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authorGravatar Samuel Mimram <smimram@debian.org>2007-02-13 13:48:12 +0000
committerGravatar Samuel Mimram <smimram@debian.org>2007-02-13 13:48:12 +0000
commit55ce117e8083477593cf1ff2e51a3641c7973830 (patch)
treea82defb4105f175c71b0d13cae42831ce608c4d6 /contrib
parent208a0f7bfa5249f9795e6e225f309cbe715c0fad (diff)
Imported Upstream version 8.1+dfsgupstream/8.1+dfsg
Diffstat (limited to 'contrib')
-rw-r--r--contrib/dp/dp.ml15
-rw-r--r--contrib/extraction/extract_env.ml299
-rw-r--r--contrib/extraction/extraction.ml17
-rw-r--r--contrib/extraction/miniml.mli6
-rw-r--r--contrib/extraction/modutil.ml7
-rw-r--r--contrib/extraction/ocaml.ml38
-rw-r--r--contrib/extraction/test_extraction.v552
-rw-r--r--contrib/first-order/ground.ml4
-rw-r--r--contrib/funind/functional_principles_proofs.ml225
-rw-r--r--contrib/funind/functional_principles_types.ml23
-rw-r--r--contrib/funind/indfun.ml2
-rw-r--r--contrib/funind/rawtermops.ml2
-rw-r--r--contrib/interface/ascent.mli1
-rw-r--r--contrib/interface/parse.ml6
-rw-r--r--contrib/interface/vtp.ml3
-rw-r--r--contrib/interface/xlate.ml9
-rw-r--r--contrib/setoid_ring/ArithRing.v56
-rw-r--r--contrib/setoid_ring/BinList.v4
-rw-r--r--contrib/setoid_ring/Field_tac.v399
-rw-r--r--contrib/setoid_ring/Field_theory.v793
-rw-r--r--contrib/setoid_ring/InitialRing.v210
-rw-r--r--contrib/setoid_ring/NArithRing.v10
-rw-r--r--contrib/setoid_ring/RealField.v34
-rw-r--r--contrib/setoid_ring/Ring.v3
-rw-r--r--contrib/setoid_ring/Ring_polynom.v1014
-rw-r--r--contrib/setoid_ring/Ring_tac.v336
-rw-r--r--contrib/setoid_ring/Ring_theory.v101
-rw-r--r--contrib/setoid_ring/ZArithRing.v47
-rw-r--r--contrib/setoid_ring/newring.ml4242
-rw-r--r--contrib/subtac/FixSub.v82
-rw-r--r--contrib/subtac/FunctionalExtensionality.v25
-rw-r--r--contrib/subtac/Subtac.v2
-rw-r--r--contrib/subtac/Utils.v28
-rw-r--r--contrib/subtac/eterm.ml30
-rw-r--r--contrib/subtac/g_subtac.ml451
-rw-r--r--contrib/subtac/subtac.ml17
-rw-r--r--contrib/subtac/subtac_cases.ml1925
-rw-r--r--contrib/subtac/subtac_cases.mli50
-rw-r--r--contrib/subtac/subtac_coercion.ml168
-rw-r--r--contrib/subtac/subtac_command.ml282
-rw-r--r--contrib/subtac/subtac_obligations.ml321
-rw-r--r--contrib/subtac/subtac_obligations.mli17
-rw-r--r--contrib/subtac/subtac_pretyping.ml33
-rw-r--r--contrib/subtac/subtac_pretyping_F.ml13
-rw-r--r--contrib/subtac/subtac_utils.ml373
-rw-r--r--contrib/subtac/subtac_utils.mli20
-rw-r--r--contrib/subtac/test/ListsTest.v141
-rw-r--r--contrib/subtac/test/euclid.v73
-rw-r--r--contrib/xml/proof2aproof.ml2
-rw-r--r--contrib/xml/proofTree2Xml.ml47
50 files changed, 5696 insertions, 2422 deletions
diff --git a/contrib/dp/dp.ml b/contrib/dp/dp.ml
index af684e6e..131dd029 100644
--- a/contrib/dp/dp.ml
+++ b/contrib/dp/dp.ml
@@ -639,8 +639,8 @@ let remove_files = List.iter (fun f -> try Sys.remove f with _ -> ())
let sprintf = Format.sprintf
let call_simplify fwhy =
- if Sys.command (sprintf "why --simplify %s" fwhy) <> 0 then
- anomaly ("call to why --simplify " ^ fwhy ^ " failed; please report");
+ let cmd = sprintf "why --simplify %s" fwhy in
+ if Sys.command cmd <> 0 then error ("Call to " ^ cmd ^ " failed");
let fsx = Filename.chop_suffix fwhy ".why" ^ "_why.sx" in
let cmd =
sprintf "timeout 10 Simplify %s > out 2>&1 && grep -q -w Valid out" fsx
@@ -652,8 +652,7 @@ let call_simplify fwhy =
let call_zenon fwhy =
let cmd = sprintf "why --no-prelude --no-zenon-prelude --zenon %s" fwhy in
- if Sys.command cmd <> 0 then
- anomaly ("call to " ^ cmd ^ " failed; please report");
+ if Sys.command cmd <> 0 then error ("call to " ^ cmd ^ " failed");
let fznn = Filename.chop_suffix fwhy ".why" ^ "_why.znn" in
let cmd =
sprintf "timeout 10 zenon %s > out 2>&1 && grep -q PROOF-FOUND out" fznn
@@ -669,8 +668,8 @@ let call_zenon fwhy =
r
let call_cvcl fwhy =
- if Sys.command (sprintf "why --cvcl %s" fwhy) <> 0 then
- anomaly ("call to why --cvcl " ^ fwhy ^ " failed; please report");
+ let cmd = sprintf "why --cvcl %s" fwhy in
+ if Sys.command cmd <> 0 then error ("call to " ^ cmd ^ " failed");
let fcvc = Filename.chop_suffix fwhy ".why" ^ "_why.cvc" in
let cmd =
sprintf "timeout 10 cvcl < %s > out 2>&1 && grep -q -w Valid out" fcvc
@@ -681,8 +680,8 @@ let call_cvcl fwhy =
r
let call_harvey fwhy =
- if Sys.command (sprintf "why --harvey %s" fwhy) <> 0 then
- anomaly ("call to why --harvey " ^ fwhy ^ " failed; please report");
+ let cmd = sprintf "why --harvey %s" fwhy in
+ if Sys.command cmd <> 0 then error ("call to " ^ cmd ^ " failed");
let frv = Filename.chop_suffix fwhy ".why" ^ "_why.rv" in
let out = Sys.command (sprintf "rvc -e -t %s > /dev/null 2>&1" frv) in
if out <> 0 then anomaly ("call to rvc -e -t " ^ frv ^ " failed");
diff --git a/contrib/extraction/extract_env.ml b/contrib/extraction/extract_env.ml
index 2d425e9f..e31b701c 100644
--- a/contrib/extraction/extract_env.ml
+++ b/contrib/extraction/extract_env.ml
@@ -6,7 +6,7 @@
(* * GNU Lesser General Public License Version 2.1 *)
(************************************************************************)
-(*i $Id: extract_env.ml 9310 2006-10-28 19:35:09Z herbelin $ i*)
+(*i $Id: extract_env.ml 9486 2007-01-15 19:11:28Z letouzey $ i*)
open Term
open Declarations
@@ -53,23 +53,55 @@ let environment_until dir_opt =
| _ -> assert false
in parse (Library.loaded_libraries ())
-type visit =
- { mutable kn : KNset.t; mutable ref : Refset.t; mutable mp : MPset.t }
-let in_kn v kn = KNset.mem kn v.kn
-let in_ref v ref = Refset.mem ref v.ref
-let in_mp v mp = MPset.mem mp v.mp
-
-let visit_mp v mp = v.mp <- MPset.union (prefixes_mp mp) v.mp
-let visit_kn v kn = v.kn <- KNset.add kn v.kn; visit_mp v (modpath kn)
-let visit_ref v r =
- let r =
- (* if we meet a constructor we must export the inductive definition *)
- match r with
- ConstructRef (r,_) -> IndRef r
- | _ -> r
- in
- v.ref <- Refset.add r v.ref; visit_mp v (modpath_of_r r)
+(*s Visit:
+ a structure recording the needed dependencies for the current extraction *)
+
+module type VISIT = sig
+ (* Reset the dependencies by emptying the visit lists *)
+ val reset : unit -> unit
+
+ (* Add the module_path and all its prefixes to the mp visit list *)
+ val add_mp : module_path -> unit
+
+ (* Add kernel_name / constant / reference / ... in the visit lists.
+ These functions silently add the mp of their arg in the mp list *)
+ val add_kn : kernel_name -> unit
+ val add_con : constant -> unit
+ val add_ref : global_reference -> unit
+ val add_decl_deps : ml_decl -> unit
+ val add_spec_deps : ml_spec -> unit
+
+ (* Test functions:
+ is a particular object a needed dependency for the current extraction ? *)
+ val needed_kn : kernel_name -> bool
+ val needed_con : constant -> bool
+ val needed_mp : module_path -> bool
+end
+
+module Visit : VISIT = struct
+ (* Thanks to C.S.C, what used to be in a single KNset should now be split
+ into a KNset (for inductives and modules names) and a Cset for constants
+ (and still the remaining MPset) *)
+ type must_visit =
+ { mutable kn : KNset.t; mutable con : Cset.t; mutable mp : MPset.t }
+ (* the imperative internal visit lists *)
+ let v = { kn = KNset.empty ; con = Cset.empty ; mp = MPset.empty }
+ (* the accessor functions *)
+ let reset () = v.kn <- KNset.empty; v.con <- Cset.empty; v.mp <- MPset.empty
+ let needed_kn kn = KNset.mem kn v.kn
+ let needed_con c = Cset.mem c v.con
+ let needed_mp mp = MPset.mem mp v.mp
+ let add_mp mp = v.mp <- MPset.union (prefixes_mp mp) v.mp
+ let add_kn kn = v.kn <- KNset.add kn v.kn; add_mp (modpath kn)
+ let add_con c = v.con <- Cset.add c v.con; add_mp (con_modpath c)
+ let add_ref = function
+ | ConstRef c -> add_con c
+ | IndRef (kn,_) | ConstructRef ((kn,_),_) -> add_kn kn
+ | VarRef _ -> assert false
+ let add_decl_deps = decl_iter_references add_ref add_ref add_ref
+ let add_spec_deps = spec_iter_references add_ref add_ref add_ref
+end
exception Impossible
@@ -104,115 +136,108 @@ let factor_fix env l cb msb =
labels, recd, msb''
end
-let get_decl_references v d =
- let f = visit_ref v in decl_iter_references f f f d
-
-let get_spec_references v s =
- let f = visit_ref v in spec_iter_references f f f s
-
-let rec extract_msig env v mp = function
+let rec extract_msig env mp = function
| [] -> []
| (l,SPBconst cb) :: msig ->
let kn = make_con mp empty_dirpath l in
let s = extract_constant_spec env kn cb in
- if logical_spec s then extract_msig env v mp msig
+ if logical_spec s then extract_msig env mp msig
else begin
- get_spec_references v s;
- (l,Spec s) :: (extract_msig env v mp msig)
+ Visit.add_spec_deps s;
+ (l,Spec s) :: (extract_msig env mp msig)
end
| (l,SPBmind cb) :: msig ->
let kn = make_kn mp empty_dirpath l in
let s = Sind (kn, extract_inductive env kn) in
- if logical_spec s then extract_msig env v mp msig
+ if logical_spec s then extract_msig env mp msig
else begin
- get_spec_references v s;
- (l,Spec s) :: (extract_msig env v mp msig)
+ Visit.add_spec_deps s;
+ (l,Spec s) :: (extract_msig env mp msig)
end
| (l,SPBmodule {msb_modtype=mtb}) :: msig ->
-(*i let mpo = Some (MPdot (mp,l)) in i*)
- (l,Smodule (extract_mtb env v None (*i mpo i*) mtb)) :: (extract_msig env v mp msig)
+ (l,Smodule (extract_mtb env None mtb)) :: (extract_msig env mp msig)
| (l,SPBmodtype mtb) :: msig ->
- (l,Smodtype (extract_mtb env v None mtb)) :: (extract_msig env v mp msig)
+ (l,Smodtype (extract_mtb env None mtb)) :: (extract_msig env mp msig)
-and extract_mtb env v mpo = function
- | MTBident kn -> visit_kn v kn; MTident kn
+and extract_mtb env mpo = function
+ | MTBident kn -> Visit.add_kn kn; MTident kn
| MTBfunsig (mbid, mtb, mtb') ->
let mp = MPbound mbid in
let env' = Modops.add_module mp (Modops.module_body_of_type mtb) env in
- MTfunsig (mbid, extract_mtb env v None mtb,
- extract_mtb env' v None mtb')
+ MTfunsig (mbid, extract_mtb env None mtb,
+ extract_mtb env' None mtb')
| MTBsig (msid, msig) ->
let mp, msig = match mpo with
| None -> MPself msid, msig
| Some mp -> mp, Modops.subst_signature_msid msid mp msig
in
let env' = Modops.add_signature mp msig env in
- MTsig (msid, extract_msig env' v mp msig)
+ MTsig (msid, extract_msig env' mp msig)
-let rec extract_msb env v mp all = function
+let rec extract_msb env mp all = function
| [] -> []
| (l,SEBconst cb) :: msb ->
(try
let vl,recd,msb = factor_fix env l cb msb in
- let vkn = Array.map (fun id -> make_con mp empty_dirpath id) vl in
- let ms = extract_msb env v mp all msb in
- let b = array_exists (fun con -> in_ref v (ConstRef con)) vkn in
+ let vc = Array.map (make_con mp empty_dirpath) vl in
+ let ms = extract_msb env mp all msb in
+ let b = array_exists Visit.needed_con vc in
if all || b then
- let d = extract_fixpoint env vkn recd in
+ let d = extract_fixpoint env vc recd in
if (not b) && (logical_decl d) then ms
- else begin get_decl_references v d; (l,SEdecl d) :: ms end
+ else begin Visit.add_decl_deps d; (l,SEdecl d) :: ms end
else ms
with Impossible ->
- let ms = extract_msb env v mp all msb in
- let kn = make_con mp empty_dirpath l in
- let b = in_ref v (ConstRef kn) in
+ let ms = extract_msb env mp all msb in
+ let c = make_con mp empty_dirpath l in
+ let b = Visit.needed_con c in
if all || b then
- let d = extract_constant env kn cb in
+ let d = extract_constant env c cb in
if (not b) && (logical_decl d) then ms
- else begin get_decl_references v d; (l,SEdecl d) :: ms end
+ else begin Visit.add_decl_deps d; (l,SEdecl d) :: ms end
else ms)
| (l,SEBmind mib) :: msb ->
- let ms = extract_msb env v mp all msb in
+ let ms = extract_msb env mp all msb in
let kn = make_kn mp empty_dirpath l in
- let b = in_ref v (IndRef (kn,0)) in (* 0 is dummy *)
+ let b = Visit.needed_kn kn in
if all || b then
let d = Dind (kn, extract_inductive env kn) in
if (not b) && (logical_decl d) then ms
- else begin get_decl_references v d; (l,SEdecl d) :: ms end
+ else begin Visit.add_decl_deps d; (l,SEdecl d) :: ms end
else ms
| (l,SEBmodule mb) :: msb ->
- let ms = extract_msb env v mp all msb in
+ let ms = extract_msb env mp all msb in
let mp = MPdot (mp,l) in
- if all || in_mp v mp then
- (l,SEmodule (extract_module env v mp true mb)) :: ms
+ if all || Visit.needed_mp mp then
+ (l,SEmodule (extract_module env mp true mb)) :: ms
else ms
| (l,SEBmodtype mtb) :: msb ->
- let ms = extract_msb env v mp all msb in
+ let ms = extract_msb env mp all msb in
let kn = make_kn mp empty_dirpath l in
- if all || in_kn v kn then
- (l,SEmodtype (extract_mtb env v None mtb)) :: ms
+ if all || Visit.needed_kn kn then
+ (l,SEmodtype (extract_mtb env None mtb)) :: ms
else ms
-and extract_meb env v mpo all = function
+and extract_meb env mpo all = function
| MEBident (MPfile d) -> error_MPfile_as_mod d (* temporary (I hope) *)
- | MEBident mp -> visit_mp v mp; MEident mp
+ | MEBident mp -> Visit.add_mp mp; MEident mp
| MEBapply (meb, meb',_) ->
- MEapply (extract_meb env v None true meb,
- extract_meb env v None true meb')
+ MEapply (extract_meb env None true meb,
+ extract_meb env None true meb')
| MEBfunctor (mbid, mtb, meb) ->
let mp = MPbound mbid in
let env' = Modops.add_module mp (Modops.module_body_of_type mtb) env in
- MEfunctor (mbid, extract_mtb env v None mtb,
- extract_meb env' v None true meb)
+ MEfunctor (mbid, extract_mtb env None mtb,
+ extract_meb env' None true meb)
| MEBstruct (msid, msb) ->
let mp,msb = match mpo with
| None -> MPself msid, msb
| Some mp -> mp, subst_msb (map_msid msid mp) msb
in
let env' = add_structure mp msb env in
- MEstruct (msid, extract_msb env' v mp all msb)
+ MEstruct (msid, extract_msb env' mp all msb)
-and extract_module env v mp all mb =
+and extract_module env mp all mb =
(* [mb.mod_expr <> None ], since we look at modules from outside. *)
(* Example of module with empty [mod_expr] is X inside a Module F [X:SIG]. *)
let meb = out_some mb.mod_expr in
@@ -220,25 +245,21 @@ and extract_module env v mp all mb =
(* Because of the "with" construct, the module type can be [MTBsig] with *)
(* a msid different from the one of the module. Here is the patch. *)
let mtb = replicate_msid meb mtb in
- { ml_mod_expr = extract_meb env v (Some mp) all meb;
- ml_mod_type = extract_mtb env v None mtb }
+ { ml_mod_expr = extract_meb env (Some mp) all meb;
+ ml_mod_type = extract_mtb env None mtb }
let unpack = function MEstruct (_,sel) -> sel | _ -> assert false
let mono_environment refs mpl =
- let l = environment_until None in
- let v =
- let add_ref r = Refset.add r in
- let refs = List.fold_right add_ref refs Refset.empty in
- let add_mp mp = MPset.union (prefixes_mp mp) in
- let mps = List.fold_right add_mp mpl MPset.empty in
- let mps = Refset.fold (fun k -> add_mp (modpath_of_r k)) refs mps in
- { kn = KNset.empty; ref = refs; mp = mps }
- in
+ Visit.reset ();
+ List.iter Visit.add_ref refs;
+ List.iter Visit.add_mp mpl;
let env = Global.env () in
- List.rev_map (fun (mp,m) -> mp, unpack (extract_meb env v (Some mp) false m))
- (List.rev l)
+ let l = List.rev (environment_until None) in
+ List.rev_map
+ (fun (mp,m) -> mp, unpack (extract_meb env (Some mp) false m)) l
+
(*s Recursive extraction in the Coq toplevel. The vernacular command is
\verb!Recursive Extraction! [qualid1] ... [qualidn]. We use [extract_env]
to get the saturated environment to extract. *)
@@ -259,6 +280,7 @@ let mono_extraction (f,m) qualids =
let prm = {modular=false; mod_name = m; to_appear= refs} in
let struc = optimize_struct prm None (mono_environment refs mps) in
print_structure_to_file f prm struc;
+ Visit.reset ();
reset_tables ()
let extraction_rec = mono_extraction (None,id_of_string "Main")
@@ -277,15 +299,15 @@ let extraction qid =
let r = Nametab.global qid in
if is_custom r then
msgnl (str "User defined extraction:" ++ spc () ++
- str (find_custom r) ++ fnl ())
- else begin
+ str (find_custom r) ++ fnl ())
+ else
let prm =
- { modular = false; mod_name = id_of_string "Main"; to_appear = [r]} in
+ { modular = false; mod_name = id_of_string "Main"; to_appear = [r]} in
let struc = optimize_struct prm None (mono_environment [r] []) in
let d = get_decl_in_structure r struc in
print_one_decl struc (modpath_of_r r) d;
- reset_tables ()
- end
+ Visit.reset ();
+ reset_tables ()
(*s Extraction to a file (necessarily recursive).
The vernacular command is
@@ -313,32 +335,33 @@ let extraction_file f vl =
let extraction_module m =
check_inside_section ();
check_inside_module ();
- match lang () with
+ begin match lang () with
| Toplevel -> error_toplevel ()
| Scheme -> error_scheme ()
- | _ ->
- let q = snd (qualid_of_reference m) in
- let mp =
- try Nametab.locate_module q
- with Not_found -> error_unknown_module q
- in
- let b = is_modfile mp in
- let prm = {modular=b; mod_name = id_of_string ""; to_appear= []} in
- let l = environment_until None in
- let v={ kn = KNset.empty ; ref = Refset.empty; mp = prefixes_mp mp } in
- let env = Global.env () in
- let struc =
- List.rev_map
- (fun (mp,m) -> mp, unpack (extract_meb env v (Some mp) b m))
- (List.rev l)
- in
- let struc = optimize_struct prm None struc in
- let struc =
- let bmp = base_mp mp in
- try [bmp, List.assoc bmp struc] with Not_found -> assert false
- in
- print_structure_to_file None prm struc;
- reset_tables ()
+ | _ -> ()
+ end;
+ let q = snd (qualid_of_reference m) in
+ let mp =
+ try Nametab.locate_module q with Not_found -> error_unknown_module q
+ in
+ let b = is_modfile mp in
+ let prm = {modular=b; mod_name = id_of_string ""; to_appear= []} in
+ Visit.reset ();
+ Visit.add_mp mp;
+ let env = Global.env () in
+ let l = List.rev (environment_until None) in
+ let struc =
+ List.rev_map (fun (mp,m) -> mp, unpack (extract_meb env (Some mp) b m)) l
+ in
+ let struc = optimize_struct prm None struc in
+ let struc =
+ let bmp = base_mp mp in
+ try [bmp, List.assoc bmp struc] with Not_found -> assert false
+ in
+ print_structure_to_file None prm struc;
+ Visit.reset ();
+ reset_tables ()
+
(*s (Recursive) Extraction of a library. The vernacular command is
\verb!(Recursive) Extraction Library! [M]. *)
@@ -355,38 +378,38 @@ let dir_module_of_id m =
let extraction_library is_rec m =
check_inside_section ();
check_inside_module ();
- match lang () with
+ begin match lang () with
| Toplevel -> error_toplevel ()
| Scheme -> error_scheme ()
- | _ ->
- let dir_m = dir_module_of_id m in
- let v =
- { kn = KNset.empty; ref = Refset.empty;
- mp = MPset.singleton (MPfile dir_m) } in
- let l = environment_until (Some dir_m) in
- let struc =
- let env = Global.env () in
- let select l (mp,meb) =
- if in_mp v mp (* [mp] est long -> [in_mp] peut etre sans [long_mp] *)
- then (mp, unpack (extract_meb env v (Some mp) true meb)) :: l
- else l
- in
- List.fold_left select [] (List.rev l)
- in
- let dummy_prm = {modular=true; mod_name=m; to_appear=[]} in
- let struc = optimize_struct dummy_prm None struc in
- let rec print = function
- | [] -> ()
- | (MPfile dir, _) :: l when not is_rec && dir <> dir_m -> print l
- | (MPfile dir, sel) as e :: l ->
- let short_m = snd (split_dirpath dir) in
- let f = module_file_name short_m in
- let prm = {modular=true;mod_name=short_m;to_appear=[]} in
- print_structure_to_file (Some f) prm [e];
- print l
- | _ -> assert false
- in print struc;
- reset_tables ()
+ | _ -> ()
+ end;
+ let dir_m = dir_module_of_id m in
+ Visit.reset ();
+ Visit.add_mp (MPfile dir_m);
+ let env = Global.env () in
+ let l = List.rev (environment_until (Some dir_m)) in
+ let select l (mp,meb) =
+ if Visit.needed_mp mp
+ then (mp, unpack (extract_meb env (Some mp) true meb)) :: l
+ else l
+ in
+ let struc = List.fold_left select [] l in
+ let dummy_prm = {modular=true; mod_name=m; to_appear=[]} in
+ let struc = optimize_struct dummy_prm None struc in
+ let rec print = function
+ | [] -> ()
+ | (MPfile dir, _) :: l when not is_rec && dir <> dir_m -> print l
+ | (MPfile dir, sel) as e :: l ->
+ let short_m = snd (split_dirpath dir) in
+ let f = module_file_name short_m in
+ let prm = {modular=true;mod_name=short_m;to_appear=[]} in
+ print_structure_to_file (Some f) prm [e];
+ print l
+ | _ -> assert false
+ in
+ print struc;
+ Visit.reset ();
+ reset_tables ()
diff --git a/contrib/extraction/extraction.ml b/contrib/extraction/extraction.ml
index 52e7f1dd..6fd4a3cc 100644
--- a/contrib/extraction/extraction.ml
+++ b/contrib/extraction/extraction.ml
@@ -6,7 +6,7 @@
(* * GNU Lesser General Public License Version 2.1 *)
(************************************************************************)
-(*i $Id: extraction.ml 9310 2006-10-28 19:35:09Z herbelin $ i*)
+(*i $Id: extraction.ml 9456 2006-12-17 20:08:38Z letouzey $ i*)
(*i*)
open Util
@@ -310,6 +310,9 @@ and extract_ind env kn = (* kn is supposed to be in long form *)
with Not_found ->
internal_call := KNset.add kn !internal_call;
let mib = Environ.lookup_mind kn env in
+ (* First, if this inductive is aliased via a Module, *)
+ (* we process the original inductive. *)
+ option_iter (fun kn -> ignore (extract_ind env kn)) mib.mind_equiv;
(* Everything concerning parameters. *)
(* We do that first, since they are common to all the [mib]. *)
let mip0 = mib.mind_packets.(0) in
@@ -332,7 +335,11 @@ and extract_ind env kn = (* kn is supposed to be in long form *)
ip_types = t })
mib.mind_packets
in
- add_ind kn {ind_info = Standard; ind_nparams = npar; ind_packets = packets};
+ add_ind kn
+ {ind_info = Standard;
+ ind_nparams = npar;
+ ind_packets = packets;
+ ind_equiv = mib.mind_equiv };
(* Second pass: we extract constructors *)
for i = 0 to mib.mind_ntypes - 1 do
let p = packets.(i) in
@@ -413,7 +420,11 @@ and extract_ind env kn = (* kn is supposed to be in long form *)
Record field_glob
with (I info) -> info
in
- let i = {ind_info = ind_info; ind_nparams = npar; ind_packets = packets} in
+ let i = {ind_info = ind_info;
+ ind_nparams = npar;
+ ind_packets = packets;
+ ind_equiv = mib.mind_equiv}
+ in
add_ind kn i;
internal_call := KNset.remove kn !internal_call;
i
diff --git a/contrib/extraction/miniml.mli b/contrib/extraction/miniml.mli
index e34abe02..3b4146f8 100644
--- a/contrib/extraction/miniml.mli
+++ b/contrib/extraction/miniml.mli
@@ -6,7 +6,7 @@
(* * GNU Lesser General Public License Version 2.1 *)
(************************************************************************)
-(*i $Id: miniml.mli 8724 2006-04-20 09:57:01Z letouzey $ i*)
+(*i $Id: miniml.mli 9456 2006-12-17 20:08:38Z letouzey $ i*)
(*s Target language for extraction: a core ML called MiniML. *)
@@ -79,7 +79,9 @@ type ml_ind_packet = {
type ml_ind = {
ind_info : inductive_info;
ind_nparams : int;
- ind_packets : ml_ind_packet array }
+ ind_packets : ml_ind_packet array;
+ ind_equiv : kernel_name option
+}
(*s ML terms. *)
diff --git a/contrib/extraction/modutil.ml b/contrib/extraction/modutil.ml
index 46d4a5a6..c9d4e237 100644
--- a/contrib/extraction/modutil.ml
+++ b/contrib/extraction/modutil.ml
@@ -6,7 +6,7 @@
(* * GNU Lesser General Public License Version 2.1 *)
(************************************************************************)
-(*i $Id: modutil.ml 8724 2006-04-20 09:57:01Z letouzey $ i*)
+(*i $Id: modutil.ml 9456 2006-12-17 20:08:38Z letouzey $ i*)
open Names
open Declarations
@@ -195,7 +195,10 @@ let ind_iter_references do_term do_cons do_type kn ind =
let type_iter = type_iter_references do_type in
let cons_iter cp l = do_cons (ConstructRef cp); List.iter type_iter l in
let packet_iter ip p =
- do_type (IndRef ip); Array.iteri (fun j -> cons_iter (ip,j+1)) p.ip_types
+ do_type (IndRef ip);
+ if lang () = Ocaml then
+ option_iter (fun kne -> do_type (IndRef (kne,snd ip))) ind.ind_equiv;
+ Array.iteri (fun j -> cons_iter (ip,j+1)) p.ip_types
in
if lang () = Ocaml then record_iter_references do_term ind.ind_info;
Array.iteri (fun i -> packet_iter (kn,i)) ind.ind_packets
diff --git a/contrib/extraction/ocaml.ml b/contrib/extraction/ocaml.ml
index 483da236..35f9a83c 100644
--- a/contrib/extraction/ocaml.ml
+++ b/contrib/extraction/ocaml.ml
@@ -6,7 +6,7 @@
(* * GNU Lesser General Public License Version 2.1 *)
(************************************************************************)
-(*i $Id: ocaml.ml 8930 2006-06-09 02:14:34Z letouzey $ i*)
+(*i $Id: ocaml.ml 9472 2007-01-05 15:49:32Z letouzey $ i*)
(*s Production of Ocaml syntax. *)
@@ -392,7 +392,14 @@ let rec pp_Dfix init i ((rv,c,t) as fix) =
(*s Pretty-printing of inductive types declaration. *)
-let pp_one_ind prefix ip pl cv =
+let pp_equiv param_list = function
+ | None -> mt ()
+ | Some ip_equiv ->
+ str " = " ++ pp_parameters param_list ++ pp_global (IndRef ip_equiv)
+
+let pp_comment s = str "(* " ++ s ++ str " *)"
+
+let pp_one_ind prefix ip ip_equiv pl cv =
let pl = rename_tvars keywords pl in
let pp_constructor (r,l) =
hov 2 (str " | " ++ pp_global r ++
@@ -402,13 +409,12 @@ let pp_one_ind prefix ip pl cv =
prlist_with_sep
(fun () -> spc () ++ str "* ") (pp_type true pl) l))
in
- pp_parameters pl ++ str prefix ++ pp_global (IndRef ip) ++ str " =" ++
+ pp_parameters pl ++ str prefix ++ pp_global (IndRef ip) ++
+ pp_equiv pl ip_equiv ++ str " =" ++
if Array.length cv = 0 then str " unit (* empty inductive *)"
else fnl () ++ v 0 (prvect_with_sep fnl pp_constructor
(Array.mapi (fun i c -> ConstructRef (ip,i+1), c) cv))
-let pp_comment s = str "(* " ++ s ++ str " *)"
-
let pp_logical_ind packet =
pp_comment (pr_id packet.ip_typename ++ str " : logical inductive") ++
fnl () ++ pp_comment (str "with constructors : " ++
@@ -422,10 +428,11 @@ let pp_singleton kn packet =
pp_comment (str "singleton inductive, whose constructor was " ++
pr_id packet.ip_consnames.(0)))
-let pp_record kn projs packet =
+let pp_record kn projs ip_equiv packet =
let l = List.combine projs packet.ip_types.(0) in
let pl = rename_tvars keywords packet.ip_vars in
- str "type " ++ pp_parameters pl ++ pp_global (IndRef (kn,0)) ++ str " = { "++
+ str "type " ++ pp_parameters pl ++ pp_global (IndRef (kn,0)) ++
+ pp_equiv pl ip_equiv ++ str " = { "++
hov 0 (prlist_with_sep (fun () -> str ";" ++ spc ())
(fun (r,t) -> pp_global r ++ str " : " ++ pp_type true pl t) l)
++ str " }"
@@ -434,17 +441,20 @@ let pp_coind ip pl =
let r = IndRef ip in
let pl = rename_tvars keywords pl in
pp_parameters pl ++ pp_global r ++ str " = " ++
- pp_parameters pl ++ str "__" ++ pp_global r ++ str " Lazy.t"
+ pp_parameters pl ++ str "__" ++ pp_global r ++ str " Lazy.t" ++
+ fnl() ++ str "and "
let pp_ind co kn ind =
+ let prefix = if co then "__" else "" in
let some = ref false in
let init= ref (str "type ") in
let rec pp i =
if i >= Array.length ind.ind_packets then mt ()
else
let ip = (kn,i) in
+ let ip_equiv = option_map (fun kn -> (kn,i)) ind.ind_equiv in
let p = ind.ind_packets.(i) in
- if is_custom (IndRef (kn,i)) then pp (i+1)
+ if is_custom (IndRef ip) then pp (i+1)
else begin
some := true;
if p.ip_logical then pp_logical_ind p ++ pp (i+1)
@@ -453,8 +463,8 @@ let pp_ind co kn ind =
begin
init := (fnl () ++ str "and ");
s ++
- (if co then pp_coind ip p.ip_vars ++ fnl () ++ str "and " else mt ())
- ++ pp_one_ind (if co then "__" else "") ip p.ip_vars p.ip_types ++
+ (if co then pp_coind ip p.ip_vars else mt ())
+ ++ pp_one_ind prefix ip ip_equiv p.ip_vars p.ip_types ++
pp (i+1)
end
end
@@ -468,7 +478,9 @@ let pp_mind kn i =
match i.ind_info with
| Singleton -> pp_singleton kn i.ind_packets.(0)
| Coinductive -> pp_ind true kn i
- | Record projs -> pp_record kn projs i.ind_packets.(0)
+ | Record projs ->
+ let ip_equiv = option_map (fun kn -> (kn,0)) i.ind_equiv in
+ pp_record kn projs ip_equiv i.ind_packets.(0)
| Standard -> pp_ind false kn i
let pp_decl mpl =
@@ -574,7 +586,7 @@ let rec pp_structure_elem mpl = function
| (l,SEmodule m) ->
hov 1
(str "module " ++ P.pp_module mpl (MPdot (List.hd mpl, l)) ++
- (* if you want signatures everywhere: *)
+ (*i if you want signatures everywhere: i*)
(*i str " :" ++ fnl () ++ i*)
(*i pp_module_type mpl None m.ml_mod_type ++ fnl () ++ i*)
str " = " ++
diff --git a/contrib/extraction/test_extraction.v b/contrib/extraction/test_extraction.v
deleted file mode 100644
index 0745f62d..00000000
--- a/contrib/extraction/test_extraction.v
+++ /dev/null
@@ -1,552 +0,0 @@
-(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
-(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
-(************************************************************************)
-
-Require Import Arith.
-Require Import List.
-
-(*** STANDARD EXAMPLES *)
-
-(** Functions. *)
-
-Definition idnat (x:nat) := x.
-Extraction idnat.
-(* let idnat x = x *)
-
-Definition id (X:Type) (x:X) := x.
-Extraction id. (* let id x = x *)
-Definition id' := id Set nat.
-Extraction id'. (* type id' = nat *)
-
-Definition test2 (f:nat -> nat) (x:nat) := f x.
-Extraction test2.
-(* let test2 f x = f x *)
-
-Definition test3 (f:nat -> Set -> nat) (x:nat) := f x nat.
-Extraction test3.
-(* let test3 f x = f x __ *)
-
-Definition test4 (f:(nat -> nat) -> nat) (x:nat) (g:nat -> nat) := f g.
-Extraction test4.
-(* let test4 f x g = f g *)
-
-Definition test5 := (1, 0).
-Extraction test5.
-(* let test5 = Pair ((S O), O) *)
-
-Definition cf (x:nat) (_:x <= 0) := S x.
-Extraction NoInline cf.
-Definition test6 := cf 0 (le_n 0).
-Extraction test6.
-(* let test6 = cf O *)
-
-Definition test7 := (fun (X:Set) (x:X) => x) nat.
-Extraction test7.
-(* let test7 x = x *)
-
-Definition d (X:Type) := X.
-Extraction d. (* type 'x d = 'x *)
-Definition d2 := d Set.
-Extraction d2. (* type d2 = __ d *)
-Definition d3 (x:d Set) := 0.
-Extraction d3. (* let d3 _ = O *)
-Definition d4 := d nat.
-Extraction d4. (* type d4 = nat d *)
-Definition d5 := (fun x:d Type => 0) Type.
-Extraction d5. (* let d5 = O *)
-Definition d6 (x:d Type) := x.
-Extraction d6. (* type 'x d6 = 'x *)
-
-Definition test8 := (fun (X:Type) (x:X) => x) Set nat.
-Extraction test8. (* type test8 = nat *)
-
-Definition test9 := let t := nat in id Set t.
-Extraction test9. (* type test9 = nat *)
-
-Definition test10 := (fun (X:Type) (x:X) => 0) Type Type.
-Extraction test10. (* let test10 = O *)
-
-Definition test11 := let n := 0 in let p := S n in S p.
-Extraction test11. (* let test11 = S (S O) *)
-
-Definition test12 := forall x:forall X:Type, X -> X, x Type Type.
-Extraction test12.
-(* type test12 = (__ -> __ -> __) -> __ *)
-
-
-Definition test13 := match left True I with
- | left x => 1
- | right x => 0
- end.
-Extraction test13. (* let test13 = S O *)
-
-
-(** example with more arguments that given by the type *)
-
-Definition test19 :=
- nat_rec (fun n:nat => nat -> nat) (fun n:nat => 0)
- (fun (n:nat) (f:nat -> nat) => f) 0 0.
-Extraction test19.
-(* let test19 =
- let rec f = function
- | O -> (fun n0 -> O)
- | S n0 -> f n0
- in f O O
-*)
-
-
-(** casts *)
-
-Definition test20 := True:Type.
-Extraction test20.
-(* type test20 = __ *)
-
-
-(** Simple inductive type and recursor. *)
-
-Extraction nat.
-(*
-type nat =
- | O
- | S of nat
-*)
-
-Extraction sumbool_rect.
-(*
-let sumbool_rect f f0 = function
- | Left -> f __
- | Right -> f0 __
-*)
-
-(** Less simple inductive type. *)
-
-Inductive c (x:nat) : nat -> Set :=
- | refl : c x x
- | trans : forall y z:nat, c x y -> y <= z -> c x z.
-Extraction c.
-(*
-type c =
- | Refl
- | Trans of nat * nat * c
-*)
-
-Definition Ensemble (U:Type) := U -> Prop.
-Definition Empty_set (U:Type) (x:U) := False.
-Definition Add (U:Type) (A:Ensemble U) (x y:U) := A y \/ x = y.
-
-Inductive Finite (U:Type) : Ensemble U -> Set :=
- | Empty_is_finite : Finite U (Empty_set U)
- | Union_is_finite :
- forall A:Ensemble U,
- Finite U A -> forall x:U, ~ A x -> Finite U (Add U A x).
-Extraction Finite.
-(*
-type 'u finite =
- | Empty_is_finite
- | Union_is_finite of 'u finite * 'u
-*)
-
-
-(** Mutual Inductive *)
-
-Inductive tree : Set :=
- Node : nat -> forest -> tree
-with forest : Set :=
- | Leaf : nat -> forest
- | Cons : tree -> forest -> forest.
-
-Extraction tree.
-(*
-type tree =
- | Node of nat * forest
-and forest =
- | Leaf of nat
- | Cons of tree * forest
-*)
-
-Fixpoint tree_size (t:tree) : nat :=
- match t with
- | Node a f => S (forest_size f)
- end
-
- with forest_size (f:forest) : nat :=
- match f with
- | Leaf b => 1
- | Cons t f' => tree_size t + forest_size f'
- end.
-
-Extraction tree_size.
-(*
-let rec tree_size = function
- | Node (a, f) -> S (forest_size f)
-and forest_size = function
- | Leaf b -> S O
- | Cons (t, f') -> plus (tree_size t) (forest_size f')
-*)
-
-
-(** Eta-expansions of inductive constructor *)
-
-Inductive titi : Set :=
- tata : nat -> nat -> nat -> nat -> titi.
-Definition test14 := tata 0.
-Extraction test14.
-(* let test14 x x0 x1 = Tata (O, x, x0, x1) *)
-Definition test15 := tata 0 1.
-Extraction test15.
-(* let test15 x x0 = Tata (O, (S O), x, x0) *)
-
-Inductive eta : Set :=
- eta_c : nat -> Prop -> nat -> Prop -> eta.
-Extraction eta_c.
-(*
-type eta =
- | Eta_c of nat * nat
-*)
-Definition test16 := eta_c 0.
-Extraction test16.
-(* let test16 x = Eta_c (O, x) *)
-Definition test17 := eta_c 0 True.
-Extraction test17.
-(* let test17 x = Eta_c (O, x) *)
-Definition test18 := eta_c 0 True 0.
-Extraction test18.
-(* let test18 _ = Eta_c (O, O) *)
-
-
-(** Example of singleton inductive type *)
-
-Inductive bidon (A:Prop) (B:Type) : Set :=
- tb : forall (x:A) (y:B), bidon A B.
-Definition fbidon (A B:Type) (f:A -> B -> bidon True nat)
- (x:A) (y:B) := f x y.
-Extraction bidon.
-(* type 'b bidon = 'b *)
-Extraction tb.
-(* tb : singleton inductive constructor *)
-Extraction fbidon.
-(* let fbidon f x y =
- f x y
-*)
-
-Definition fbidon2 := fbidon True nat (tb True nat).
-Extraction fbidon2. (* let fbidon2 y = y *)
-Extraction NoInline fbidon.
-Extraction fbidon2.
-(* let fbidon2 y = fbidon (fun _ x -> x) __ y *)
-
-(* NB: first argument of fbidon2 has type [True], so it disappears. *)
-
-(** mutual inductive on many sorts *)
-
-Inductive test_0 : Prop :=
- ctest0 : test_0
-with test_1 : Set :=
- ctest1 : test_0 -> test_1.
-Extraction test_0.
-(* test0 : logical inductive *)
-Extraction test_1.
-(*
-type test1 =
- | Ctest1
-*)
-
-(** logical singleton *)
-
-Extraction eq.
-(* eq : logical inductive *)
-Extraction eq_rect.
-(* let eq_rect x f y =
- f
-*)
-
-(** No more propagation of type parameters. Obj.t instead. *)
-
-Inductive tp1 : Set :=
- T : forall (C:Set) (c:C), tp2 -> tp1
-with tp2 : Set :=
- T' : tp1 -> tp2.
-Extraction tp1.
-(*
-type tp1 =
- | T of __ * tp2
-and tp2 =
- | T' of tp1
-*)
-
-Inductive tp1bis : Set :=
- Tbis : tp2bis -> tp1bis
-with tp2bis : Set :=
- T'bis : forall (C:Set) (c:C), tp1bis -> tp2bis.
-Extraction tp1bis.
-(*
-type tp1bis =
- | Tbis of tp2bis
-and tp2bis =
- | T'bis of __ * tp1bis
-*)
-
-
-(** Strange inductive type. *)
-
-Inductive Truc : Set -> Set :=
- | chose : forall A:Set, Truc A
- | machin : forall A:Set, A -> Truc bool -> Truc A.
-Extraction Truc.
-(*
-type 'x truc =
- | Chose
- | Machin of 'x * bool truc
-*)
-
-
-(** Dependant type over Type *)
-
-Definition test24 := sigT (fun a:Set => option a).
-Extraction test24.
-(* type test24 = (__, __ option) sigT *)
-
-
-(** Coq term non strongly-normalizable after extraction *)
-
-Require Import Gt.
-Definition loop (Ax:Acc gt 0) :=
- (fix F (a:nat) (b:Acc gt a) {struct b} : nat :=
- F (S a) (Acc_inv b (S a) (gt_Sn_n a))) 0 Ax.
-Extraction loop.
-(* let loop _ =
- let rec f a =
- f (S a)
- in f O
-*)
-
-(*** EXAMPLES NEEDING OBJ.MAGIC *)
-
-(** False conversion of type: *)
-
-Lemma oups : forall H:nat = list nat, nat -> nat.
-intros.
-generalize H0; intros.
-rewrite H in H1.
-case H1.
-exact H0.
-intros.
-exact n.
-Qed.
-Extraction oups.
-(*
-let oups h0 =
- match Obj.magic h0 with
- | Nil -> h0
- | Cons0 (n, l) -> n
-*)
-
-
-(** hybrids *)
-
-Definition horibilis (b:bool) :=
- if b as b return (if b then Type else nat) then Set else 0.
-Extraction horibilis.
-(*
-let horibilis = function
- | True -> Obj.magic __
- | False -> Obj.magic O
-*)
-
-Definition PropSet (b:bool) := if b then Prop else Set.
-Extraction PropSet. (* type propSet = __ *)
-
-Definition natbool (b:bool) := if b then nat else bool.
-Extraction natbool. (* type natbool = __ *)
-
-Definition zerotrue (b:bool) := if b as x return natbool x then 0 else true.
-Extraction zerotrue.
-(*
-let zerotrue = function
- | True -> Obj.magic O
- | False -> Obj.magic True
-*)
-
-Definition natProp (b:bool) := if b return Type then nat else Prop.
-
-Definition natTrue (b:bool) := if b return Type then nat else True.
-
-Definition zeroTrue (b:bool) := if b as x return natProp x then 0 else True.
-Extraction zeroTrue.
-(*
-let zeroTrue = function
- | True -> Obj.magic O
- | False -> Obj.magic __
-*)
-
-Definition natTrue2 (b:bool) := if b return Type then nat else True.
-
-Definition zeroprop (b:bool) := if b as x return natTrue x then 0 else I.
-Extraction zeroprop.
-(*
-let zeroprop = function
- | True -> Obj.magic O
- | False -> Obj.magic __
-*)
-
-(** polymorphic f applied several times *)
-
-Definition test21 := (id nat 0, id bool true).
-Extraction test21.
-(* let test21 = Pair ((id O), (id True)) *)
-
-(** ok *)
-
-Definition test22 :=
- (fun f:forall X:Type, X -> X => (f nat 0, f bool true))
- (fun (X:Type) (x:X) => x).
-Extraction test22.
-(* let test22 =
- let f = fun x -> x in Pair ((f O), (f True)) *)
-
-(* still ok via optim beta -> let *)
-
-Definition test23 (f:forall X:Type, X -> X) := (f nat 0, f bool true).
-Extraction test23.
-(* let test23 f = Pair ((Obj.magic f __ O), (Obj.magic f __ True)) *)
-
-(* problem: fun f -> (f 0, f true) not legal in ocaml *)
-(* solution: magic ... *)
-
-
-(** Dummy constant __ can be applied.... *)
-
-Definition f (X:Type) (x:nat -> X) (y:X -> bool) : bool := y (x 0).
-Extraction f.
-(* let f x y =
- y (x O)
-*)
-
-Definition f_prop := f (0 = 0) (fun _ => refl_equal 0) (fun _ => true).
-Extraction NoInline f.
-Extraction f_prop.
-(* let f_prop =
- f (Obj.magic __) (fun _ -> True)
-*)
-
-Definition f_arity := f Set (fun _:nat => nat) (fun _:Set => true).
-Extraction f_arity.
-(* let f_arity =
- f (Obj.magic __) (fun _ -> True)
-*)
-
-Definition f_normal :=
- f nat (fun x => x) (fun x => match x with
- | O => true
- | _ => false
- end).
-Extraction f_normal.
-(* let f_normal =
- f (fun x -> x) (fun x -> match x with
- | O -> True
- | S n -> False)
-*)
-
-
-(* inductive with magic needed *)
-
-Inductive Boite : Set :=
- boite : forall b:bool, (if b then nat else (nat * nat)%type) -> Boite.
-Extraction Boite.
-(*
-type boite =
- | Boite of bool * __
-*)
-
-
-Definition boite1 := boite true 0.
-Extraction boite1.
-(* let boite1 = Boite (True, (Obj.magic O)) *)
-
-Definition boite2 := boite false (0, 0).
-Extraction boite2.
-(* let boite2 = Boite (False, (Obj.magic (Pair (O, O)))) *)
-
-Definition test_boite (B:Boite) :=
- match B return nat with
- | boite true n => n
- | boite false n => fst n + snd n
- end.
-Extraction test_boite.
-(*
-let test_boite = function
- | Boite (b0, n) ->
- (match b0 with
- | True -> Obj.magic n
- | False -> plus (fst (Obj.magic n)) (snd (Obj.magic n)))
-*)
-
-(* singleton inductive with magic needed *)
-
-Inductive Box : Set :=
- box : forall A:Set, A -> Box.
-Extraction Box.
-(* type box = __ *)
-
-Definition box1 := box nat 0.
-Extraction box1. (* let box1 = Obj.magic O *)
-
-(* applied constant, magic needed *)
-
-Definition idzarb (b:bool) (x:if b then nat else bool) := x.
-Definition zarb := idzarb true 0.
-Extraction NoInline idzarb.
-Extraction zarb.
-(* let zarb = Obj.magic idzarb True (Obj.magic O) *)
-
-(** function of variable arity. *)
-(** Fun n = nat -> nat -> ... -> nat *)
-
-Fixpoint Fun (n:nat) : Set :=
- match n with
- | O => nat
- | S n => nat -> Fun n
- end.
-
-Fixpoint Const (k n:nat) {struct n} : Fun n :=
- match n as x return Fun x with
- | O => k
- | S n => fun p:nat => Const k n
- end.
-
-Fixpoint proj (k n:nat) {struct n} : Fun n :=
- match n as x return Fun x with
- | O => 0 (* ou assert false ....*)
- | S n =>
- match k with
- | O => fun x => Const x n
- | S k => fun x => proj k n
- end
- end.
-
-Definition test_proj := proj 2 4 0 1 2 3.
-
-Eval compute in test_proj.
-
-Recursive Extraction test_proj.
-
-
-
-(*** TO SUM UP: ***)
-
-
-Extraction
- "test_extraction.ml" idnat id id' test2 test3 test4 test5 test6 test7 d d2
- d3 d4 d5 d6 test8 id id' test9 test10 test11 test12
- test13 test19 test20 nat sumbool_rect c Finite tree
- tree_size test14 test15 eta_c test16 test17 test18 bidon
- tb fbidon fbidon2 fbidon2 test_0 test_1 eq eq_rect tp1
- tp1bis Truc oups test24 loop horibilis PropSet natbool
- zerotrue zeroTrue zeroprop test21 test22 test23 f f_prop
- f_arity f_normal Boite boite1 boite2 test_boite Box box1
- zarb test_proj.
-
diff --git a/contrib/first-order/ground.ml b/contrib/first-order/ground.ml
index bb096308..bccac6df 100644
--- a/contrib/first-order/ground.ml
+++ b/contrib/first-order/ground.ml
@@ -6,7 +6,7 @@
(* * GNU Lesser General Public License Version 2.1 *)
(************************************************************************)
-(* $Id: ground.ml 7909 2006-01-21 11:09:18Z herbelin $ *)
+(* $Id: ground.ml 9537 2007-01-26 10:05:04Z corbinea $ *)
open Formula
open Sequent
@@ -81,7 +81,7 @@ let ground_tac solver startseq gl=
tclFAIL 0 (Pp.str "reversible in 1st order mode")
else
backtrack in
- forall_tac backtrack continue (re_add seq1)
+ forall_tac backtrack1 continue (re_add seq1)
| Rarrow->
arrow_tac backtrack continue (re_add seq1)
| Ror->
diff --git a/contrib/funind/functional_principles_proofs.ml b/contrib/funind/functional_principles_proofs.ml
index 14e2233f..ff4f7499 100644
--- a/contrib/funind/functional_principles_proofs.ml
+++ b/contrib/funind/functional_principles_proofs.ml
@@ -1380,219 +1380,6 @@ let is_valid_hypothesis predicates_name =
| _ -> false
in
is_valid_hypothesis
-(*
-let fresh_id avoid na =
- let id =
- match na with
- | Name id -> id
- | Anonymous -> h_id
- in
- next_global_ident_away true id avoid
-
-
-let prove_principle_for_gen
- (f_ref,functional_ref,eq_ref) tcc_lemma_ref is_mes
- rec_arg_num rec_arg_type relation =
- fun g ->
- let type_of_goal = pf_concl g in
- let goal_ids = pf_ids_of_hyps g in
- let goal_elim_infos = compute_elim_sig type_of_goal in
- let params_names,ids = List.fold_left
- (fun (params_names,avoid) (na,_,_) ->
- let new_id = fresh_id avoid na in
- (new_id::params_names,new_id::avoid)
- )
- ([],goal_ids)
- goal_elim_infos.params
- in
- let predicates_names,ids =
- List.fold_left
- (fun (predicates_names,avoid) (na,_,_) ->
- let new_id = fresh_id avoid na in
- (new_id::predicates_names,new_id::avoid)
- )
- ([],ids)
- goal_elim_infos.predicates
- in
- let branches_names,ids =
- List.fold_left
- (fun (branches_names,avoid) (na,_,_) ->
- let new_id = fresh_id avoid na in
- (new_id::branches_names,new_id::avoid)
- )
- ([],ids)
- goal_elim_infos.branches
- in
- let to_intro = params_names@predicates_names@branches_names in
- let nparams = List.length params_names in
- let rec_arg_num = rec_arg_num - nparams in
- let tac_intro_static = h_intros to_intro in
- let args_info = ref None in
- let arg_tac g = (* introducing args *)
- let ids = pf_ids_of_hyps g in
- let func_body = def_of_const (mkConst functional_ref) in
- (* let _ = Pp.msgnl (Printer.pr_lconstr func_body) in *)
- let (f_name, _, body1) = destLambda func_body in
- let f_id =
- match f_name with
- | Name f_id -> next_global_ident_away true f_id ids
- | Anonymous -> anomaly "anonymous function"
- in
- let n_names_types,_ = decompose_lam body1 in
- let n_ids,ids =
- List.fold_left
- (fun (n_ids,ids) (n_name,_) ->
- match n_name with
- | Name id ->
- let n_id = next_global_ident_away true id ids in
- n_id::n_ids,n_id::ids
- | _ -> anomaly "anonymous argument"
- )
- ([],(f_id::ids))
- n_names_types
- in
- let rec_arg_id = List.nth n_ids (rec_arg_num - 1 ) in
- let args_ids = snd (list_chop nparams n_ids) in
- args_info := Some (ids,args_ids,rec_arg_id);
- h_intros args_ids g
- in
- let wf_tac =
- if is_mes
- then
- (fun b -> Recdef.tclUSER_if_not_mes b None)
- else fun _ -> prove_with_tcc tcc_lemma_ref []
- in
- let start_tac g =
- let ids,args_ids,rec_arg_id = out_some !args_info in
- let nargs = List.length args_ids in
- let pre_rec_arg =
- List.rev_map
- mkVar
- (fst (list_chop (rec_arg_num - 1) args_ids))
- in
- let args_before_rec = pre_rec_arg@(List.map mkVar params_names) in
- let relation = substl args_before_rec relation in
- let input_type = substl args_before_rec rec_arg_type in
- let wf_thm = next_global_ident_away true (id_of_string ("wf_R")) ids in
- let wf_rec_arg =
- next_global_ident_away true
- (id_of_string ("Acc_"^(string_of_id rec_arg_id)))
- (wf_thm::ids)
- in
- let hrec = next_global_ident_away true hrec_id (wf_rec_arg::wf_thm::ids) in
- let acc_inv =
- lazy (
- mkApp (
- delayed_force acc_inv_id,
- [|input_type;relation;mkVar rec_arg_id|]
- )
- )
- in
- (tclTHENS
- (observe_tac
- "first assert"
- (assert_tac
- true (* the assert thm is in first subgoal *)
- (Name wf_rec_arg)
- (mkApp (delayed_force acc_rel,
- [|input_type;relation;mkVar rec_arg_id|])
- )
- )
- )
- [
- (* accesibility proof *)
- tclTHENS
- (observe_tac
- "second assert"
- (assert_tac
- true
- (Name wf_thm)
- (mkApp (delayed_force well_founded,[|input_type;relation|]))
- )
- )
- [
- (* interactive proof of the well_foundness of the relation *)
- wf_tac is_mes;
- (* well_foundness -> Acc for any element *)
- observe_tac
- "apply wf_thm"
- (h_apply ((mkApp(mkVar wf_thm,
- [|mkVar rec_arg_id |])),Rawterm.NoBindings)
- )
- ]
- ;
- (* rest of the proof *)
- tclTHENSEQ
- [
- observe_tac "generalize" (fun g ->
- let to_thin =
- fst (list_chop ( nargs + 1) (pf_ids_of_hyps g))
- in
- let to_thin_c = List.rev_map mkVar to_thin in
- tclTHEN (generalize to_thin_c) (observe_tac "thin" (h_clear false to_thin)) g
- );
- observe_tac "h_fix" (h_fix (Some hrec) (nargs+1));
- h_intros args_ids;
- h_intro wf_rec_arg;
- Equality.rewriteLR (mkConst eq_ref);
- (fun g' ->
- let body =
- let _,args = destApp (pf_concl g') in
- array_last args
- in
- let body_info rec_hyps =
- {
- nb_rec_hyps = List.length rec_hyps;
- rec_hyps = rec_hyps;
- eq_hyps = [];
- info = body
- }
- in
- let acc_inv = lazy (mkApp(Lazy.force acc_inv, [|mkVar wf_rec_arg|]) ) in
- let pte_info =
- { proving_tac =
- (fun eqs ->
- observe_tac "new_prove_with_tcc"
- (new_prove_with_tcc is_mes acc_inv hrec tcc_lemma_ref (List.map mkVar eqs))
- );
- is_valid = is_valid_hypothesis predicates_names
- }
- in
- let ptes_info : pte_info Idmap.t =
- List.fold_left
- (fun map pte_id ->
- Idmap.add pte_id
- pte_info
- map
- )
- Idmap.empty
- predicates_names
- in
- let make_proof rec_hyps =
- build_proof
- false
- [f_ref]
- ptes_info
- (body_info rec_hyps)
- in
- instanciate_hyps_with_args
- make_proof
- branches_names
- args_ids
- g'
-
- )
- ]
- ]
- g
- )
- in
- tclTHENSEQ
- [tac_intro_static;
- arg_tac;
- start_tac
- ] g
-*)
let prove_principle_for_gen
(f_ref,functional_ref,eq_ref) tcc_lemma_ref is_mes
@@ -1627,14 +1414,22 @@ let prove_principle_for_gen
in
let real_rec_arg_num = rec_arg_num - princ_info.nparams in
let npost_rec_arg = princ_info.nargs - real_rec_arg_num + 1 in
+ observe (
+ str "princ_type := " ++ pr_lconstr princ_type ++ fnl () ++
+ str "princ_info.nparams := " ++ int princ_info.nparams ++ fnl () ++
+ str "princ_info.nargs := " ++ int princ_info.nargs ++ fnl () ++
+ str "rec_arg_num := " ++ int rec_arg_num ++ fnl() ++
+ str "real_rec_arg_num := " ++ int real_rec_arg_num ++ fnl () ++
+ str "npost_rec_arg := " ++ int npost_rec_arg );
let (post_rec_arg,pre_rec_arg) =
Util.list_chop npost_rec_arg princ_info.args
in
let rec_arg_id =
- match post_rec_arg with
+ match List.rev post_rec_arg with
| (Name id,_,_)::_ -> id
| _ -> assert false
in
+ observe (str "rec_arg_id := " ++ pr_lconstr (mkVar rec_arg_id));
let subst_constrs = List.map (fun (na,_,_) -> mkVar (Nameops.out_name na)) (pre_rec_arg@princ_info.params) in
let relation = substl subst_constrs relation in
let input_type = substl subst_constrs rec_arg_type in
@@ -1679,7 +1474,7 @@ let prove_principle_for_gen
(mkApp (delayed_force acc_rel,[|input_type;relation;mkVar rec_arg_id|]))
);
observe_tac "reverting" (revert (List.rev (acc_rec_arg_id::args_ids)));
- observe_tac "h_fix" (h_fix (Some fix_id) (real_rec_arg_num + 1));
+ observe_tac "h_fix" (h_fix (Some fix_id) (npost_rec_arg + 1));
h_intros (List.rev (acc_rec_arg_id::args_ids));
Equality.rewriteLR (mkConst eq_ref);
observe_tac "finish" (fun gl' ->
diff --git a/contrib/funind/functional_principles_types.ml b/contrib/funind/functional_principles_types.ml
index 89ebb75a..8ad2e72b 100644
--- a/contrib/funind/functional_principles_types.ml
+++ b/contrib/funind/functional_principles_types.ml
@@ -405,11 +405,26 @@ let generate_functional_principle
let (id,(entry,g_kind,hook)) =
build_functional_principle interactive_proof old_princ_type new_sorts funs i proof_tac hook
in
+ (* Pr 1278 :
+ Don't forget to close the goal if an error is raised !!!!
+ *)
save false new_princ_name entry g_kind hook
- with
- | Defining_principle _ as e -> raise e
- | e -> raise (Defining_principle e)
-
+ with e ->
+ begin
+ begin
+ try
+ let id = Pfedit.get_current_proof_name () in
+ let s = string_of_id id in
+ let n = String.length "___________princ_________" in
+ if String.length s >= n
+ then if String.sub s 0 n = "___________princ_________"
+ then Pfedit.delete_current_proof ()
+ else ()
+ else ()
+ with _ -> ()
+ end;
+ raise (Defining_principle e)
+ end
(* defined () *)
diff --git a/contrib/funind/indfun.ml b/contrib/funind/indfun.ml
index 82bb2869..6e2af224 100644
--- a/contrib/funind/indfun.ml
+++ b/contrib/funind/indfun.ml
@@ -266,7 +266,7 @@ let derive_inversion fix_names =
)
with e ->
msg_warning
- (str "Cannot built inversion information" ++
+ (str "Cannot build functional inversion principle" ++
if do_observe () then Cerrors.explain_exn e else mt ())
with _ -> ()
diff --git a/contrib/funind/rawtermops.ml b/contrib/funind/rawtermops.ml
index ed46ec72..ba5c2bbd 100644
--- a/contrib/funind/rawtermops.ml
+++ b/contrib/funind/rawtermops.ml
@@ -561,7 +561,7 @@ let ids_of_rawterm c =
| RCases (loc,rtntypopt,tml,brchl) ->
List.flatten (List.map (fun (_,idl,patl,c) -> idl @ ids_of_rawterm [] c) brchl)
| RRec _ -> failwith "Fix inside a constructor branch"
- | (RSort _ | RHole _ | RRef _ | REvar _ | RPatVar _ | RDynamic _) as x -> []
+ | (RSort _ | RHole _ | RRef _ | REvar _ | RPatVar _ | RDynamic _) -> []
in
(* build the set *)
List.fold_left (fun acc x -> Idset.add x acc) Idset.empty (ids_of_rawterm [] c)
diff --git a/contrib/interface/ascent.mli b/contrib/interface/ascent.mli
index b6cc55f6..ef1d095e 100644
--- a/contrib/interface/ascent.mli
+++ b/contrib/interface/ascent.mli
@@ -642,6 +642,7 @@ and ct_TACTIC_COM =
| CT_elim_type of ct_FORMULA
| CT_exact of ct_FORMULA
| CT_exact_no_check of ct_FORMULA
+ | CT_vm_cast_no_check of ct_FORMULA
| CT_exists of ct_SPEC_LIST
| CT_fail of ct_ID_OR_INT * ct_STRING_OPT
| CT_first of ct_TACTIC_COM * ct_TACTIC_COM list
diff --git a/contrib/interface/parse.ml b/contrib/interface/parse.ml
index 4d4df59f..8cca7614 100644
--- a/contrib/interface/parse.ml
+++ b/contrib/interface/parse.ml
@@ -315,21 +315,21 @@ let parse_file_action reqid file_name =
fnl () ++ Cerrors.explain_exn e));;
let add_rec_path_action reqid string_arg ident_arg =
- let directory_name = glob string_arg in
+ let directory_name = expand_path_macros string_arg in
begin
add_rec_path directory_name (Libnames.dirpath_of_string ident_arg)
end;;
let add_path_action reqid string_arg =
- let directory_name = glob string_arg in
+ let directory_name = expand_path_macros string_arg in
begin
add_path directory_name Names.empty_dirpath
end;;
let print_version_action () =
msgnl (mt ());
- msgnl (str "$Id: parse.ml 7844 2006-01-11 16:36:14Z bertot $");;
+ msgnl (str "$Id: parse.ml 9397 2006-11-21 21:50:54Z herbelin $");;
let load_syntax_action reqid module_name =
msg (str "loading " ++ str module_name ++ str "... ");
diff --git a/contrib/interface/vtp.ml b/contrib/interface/vtp.ml
index fe227f99..166a0cbf 100644
--- a/contrib/interface/vtp.ml
+++ b/contrib/interface/vtp.ml
@@ -1549,6 +1549,9 @@ and fTACTIC_COM = function
| CT_exact_no_check(x1) ->
fFORMULA x1;
fNODE "exact_no_check" 1
+| CT_vm_cast_no_check(x1) ->
+ fFORMULA x1;
+ fNODE "vm_cast_no_check" 1
| CT_exists(x1) ->
fSPEC_LIST x1;
fNODE "exists" 1
diff --git a/contrib/interface/xlate.ml b/contrib/interface/xlate.ml
index 6c9e8239..60195229 100644
--- a/contrib/interface/xlate.ml
+++ b/contrib/interface/xlate.ml
@@ -1060,6 +1060,7 @@ and xlate_tac =
| TacAssumption -> CT_assumption
| TacExact c -> CT_exact (xlate_formula c)
| TacExactNoCheck c -> CT_exact_no_check (xlate_formula c)
+ | TacVmCastNoCheck c -> CT_vm_cast_no_check (xlate_formula c)
| TacDestructHyp (true, (_,id)) -> CT_cdhyp (xlate_ident id)
| TacDestructHyp (false, (_,id)) -> CT_dhyp (xlate_ident id)
| TacDestructConcl -> CT_dconcl
@@ -1978,7 +1979,7 @@ let rec xlate_vernac =
| VernacOpenCloseScope(false, true, s) -> CT_open_scope(CT_ident s)
| VernacOpenCloseScope(true, false, s) -> CT_local_close_scope(CT_ident s)
| VernacOpenCloseScope(false, false, s) -> CT_close_scope(CT_ident s)
- | VernacArgumentsScope(qid, l) ->
+ | VernacArgumentsScope(true, qid, l) ->
CT_arguments_scope(loc_qualid_to_ct_ID qid,
CT_id_opt_list
(List.map
@@ -1986,6 +1987,8 @@ let rec xlate_vernac =
match x with
None -> ctv_ID_OPT_NONE
| Some x -> ctf_ID_OPT_SOME(CT_ident x)) l))
+ | VernacArgumentsScope(false, qid, l) ->
+ xlate_error "TODO: Arguments Scope Global"
| VernacDelimiters(s1,s2) -> CT_delim_scope(CT_ident s1, CT_ident s2)
| VernacBindScope(id, a::l) ->
let xlate_class_rawexpr = function
@@ -2060,7 +2063,7 @@ let rec xlate_vernac =
| VernacNop -> CT_proof_no_op
| VernacComments l ->
CT_scomments(CT_scomment_content_list (List.map xlate_comment l))
- | VernacDeclareImplicits(id, opt_positions) ->
+ | VernacDeclareImplicits(true, id, opt_positions) ->
CT_implicits
(reference_to_ct_ID id,
match opt_positions with
@@ -2073,6 +2076,8 @@ let rec xlate_vernac =
-> xlate_error
"explication argument by rank is obsolete"
| ExplByName id -> CT_ident (string_of_id id)) l)))
+ | VernacDeclareImplicits(false, id, opt_positions) ->
+ xlate_error "TODO: Implicit Arguments Global"
| VernacReserve((_,a)::l, f) ->
CT_reserve(CT_id_ne_list(xlate_ident a,
List.map (fun (_,x) -> xlate_ident x) l),
diff --git a/contrib/setoid_ring/ArithRing.v b/contrib/setoid_ring/ArithRing.v
index 5060bc69..074f6ef7 100644
--- a/contrib/setoid_ring/ArithRing.v
+++ b/contrib/setoid_ring/ArithRing.v
@@ -7,20 +7,32 @@
(************************************************************************)
Require Import Mult.
+Require Import BinNat.
+Require Import Nnat.
Require Export Ring.
Set Implicit Arguments.
-Ltac isnatcst t :=
- let t := eval hnf in t in
- match t with
- O => true
- | S ?p => isnatcst p
- | _ => false
- end.
+Lemma natSRth : semi_ring_theory O (S O) plus mult (@eq nat).
+ Proof.
+ constructor. exact plus_0_l. exact plus_comm. exact plus_assoc.
+ exact mult_1_l. exact mult_0_l. exact mult_comm. exact mult_assoc.
+ exact mult_plus_distr_r.
+ Qed.
+
+Lemma nat_morph_N :
+ semi_morph 0 1 plus mult (eq (A:=nat))
+ 0%N 1%N Nplus Nmult Neq_bool nat_of_N.
+Proof.
+ constructor;trivial.
+ exact nat_of_Nplus.
+ exact nat_of_Nmult.
+ intros x y H;rewrite (Neq_bool_ok _ _ H);trivial.
+Qed.
+
Ltac natcst t :=
match isnatcst t with
- true => t
- | _ => NotConstant
+ true => constr:(N_of_nat t)
+ | _ => InitialRing.NotConstant
end.
Ltac Ss_to_add f acc :=
@@ -43,28 +55,6 @@ Ltac natprering :=
| _ => idtac
end.
- Lemma natSRth : semi_ring_theory O (S O) plus mult (@eq nat).
- Proof.
- constructor. exact plus_0_l. exact plus_comm. exact plus_assoc.
- exact mult_1_l. exact mult_0_l. exact mult_comm. exact mult_assoc.
- exact mult_plus_distr_r.
- Qed.
-
-
-Unboxed Fixpoint nateq (n m:nat) {struct m} : bool :=
- match n, m with
- | O, O => true
- | S n', S m' => nateq n' m'
- | _, _ => false
- end.
-
-Lemma nateq_ok : forall n m:nat, nateq n m = true -> n = m.
-Proof.
- simple induction n; simple induction m; simpl; intros; try discriminate.
- trivial.
- rewrite (H n1 H1).
- trivial.
-Qed.
-
Add Ring natr : natSRth
- (decidable nateq_ok, constants [natcst], preprocess [natprering]).
+ (morphism nat_morph_N, constants [natcst], preprocess [natprering]).
+
diff --git a/contrib/setoid_ring/BinList.v b/contrib/setoid_ring/BinList.v
index 0d0fe5a4..50902004 100644
--- a/contrib/setoid_ring/BinList.v
+++ b/contrib/setoid_ring/BinList.v
@@ -10,7 +10,7 @@ Set Implicit Arguments.
Require Import BinPos.
Require Export List.
Require Export ListTactics.
-Open Scope positive_scope.
+Open Local Scope positive_scope.
Section MakeBinList.
Variable A : Type.
@@ -89,3 +89,5 @@ Section MakeBinList.
Qed.
End MakeBinList.
+
+
diff --git a/contrib/setoid_ring/Field_tac.v b/contrib/setoid_ring/Field_tac.v
index 786654ab..aad3a580 100644
--- a/contrib/setoid_ring/Field_tac.v
+++ b/contrib/setoid_ring/Field_tac.v
@@ -10,10 +10,10 @@ Require Import Ring_tac BinList Ring_polynom InitialRing.
Require Export Field_theory.
(* syntaxification *)
- Ltac mkFieldexpr C Cst radd rmul rsub ropp rdiv rinv t fv :=
+ Ltac mkFieldexpr C Cst CstPow radd rmul rsub ropp rdiv rinv rpow t fv :=
let rec mkP t :=
match Cst t with
- | Ring_tac.NotConstant =>
+ | InitialRing.NotConstant =>
match t with
| (radd ?t1 ?t2) =>
let e1 := mkP t1 in
@@ -31,6 +31,13 @@ Require Export Field_theory.
let e2 := mkP t2 in constr:(FEdiv e1 e2)
| (rinv ?t1) =>
let e1 := mkP t1 in constr:(FEinv e1)
+ | (rpow ?t1 ?n) =>
+ match CstPow n with
+ | InitialRing.NotConstant =>
+ let p := Find_at t fv in constr:(@FEX C p)
+ | ?c => let e1 := mkP t1 in constr:(FEpow e1 c)
+ end
+
| _ =>
let p := Find_at t fv in constr:(@FEX C p)
end
@@ -38,10 +45,10 @@ Require Export Field_theory.
end
in mkP t.
-Ltac FFV Cst add mul sub opp div inv t fv :=
+Ltac FFV Cst CstPow add mul sub opp div inv pow t fv :=
let rec TFV t fv :=
match Cst t with
- | Ring_tac.NotConstant =>
+ | InitialRing.NotConstant =>
match t with
| (add ?t1 ?t2) => TFV t2 ltac:(TFV t1 fv)
| (mul ?t1 ?t2) => TFV t2 ltac:(TFV t1 fv)
@@ -49,16 +56,24 @@ Ltac FFV Cst add mul sub opp div inv t fv :=
| (opp ?t1) => TFV t1 fv
| (div ?t1 ?t2) => TFV t2 ltac:(TFV t1 fv)
| (inv ?t1) => TFV t1 fv
+ | (pow ?t1 ?n) =>
+ match CstPow n with
+ | InitialRing.NotConstant => AddFvTail t fv
+ | _ => TFV t1 fv
+ end
| _ => AddFvTail t fv
end
| _ => fv
end
in TFV t fv.
-Ltac ParseFieldComponents lemma req :=
+Ltac ParseFieldComponents lemma :=
match type of lemma with
- | context [@FEeval ?R ?rO ?add ?mul ?sub ?opp ?div ?inv ?C ?phi _ _] =>
- (fun f => f add mul sub opp div inv C)
+ | context [
+ (* PCond _ _ _ _ _ _ _ _ _ _ _ -> *)
+ (@FEeval ?R ?rO ?radd ?rmul ?rsub ?ropp ?rdiv ?rinv
+ ?C ?phi ?Cpow ?Cp_phi ?rpow _ _) ] =>
+ (fun f => f radd rmul rsub ropp rdiv rinv rpow C)
| _ => fail 1 "field anomaly: bad correctness lemma (parse)"
end.
@@ -78,91 +93,244 @@ Ltac fold_field_cond req :=
Ltac simpl_PCond req :=
protect_fv "field_cond";
- try (exact I);
+ (try exact I);
+ fold_field_cond req.
+
+Ltac simpl_PCond_BEURK req :=
+ protect_fv "field_cond";
fold_field_cond req.
(* Rewriting (field_simplify) *)
-Ltac Field_simplify lemma Cond_lemma req Cst_tac :=
- let Make_tac :=
- match type of lemma with
- | forall l fe nfe,
- _ = nfe ->
- PCond _ _ _ _ _ _ _ _ _ ->
- req (FEeval ?rO ?radd ?rmul ?rsub ?ropp ?rdiv ?rinv (C:=?C) ?phi l fe)
- _ =>
- let mkFV := FFV Cst_tac radd rmul rsub ropp rdiv rinv in
- let mkFE := mkFieldexpr C Cst_tac radd rmul rsub ropp rdiv rinv in
- let simpl_field H := protect_fv "field" in H in
- fun f rl => f mkFV mkFE simpl_field lemma req rl;
- try (apply Cond_lemma; simpl_PCond req)
- | _ => fail 1 "field anomaly: bad correctness lemma (rewr)"
- end in
- Make_tac ReflexiveRewriteTactic.
-(* Pb: second rewrite are applied to non-zero condition of first rewrite... *)
-
-Tactic Notation (at level 0) "field_simplify" constr_list(rl) :=
- field_lookup
- (fun req cst_tac _ _ field_simplify_ok cond_ok pre post rl =>
- pre(); Field_simplify field_simplify_ok cond_ok req cst_tac rl; post()).
-
-
-(* Generic form of field tactics *)
-Ltac Field_Scheme FV_tac SYN_tac SIMPL_tac lemma Cond_lemma req :=
- let R := match type of req with ?R -> _ => R end in
- let rec ParseExpr ilemma :=
- match type of ilemma with
- forall nfe, ?fe = nfe -> _ =>
- (fun t =>
- let x := fresh "fld_expr" in
- let H := fresh "norm_fld_expr" in
- compute_assertion H x fe;
- ParseExpr (ilemma x H) t;
- try clear x H)
- | _ => (fun t => t ilemma)
- end in
- let Main r1 r2 :=
- let fv := FV_tac r1 (@List.nil R) in
- let fv := FV_tac r2 fv in
- let fe1 := SYN_tac r1 fv in
- let fe2 := SYN_tac r2 fv in
- ParseExpr (lemma fv fe1 fe2)
- ltac:(fun ilemma =>
- apply ilemma || fail "field anomaly: failed in applying lemma";
- [ SIMPL_tac | apply Cond_lemma; simpl_PCond req]) in
- OnEquation req Main.
+Ltac Field_norm_gen f Cst_tac Pow_tac lemma Cond_lemma req n lH rl :=
+ let Main radd rmul rsub ropp rdiv rinv rpow C :=
+ let mkFV := FV Cst_tac Pow_tac radd rmul rsub ropp rpow in
+ let mkPol := mkPolexpr C Cst_tac Pow_tac radd rmul rsub ropp rpow in
+ let mkFFV := FFV Cst_tac Pow_tac radd rmul rsub ropp rdiv rinv rpow in
+ let mkFE :=
+ mkFieldexpr C Cst_tac Pow_tac radd rmul rsub ropp rdiv rinv rpow in
+ let fv := FV_hypo_tac mkFV req lH in
+ let simpl_field H := (protect_fv "field" in H;f H) in
+ let lemma_tac fv RW_tac :=
+ let rr_lemma := fresh "f_rw_lemma" in
+ let lpe := mkHyp_tac C req ltac:(fun t => mkPol t fv) lH in
+ let vlpe := fresh "list_hyp" in
+ let vlmp := fresh "list_hyp_norm" in
+ let vlmp_eq := fresh "list_hyp_norm_eq" in
+ let prh := proofHyp_tac lH in
+ pose (vlpe := lpe);
+ match type of lemma with
+ | context [mk_monpol_list ?cO ?cI ?cadd ?cmul ?csub ?copp ?ceqb _] =>
+ compute_assertion vlmp_eq vlmp
+ (mk_monpol_list cO cI cadd cmul csub copp ceqb vlpe);
+ (assert (rr_lemma := lemma n vlpe fv prh vlmp vlmp_eq)
+ || fail "type error when build the rewriting lemma");
+ RW_tac rr_lemma;
+ try clear rr_lemma vlmp_eq vlmp vlpe
+ | _ => fail 1 "field_simplify anomaly: bad correctness lemma"
+ end in
+ ReflexiveRewriteTactic mkFFV mkFE simpl_field lemma_tac fv rl;
+ try (apply Cond_lemma; simpl_PCond req) in
+ ParseFieldComponents lemma Main.
+
+Ltac Field_simplify_gen f :=
+ fun req cst_tac pow_tac _ _ field_simplify_ok _ cond_ok pre post lH rl =>
+ pre();
+ Field_norm_gen f cst_tac pow_tac field_simplify_ok cond_ok req
+ ring_subst_niter lH rl;
+ post().
+
+Ltac Field_simplify := Field_simplify_gen ltac:(fun H => rewrite H).
+
+Tactic Notation (at level 0)
+ "field_simplify" constr_list(rl) :=
+ match goal with [|- ?G] => field_lookup Field_simplify [] rl [G] end.
+
+Tactic Notation (at level 0)
+ "field_simplify" "[" constr_list(lH) "]" constr_list(rl) :=
+ match goal with [|- ?G] => field_lookup Field_simplify [lH] rl [G] end.
+
+Tactic Notation "field_simplify" constr_list(rl) "in" hyp(H):=
+ let G := getGoal in
+ let t := type of H in
+ let g := fresh "goal" in
+ set (g:= G);
+ generalize H;clear H;
+ field_lookup Field_simplify [] rl [t];
+ intro H;
+ unfold g;clear g.
+
+Tactic Notation "field_simplify" "["constr_list(lH) "]" constr_list(rl) "in" hyp(H):=
+ let G := getGoal in
+ let t := type of H in
+ let g := fresh "goal" in
+ set (g:= G);
+ generalize H;clear H;
+ field_lookup Field_simplify [lH] rl [t];
+ intro H;
+ unfold g;clear g.
+
+(*
+Ltac Field_simplify_in hyp:=
+ Field_simplify_gen ltac:(fun H => rewrite H in hyp).
+
+Tactic Notation (at level 0)
+ "field_simplify" constr_list(rl) "in" hyp(h) :=
+ let t := type of h in
+ field_lookup (Field_simplify_in h) [] rl [t].
+
+Tactic Notation (at level 0)
+ "field_simplify" "[" constr_list(lH) "]" constr_list(rl) "in" hyp(h) :=
+ let t := type of h in
+ field_lookup (Field_simplify_in h) [lH] rl [t].
+*)
+
+(** Generic tactic for solving equations *)
+
+Ltac Field_Scheme Simpl_tac Cst_tac Pow_tac lemma Cond_lemma req n lH :=
+ let Main radd rmul rsub ropp rdiv rinv rpow C :=
+ let mkFV := FV Cst_tac Pow_tac radd rmul rsub ropp rpow in
+ let mkPol := mkPolexpr C Cst_tac Pow_tac radd rmul rsub ropp rpow in
+ let mkFFV := FFV Cst_tac Pow_tac radd rmul rsub ropp rdiv rinv rpow in
+ let mkFE :=
+ mkFieldexpr C Cst_tac Pow_tac radd rmul rsub ropp rdiv rinv rpow in
+ let rec ParseExpr ilemma :=
+ match type of ilemma with
+ forall nfe, ?fe = nfe -> _ =>
+ (fun t =>
+ let x := fresh "fld_expr" in
+ let H := fresh "norm_fld_expr" in
+ compute_assertion H x fe;
+ ParseExpr (ilemma x H) t;
+ try clear x H)
+ | _ => (fun t => t ilemma)
+ end in
+ let Main_eq t1 t2 :=
+ let fv := FV_hypo_tac mkFV req lH in
+ let fv := mkFFV t1 fv in
+ let fv := mkFFV t2 fv in
+ let lpe := mkHyp_tac C req ltac:(fun t => mkPol t fv) lH in
+ let prh := proofHyp_tac lH in
+ let vlpe := fresh "list_hyp" in
+ let fe1 := mkFE t1 fv in
+ let fe2 := mkFE t2 fv in
+ pose (vlpe := lpe);
+ let nlemma := fresh "field_lemma" in
+ (assert (nlemma := lemma n fv vlpe fe1 fe2 prh)
+ || fail "field anomaly:failed to build lemma");
+ ParseExpr nlemma
+ ltac:(fun ilemma =>
+ apply ilemma
+ || fail "field anomaly: failed in applying lemma";
+ [ Simpl_tac | apply Cond_lemma; simpl_PCond req]);
+ clear vlpe nlemma in
+ OnEquation req Main_eq in
+ ParseFieldComponents lemma Main.
(* solve completely a field equation, leaving non-zero conditions to be
proved (field) *)
-Ltac Field lemma Cond_lemma req Cst_tac :=
- let Main radd rmul rsub ropp rdiv rinv C :=
- let mkFV := FFV Cst_tac radd rmul rsub ropp rdiv rinv in
- let mkFE := mkFieldexpr C Cst_tac radd rmul rsub ropp rdiv rinv in
- let Simpl :=
- vm_compute; reflexivity || fail "not a valid field equation" in
- Field_Scheme mkFV mkFE Simpl lemma Cond_lemma req in
- ParseFieldComponents lemma req Main.
+Ltac FIELD :=
+ let Simpl := vm_compute; reflexivity || fail "not a valid field equation" in
+ fun req cst_tac pow_tac field_ok _ _ _ cond_ok pre post lH rl =>
+ pre();
+ Field_Scheme Simpl cst_tac pow_tac field_ok cond_ok req
+ Ring_tac.ring_subst_niter lH;
+ try exact I;
+ post().
+
Tactic Notation (at level 0) "field" :=
- field_lookup
- (fun req cst_tac field_ok _ _ cond_ok pre post rl =>
- pre(); Field field_ok cond_ok req cst_tac; post()).
+ let G := getGoal in field_lookup FIELD [] [G].
+
+Tactic Notation (at level 0) "field" "[" constr_list(lH) "]" :=
+ let G := getGoal in field_lookup FIELD [lH] [G].
(* transforms a field equation to an equivalent (simplified) ring equation,
and leaves non-zero conditions to be proved (field_simplify_eq) *)
-Ltac Field_simplify_eq lemma Cond_lemma req Cst_tac :=
- let Main radd rmul rsub ropp rdiv rinv C :=
- let mkFV := FFV Cst_tac radd rmul rsub ropp rdiv rinv in
- let mkFE := mkFieldexpr C Cst_tac radd rmul rsub ropp rdiv rinv in
- let Simpl := (protect_fv "field") in
- Field_Scheme mkFV mkFE Simpl lemma Cond_lemma req in
- ParseFieldComponents lemma req Main.
-
-Tactic Notation (at level 0) "field_simplify_eq" :=
- field_lookup
- (fun req cst_tac _ field_simplify_eq_ok _ cond_ok pre post rl =>
- pre(); Field_simplify_eq field_simplify_eq_ok cond_ok req cst_tac;
- post()).
+Ltac FIELD_SIMPL :=
+ let Simpl := (protect_fv "field") in
+ fun req cst_tac pow_tac _ field_simplify_eq_ok _ _ cond_ok pre post lH rl =>
+ pre();
+ Field_Scheme Simpl cst_tac pow_tac field_simplify_eq_ok cond_ok
+ req Ring_tac.ring_subst_niter lH;
+ post().
+
+Tactic Notation (at level 0) "field_simplify_eq" :=
+ let G := getGoal in field_lookup FIELD_SIMPL [] [G].
+
+Tactic Notation (at level 0) "field_simplify_eq" "[" constr_list(lH) "]" :=
+ let G := getGoal in field_lookup FIELD_SIMPL [lH] [G].
+
+(* Same as FIELD_SIMPL but in hypothesis *)
+
+Ltac Field_simplify_eq Cst_tac Pow_tac lemma Cond_lemma req n lH :=
+ let Main radd rmul rsub ropp rdiv rinv rpow C :=
+ let hyp := fresh "hyp" in
+ intro hyp;
+ match type of hyp with
+ | req ?t1 ?t2 =>
+ let mkFV := FV Cst_tac Pow_tac radd rmul rsub ropp rpow in
+ let mkPol := mkPolexpr C Cst_tac Pow_tac radd rmul rsub ropp rpow in
+ let mkFFV := FFV Cst_tac Pow_tac radd rmul rsub ropp rdiv rinv rpow in
+ let mkFE :=
+ mkFieldexpr C Cst_tac Pow_tac radd rmul rsub ropp rdiv rinv rpow in
+ let rec ParseExpr ilemma :=
+ match type of ilemma with
+ | forall nfe, ?fe = nfe -> _ =>
+ (fun t =>
+ let x := fresh "fld_expr" in
+ let H := fresh "norm_fld_expr" in
+ compute_assertion H x fe;
+ ParseExpr (ilemma x H) t;
+ try clear H x)
+ | _ => (fun t => t ilemma)
+ end in
+ let fv := FV_hypo_tac mkFV req lH in
+ let fv := mkFFV t1 fv in
+ let fv := mkFFV t2 fv in
+ let lpe := mkHyp_tac C req ltac:(fun t => mkPol t fv) lH in
+ let prh := proofHyp_tac lH in
+ let fe1 := mkFE t1 fv in
+ let fe2 := mkFE t2 fv in
+ let vlpe := fresh "vlpe" in
+ ParseExpr (lemma n fv lpe fe1 fe2 prh)
+ ltac:(fun ilemma =>
+ match type of ilemma with
+ | req _ _ -> _ -> ?EQ =>
+ let tmp := fresh "tmp" in
+ assert (tmp : EQ);
+ [ apply ilemma;
+ [ exact hyp | apply Cond_lemma; simpl_PCond_BEURK req]
+ | protect_fv "field" in tmp;
+ generalize tmp;clear tmp ];
+ clear hyp
+ end)
+ end in
+ ParseFieldComponents lemma Main.
+
+Ltac FIELD_SIMPL_EQ :=
+ fun req cst_tac pow_tac _ _ _ lemma cond_ok pre post lH rl =>
+ pre();
+ Field_simplify_eq cst_tac pow_tac lemma cond_ok req
+ Ring_tac.ring_subst_niter lH;
+ post().
+
+Tactic Notation (at level 0) "field_simplify_eq" "in" hyp(H) :=
+ let t := type of H in
+ generalize H;
+ field_lookup FIELD_SIMPL_EQ [] [t];
+ [ try exact I
+ | clear H;intro H].
+
+
+Tactic Notation (at level 0)
+ "field_simplify_eq" "[" constr_list(lH) "]" "in" hyp(H) :=
+ let t := type of H in
+ generalize H;
+ field_lookup FIELD_SIMPL_EQ [lH] [t];
+ [ try exact I
+ |clear H;intro H].
+
(* Adding a new field *)
Ltac ring_of_field f :=
@@ -179,22 +347,59 @@ Ltac coerce_to_almost_field set ext f :=
| semi_field_theory _ _ _ _ _ _ _ => constr:(SF2AF set f)
end.
-Ltac field_elements set ext fspec rk :=
+Ltac field_elements set ext fspec pspec sspec rk :=
let afth := coerce_to_almost_field set ext fspec in
let rspec := ring_of_field fspec in
- ring_elements set ext rspec rk
- ltac:(fun arth ext_r morph f => f afth ext_r morph).
-
-
-Ltac field_lemmas set ext inv_m fspec rk :=
- field_elements set ext fspec rk
- ltac:(fun afth ext_r morph =>
- let field_ok := constr:(Field_correct set ext_r inv_m afth morph) in
- let field_simpl_ok :=
- constr:(Pphi_dev_div_ok set ext_r inv_m afth morph) in
- let field_simpl_eq_ok :=
- constr:(Field_simplify_eq_correct set ext_r inv_m afth morph) in
- let cond1_ok := constr:(Pcond_simpl_gen set ext_r afth morph) in
- let cond2_ok := constr:(Pcond_simpl_complete set ext_r afth morph) in
- (fun f => f afth ext_r morph field_ok field_simpl_ok field_simpl_eq_ok
- cond1_ok cond2_ok)).
+ ring_elements set ext rspec pspec sspec rk
+ ltac:(fun arth ext_r morph p_spec s_spec f => f afth ext_r morph p_spec s_spec).
+
+Ltac field_lemmas set ext inv_m fspec pspec sspec rk :=
+ let simpl_eq_lemma :=
+ match pspec with
+ | None => constr:(Field_simplify_eq_correct)
+ | Some _ => constr:(Field_simplify_eq_pow_correct)
+ end in
+ let simpl_eq_in_lemma :=
+ match pspec with
+ | None => constr:(Field_simplify_eq_in_correct)
+ | Some _ => constr:(Field_simplify_eq_pow_in_correct)
+ end in
+ let rw_lemma :=
+ match pspec with
+ | None => constr:(Field_rw_correct)
+ | Some _ => constr:(Field_rw_pow_correct)
+ end in
+ field_elements set ext fspec pspec sspec rk
+ ltac:(fun afth ext_r morph p_spec s_spec =>
+ match p_spec with
+ | mkhypo ?pp_spec => match s_spec with
+ | mkhypo ?ss_spec =>
+ let field_simpl_eq_ok :=
+ constr:(simpl_eq_lemma _ _ _ _ _ _ _ _ _ _
+ set ext_r inv_m afth
+ _ _ _ _ _ _ _ _ _ morph
+ _ _ _ pp_spec _ ss_spec) in
+ let field_simpl_ok :=
+ constr:(rw_lemma _ _ _ _ _ _ _ _ _ _
+ set ext_r inv_m afth
+ _ _ _ _ _ _ _ _ _ morph
+ _ _ _ pp_spec _ ss_spec) in
+ let field_simpl_eq_in :=
+ constr:(simpl_eq_in_lemma _ _ _ _ _ _ _ _ _ _
+ set ext_r inv_m afth
+ _ _ _ _ _ _ _ _ _ morph
+ _ _ _ pp_spec _ ss_spec) in
+ let field_ok :=
+ constr:(Field_correct set ext_r inv_m afth morph pp_spec ss_spec) in
+ let cond1_ok :=
+ constr:(Pcond_simpl_gen set ext_r afth morph pp_spec) in
+ let cond2_ok :=
+ constr:(Pcond_simpl_complete set ext_r afth morph pp_spec) in
+ (fun f =>
+ f afth ext_r morph field_ok field_simpl_ok field_simpl_eq_ok field_simpl_eq_in
+ cond1_ok cond2_ok)
+ | _ => fail 2 "bad sign specification"
+ end
+ | _ => fail 1 "bad power specification"
+ end).
+
diff --git a/contrib/setoid_ring/Field_theory.v b/contrib/setoid_ring/Field_theory.v
index f810859c..ea8421cf 100644
--- a/contrib/setoid_ring/Field_theory.v
+++ b/contrib/setoid_ring/Field_theory.v
@@ -9,6 +9,7 @@
Require Ring.
Import Ring_polynom Ring_tac Ring_theory InitialRing Setoid List.
Require Import ZArith_base.
+(*Require Import Omega.*)
Set Implicit Arguments.
Section MakeFieldPol.
@@ -29,7 +30,7 @@ Section MakeFieldPol.
Variable Rsth : Setoid_Theory R req.
Variable Reqe : ring_eq_ext radd rmul ropp req.
Variable SRinv_ext : forall p q, p == q -> / p == / q.
-
+
(* Field properties *)
Record almost_field_theory : Prop := mk_afield {
AF_AR : almost_ring_theory rO rI radd rmul rsub ropp req;
@@ -94,9 +95,20 @@ Hint Resolve (ARadd_0_l ARth) (ARadd_comm ARth) (ARadd_assoc ARth)
(ARopp_mul_l ARth) (ARopp_add ARth)
(ARsub_def ARth) .
-Notation NPEeval := (PEeval rO radd rmul rsub ropp phi).
-Notation Nnorm := (norm cO cI cadd cmul csub copp ceqb).
-Notation NPphi_dev := (Pphi_dev rO rI radd rmul cO cI ceqb phi).
+ (* Power coefficients *)
+ Variable Cpow : Set.
+ Variable Cp_phi : N -> Cpow.
+ Variable rpow : R -> Cpow -> R.
+ Variable pow_th : power_theory rI rmul req Cp_phi rpow.
+ (* sign function *)
+ Variable get_sign : C -> option C.
+ Variable get_sign_spec : sign_theory ropp req phi get_sign.
+
+Notation NPEeval := (PEeval rO radd rmul rsub ropp phi Cp_phi rpow).
+Notation Nnorm := (norm_subst cO cI cadd cmul csub copp ceqb).
+
+Notation NPphi_dev := (Pphi_dev rO rI radd rmul rsub ropp cO cI ceqb phi get_sign).
+Notation NPphi_pow := (Pphi_pow rO rI radd rmul rsub ropp cO cI ceqb phi Cp_phi rpow get_sign).
(* add abstract semi-ring to help with some proofs *)
Add Ring Rring : (ARth_SRth ARth).
@@ -105,7 +117,7 @@ Add Ring Rring : (ARth_SRth ARth).
(* additional ring properties *)
Lemma rsub_0_l : forall r, 0 - r == - r.
-intros; rewrite (ARsub_def ARth) in |- *; ring.
+intros; rewrite (ARsub_def ARth) in |- *;ring.
Qed.
Lemma rsub_0_r : forall r, r - 0 == r.
@@ -352,6 +364,20 @@ intros H1; apply f_equal with ( f := xO ); auto.
intros H1 H2; case H1; injection H2; auto.
Qed.
+Definition N_eq n1 n2 :=
+ match n1, n2 with
+ | N0, N0 => true
+ | Npos p1, Npos p2 => positive_eq p1 p2
+ | _, _ => false
+ end.
+
+Lemma N_eq_correct : forall n1 n2, if N_eq n1 n2 then n1 = n2 else n1 <> n2.
+Proof.
+ intros [ |p1] [ |p2];simpl;trivial;try(intro H;discriminate H;fail).
+ assert (H:=positive_eq_correct p1 p2);destruct (positive_eq p1 p2);
+ [rewrite H;trivial | intro H1;injection H1;subst;apply H;trivial].
+Qed.
+
(* equality test *)
Fixpoint PExpr_eq (e1 e2 : PExpr C) {struct e1} : bool :=
match e1, e2 with
@@ -361,9 +387,25 @@ Fixpoint PExpr_eq (e1 e2 : PExpr C) {struct e1} : bool :=
| PEsub e3 e5, PEsub e4 e6 => if PExpr_eq e3 e4 then PExpr_eq e5 e6 else false
| PEmul e3 e5, PEmul e4 e6 => if PExpr_eq e3 e4 then PExpr_eq e5 e6 else false
| PEopp e3, PEopp e4 => PExpr_eq e3 e4
+ | PEpow e3 n3, PEpow e4 n4 => if N_eq n3 n4 then PExpr_eq e3 e4 else false
| _, _ => false
end.
+Add Morphism (pow_pos rmul) : pow_morph.
+intros x y H p;induction p as [p IH| p IH|];simpl;auto;ring[IH].
+Qed.
+
+Add Morphism (pow_N rI rmul) : pow_N_morph.
+intros x y H [|p];simpl;auto. apply pow_morph;trivial.
+Qed.
+(*
+Lemma rpow_morph : forall x y n, x == y ->rpow x (Cp_phi n) == rpow y (Cp_phi n).
+Proof.
+ intros; repeat rewrite pow_th.(rpow_pow_N).
+ destruct n;simpl. apply eq_refl.
+ induction p;simpl;try rewrite IHp;try rewrite H; apply eq_refl.
+Qed.
+*)
Theorem PExpr_eq_semi_correct:
forall l e1 e2, PExpr_eq e1 e2 = true -> NPEeval l e1 == NPEeval l e2.
intros l e1; elim e1.
@@ -387,6 +429,10 @@ intros e4 e6; generalize (rec1 e4); case (PExpr_eq e3 e4);
intros e3 rec e2; (case e2; simpl; (try (intros; discriminate))).
intros e4; generalize (rec e4); case (PExpr_eq e3 e4);
(try (intros; discriminate)); auto.
+intros e3 rec n3 e2;(case e2;simpl;(try (intros;discriminate))).
+intros e4 n4;generalize (N_eq_correct n3 n4);destruct (N_eq n3 n4);
+intros;try discriminate.
+repeat rewrite pow_th.(rpow_pow_N);rewrite H;rewrite (rec _ H0);auto.
Qed.
(* add *)
@@ -395,6 +441,7 @@ Definition NPEadd e1 e2 :=
PEc c1, PEc c2 => PEc (cadd c1 c2)
| PEc c, _ => if ceqb c cO then e2 else PEadd e1 e2
| _, PEc c => if ceqb c cO then e1 else PEadd e1 e2
+ (* Peut t'on factoriser ici ??? *)
| _, _ => PEadd e1 e2
end.
@@ -403,32 +450,68 @@ Theorem NPEadd_correct:
Proof.
intros l e1 e2.
destruct e1; destruct e2; simpl in |- *; try reflexivity; try apply ceqb_rect;
- try (intro eq_c; rewrite eq_c in |- *); simpl in |- *;
- try rewrite (morph0 CRmorph) in |- *; try ring.
-apply (morph_add CRmorph).
+ try (intro eq_c; rewrite eq_c in |- *); simpl in |- *;try apply eq_refl;
+ try ring [(morph0 CRmorph)].
+ apply (morph_add CRmorph).
+Qed.
+
+Definition NPEpow x n :=
+ match n with
+ | N0 => PEc cI
+ | Npos p =>
+ if positive_eq p xH then x else
+ match x with
+ | PEc c =>
+ if ceqb c cI then PEc cI else if ceqb c cO then PEc cO else PEc (pow_pos cmul c p)
+ | _ => PEpow x n
+ end
+ end.
+
+Theorem NPEpow_correct : forall l e n,
+ NPEeval l (NPEpow e n) == NPEeval l (PEpow e n).
+Proof.
+ destruct n;simpl.
+ rewrite pow_th.(rpow_pow_N);simpl;auto.
+ generalize (positive_eq_correct p xH).
+ destruct (positive_eq p 1);intros.
+ rewrite H;rewrite pow_th.(rpow_pow_N). trivial.
+ clear H;destruct e;simpl;auto.
+ repeat apply ceqb_rect;simpl;intros;rewrite pow_th.(rpow_pow_N);simpl.
+ symmetry;induction p;simpl;trivial; ring [IHp H CRmorph.(morph1)].
+ symmetry; induction p;simpl;trivial;ring [IHp CRmorph.(morph0)].
+ induction p;simpl;auto;repeat rewrite CRmorph.(morph_mul);ring [IHp].
Qed.
(* mul *)
-Definition NPEmul x y :=
+Fixpoint NPEmul (x y : PExpr C) {struct x} : PExpr C :=
match x, y with
PEc c1, PEc c2 => PEc (cmul c1 c2)
| PEc c, _ =>
if ceqb c cI then y else if ceqb c cO then PEc cO else PEmul x y
| _, PEc c =>
if ceqb c cI then x else if ceqb c cO then PEc cO else PEmul x y
- | _, _ => PEmul x y
+ | PEpow e1 n1, PEpow e2 n2 =>
+ if N_eq n1 n2 then NPEpow (NPEmul e1 e2) n1 else PEmul x y
+ | _, _ => PEmul x y
end.
-
+
+Lemma pow_pos_mul : forall x y p, pow_pos rmul (x * y) p == pow_pos rmul x p * pow_pos rmul y p.
+induction p;simpl;auto;try ring [IHp].
+Qed.
+
Theorem NPEmul_correct : forall l e1 e2,
NPEeval l (NPEmul e1 e2) == NPEeval l (PEmul e1 e2).
-intros l e1 e2.
-destruct e1; destruct e2; simpl in |- *; try reflexivity;
+induction e1;destruct e2; simpl in |- *;try reflexivity;
repeat apply ceqb_rect;
- try (intro eq_c; rewrite eq_c in |- *); simpl in |- *;
- try rewrite (morph0 CRmorph) in |- *;
- try rewrite (morph1 CRmorph) in |- *;
- try ring.
-apply (morph_mul CRmorph).
+ try (intro eq_c; rewrite eq_c in |- *); simpl in |- *; try reflexivity;
+ try ring [(morph0 CRmorph) (morph1 CRmorph)].
+ apply (morph_mul CRmorph).
+assert (H:=N_eq_correct n n0);destruct (N_eq n n0).
+rewrite NPEpow_correct. simpl.
+repeat rewrite pow_th.(rpow_pow_N).
+rewrite IHe1;rewrite <- H;destruct n;simpl;try ring.
+apply pow_pos_mul.
+simpl;auto.
Qed.
(* sub *)
@@ -437,6 +520,7 @@ Definition NPEsub e1 e2 :=
PEc c1, PEc c2 => PEc (csub c1 c2)
| PEc c, _ => if ceqb c cO then PEopp e2 else PEsub e1 e2
| _, PEc c => if ceqb c cO then e1 else PEsub e1 e2
+ (* Peut-on factoriser ici *)
| _, _ => PEsub e1 e2
end.
@@ -467,6 +551,7 @@ Fixpoint PExpr_simp (e : PExpr C) : PExpr C :=
| PEmul e1 e2 => NPEmul (PExpr_simp e1) (PExpr_simp e2)
| PEsub e1 e2 => NPEsub (PExpr_simp e1) (PExpr_simp e2)
| PEopp e1 => NPEopp (PExpr_simp e1)
+ | PEpow e1 n1 => NPEpow (PExpr_simp e1) n1
| _ => e
end.
@@ -489,6 +574,10 @@ intros e1 He1.
transitivity (NPEeval l (PEopp (PExpr_simp e1))); auto.
apply NPEopp_correct.
simpl; auto.
+intros e1 He1 n;simpl.
+rewrite NPEpow_correct;simpl.
+repeat rewrite pow_th.(rpow_pow_N).
+rewrite He1;auto.
Qed.
@@ -508,8 +597,9 @@ Inductive FExpr : Type :=
| FEmul: FExpr -> FExpr -> FExpr
| FEopp: FExpr -> FExpr
| FEinv: FExpr -> FExpr
- | FEdiv: FExpr -> FExpr -> FExpr .
-
+ | FEdiv: FExpr -> FExpr -> FExpr
+ | FEpow: FExpr -> N -> FExpr .
+
Fixpoint FEeval (l : list R) (pe : FExpr) {struct pe} : R :=
match pe with
| FEc c => phi c
@@ -520,6 +610,7 @@ Fixpoint FEeval (l : list R) (pe : FExpr) {struct pe} : R :=
| FEopp x => - FEeval l x
| FEinv x => / FEeval l x
| FEdiv x y => FEeval l x / FEeval l y
+ | FEpow x n => rpow (FEeval l x) (Cp_phi n)
end.
(* The result of the normalisation *)
@@ -538,8 +629,8 @@ Record linear : Type := mk_linear {
Fixpoint PCond (l : list R) (le : list (PExpr C)) {struct le} : Prop :=
match le with
| nil => True
- | e1 :: nil => ~ req (PEeval rO radd rmul rsub ropp phi l e1) rO
- | e1 :: l1 => ~ req (PEeval rO radd rmul rsub ropp phi l e1) rO /\ PCond l l1
+ | e1 :: nil => ~ req (NPEeval l e1) rO
+ | e1 :: l1 => ~ req (NPEeval l e1) rO /\ PCond l l1
end.
Theorem PCond_cons_inv_l :
@@ -584,66 +675,170 @@ Qed.
***************************************************************************)
-
-Fixpoint isIn (e1 e2: PExpr C) {struct e2}: option (PExpr C) :=
+Fixpoint isIn (e1:PExpr C) (p1:positive)
+ (e2:PExpr C) (p2:positive) {struct e2}: option (N * PExpr C) :=
match e2 with
| PEmul e3 e4 =>
- match isIn e1 e3 with
- Some e5 => Some (NPEmul e5 e4)
- | None => match isIn e1 e4 with
- | Some e5 => Some (NPEmul e3 e5)
- | None => None
- end
+ match isIn e1 p1 e3 p2 with
+ | Some (N0, e5) => Some (N0, NPEmul e5 (NPEpow e4 (Npos p2)))
+ | Some (Npos p, e5) =>
+ match isIn e1 p e4 p2 with
+ | Some (n, e6) => Some (n, NPEmul e5 e6)
+ | None => Some (Npos p, NPEmul e5 (NPEpow e4 (Npos p2)))
+ end
+ | None =>
+ match isIn e1 p1 e4 p2 with
+ | Some (n, e5) => Some (n,NPEmul (NPEpow e3 (Npos p2)) e5)
+ | None => None
+ end
end
+ | PEpow e3 N0 => None
+ | PEpow e3 (Npos p3) => isIn e1 p1 e3 (Pmult p3 p2)
| _ =>
- if PExpr_eq e1 e2 then Some (PEc cI) else None
+ if PExpr_eq e1 e2 then
+ match Zminus (Zpos p1) (Zpos p2) with
+ | Zpos p => Some (Npos p, PEc cI)
+ | Z0 => Some (N0, PEc cI)
+ | Zneg p => Some (N0, NPEpow e2 (Npos p))
+ end
+ else None
end.
+
+ Definition ZtoN z := match z with Zpos p => Npos p | _ => N0 end.
+ Definition NtoZ n := match n with Npos p => Zpos p | _ => Z0 end.
+
+ Notation pow_pos_plus := (Ring_theory.pow_pos_Pplus _ Rsth Reqe.(Rmul_ext)
+ ARth.(ARmul_comm) ARth.(ARmul_assoc)).
+
+ Lemma isIn_correct_aux : forall l e1 e2 p1 p2,
+ match
+ (if PExpr_eq e1 e2 then
+ match Zminus (Zpos p1) (Zpos p2) with
+ | Zpos p => Some (Npos p, PEc cI)
+ | Z0 => Some (N0, PEc cI)
+ | Zneg p => Some (N0, NPEpow e2 (Npos p))
+ end
+ else None)
+ with
+ | Some(n, e3) =>
+ NPEeval l (PEpow e2 (Npos p2)) ==
+ NPEeval l (PEmul (PEpow e1 (ZtoN (Zpos p1 - NtoZ n))) e3) /\
+ (Zpos p1 > NtoZ n)%Z
+ | _ => True
+ end.
+Proof.
+ intros l e1 e2 p1 p2; generalize (PExpr_eq_semi_correct l e1 e2);
+ case (PExpr_eq e1 e2); simpl; auto; intros H.
+ case_eq ((p1 ?= p2)%positive Eq);intros;simpl.
+ repeat rewrite pow_th.(rpow_pow_N);simpl. split. 2:refine (refl_equal _).
+ rewrite (Pcompare_Eq_eq _ _ H0).
+ rewrite H;[trivial | ring [ (morph1 CRmorph)]].
+ fold (NPEpow e2 (Npos (p2 - p1))).
+ rewrite NPEpow_correct;simpl.
+ repeat rewrite pow_th.(rpow_pow_N);simpl.
+ rewrite H;trivial. split. 2:refine (refl_equal _).
+ rewrite <- pow_pos_plus; rewrite Pplus_minus;auto. apply ZC2;trivial.
+ repeat rewrite pow_th.(rpow_pow_N);simpl.
+ rewrite H;trivial.
+ change (ZtoN
+ match (p1 ?= p1 - p2)%positive Eq with
+ | Eq => 0
+ | Lt => Zneg (p1 - p2 - p1)
+ | Gt => Zpos (p1 - (p1 - p2))
+ end) with (ZtoN (Zpos p1 - Zpos (p1 -p2))).
+ replace (Zpos (p1 - p2)) with (Zpos p1 - Zpos p2)%Z.
+ split.
+ repeat rewrite Zth.(Rsub_def). rewrite (Ring_theory.Ropp_add Zsth Zeqe Zth).
+ rewrite Zplus_assoc. simpl. rewrite Pcompare_refl. simpl.
+ ring [ (morph1 CRmorph)].
+ assert (Zpos p1 > 0 /\ Zpos p2 > 0)%Z. split;refine (refl_equal _).
+ apply Zplus_gt_reg_l with (Zpos p2).
+ rewrite Zplus_minus. change (Zpos p2 + Zpos p1 > 0 + Zpos p1)%Z.
+ apply Zplus_gt_compat_r. refine (refl_equal _).
+ simpl;rewrite H0;trivial.
+Qed.
+
+Lemma pow_pos_pow_pos : forall x p1 p2, pow_pos rmul (pow_pos rmul x p1) p2 == pow_pos rmul x (p1*p2).
+induction p1;simpl;intros;repeat rewrite pow_pos_mul;repeat rewrite pow_pos_plus;simpl.
+ring [(IHp1 p2)]. ring [(IHp1 p2)]. auto.
+Qed.
+
-Theorem isIn_correct: forall l e1 e2,
- match isIn e1 e2 with
- (Some e3) => NPEeval l e2 == NPEeval l (NPEmul e1 e3)
- | _ => True
+Theorem isIn_correct: forall l e1 p1 e2 p2,
+ match isIn e1 p1 e2 p2 with
+ | Some(n, e3) =>
+ NPEeval l (PEpow e2 (Npos p2)) ==
+ NPEeval l (PEmul (PEpow e1 (ZtoN (Zpos p1 - NtoZ n))) e3) /\
+ (Zpos p1 > NtoZ n)%Z
+ | _ => True
end.
Proof.
-intros l e1 e2; elim e2; simpl; auto.
- intros c;
- generalize (PExpr_eq_semi_correct l e1 (PEc c));
- case (PExpr_eq e1 (PEc c)); simpl; auto; intros H.
- rewrite NPEmul_correct; simpl; auto.
- rewrite H; auto; simpl.
- rewrite (morph1 CRmorph); rewrite (ARmul_1_r Rsth ARth); auto.
- intros p;
- generalize (PExpr_eq_semi_correct l e1 (PEX C p));
- case (PExpr_eq e1 (PEX C p)); simpl; auto; intros H.
- rewrite NPEmul_correct; simpl; auto.
- rewrite H; auto; simpl.
- rewrite (morph1 CRmorph); rewrite (ARmul_1_r Rsth ARth); auto.
- intros p Hrec p1 Hrec1.
- generalize (PExpr_eq_semi_correct l e1 (PEadd p p1));
- case (PExpr_eq e1 (PEadd p p1)); simpl; auto; intros H.
- rewrite NPEmul_correct; simpl; auto.
- rewrite H; auto; simpl.
- rewrite (morph1 CRmorph); rewrite (ARmul_1_r Rsth ARth); auto.
- intros p Hrec p1 Hrec1.
- generalize (PExpr_eq_semi_correct l e1 (PEsub p p1));
- case (PExpr_eq e1 (PEsub p p1)); simpl; auto; intros H.
- rewrite NPEmul_correct; simpl; auto.
- rewrite H; auto; simpl.
- rewrite (morph1 CRmorph); rewrite (ARmul_1_r Rsth ARth); auto.
- intros p; case (isIn e1 p).
- intros p2 Hrec p1 Hrec1.
- rewrite Hrec; auto; simpl.
- repeat (rewrite NPEmul_correct; simpl; auto).
- intros _ p1; case (isIn e1 p1); auto.
- intros p2 H; rewrite H.
- repeat (rewrite NPEmul_correct; simpl; auto).
- ring.
- intros p;
- generalize (PExpr_eq_semi_correct l e1 (PEopp p));
- case (PExpr_eq e1 (PEopp p)); simpl; auto; intros H.
- rewrite NPEmul_correct; simpl; auto.
- rewrite H; auto; simpl.
- rewrite (morph1 CRmorph); rewrite (ARmul_1_r Rsth ARth); auto.
+Opaque NPEpow.
+intros l e1 p1 e2; generalize p1;clear p1;elim e2; intros;
+ try (refine (isIn_correct_aux l e1 _ p1 p2);fail);simpl isIn.
+generalize (H p1 p2);clear H;destruct (isIn e1 p1 p p2). destruct p3.
+destruct n.
+ simpl. rewrite NPEmul_correct. simpl; rewrite NPEpow_correct;simpl.
+ repeat rewrite pow_th.(rpow_pow_N);simpl.
+ rewrite pow_pos_mul;intros (H,H1);split;[ring[H]|trivial].
+ generalize (H0 p4 p2);clear H0;destruct (isIn e1 p4 p0 p2). destruct p5.
+ destruct n;simpl.
+ rewrite NPEmul_correct;repeat rewrite pow_th.(rpow_pow_N);simpl.
+ intros (H1,H2) (H3,H4).
+ unfold Zgt in H2, H4;simpl in H2,H4. rewrite H4 in H3;simpl in H3.
+ rewrite pow_pos_mul. rewrite H1;rewrite H3.
+ assert (pow_pos rmul (NPEeval l e1) (p1 - p4) * NPEeval l p3 *
+ (pow_pos rmul (NPEeval l e1) p4 * NPEeval l p5) ==
+ pow_pos rmul (NPEeval l e1) p4 * pow_pos rmul (NPEeval l e1) (p1 - p4) *
+ NPEeval l p3 *NPEeval l p5) by ring. rewrite H;clear H.
+ rewrite <- pow_pos_plus. rewrite Pplus_minus.
+ split. symmetry;apply ARth.(ARmul_assoc). refine (refl_equal _). trivial.
+ repeat rewrite pow_th.(rpow_pow_N);simpl.
+ intros (H1,H2) (H3,H4).
+ unfold Zgt in H2, H4;simpl in H2,H4. rewrite H4 in H3;simpl in H3.
+ rewrite H2 in H1;simpl in H1.
+ assert (Zpos p1 > Zpos p6)%Z.
+ apply Zgt_trans with (Zpos p4). exact H4. exact H2.
+ unfold Zgt in H;simpl in H;rewrite H.
+ split. 2:exact H.
+ rewrite pow_pos_mul. simpl;rewrite H1;rewrite H3.
+ assert (pow_pos rmul (NPEeval l e1) (p1 - p4) * NPEeval l p3 *
+ (pow_pos rmul (NPEeval l e1) (p4 - p6) * NPEeval l p5) ==
+ pow_pos rmul (NPEeval l e1) (p1 - p4) * pow_pos rmul (NPEeval l e1) (p4 - p6) *
+ NPEeval l p3 * NPEeval l p5) by ring. rewrite H0;clear H0.
+ rewrite <- pow_pos_plus.
+ replace (p1 - p4 + (p4 - p6))%positive with (p1 - p6)%positive.
+ rewrite NPEmul_correct. simpl;ring.
+ assert
+ (Zpos p1 - Zpos p6 = Zpos p1 - Zpos p4 + (Zpos p4 - Zpos p6))%Z.
+ change ((Zpos p1 - Zpos p6)%Z = (Zpos p1 + (- Zpos p4) + (Zpos p4 +(- Zpos p6)))%Z).
+ rewrite <- Zplus_assoc. rewrite (Zplus_assoc (- Zpos p4)).
+ simpl. rewrite Pcompare_refl. reflexivity.
+ unfold Zminus, Zopp in H0. simpl in H0.
+ rewrite H2 in H0;rewrite H4 in H0;rewrite H in H0. inversion H0;trivial.
+ simpl. repeat rewrite pow_th.(rpow_pow_N).
+ intros H1 (H2,H3). unfold Zgt in H3;simpl in H3. rewrite H3 in H2;rewrite H3.
+ rewrite NPEmul_correct;simpl;rewrite NPEpow_correct;simpl.
+ simpl in H2. rewrite pow_th.(rpow_pow_N);simpl.
+ rewrite pow_pos_mul. split. ring [H2]. exact H3.
+ generalize (H0 p1 p2);clear H0;destruct (isIn e1 p1 p0 p2). destruct p3.
+ destruct n;simpl. rewrite NPEmul_correct;simpl;rewrite NPEpow_correct;simpl.
+ repeat rewrite pow_th.(rpow_pow_N);simpl.
+ intros (H1,H2);split;trivial. rewrite pow_pos_mul;ring [H1].
+ rewrite NPEmul_correct;simpl;rewrite NPEpow_correct;simpl.
+ repeat rewrite pow_th.(rpow_pow_N);simpl. rewrite pow_pos_mul.
+ intros (H1, H2);rewrite H1;split.
+ unfold Zgt in H2;simpl in H2;rewrite H2;rewrite H2 in H1.
+ simpl in H1;ring [H1]. trivial.
+ trivial.
+ destruct n. trivial.
+ generalize (H p1 (p0*p2)%positive);clear H;destruct (isIn e1 p1 p (p0*p2)). destruct p3.
+ destruct n;simpl. repeat rewrite pow_th.(rpow_pow_N). simpl.
+ intros (H1,H2);split. rewrite pow_pos_pow_pos. trivial. trivial.
+ repeat rewrite pow_th.(rpow_pow_N). simpl.
+ intros (H1,H2);split;trivial.
+ rewrite pow_pos_pow_pos;trivial.
+ trivial.
Qed.
Record rsplit : Type := mk_rsplit {
@@ -652,90 +847,94 @@ Record rsplit : Type := mk_rsplit {
rsplit_right : PExpr C}.
(* Stupid name clash *)
-Let left := rsplit_left.
-Let right := rsplit_right.
-Let common := rsplit_common.
+Notation left := rsplit_left.
+Notation right := rsplit_right.
+Notation common := rsplit_common.
-Fixpoint split (e1 e2: PExpr C) {struct e1}: rsplit :=
+Fixpoint split_aux (e1: PExpr C) (p:positive) (e2:PExpr C) {struct e1}: rsplit :=
match e1 with
| PEmul e3 e4 =>
- let r1 := split e3 e2 in
- let r2 := split e4 (right r1) in
+ let r1 := split_aux e3 p e2 in
+ let r2 := split_aux e4 p (right r1) in
mk_rsplit (NPEmul (left r1) (left r2))
(NPEmul (common r1) (common r2))
(right r2)
+ | PEpow e3 N0 => mk_rsplit (PEc cI) (PEc cI) e2
+ | PEpow e3 (Npos p3) => split_aux e3 (Pmult p3 p) e2
| _ =>
- match isIn e1 e2 with
- Some e3 => mk_rsplit (PEc cI) e1 e3
- | None => mk_rsplit e1 (PEc cI) e2
+ match isIn e1 p e2 xH with
+ | Some (N0,e3) => mk_rsplit (PEc cI) (NPEpow e1 (Npos p)) e3
+ | Some (Npos q, e3) => mk_rsplit (NPEpow e1 (Npos q)) (NPEpow e1 (Npos (p - q))) e3
+ | None => mk_rsplit (NPEpow e1 (Npos p)) (PEc cI) e2
end
end.
-Theorem split_correct: forall l e1 e2,
- NPEeval l e1 == NPEeval l (NPEmul (left (split e1 e2))
- (common (split e1 e2)))
-/\
- NPEeval l e2 == NPEeval l (NPEmul (right (split e1 e2))
- (common (split e1 e2))).
+Lemma split_aux_correct_1 : forall l e1 p e2,
+ let res := match isIn e1 p e2 xH with
+ | Some (N0,e3) => mk_rsplit (PEc cI) (NPEpow e1 (Npos p)) e3
+ | Some (Npos q, e3) => mk_rsplit (NPEpow e1 (Npos q)) (NPEpow e1 (Npos (p - q))) e3
+ | None => mk_rsplit (NPEpow e1 (Npos p)) (PEc cI) e2
+ end in
+ NPEeval l (PEpow e1 (Npos p)) == NPEeval l (NPEmul (left res) (common res))
+ /\
+ NPEeval l e2 == NPEeval l (NPEmul (right res) (common res)).
Proof.
-intros l e1; elim e1; simpl; auto.
- intros c e2; generalize (isIn_correct l (PEc c) e2);
- case (isIn (PEc c) e2); auto; intros p;
- [intros Hp1; rewrite Hp1 | idtac];
- simpl left; simpl common; simpl right; auto;
- repeat rewrite NPEmul_correct; simpl; split;
- try rewrite (morph1 CRmorph); ring.
- intros p e2; generalize (isIn_correct l (PEX C p) e2);
- case (isIn (PEX C p) e2); auto; intros p1;
- [intros Hp1; rewrite Hp1 | idtac];
- simpl left; simpl common; simpl right; auto;
- repeat rewrite NPEmul_correct; simpl; split;
- try rewrite (morph1 CRmorph); ring.
- intros p1 _ p2 _ e2; generalize (isIn_correct l (PEadd p1 p2) e2);
- case (isIn (PEadd p1 p2) e2); auto; intros p;
- [intros Hp1; rewrite Hp1 | idtac];
- simpl left; simpl common; simpl right; auto;
- repeat rewrite NPEmul_correct; simpl; split;
- try rewrite (morph1 CRmorph); ring.
- intros p1 _ p2 _ e2; generalize (isIn_correct l (PEsub p1 p2) e2);
- case (isIn (PEsub p1 p2) e2); auto; intros p;
- [intros Hp1; rewrite Hp1 | idtac];
- simpl left; simpl common; simpl right; auto;
- repeat rewrite NPEmul_correct; simpl; split;
- try rewrite (morph1 CRmorph); ring.
- intros p1 Hp1 p2 Hp2 e2.
- repeat rewrite NPEmul_correct; simpl; split.
- case (Hp1 e2); case (Hp2 (right (split p1 e2))).
- intros tmp1 _ tmp2 _; rewrite tmp1; rewrite tmp2.
- repeat rewrite NPEmul_correct; simpl.
- ring.
- case (Hp1 e2); case (Hp2 (right (split p1 e2))).
- intros _ tmp1 _ tmp2; rewrite tmp2;
- repeat rewrite NPEmul_correct; simpl.
- rewrite tmp1.
- repeat rewrite NPEmul_correct; simpl.
- ring.
- intros p _ e2; generalize (isIn_correct l (PEopp p) e2);
- case (isIn (PEopp p) e2); auto; intros p1;
- [intros Hp1; rewrite Hp1 | idtac];
- simpl left; simpl common; simpl right; auto;
- repeat rewrite NPEmul_correct; simpl; split;
- try rewrite (morph1 CRmorph); ring.
+ intros. unfold res;clear res; generalize (isIn_correct l e1 p e2 xH).
+ destruct (isIn e1 p e2 1). destruct p0.
+ Opaque NPEpow NPEmul.
+ destruct n;simpl;
+ (repeat rewrite NPEmul_correct;simpl;
+ repeat rewrite NPEpow_correct;simpl;
+ repeat rewrite pow_th.(rpow_pow_N);simpl).
+ intros (H, Hgt);split;try ring [H CRmorph.(morph1)].
+ intros (H, Hgt). unfold Zgt in Hgt;simpl in Hgt;rewrite Hgt in H.
+ simpl in H;split;try ring [H].
+ rewrite <- pow_pos_plus. rewrite Pplus_minus. reflexivity. trivial.
+ simpl;intros. repeat rewrite NPEmul_correct;simpl.
+ rewrite NPEpow_correct;simpl. split;ring [CRmorph.(morph1)].
Qed.
+Theorem split_aux_correct: forall l e1 p e2,
+ NPEeval l (PEpow e1 (Npos p)) ==
+ NPEeval l (NPEmul (left (split_aux e1 p e2)) (common (split_aux e1 p e2)))
+/\
+ NPEeval l e2 == NPEeval l (NPEmul (right (split_aux e1 p e2))
+ (common (split_aux e1 p e2))).
+Proof.
+intros l; induction e1;intros k e2; try refine (split_aux_correct_1 l _ k e2);simpl.
+generalize (IHe1_1 k e2); clear IHe1_1.
+generalize (IHe1_2 k (rsplit_right (split_aux e1_1 k e2))); clear IHe1_2.
+simpl. repeat (rewrite NPEmul_correct;simpl).
+repeat rewrite pow_th.(rpow_pow_N);simpl.
+intros (H1,H2) (H3,H4);split.
+rewrite pow_pos_mul. rewrite H1;rewrite H3. ring.
+rewrite H4;rewrite H2;ring.
+destruct n;simpl.
+split. repeat rewrite pow_th.(rpow_pow_N);simpl.
+rewrite NPEmul_correct. simpl.
+ induction k;simpl;try ring [CRmorph.(morph1)]; ring [IHk CRmorph.(morph1)].
+ rewrite NPEmul_correct;simpl. ring [CRmorph.(morph1)].
+generalize (IHe1 (p*k)%positive e2);clear IHe1;simpl.
+repeat rewrite NPEmul_correct;simpl.
+repeat rewrite pow_th.(rpow_pow_N);simpl.
+rewrite pow_pos_pow_pos. intros [H1 H2];split;ring [H1 H2].
+Qed.
+Definition split e1 e2 := split_aux e1 xH e2.
+
Theorem split_correct_l: forall l e1 e2,
NPEeval l e1 == NPEeval l (NPEmul (left (split e1 e2))
(common (split e1 e2))).
Proof.
-intros l e1 e2; case (split_correct l e1 e2); auto.
+intros l e1 e2; case (split_aux_correct l e1 xH e2);simpl.
+rewrite pow_th.(rpow_pow_N);simpl;auto.
Qed.
Theorem split_correct_r: forall l e1 e2,
NPEeval l e2 == NPEeval l (NPEmul (right (split e1 e2))
(common (split e1 e2))).
Proof.
-intros l e1 e2; case (split_correct l e1 e2); auto.
+intros l e1 e2; case (split_aux_correct l e1 xH e2);simpl;auto.
Qed.
Fixpoint Fnorm (e : FExpr) : linear :=
@@ -777,6 +976,9 @@ Fixpoint Fnorm (e : FExpr) : linear :=
mk_linear (NPEmul (num x) (denum y))
(NPEmul (denum x) (num y))
(num y :: condition x ++ condition y)
+ | FEpow e1 n =>
+ let x := Fnorm e1 in
+ mk_linear (NPEpow (num x) n) (NPEpow (denum x) n) (condition x)
end.
@@ -789,6 +991,17 @@ Eval compute
(FEadd (FEinv (FEX xH%positive)) (FEinv (FEX (xO xH)%positive))))).
*)
+ Lemma pow_pos_not_0 : forall x, ~x==0 -> forall p, ~pow_pos rmul x p == 0.
+Proof.
+ induction p;simpl.
+ intro Hp;assert (H1 := @rmul_reg_l _ (pow_pos rmul x p * pow_pos rmul x p) 0 H).
+ apply IHp.
+ rewrite (@rmul_reg_l _ (pow_pos rmul x p) 0 IHp). rewrite H1. rewrite Hp;ring. ring.
+ reflexivity.
+ intro Hp;apply IHp. rewrite (@rmul_reg_l _ (pow_pos rmul x p) 0 IHp).
+ rewrite Hp;ring. reflexivity. trivial.
+Qed.
+
Theorem Pcond_Fnorm:
forall l e,
PCond l (condition (Fnorm e)) -> ~ NPEeval l (denum (Fnorm e)) == 0.
@@ -849,6 +1062,11 @@ intros l e; elim e.
specialize PCond_cons_inv_r with (1:=Hcond); intro Hcond1.
apply PCond_app_inv_l with (1 := Hcond1).
apply PCond_cons_inv_l with (1:=Hcond).
+ simpl;intros e1 Hrec1 n Hcond.
+ rewrite NPEpow_correct.
+ simpl;rewrite pow_th.(rpow_pow_N).
+ destruct n;simpl;intros.
+ apply AFth.(AF_1_neq_0). apply pow_pos_not_0;auto.
Qed.
Hint Resolve Pcond_Fnorm.
@@ -928,6 +1146,23 @@ rewrite (He1 HH1); rewrite (He2 HH2).
repeat rewrite NPEmul_correct;simpl.
apply rdiv7; auto.
apply PCond_cons_inv_l with ( 1 := HH ).
+
+intros e1 He1 n Hcond;assert (He1' := He1 Hcond);clear He1.
+repeat rewrite NPEpow_correct;simpl;repeat rewrite pow_th.(rpow_pow_N).
+rewrite He1';clear He1'.
+destruct n;simpl. apply rdiv1.
+generalize (NPEeval l (num (Fnorm e1))) (NPEeval l (denum (Fnorm e1)))
+ (Pcond_Fnorm _ _ Hcond).
+intros r r0 Hdiff;induction p;simpl.
+repeat (rewrite <- rdiv4;trivial).
+intro Hp;apply (pow_pos_not_0 Hdiff p).
+rewrite (@rmul_reg_l (pow_pos rmul r0 p) (pow_pos rmul r0 p) 0).
+ apply pow_pos_not_0;trivial. ring [Hp]. reflexivity.
+apply pow_pos_not_0;trivial. apply pow_pos_not_0;trivial.
+rewrite IHp;reflexivity.
+rewrite <- rdiv4;trivial. apply pow_pos_not_0;trivial. apply pow_pos_not_0;trivial.
+rewrite IHp;reflexivity.
+reflexivity.
Qed.
Theorem Fnorm_crossproduct:
@@ -951,17 +1186,22 @@ rewrite Fnorm_FEeval_PEeval in |- *.
Qed.
(* Correctness lemmas of reflexive tactics *)
+Notation Ninterp_PElist := (interp_PElist rO radd rmul rsub ropp req phi Cp_phi rpow).
+Notation Nmk_monpol_list := (mk_monpol_list cO cI cadd cmul csub copp ceqb).
Theorem Fnorm_correct:
- forall l fe,
- Peq ceqb (Nnorm (num (Fnorm fe))) (Pc cO) = true ->
- PCond l (condition (Fnorm fe)) -> FEeval l fe == 0.
-intros l fe H H1;
+ forall n l lpe fe,
+ Ninterp_PElist l lpe ->
+ Peq ceqb (Nnorm n (Nmk_monpol_list lpe) (num (Fnorm fe))) (Pc cO) = true ->
+ PCond l (condition (Fnorm fe)) -> FEeval l fe == 0.
+intros n l lpe fe Hlpe H H1;
apply eq_trans with (1 := Fnorm_FEeval_PEeval l fe H1).
apply rdiv8; auto.
transitivity (NPEeval l (PEc cO)); auto.
-apply (ring_correct Rsth Reqe ARth CRmorph); auto.
-simpl; apply (morph0 CRmorph); auto.
+rewrite (norm_subst_ok Rsth Reqe ARth CRmorph pow_th n l lpe);auto.
+change (NPEeval l (PEc cO)) with (Pphi 0 radd rmul phi l (Pc cO)).
+apply (Peq_ok Rsth Reqe CRmorph);auto.
+simpl. apply (morph0 CRmorph); auto.
Qed.
(* simplify a field expression into a fraction *)
@@ -969,31 +1209,50 @@ Qed.
Definition display_linear l num den :=
NPphi_dev l num / NPphi_dev l den.
-Theorem Pphi_dev_div_ok:
- forall l fe nfe,
- Fnorm fe = nfe ->
- PCond l (condition nfe) ->
- FEeval l fe == display_linear l (Nnorm (num nfe)) (Nnorm (denum nfe)).
+Definition display_pow_linear l num den :=
+ NPphi_pow l num / NPphi_pow l den.
+
+Theorem Field_rw_correct :
+ forall n lpe l,
+ Ninterp_PElist l lpe ->
+ forall lmp, Nmk_monpol_list lpe = lmp ->
+ forall fe nfe, Fnorm fe = nfe ->
+ PCond l (condition nfe) ->
+ FEeval l fe == display_linear l (Nnorm n lmp (num nfe)) (Nnorm n lmp (denum nfe)).
Proof.
- intros l fe nfe eq_nfe H; subst nfe.
+ intros n lpe l Hlpe lmp lmp_eq fe nfe eq_nfe H; subst nfe lmp.
apply eq_trans with (1 := Fnorm_FEeval_PEeval _ _ H).
unfold display_linear; apply SRdiv_ext;
- apply (Pphi_dev_ok Rsth Reqe ARth CRmorph); reflexivity.
+ eapply (ring_rw_correct Rsth Reqe ARth CRmorph);eauto.
+Qed.
+
+Theorem Field_rw_pow_correct :
+ forall n lpe l,
+ Ninterp_PElist l lpe ->
+ forall lmp, Nmk_monpol_list lpe = lmp ->
+ forall fe nfe, Fnorm fe = nfe ->
+ PCond l (condition nfe) ->
+ FEeval l fe == display_pow_linear l (Nnorm n lmp (num nfe)) (Nnorm n lmp (denum nfe)).
+Proof.
+ intros n lpe l Hlpe lmp lmp_eq fe nfe eq_nfe H; subst nfe lmp.
+ apply eq_trans with (1 := Fnorm_FEeval_PEeval _ _ H).
+ unfold display_pow_linear; apply SRdiv_ext;
+ eapply (ring_rw_pow_correct Rsth Reqe ARth CRmorph);eauto.
Qed.
-(* solving a field equation *)
Theorem Field_correct :
- forall l fe1 fe2,
+ forall n l lpe fe1 fe2, Ninterp_PElist l lpe ->
+ forall lmp, Nmk_monpol_list lpe = lmp ->
forall nfe1, Fnorm fe1 = nfe1 ->
forall nfe2, Fnorm fe2 = nfe2 ->
- Peq ceqb (Nnorm (PEmul (num nfe1) (denum nfe2)))
- (Nnorm (PEmul (num nfe2) (denum nfe1))) = true ->
+ Peq ceqb (Nnorm n lmp (PEmul (num nfe1) (denum nfe2)))
+ (Nnorm n lmp (PEmul (num nfe2) (denum nfe1))) = true ->
PCond l (condition nfe1 ++ condition nfe2) ->
FEeval l fe1 == FEeval l fe2.
Proof.
-intros l fe1 fe2 nfe1 eq1 nfe2 eq2 Hnorm Hcond; subst nfe1 nfe2.
+intros n l lpe fe1 fe2 Hlpe lmp eq_lmp nfe1 eq1 nfe2 eq2 Hnorm Hcond; subst nfe1 nfe2 lmp.
apply Fnorm_crossproduct; trivial.
-apply (ring_correct Rsth Reqe ARth CRmorph); trivial.
+eapply (ring_correct Rsth Reqe ARth CRmorph); eauto.
Qed.
(* simplify a field equation : generate the crossproduct and simplify
@@ -1002,47 +1261,204 @@ Theorem Field_simplify_eq_old_correct :
forall l fe1 fe2 nfe1 nfe2,
Fnorm fe1 = nfe1 ->
Fnorm fe2 = nfe2 ->
- NPphi_dev l (Nnorm (PEmul (num nfe1) (denum nfe2))) ==
- NPphi_dev l (Nnorm (PEmul (num nfe2) (denum nfe1))) ->
+ NPphi_dev l (Nnorm O nil (PEmul (num nfe1) (denum nfe2))) ==
+ NPphi_dev l (Nnorm O nil (PEmul (num nfe2) (denum nfe1))) ->
PCond l (condition nfe1 ++ condition nfe2) ->
FEeval l fe1 == FEeval l fe2.
Proof.
intros l fe1 fe2 nfe1 nfe2 eq1 eq2 Hcrossprod Hcond; subst nfe1 nfe2.
apply Fnorm_crossproduct; trivial.
-rewrite (Pphi_dev_gen_ok Rsth Reqe ARth CRmorph) in |- *.
-rewrite (Pphi_dev_gen_ok Rsth Reqe ARth CRmorph) in |- *.
+match goal with
+ [ |- NPEeval l ?x == NPEeval l ?y] =>
+ rewrite (ring_rw_correct Rsth Reqe ARth CRmorph pow_th get_sign_spec
+ O nil l I (refl_equal nil) x (refl_equal (Nnorm O nil x)));
+ rewrite (ring_rw_correct Rsth Reqe ARth CRmorph pow_th get_sign_spec
+ O nil l I (refl_equal nil) y (refl_equal (Nnorm O nil y)))
+ end.
trivial.
Qed.
Theorem Field_simplify_eq_correct :
- forall l fe1 fe2,
+ forall n l lpe fe1 fe2,
+ Ninterp_PElist l lpe ->
+ forall lmp, Nmk_monpol_list lpe = lmp ->
forall nfe1, Fnorm fe1 = nfe1 ->
forall nfe2, Fnorm fe2 = nfe2 ->
forall den, split (denum nfe1) (denum nfe2) = den ->
- NPphi_dev l (Nnorm (PEmul (num nfe1) (right den))) ==
- NPphi_dev l (Nnorm (PEmul (num nfe2) (left den))) ->
+ NPphi_dev l (Nnorm n lmp (PEmul (num nfe1) (right den))) ==
+ NPphi_dev l (Nnorm n lmp (PEmul (num nfe2) (left den))) ->
PCond l (condition nfe1 ++ condition nfe2) ->
FEeval l fe1 == FEeval l fe2.
Proof.
-intros l fe1 fe2 nfe1 eq1 nfe2 eq2 den eq3 Hcrossprod Hcond;
- subst nfe1 nfe2 den.
+intros n l lpe fe1 fe2 Hlpe lmp Hlmp nfe1 eq1 nfe2 eq2 den eq3 Hcrossprod Hcond;
+ subst nfe1 nfe2 den lmp.
apply Fnorm_crossproduct; trivial.
simpl in |- *.
-elim (split_correct l (denum (Fnorm fe1)) (denum (Fnorm fe2))); intros.
-rewrite H in |- *.
-rewrite H0 in |- *.
-clear H H0.
+rewrite (split_correct_l l (denum (Fnorm fe1)) (denum (Fnorm fe2))) in |- *.
+rewrite (split_correct_r l (denum (Fnorm fe1)) (denum (Fnorm fe2))) in |- *.
rewrite NPEmul_correct in |- *.
rewrite NPEmul_correct in |- *.
simpl in |- *.
repeat rewrite (ARmul_assoc ARth) in |- *.
-rewrite <- (Pphi_dev_gen_ok Rsth Reqe ARth CRmorph) in Hcrossprod.
-rewrite <- (Pphi_dev_gen_ok Rsth Reqe ARth CRmorph) in Hcrossprod.
+rewrite <-(
+ let x := PEmul (num (Fnorm fe1))
+ (rsplit_right (split (denum (Fnorm fe1)) (denum (Fnorm fe2)))) in
+ring_rw_correct Rsth Reqe ARth CRmorph pow_th get_sign_spec n lpe l
+ Hlpe (refl_equal (Nmk_monpol_list lpe))
+ x (refl_equal (Nnorm n (Nmk_monpol_list lpe) x))) in Hcrossprod.
+rewrite <-(
+ let x := (PEmul (num (Fnorm fe2))
+ (rsplit_left
+ (split (denum (Fnorm fe1)) (denum (Fnorm fe2))))) in
+ ring_rw_correct Rsth Reqe ARth CRmorph pow_th get_sign_spec n lpe l
+ Hlpe (refl_equal (Nmk_monpol_list lpe))
+ x (refl_equal (Nnorm n (Nmk_monpol_list lpe) x))) in Hcrossprod.
simpl in Hcrossprod.
rewrite Hcrossprod in |- *.
reflexivity.
Qed.
+Theorem Field_simplify_eq_pow_correct :
+ forall n l lpe fe1 fe2,
+ Ninterp_PElist l lpe ->
+ forall lmp, Nmk_monpol_list lpe = lmp ->
+ forall nfe1, Fnorm fe1 = nfe1 ->
+ forall nfe2, Fnorm fe2 = nfe2 ->
+ forall den, split (denum nfe1) (denum nfe2) = den ->
+ NPphi_pow l (Nnorm n lmp (PEmul (num nfe1) (right den))) ==
+ NPphi_pow l (Nnorm n lmp (PEmul (num nfe2) (left den))) ->
+ PCond l (condition nfe1 ++ condition nfe2) ->
+ FEeval l fe1 == FEeval l fe2.
+Proof.
+intros n l lpe fe1 fe2 Hlpe lmp Hlmp nfe1 eq1 nfe2 eq2 den eq3 Hcrossprod Hcond;
+ subst nfe1 nfe2 den lmp.
+apply Fnorm_crossproduct; trivial.
+simpl in |- *.
+rewrite (split_correct_l l (denum (Fnorm fe1)) (denum (Fnorm fe2))) in |- *.
+rewrite (split_correct_r l (denum (Fnorm fe1)) (denum (Fnorm fe2))) in |- *.
+rewrite NPEmul_correct in |- *.
+rewrite NPEmul_correct in |- *.
+simpl in |- *.
+repeat rewrite (ARmul_assoc ARth) in |- *.
+rewrite <-(
+ let x := PEmul (num (Fnorm fe1))
+ (rsplit_right (split (denum (Fnorm fe1)) (denum (Fnorm fe2)))) in
+ring_rw_pow_correct Rsth Reqe ARth CRmorph pow_th get_sign_spec n lpe l
+ Hlpe (refl_equal (Nmk_monpol_list lpe))
+ x (refl_equal (Nnorm n (Nmk_monpol_list lpe) x))) in Hcrossprod.
+rewrite <-(
+ let x := (PEmul (num (Fnorm fe2))
+ (rsplit_left
+ (split (denum (Fnorm fe1)) (denum (Fnorm fe2))))) in
+ ring_rw_pow_correct Rsth Reqe ARth CRmorph pow_th get_sign_spec n lpe l
+ Hlpe (refl_equal (Nmk_monpol_list lpe))
+ x (refl_equal (Nnorm n (Nmk_monpol_list lpe) x))) in Hcrossprod.
+simpl in Hcrossprod.
+rewrite Hcrossprod in |- *.
+reflexivity.
+Qed.
+
+Theorem Field_simplify_eq_pow_in_correct :
+ forall n l lpe fe1 fe2,
+ Ninterp_PElist l lpe ->
+ forall lmp, Nmk_monpol_list lpe = lmp ->
+ forall nfe1, Fnorm fe1 = nfe1 ->
+ forall nfe2, Fnorm fe2 = nfe2 ->
+ forall den, split (denum nfe1) (denum nfe2) = den ->
+ forall np1, Nnorm n lmp (PEmul (num nfe1) (right den)) = np1 ->
+ forall np2, Nnorm n lmp (PEmul (num nfe2) (left den)) = np2 ->
+ FEeval l fe1 == FEeval l fe2 ->
+ PCond l (condition nfe1 ++ condition nfe2) ->
+ NPphi_pow l np1 ==
+ NPphi_pow l np2.
+Proof.
+ intros. subst nfe1 nfe2 lmp np1 np2.
+ repeat rewrite (Pphi_pow_ok Rsth Reqe ARth CRmorph pow_th get_sign_spec).
+ repeat (rewrite <- (norm_subst_ok Rsth Reqe ARth CRmorph pow_th);trivial). simpl.
+ assert (N1 := Pcond_Fnorm _ _ (PCond_app_inv_l _ _ _ H7)).
+ assert (N2 := Pcond_Fnorm _ _ (PCond_app_inv_r _ _ _ H7)).
+ apply (@rmul_reg_l (NPEeval l (rsplit_common den))).
+ intro Heq;apply N1.
+ rewrite (split_correct_l l (denum (Fnorm fe1)) (denum (Fnorm fe2))).
+ rewrite H3. rewrite NPEmul_correct. simpl. ring [Heq].
+ repeat rewrite (ARth.(ARmul_comm) (NPEeval l (rsplit_common den))).
+ repeat rewrite <- ARth.(ARmul_assoc).
+ change (NPEeval l (rsplit_right den) * NPEeval l (rsplit_common den)) with
+ (NPEeval l (PEmul (rsplit_right den) (rsplit_common den))).
+ change (NPEeval l (rsplit_left den) * NPEeval l (rsplit_common den)) with
+ (NPEeval l (PEmul (rsplit_left den) (rsplit_common den))).
+ repeat rewrite <- NPEmul_correct. rewrite <- H3. rewrite <- split_correct_l.
+ rewrite <- split_correct_r.
+ apply (@rmul_reg_l (/NPEeval l (denum (Fnorm fe2)))).
+ intro Heq; apply AFth.(AF_1_neq_0).
+ rewrite <- (@AFinv_l AFth (NPEeval l (denum (Fnorm fe2))));trivial.
+ ring [Heq]. rewrite (ARth.(ARmul_comm) (/ NPEeval l (denum (Fnorm fe2)))).
+ repeat rewrite <- (ARth.(ARmul_assoc)).
+ rewrite <- (AFth.(AFdiv_def)). rewrite rdiv_r_r. trivial.
+ apply (@rmul_reg_l (/NPEeval l (denum (Fnorm fe1)))).
+ intro Heq; apply AFth.(AF_1_neq_0).
+ rewrite <- (@AFinv_l AFth (NPEeval l (denum (Fnorm fe1))));trivial.
+ ring [Heq]. repeat rewrite (ARth.(ARmul_comm) (/ NPEeval l (denum (Fnorm fe1)))).
+ repeat rewrite <- (ARth.(ARmul_assoc)).
+ repeat rewrite <- (AFth.(AFdiv_def)). rewrite rdiv_r_r. trivial.
+ rewrite (AFth.(AFdiv_def)). ring_simplify. unfold SRopp.
+ rewrite (ARth.(ARmul_comm) (/ NPEeval l (denum (Fnorm fe2)))).
+ repeat rewrite <- (AFth.(AFdiv_def)).
+ repeat rewrite <- Fnorm_FEeval_PEeval;trivial.
+ apply (PCond_app_inv_l _ _ _ H7). apply (PCond_app_inv_r _ _ _ H7).
+Qed.
+
+Theorem Field_simplify_eq_in_correct :
+forall n l lpe fe1 fe2,
+ Ninterp_PElist l lpe ->
+ forall lmp, Nmk_monpol_list lpe = lmp ->
+ forall nfe1, Fnorm fe1 = nfe1 ->
+ forall nfe2, Fnorm fe2 = nfe2 ->
+ forall den, split (denum nfe1) (denum nfe2) = den ->
+ forall np1, Nnorm n lmp (PEmul (num nfe1) (right den)) = np1 ->
+ forall np2, Nnorm n lmp (PEmul (num nfe2) (left den)) = np2 ->
+ FEeval l fe1 == FEeval l fe2 ->
+ PCond l (condition nfe1 ++ condition nfe2) ->
+ NPphi_dev l np1 ==
+ NPphi_dev l np2.
+Proof.
+ intros. subst nfe1 nfe2 lmp np1 np2.
+ repeat rewrite (Pphi_dev_ok Rsth Reqe ARth CRmorph get_sign_spec).
+ repeat (rewrite <- (norm_subst_ok Rsth Reqe ARth CRmorph pow_th);trivial). simpl.
+ assert (N1 := Pcond_Fnorm _ _ (PCond_app_inv_l _ _ _ H7)).
+ assert (N2 := Pcond_Fnorm _ _ (PCond_app_inv_r _ _ _ H7)).
+ apply (@rmul_reg_l (NPEeval l (rsplit_common den))).
+ intro Heq;apply N1.
+ rewrite (split_correct_l l (denum (Fnorm fe1)) (denum (Fnorm fe2))).
+ rewrite H3. rewrite NPEmul_correct. simpl. ring [Heq].
+ repeat rewrite (ARth.(ARmul_comm) (NPEeval l (rsplit_common den))).
+ repeat rewrite <- ARth.(ARmul_assoc).
+ change (NPEeval l (rsplit_right den) * NPEeval l (rsplit_common den)) with
+ (NPEeval l (PEmul (rsplit_right den) (rsplit_common den))).
+ change (NPEeval l (rsplit_left den) * NPEeval l (rsplit_common den)) with
+ (NPEeval l (PEmul (rsplit_left den) (rsplit_common den))).
+ repeat rewrite <- NPEmul_correct;rewrite <- H3. rewrite <- split_correct_l.
+ rewrite <- split_correct_r.
+ apply (@rmul_reg_l (/NPEeval l (denum (Fnorm fe2)))).
+ intro Heq; apply AFth.(AF_1_neq_0).
+ rewrite <- (@AFinv_l AFth (NPEeval l (denum (Fnorm fe2))));trivial.
+ ring [Heq]. rewrite (ARth.(ARmul_comm) (/ NPEeval l (denum (Fnorm fe2)))).
+ repeat rewrite <- (ARth.(ARmul_assoc)).
+ rewrite <- (AFth.(AFdiv_def)). rewrite rdiv_r_r. trivial.
+ apply (@rmul_reg_l (/NPEeval l (denum (Fnorm fe1)))).
+ intro Heq; apply AFth.(AF_1_neq_0).
+ rewrite <- (@AFinv_l AFth (NPEeval l (denum (Fnorm fe1))));trivial.
+ ring [Heq]. repeat rewrite (ARth.(ARmul_comm) (/ NPEeval l (denum (Fnorm fe1)))).
+ repeat rewrite <- (ARth.(ARmul_assoc)).
+ repeat rewrite <- (AFth.(AFdiv_def)). rewrite rdiv_r_r. trivial.
+ rewrite (AFth.(AFdiv_def)). ring_simplify. unfold SRopp.
+ rewrite (ARth.(ARmul_comm) (/ NPEeval l (denum (Fnorm fe2)))).
+ repeat rewrite <- (AFth.(AFdiv_def)).
+ repeat rewrite <- Fnorm_FEeval_PEeval;trivial.
+ apply (PCond_app_inv_l _ _ _ H7). apply (PCond_app_inv_r _ _ _ H7).
+Qed.
+
+
Section Fcons_impl.
Variable Fcons : PExpr C -> list (PExpr C) -> list (PExpr C).
@@ -1100,7 +1516,7 @@ Fixpoint Fcons0 (e:PExpr C) (l:list (PExpr C)) {struct l} : list (PExpr C) :=
match l with
nil => cons e nil
| cons a l1 =>
- if Peq ceqb (Nnorm e) (Nnorm a) then l else cons a (Fcons0 e l1)
+ if Peq ceqb (Nnorm O nil e) (Nnorm O nil a) then l else cons a (Fcons0 e l1)
end.
Theorem PFcons0_fcons_inv:
@@ -1108,8 +1524,8 @@ Theorem PFcons0_fcons_inv:
intros l a l1; elim l1; simpl Fcons0; auto.
simpl; auto.
intros a0 l0.
-generalize (ring_correct Rsth Reqe ARth CRmorph l a a0);
- case (Peq ceqb (Nnorm a) (Nnorm a0)).
+generalize (ring_correct Rsth Reqe ARth CRmorph pow_th O l nil a a0). simpl.
+ case (Peq ceqb (Nnorm O nil a) (Nnorm O nil a0)).
intros H H0 H1; split; auto.
rewrite H; auto.
generalize (PCond_cons_inv_l _ _ _ H1); simpl; auto.
@@ -1125,6 +1541,7 @@ Qed.
Fixpoint Fcons00 (e:PExpr C) (l:list (PExpr C)) {struct e} : list (PExpr C) :=
match e with
PEmul e1 e2 => Fcons00 e1 (Fcons00 e2 l)
+ | PEpow e1 _ => Fcons00 e1 l
| _ => Fcons0 e l
end.
@@ -1137,9 +1554,12 @@ intros l a; elim a; try (intros; apply PFcons0_fcons_inv; auto; fail).
case (H0 _ H3); intros H4 H5; split; auto.
simpl in |- *.
apply field_is_integral_domain; trivial.
+ simpl;intros. rewrite pow_th.(rpow_pow_N).
+ destruct (H _ H0);split;auto.
+ destruct n;simpl. apply AFth.(AF_1_neq_0).
+ apply pow_pos_not_0;trivial.
Qed.
-
Definition Pcond_simpl_gen :=
fcons_correct _ PFcons00_fcons_inv.
@@ -1167,6 +1587,7 @@ Qed.
Fixpoint Fcons1 (e:PExpr C) (l:list (PExpr C)) {struct e} : list (PExpr C) :=
match e with
PEmul e1 e2 => Fcons1 e1 (Fcons1 e2 l)
+ | PEpow e _ => Fcons1 e l
| PEopp e => if ceqb (copp cI) cO then absurd_PCond else Fcons1 e l
| PEc c => if ceqb c cO then absurd_PCond else l
| _ => Fcons0 e l
@@ -1196,6 +1617,9 @@ intros l a; elim a; try (intros; apply PFcons0_fcons_inv; auto; fail).
rewrite (morph1 CRmorph) in H0.
rewrite (morph0 CRmorph) in H0.
trivial.
+ intros;simpl. destruct (H _ H0);split;trivial.
+ rewrite pow_th.(rpow_pow_N). destruct n;simpl.
+ apply AFth.(AF_1_neq_0). apply pow_pos_not_0;trivial.
Qed.
Definition Fcons2 e l := Fcons1 (PExpr_simp e) l.
@@ -1214,30 +1638,6 @@ Definition Pcond_simpl_complete :=
End Fcons_simpl.
-Let Mpc := MPcond_map cO cI cadd cmul csub copp ceqb.
-Let Mp := MPcond_dev rO rI radd rmul req cO cI ceqb phi.
-Let Subst := PNSubstL cO cI cadd cmul ceqb.
-
-(* simplification + rewriting *)
-Theorem Field_subst_correct :
-forall l ul fe m n,
- PCond l (Fapp Fcons00 (condition (Fnorm fe)) nil) ->
- Mp (Mpc ul) l ->
- Peq ceqb (Subst (Nnorm (num (Fnorm fe))) (Mpc ul) m n) (Pc cO) = true ->
- FEeval l fe == 0.
-intros l ul fe m n H H1 H2.
-assert (H3 := (Pcond_simpl_gen _ _ H)).
-apply eq_trans with (1 := Fnorm_FEeval_PEeval l fe
- (Pcond_simpl_gen _ _ H)).
-apply rdiv8; auto.
-rewrite (PNSubstL_dev_ok Rsth Reqe ARth CRmorph m n
- _ (num (Fnorm fe)) l H1).
-rewrite <-(Ring_polynom.Pphi_Pphi_dev Rsth Reqe ARth CRmorph).
-rewrite (fun x => Peq_ok Rsth Reqe CRmorph x (Pc cO)); auto.
-simpl; apply (morph0 CRmorph); auto.
-Qed.
-
-
End AlmostField.
Section FieldAndSemiField.
@@ -1457,4 +1857,3 @@ Qed.
End Field.
End Complete.
-
diff --git a/contrib/setoid_ring/InitialRing.v b/contrib/setoid_ring/InitialRing.v
index 7df68cc0..bbdcd443 100644
--- a/contrib/setoid_ring/InitialRing.v
+++ b/contrib/setoid_ring/InitialRing.v
@@ -7,16 +7,21 @@
(************************************************************************)
Require Import ZArith_base.
+Require Import Zpow_def.
Require Import BinInt.
Require Import BinNat.
Require Import Setoid.
Require Import Ring_theory.
-Require Import Ring_tac.
Require Import Ring_polynom.
+
Set Implicit Arguments.
Import RingSyntax.
+
+(* An object to return when an expression is not recognized as a constant *)
+Definition NotConstant := false.
+
(** Z is a ring and a setoid*)
Lemma Zsth : Setoid_Theory Z (@eq Z).
@@ -88,6 +93,21 @@ Section ZMORPHISM.
| Zneg p => -(gen_phiPOS p)
end.
Notation "[ x ]" := (gen_phiZ x).
+
+ Definition get_signZ z :=
+ match z with
+ | Zneg p => Some (Zpos p)
+ | _ => None
+ end.
+
+ Lemma get_signZ_th : sign_theory ropp req gen_phiZ get_signZ.
+ Proof.
+ constructor.
+ destruct c;intros;try discriminate.
+ injection H;clear H;intros H1;subst c'.
+ simpl;rrefl.
+ Qed.
+
Section ALMOST_RING.
Variable ARth : almost_ring_theory 0 1 radd rmul rsub ropp req.
@@ -346,7 +366,8 @@ Section NMORPHISM.
End NMORPHISM.
(* syntaxification of constants in an abstract ring:
- the inverse of gen_phiPOS *)
+ the inverse of gen_phiPOS
+ Why we do not reconnize only rI ?????? *)
Ltac inv_gen_phi_pos rI add mul t :=
let rec inv_cst t :=
match t with
@@ -396,65 +417,8 @@ End NMORPHISM.
end
end.
-(* coefs = Z (abstract ring) *)
-Module Zpol.
-
-Definition ring_gen_correct
- R rO rI radd rmul rsub ropp req rSet req_th Rth :=
- @ring_correct R rO rI radd rmul rsub ropp req rSet req_th
- (Rth_ARth rSet req_th Rth)
- Z 0%Z 1%Z Zplus Zmult Zminus Zopp Zeq_bool
- (@gen_phiZ R rO rI radd rmul ropp)
- (gen_phiZ_morph rSet req_th Rth).
-
-Definition ring_rw_gen_correct
- R rO rI radd rmul rsub ropp req rSet req_th Rth :=
- @Pphi_dev_ok R rO rI radd rmul rsub ropp req rSet req_th
- (Rth_ARth rSet req_th Rth)
- Z 0%Z 1%Z Zplus Zmult Zminus Zopp Zeq_bool
- (@gen_phiZ R rO rI radd rmul ropp)
- (gen_phiZ_morph rSet req_th Rth).
-
-Definition ring_gen_eq_correct R rO rI radd rmul rsub ropp Rth :=
- @ring_gen_correct
- R rO rI radd rmul rsub ropp (@eq R) (Eqsth R) (Eq_ext _ _ _) Rth.
-
-Definition ring_rw_gen_eq_correct R rO rI radd rmul rsub ropp Rth :=
- @ring_rw_gen_correct
- R rO rI radd rmul rsub ropp (@eq R) (Eqsth R) (Eq_ext _ _ _) Rth.
-
-End Zpol.
-
-(* coefs = N (abstract semi-ring) *)
-Module Npol.
-
-Definition ring_gen_correct
- R rO rI radd rmul req rSet req_th SRth :=
- @ring_correct R rO rI radd rmul (SRsub radd) (@SRopp R) req rSet
- (SReqe_Reqe req_th)
- (SRth_ARth rSet SRth)
- N 0%N 1%N Nplus Nmult (SRsub Nplus) (@SRopp N) Neq_bool
- (@gen_phiN R rO rI radd rmul)
- (gen_phiN_morph rSet req_th SRth).
-
-Definition ring_rw_gen_correct
- R rO rI radd rmul req rSet req_th SRth :=
- @Pphi_dev_ok R rO rI radd rmul (SRsub radd) (@SRopp R) req rSet
- (SReqe_Reqe req_th)
- (SRth_ARth rSet SRth)
- N 0%N 1%N Nplus Nmult (SRsub Nplus) (@SRopp N) Neq_bool
- (@gen_phiN R rO rI radd rmul)
- (gen_phiN_morph rSet req_th SRth).
-
-Definition ring_gen_eq_correct R rO rI radd rmul SRth :=
- @ring_gen_correct
- R rO rI radd rmul (@eq R) (Eqsth R) (Eq_s_ext _ _) SRth.
-
-Definition ring_rw_gen_eq_correct' R rO rI radd rmul SRth :=
- @ring_rw_gen_correct
- R rO rI radd rmul (@eq R) (Eqsth R) (Eq_s_ext _ _) SRth.
-
-End Npol.
+(* A simpl tactic reconninzing nothing *)
+ Ltac inv_morph_nothing t := constr:(NotConstant).
Ltac coerce_to_almost_ring set ext rspec :=
@@ -481,7 +445,47 @@ Ltac abstract_ring_morphism set ext rspec :=
| _ => fail 1 "bad ring structure"
end.
-Ltac ring_elements set ext rspec rk :=
+Record hypo : Type := mkhypo {
+ hypo_type : Type;
+ hypo_proof : hypo_type
+ }.
+
+Ltac gen_ring_pow set arth pspec :=
+ match pspec with
+ | None =>
+ match type of arth with
+ | @almost_ring_theory ?R ?rO ?rI ?radd ?rmul ?rsub ?ropp ?req =>
+ constr:(mkhypo (@pow_N_th R rI rmul req set))
+ | _ => fail 1 "gen_ring_pow"
+ end
+ | Some ?t => constr:(t)
+ end.
+
+Ltac default_sign_spec morph :=
+ match type of morph with
+ | @ring_morph ?R ?r0 ?rI ?radd ?rmul ?rsub ?ropp ?req
+ ?C ?c0 ?c1 ?cadd ?cmul ?csub ?copp ?ceq_b ?phi =>
+ constr:(mkhypo (@get_sign_None_th R ropp req C phi))
+ | _ => fail 1 "ring anomaly : default_sign_spec"
+ end.
+
+Ltac gen_ring_sign set rspec morph sspec rk :=
+ match sspec with
+ | None =>
+ match rk with
+ | Abstract =>
+ match type of rspec with
+ | @ring_theory ?R ?rO ?rI ?radd ?rmul ?rsub ?ropp ?req =>
+ constr:(mkhypo (@get_signZ_th R rO rI radd rmul ropp req set))
+ | _ => default_sign_spec morph
+ end
+ | _ => default_sign_spec morph
+ end
+ | Some ?t => constr:(t)
+ end.
+
+
+Ltac ring_elements set ext rspec pspec sspec rk :=
let arth := coerce_to_almost_ring set ext rspec in
let ext_r := coerce_to_ring_ext ext in
let morph :=
@@ -493,19 +497,85 @@ Ltac ring_elements set ext rspec rk :=
constr:(IDmorph rO rI add mul sub opp set _ reqb_ok)
| _ => fail 2 "ring anomaly"
end
- | @Morphism ?m => m
+ | @Morphism ?m =>
+ match type of m with
+ | ring_morph _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ => m
+ | @semi_morph _ _ _ _ _ _ _ _ _ _ _ _ _ =>
+ constr:(SRmorph_Rmorph set m)
+ | _ => fail 2 " ici"
+ end
| _ => fail 1 "ill-formed ring kind"
end in
- fun f => f arth ext_r morph.
+ let p_spec := gen_ring_pow set arth pspec in
+ let s_spec := gen_ring_sign set rspec morph sspec rk in
+ fun f => f arth ext_r morph p_spec s_spec.
(* Given a ring structure and the kind of morphism,
returns 2 lemmas (one for ring, and one for ring_simplify). *)
+Ltac ring_lemmas set ext rspec pspec sspec rk :=
+ let gen_lemma2 :=
+ match pspec with
+ | None => constr:(ring_rw_correct)
+ | Some _ => constr:(ring_rw_pow_correct)
+ end in
+ ring_elements set ext rspec pspec sspec rk
+ ltac:(fun arth ext_r morph p_spec s_spec =>
+ match p_spec with
+ | mkhypo ?pp_spec =>
+ match s_spec with
+ | mkhypo ?ps_spec =>
+ let lemma1 :=
+ constr:(ring_correct set ext_r arth morph pp_spec) in
+ let lemma2 :=
+ constr:(gen_lemma2 _ _ _ _ _ _ _ _ set ext_r arth
+ _ _ _ _ _ _ _ _ _ morph
+ _ _ _ pp_spec
+ _ ps_spec) in
+ fun f => f arth ext_r morph lemma1 lemma2
+ | _ => fail 2 "bad sign specification"
+ end
+ | _ => fail 1 "bad power specification"
+ end).
+
+(* Tactic for constant *)
+Ltac isnatcst t :=
+ match t with
+ O => true
+ | S ?p => isnatcst p
+ | _ => false
+ end.
+
+Ltac isPcst t :=
+ match t with
+ | xI ?p => isPcst p
+ | xO ?p => isPcst p
+ | xH => constr:true
+ (* nat -> positive *)
+ | P_of_succ_nat ?n => isnatcst n
+ | _ => false
+ end.
+
+Ltac isNcst t :=
+ match t with
+ N0 => constr:true
+ | Npos ?p => isPcst p
+ | _ => constr:false
+ end.
+
+Ltac isZcst t :=
+ match t with
+ Z0 => true
+ | Zpos ?p => isPcst p
+ | Zneg ?p => isPcst p
+ (* injection nat -> Z *)
+ | Z_of_nat ?n => isnatcst n
+ (* injection N -> Z *)
+ | Z_of_N ?n => isNcst n
+ (* *)
+ | _ => false
+ end.
+
+
-Ltac ring_lemmas set ext rspec rk :=
- ring_elements set ext rspec rk
- ltac:(fun arth ext_r morph =>
- let lemma1 := constr:(ring_correct set ext_r arth morph) in
- let lemma2 := constr:(Pphi_dev_ok set ext_r arth morph) in
- fun f => f arth ext_r morph lemma1 lemma2).
diff --git a/contrib/setoid_ring/NArithRing.v b/contrib/setoid_ring/NArithRing.v
index 33e3cb4e..ae067a8a 100644
--- a/contrib/setoid_ring/NArithRing.v
+++ b/contrib/setoid_ring/NArithRing.v
@@ -12,16 +12,6 @@ Import InitialRing.
Set Implicit Arguments.
-Ltac isNcst t :=
- let t := eval hnf in t in
- match t with
- N0 => constr:true
- | Npos ?p => isNcst p
- | xI ?p => isNcst p
- | xO ?p => isNcst p
- | xH => constr:true
- | _ => constr:false
- end.
Ltac Ncst t :=
match isNcst t with
true => t
diff --git a/contrib/setoid_ring/RealField.v b/contrib/setoid_ring/RealField.v
index 13896123..d0512dff 100644
--- a/contrib/setoid_ring/RealField.v
+++ b/contrib/setoid_ring/RealField.v
@@ -1,6 +1,9 @@
-Require Import Raxioms.
-Require Import Rdefinitions.
+Require Import Nnat.
+Require Import ArithRing.
Require Export Ring Field.
+Require Import Rdefinitions.
+Require Import Rpow_def.
+Require Import Raxioms.
Open Local Scope R_scope.
@@ -102,4 +105,29 @@ Lemma Zeq_bool_complete : forall x y,
Zeq_bool x y = true.
Proof gen_phiZ_complete Rset Rext Rfield Rgen_phiPOS_not_0.
-Add Field RField : Rfield (infinite Zeq_bool_complete).
+Lemma Rdef_pow_add : forall (x:R) (n m:nat), pow x (n + m) = pow x n * pow x m.
+Proof.
+ intros x n; elim n; simpl in |- *; auto with real.
+ intros n0 H' m; rewrite H'; auto with real.
+Qed.
+
+Lemma R_power_theory : power_theory 1%R Rmult (eq (A:=R)) nat_of_N pow.
+Proof.
+ constructor. destruct n. reflexivity.
+ simpl. induction p;simpl.
+ rewrite ZL6. rewrite Rdef_pow_add;rewrite IHp. reflexivity.
+ unfold nat_of_P;simpl;rewrite ZL6;rewrite Rdef_pow_add;rewrite IHp;trivial.
+ rewrite Rmult_comm;apply Rmult_1_l.
+Qed.
+
+Ltac Rpow_tac t :=
+ match isnatcst t with
+ | false => constr:(InitialRing.NotConstant)
+ | _ => constr:(N_of_nat t)
+ end.
+
+Add Field RField : Rfield
+ (completeness Zeq_bool_complete, power_tac R_power_theory [Rpow_tac]).
+
+
+
diff --git a/contrib/setoid_ring/Ring.v b/contrib/setoid_ring/Ring.v
index 167e026f..1a4e1cc7 100644
--- a/contrib/setoid_ring/Ring.v
+++ b/contrib/setoid_ring/Ring.v
@@ -9,6 +9,7 @@
Require Import Bool.
Require Export Ring_theory.
Require Export Ring_base.
+Require Export InitialRing.
Require Export Ring_tac.
Lemma BoolTheory :
@@ -25,7 +26,7 @@ reflexivity.
destruct x; reflexivity.
Qed.
-Unboxed Definition bool_eq (b1 b2:bool) :=
+Definition bool_eq (b1 b2:bool) :=
if b1 then b2 else negb b2.
Lemma bool_eq_ok : forall b1 b2, bool_eq b1 b2 = true -> b1 = b2.
diff --git a/contrib/setoid_ring/Ring_polynom.v b/contrib/setoid_ring/Ring_polynom.v
index 7317ab21..b79f2fe2 100644
--- a/contrib/setoid_ring/Ring_polynom.v
+++ b/contrib/setoid_ring/Ring_polynom.v
@@ -1,5 +1,5 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
+(* V * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
@@ -10,9 +10,11 @@ Set Implicit Arguments.
Require Import Setoid.
Require Import BinList.
Require Import BinPos.
+Require Import BinNat.
Require Import BinInt.
Require Export Ring_theory.
+Open Local Scope positive_scope.
Import RingSyntax.
Section MakeRingPol.
@@ -35,6 +37,12 @@ Section MakeRingPol.
Variable CRmorph : ring_morph rO rI radd rmul rsub ropp req
cO cI cadd cmul csub copp ceqb phi.
+ (* Power coefficients *)
+ Variable Cpow : Set.
+ Variable Cp_phi : N -> Cpow.
+ Variable rpow : R -> Cpow -> R.
+ Variable pow_th : power_theory rI rmul req Cp_phi rpow.
+
(* R notations *)
Notation "0" := rO. Notation "1" := rI.
@@ -113,12 +121,23 @@ Section MakeRingPol.
| _ => Pinj j P
end.
+ Definition mkPinj_pred j P:=
+ match j with
+ | xH => P
+ | xO j => Pinj (Pdouble_minus_one j) P
+ | xI j => Pinj (xO j) P
+ end.
+
Definition mkPX P i Q :=
match P with
| Pc c => if c ?=! cO then mkPinj xH Q else PX P i Q
| Pinj _ _ => PX P i Q
| PX P' i' Q' => if Q' ?== P0 then PX P' (i' + i) Q else PX P i Q
end.
+
+ Definition mkXi i := PX P1 i P0.
+
+ Definition mkX := mkXi 1.
(** Opposite of addition *)
@@ -305,7 +324,34 @@ Section MakeRingPol.
end.
End PmulI.
+(* A symmetric version of the multiplication *)
+ Fixpoint Pmul (P P'' : Pol) {struct P''} : Pol :=
+ match P'' with
+ | Pc c => PmulC P c
+ | Pinj j' Q' => PmulI Pmul Q' j' P
+ | PX P' i' Q' =>
+ match P with
+ | Pc c => PmulC P'' c
+ | Pinj j Q =>
+ let QQ' :=
+ match j with
+ | xH => Pmul Q Q'
+ | xO j => Pmul (Pinj (Pdouble_minus_one j) Q) Q'
+ | xI j => Pmul (Pinj (xO j) Q) Q'
+ end in
+ mkPX (Pmul P P') i' QQ'
+ | PX P i Q=>
+ let QQ' := Pmul Q Q' in
+ let PQ' := PmulI Pmul Q' xH P in
+ let QP' := Pmul (mkPinj xH Q) P' in
+ let PP' := Pmul P P' in
+ (mkPX (mkPX PP' i P0 ++ QP') i' P0) ++ mkPX PQ' i QQ'
+ end
+ end.
+
+(* Non symmetric *)
+(*
Fixpoint Pmul_aux (P P' : Pol) {struct P'} : Pol :=
match P' with
| Pc c' => PmulC P c'
@@ -319,10 +365,21 @@ Section MakeRingPol.
| Pc c => PmulC P' c
| Pinj j Q => PmulI Pmul_aux Q j P'
| PX P i Q =>
- Padd (mkPX (Pmul_aux P P') i P0) (PmulI Pmul_aux Q xH P')
+ (mkPX (Pmul_aux P P') i P0) ++ (PmulI Pmul_aux Q xH P')
end.
+*)
Notation "P ** P'" := (Pmul P P').
-
+
+ Fixpoint Psquare (P:Pol) : Pol :=
+ match P with
+ | Pc c => Pc (c *! c)
+ | Pinj j Q => Pinj j (Psquare Q)
+ | PX P i Q =>
+ let twoPQ := Pmul P (mkPinj xH (PmulC Q (cI +! cI))) in
+ let Q2 := Psquare Q in
+ let P2 := Psquare P in
+ mkPX (mkPX P2 i P0 ++ twoPQ) i Q2
+ end.
(** Monomial **)
@@ -331,29 +388,29 @@ Section MakeRingPol.
| zmon: positive -> Mon -> Mon
| vmon: positive -> Mon -> Mon.
- Fixpoint pow (x:R) (i:positive) {struct i}: R :=
- match i with
- | xH => x
- | xO i => let p := pow x i in p * p
- | xI i => let p := pow x i in x * p * p
- end.
-
Fixpoint Mphi(l:list R) (M: Mon) {struct M} : R :=
match M with
mon0 => rI
| zmon j M1 => Mphi (jump j l) M1
| vmon i M1 =>
let x := hd 0 l in
- let xi := pow x i in
+ let xi := pow_pos rmul x i in
(Mphi (tail l) M1) * xi
end.
- Definition zmon_pred j M :=
- match j with xH => M | _ => zmon (Ppred j) M end.
-
Definition mkZmon j M :=
match M with mon0 => mon0 | _ => zmon j M end.
+ Definition zmon_pred j M :=
+ match j with xH => M | _ => mkZmon (Ppred j) M end.
+
+ Definition mkVmon i M :=
+ match M with
+ | mon0 => vmon i mon0
+ | zmon j m => vmon i (zmon_pred j m)
+ | vmon i' m => vmon (i+i') m
+ end.
+
Fixpoint MFactor (P: Pol) (M: Mon) {struct P}: Pol * Pol :=
match P, M with
_, mon0 => (Pc cO, P)
@@ -434,7 +491,7 @@ Section MakeRingPol.
| Pinj j Q => Pphi (jump j l) Q
| PX P i Q =>
let x := hd 0 l in
- let xi := pow x i in
+ let xi := pow_pos rmul x i in
(Pphi l P) * xi + (Pphi (tail l) Q)
end.
@@ -469,26 +526,6 @@ Section MakeRingPol.
rewrite Psucc_o_double_minus_one_eq_xO;trivial.
simpl;trivial.
Qed.
-
- Lemma pow_Psucc : forall x j, pow x (Psucc j) == x * pow x j.
- Proof.
- induction j;simpl;rsimpl.
- rewrite IHj;rsimpl;mul_push x;rrefl.
- Qed.
-
- Lemma pow_Pplus : forall x i j, pow x (i + j) == pow x i * pow x j.
- Proof.
- intro x;induction i;intros.
- rewrite xI_succ_xO;rewrite Pplus_one_succ_r.
- rewrite <- Pplus_diag;repeat rewrite <- Pplus_assoc.
- repeat rewrite IHi.
- rewrite Pplus_comm;rewrite <- Pplus_one_succ_r;rewrite pow_Psucc.
- simpl;rsimpl.
- rewrite <- Pplus_diag;repeat rewrite <- Pplus_assoc.
- repeat rewrite IHi;rsimpl.
- rewrite Pplus_comm;rewrite <- Pplus_one_succ_r;rewrite pow_Psucc;
- simpl;rsimpl.
- Qed.
Lemma Peq_ok : forall P P',
(P ?== P') = true -> forall l, P@l == P'@ l.
@@ -523,8 +560,11 @@ Section MakeRingPol.
rewrite <-jump_Pplus;rewrite Pplus_comm;rrefl.
Qed.
+ Let pow_pos_Pplus :=
+ pow_pos_Pplus rmul Rsth Reqe.(Rmul_ext) ARth.(ARmul_comm) ARth.(ARmul_assoc).
+
Lemma mkPX_ok : forall l P i Q,
- (mkPX P i Q)@l == P@l*(pow (hd 0 l) i) + Q@(tail l).
+ (mkPX P i Q)@l == P@l*(pow_pos rmul (hd 0 l) i) + Q@(tail l).
Proof.
intros l P i Q;unfold mkPX.
destruct P;try (simpl;rrefl).
@@ -533,7 +573,7 @@ Section MakeRingPol.
rewrite mkPinj_ok;rsimpl;simpl;rrefl.
assert (H := @Peq_ok P3 P0);destruct (P3 ?== P0);simpl;try rrefl.
rewrite (H (refl_equal true));trivial.
- rewrite Pphi0;rewrite pow_Pplus;rsimpl.
+ rewrite Pphi0. rewrite pow_pos_Pplus;rsimpl.
Qed.
Ltac Esimpl :=
@@ -622,19 +662,19 @@ Section MakeRingPol.
Esimpl2;add_push [c];rrefl.
destruct p0;simpl;Esimpl2.
rewrite IHP'2;simpl.
- rsimpl;add_push (P'1@l * (pow (hd 0 l) p));rrefl.
+ rsimpl;add_push (P'1@l * (pow_pos rmul (hd 0 l) p));rrefl.
rewrite IHP'2;simpl.
- rewrite jump_Pdouble_minus_one;rsimpl;add_push (P'1@l * (pow (hd 0 l) p));rrefl.
+ rewrite jump_Pdouble_minus_one;rsimpl;add_push (P'1@l * (pow_pos rmul (hd 0 l) p));rrefl.
rewrite IHP'2;rsimpl. add_push (P @ (tail l));rrefl.
assert (H := ZPminus_spec p0 p);destruct (ZPminus p0 p);Esimpl2.
rewrite IHP'1;rewrite IHP'2;rsimpl.
add_push (P3 @ (tail l));rewrite H;rrefl.
rewrite IHP'1;rewrite IHP'2;simpl;Esimpl.
rewrite H;rewrite Pplus_comm.
- rewrite pow_Pplus;rsimpl.
+ rewrite pow_pos_Pplus;rsimpl.
add_push (P3 @ (tail l));rrefl.
assert (forall P k l,
- (PaddX Padd P'1 k P) @ l == P@l + P'1@l * pow (hd 0 l) k).
+ (PaddX Padd P'1 k P) @ l == P@l + P'1@l * pow_pos rmul (hd 0 l) k).
induction P;simpl;intros;try apply (ARadd_comm ARth).
destruct p2;simpl;try apply (ARadd_comm ARth).
rewrite jump_Pdouble_minus_one;apply (ARadd_comm ARth).
@@ -642,15 +682,15 @@ Section MakeRingPol.
rewrite IHP'1;rsimpl; rewrite H1;add_push (P5 @ (tail l0));rrefl.
rewrite IHP'1;simpl;Esimpl.
rewrite H1;rewrite Pplus_comm.
- rewrite pow_Pplus;simpl;Esimpl.
+ rewrite pow_pos_Pplus;simpl;Esimpl.
add_push (P5 @ (tail l0));rrefl.
rewrite IHP1;rewrite H1;rewrite Pplus_comm.
- rewrite pow_Pplus;simpl;rsimpl.
+ rewrite pow_pos_Pplus;simpl;rsimpl.
add_push (P5 @ (tail l0));rrefl.
rewrite H0;rsimpl.
add_push (P3 @ (tail l)).
rewrite H;rewrite Pplus_comm.
- rewrite IHP'2;rewrite pow_Pplus;rsimpl.
+ rewrite IHP'2;rewrite pow_pos_Pplus;rsimpl.
add_push (P3 @ (tail l));rrefl.
Qed.
@@ -674,20 +714,20 @@ Section MakeRingPol.
destruct P;simpl.
repeat rewrite Popp_ok;Esimpl2;rsimpl;add_push [c];try rrefl.
destruct p0;simpl;Esimpl2.
- rewrite IHP'2;simpl;rsimpl;add_push (P'1@l * (pow (hd 0 l) p));trivial.
+ rewrite IHP'2;simpl;rsimpl;add_push (P'1@l * (pow_pos rmul (hd 0 l) p));trivial.
add_push (P @ (jump p0 (jump p0 (tail l))));rrefl.
rewrite IHP'2;simpl;rewrite jump_Pdouble_minus_one;rsimpl.
- add_push (- (P'1 @ l * pow (hd 0 l) p));rrefl.
+ add_push (- (P'1 @ l * pow_pos rmul (hd 0 l) p));rrefl.
rewrite IHP'2;rsimpl;add_push (P @ (tail l));rrefl.
assert (H := ZPminus_spec p0 p);destruct (ZPminus p0 p);Esimpl2.
rewrite IHP'1; rewrite IHP'2;rsimpl.
add_push (P3 @ (tail l));rewrite H;rrefl.
rewrite IHP'1; rewrite IHP'2;rsimpl;simpl;Esimpl.
rewrite H;rewrite Pplus_comm.
- rewrite pow_Pplus;rsimpl.
+ rewrite pow_pos_Pplus;rsimpl.
add_push (P3 @ (tail l));rrefl.
assert (forall P k l,
- (PsubX Psub P'1 k P) @ l == P@l + - P'1@l * pow (hd 0 l) k).
+ (PsubX Psub P'1 k P) @ l == P@l + - P'1@l * pow_pos rmul (hd 0 l) k).
induction P;simpl;intros.
rewrite Popp_ok;rsimpl;apply (ARadd_comm ARth);trivial.
destruct p2;simpl;rewrite Popp_ok;rsimpl.
@@ -697,17 +737,44 @@ Section MakeRingPol.
assert (H1 := ZPminus_spec p2 k);destruct (ZPminus p2 k);Esimpl2;rsimpl.
rewrite IHP'1;rsimpl;add_push (P5 @ (tail l0));rewrite H1;rrefl.
rewrite IHP'1;rewrite H1;rewrite Pplus_comm.
- rewrite pow_Pplus;simpl;Esimpl.
+ rewrite pow_pos_Pplus;simpl;Esimpl.
add_push (P5 @ (tail l0));rrefl.
rewrite IHP1;rewrite H1;rewrite Pplus_comm.
- rewrite pow_Pplus;simpl;rsimpl.
+ rewrite pow_pos_Pplus;simpl;rsimpl.
add_push (P5 @ (tail l0));rrefl.
rewrite H0;rsimpl.
rewrite IHP'2;rsimpl;add_push (P3 @ (tail l)).
rewrite H;rewrite Pplus_comm.
- rewrite pow_Pplus;rsimpl.
+ rewrite pow_pos_Pplus;rsimpl.
Qed.
-
+(* Proof for the symmetriv version *)
+
+ Lemma PmulI_ok :
+ forall P',
+ (forall (P : Pol) (l : list R), (Pmul P P') @ l == P @ l * P' @ l) ->
+ forall (P : Pol) (p : positive) (l : list R),
+ (PmulI Pmul P' p P) @ l == P @ l * P' @ (jump p l).
+ Proof.
+ induction P;simpl;intros.
+ Esimpl2;apply (ARmul_comm ARth).
+ assert (H1 := ZPminus_spec p p0);destruct (ZPminus p p0);Esimpl2.
+ rewrite H1; rewrite H;rrefl.
+ rewrite H1; rewrite H.
+ rewrite Pplus_comm.
+ rewrite jump_Pplus;simpl;rrefl.
+ rewrite H1;rewrite Pplus_comm.
+ rewrite jump_Pplus;rewrite IHP;rrefl.
+ destruct p0;Esimpl2.
+ rewrite IHP1;rewrite IHP2;simpl;rsimpl.
+ mul_push (pow_pos rmul (hd 0 l) p);rrefl.
+ rewrite IHP1;rewrite IHP2;simpl;rsimpl.
+ mul_push (pow_pos rmul (hd 0 l) p); rewrite jump_Pdouble_minus_one;rrefl.
+ rewrite IHP1;simpl;rsimpl.
+ mul_push (pow_pos rmul (hd 0 l) p).
+ rewrite H;rrefl.
+ Qed.
+
+(*
Lemma PmulI_ok :
forall P',
(forall (P : Pol) (l : list R), (Pmul_aux P P') @ l == P @ l * P' @ l) ->
@@ -725,11 +792,11 @@ Section MakeRingPol.
rewrite jump_Pplus;rewrite IHP;rrefl.
destruct p0;Esimpl2.
rewrite IHP1;rewrite IHP2;simpl;rsimpl.
- mul_push (pow (hd 0 l) p);rrefl.
+ mul_push (pow_pos rmul (hd 0 l) p);rrefl.
rewrite IHP1;rewrite IHP2;simpl;rsimpl.
- mul_push (pow (hd 0 l) p); rewrite jump_Pdouble_minus_one;rrefl.
+ mul_push (pow_pos rmul (hd 0 l) p); rewrite jump_Pdouble_minus_one;rrefl.
rewrite IHP1;simpl;rsimpl.
- mul_push (pow (hd 0 l) p).
+ mul_push (pow_pos rmul (hd 0 l) p).
rewrite H;rrefl.
Qed.
@@ -741,9 +808,33 @@ Section MakeRingPol.
rewrite Padd_ok;Esimpl2.
rewrite (PmulI_ok P'2 IHP'2). rewrite IHP'1. rrefl.
Qed.
+*)
+(* Proof for the symmetric version *)
Lemma Pmul_ok : forall P P' l, (P**P')@l == P@l * P'@l.
Proof.
+ intros P P';generalize P;clear P;induction P';simpl;intros.
+ apply PmulC_ok. apply PmulI_ok;trivial.
+ destruct P.
+ rewrite (ARmul_comm ARth);Esimpl2;Esimpl2.
+ Esimpl2. rewrite IHP'1;Esimpl2.
+ assert (match p0 with
+ | xI j => Pinj (xO j) P ** P'2
+ | xO j => Pinj (Pdouble_minus_one j) P ** P'2
+ | 1 => P ** P'2
+ end @ (tail l) == P @ (jump p0 l) * P'2 @ (tail l)).
+ destruct p0;simpl;rewrite IHP'2;Esimpl.
+ rewrite jump_Pdouble_minus_one;Esimpl.
+ rewrite H;Esimpl.
+ rewrite Padd_ok; Esimpl2. rewrite Padd_ok; Esimpl2.
+ repeat (rewrite IHP'1 || rewrite IHP'2);simpl.
+ rewrite PmulI_ok;trivial.
+ mul_push (P'1@l). simpl. mul_push (P'2 @ (tail l)). Esimpl.
+ Qed.
+
+(*
+Lemma Pmul_ok : forall P P' l, (P**P')@l == P@l * P'@l.
+ Proof.
destruct P;simpl;intros.
Esimpl2;apply (ARmul_comm ARth).
rewrite (PmulI_ok P (Pmul_aux_ok P)).
@@ -753,12 +844,38 @@ Section MakeRingPol.
rewrite Pmul_aux_ok;mul_push (P' @ l).
rewrite (ARmul_comm ARth (P' @ l));rrefl.
Qed.
+*)
+
+ Lemma Psquare_ok : forall P l, (Psquare P)@l == P@l * P@l.
+ Proof.
+ induction P;simpl;intros;Esimpl2.
+ apply IHP. rewrite Padd_ok. rewrite Pmul_ok;Esimpl2.
+ rewrite IHP1;rewrite IHP2.
+ mul_push (pow_pos rmul (hd 0 l) p). mul_push (P2@l).
+ rrefl.
+ Qed.
Lemma mkZmon_ok: forall M j l,
Mphi l (mkZmon j M) == Mphi l (zmon j M).
intros M j l; case M; simpl; intros; rsimpl.
Qed.
+
+ Lemma zmon_pred_ok : forall M j l,
+ Mphi (tail l) (zmon_pred j M) == Mphi l (zmon j M).
+ Proof.
+ destruct j; simpl;intros auto; rsimpl.
+ rewrite mkZmon_ok;rsimpl.
+ rewrite mkZmon_ok;simpl. rewrite jump_Pdouble_minus_one; rsimpl.
+ Qed.
+
+ Lemma mkVmon_ok : forall M i l, Mphi l (mkVmon i M) == Mphi l M*pow_pos rmul (hd 0 l) i.
+ Proof.
+ destruct M;simpl;intros;rsimpl.
+ rewrite zmon_pred_ok;simpl;rsimpl.
+ rewrite Pplus_comm;rewrite pow_pos_Pplus;rsimpl.
+ Qed.
+
Lemma Mphi_ok: forall P M l,
let (Q,R) := MFactor P M in
@@ -798,8 +915,7 @@ Section MakeRingPol.
rewrite (ARadd_comm ARth); rsimpl.
apply radd_ext; rsimpl.
rewrite (ARadd_comm ARth); rsimpl.
- case j; simpl; auto; try intros j1; rsimpl.
- rewrite jump_Pdouble_minus_one; rsimpl.
+ rewrite zmon_pred_ok;rsimpl.
intros j M1.
case_eq ((i ?= j) Eq); intros He; simpl.
rewrite (Pcompare_Eq_eq _ _ He).
@@ -827,7 +943,7 @@ Section MakeRingPol.
apply rmul_ext; rsimpl.
rewrite (ARmul_comm ARth); rsimpl.
apply rmul_ext; rsimpl.
- rewrite <- pow_Pplus.
+ rewrite <- pow_pos_Pplus.
rewrite (Pplus_minus _ _ (ZC2 _ _ He)); rsimpl.
generalize (Hrec1 (mkZmon 1 M1) l);
case (MFactor P2 (mkZmon 1 M1));
@@ -847,13 +963,15 @@ Section MakeRingPol.
repeat (rewrite <-(ARmul_assoc ARth)).
rewrite (ARmul_comm ARth (Q3@l)); rsimpl.
apply rmul_ext; rsimpl.
- rewrite <- pow_Pplus.
+ rewrite <- pow_pos_Pplus.
rewrite (Pplus_minus _ _ He); rsimpl.
Qed.
+(* Proof for the symmetric version *)
Lemma POneSubst_ok: forall P1 M1 P2 P3 l,
POneSubst P1 M1 P2 = Some P3 -> Mphi l M1 == P2@l -> P1@l == P3@l.
+ Proof.
intros P2 M1 P3 P4 l; unfold POneSubst.
generalize (Mphi_ok P2 M1 l); case (MFactor P2 M1); simpl; auto.
intros Q1 R1; case R1.
@@ -864,16 +982,40 @@ Section MakeRingPol.
discriminate.
intros _ H1 H2; injection H1; intros; subst.
rewrite H2; rsimpl.
- rewrite Padd_ok; rewrite Pmul_ok; rsimpl.
+ (* new version *)
+ rewrite Padd_ok; rewrite PmulC_ok; rsimpl.
intros i P5 H; rewrite H.
intros HH H1; injection HH; intros; subst; rsimpl.
- rewrite Padd_ok; rewrite Pmul_ok; rewrite H1; rsimpl.
+ rewrite Padd_ok; rewrite PmulI_ok. intros;apply Pmul_ok. rewrite H1; rsimpl.
intros i P5 P6 H1 H2 H3; rewrite H1; rewrite H3.
- injection H2; intros; subst; rsimpl.
- rewrite Padd_ok; rewrite Pmul_ok; rsimpl.
+ assert (P4 = Q1 ++ P3 ** PX i P5 P6).
+ injection H2; intros; subst;trivial.
+ rewrite H;rewrite Padd_ok;rewrite Pmul_ok;rsimpl.
Qed.
-
-
+(*
+ Lemma POneSubst_ok: forall P1 M1 P2 P3 l,
+ POneSubst P1 M1 P2 = Some P3 -> Mphi l M1 == P2@l -> P1@l == P3@l.
+Proof.
+ intros P2 M1 P3 P4 l; unfold POneSubst.
+ generalize (Mphi_ok P2 M1 l); case (MFactor P2 M1); simpl; auto.
+ intros Q1 R1; case R1.
+ intros c H; rewrite H.
+ generalize (morph_eq CRmorph c cO);
+ case (c ?=! cO); simpl; auto.
+ intros H1 H2; rewrite H1; auto; rsimpl.
+ discriminate.
+ intros _ H1 H2; injection H1; intros; subst.
+ rewrite H2; rsimpl.
+ rewrite Padd_ok; rewrite Pmul_ok; rsimpl.
+ intros i P5 H; rewrite H.
+ intros HH H1; injection HH; intros; subst; rsimpl.
+ rewrite Padd_ok; rewrite Pmul_ok. rewrite H1; rsimpl.
+ intros i P5 P6 H1 H2 H3; rewrite H1; rewrite H3.
+ injection H2; intros; subst; rsimpl.
+ rewrite Padd_ok.
+ rewrite Pmul_ok; rsimpl.
+ Qed.
+*)
Lemma PNSubst1_ok: forall n P1 M1 P2 l,
Mphi l M1 == P2@l -> P1@l == (PNSubst1 P1 M1 P2 n)@l.
Proof.
@@ -947,47 +1089,28 @@ Section MakeRingPol.
| PEadd : PExpr -> PExpr -> PExpr
| PEsub : PExpr -> PExpr -> PExpr
| PEmul : PExpr -> PExpr -> PExpr
- | PEopp : PExpr -> PExpr.
-
- (** normalisation towards polynomials *)
-
- Definition X := (PX P1 xH P0).
-
- Definition mkX j :=
- match j with
- | xH => X
- | xO j => Pinj (Pdouble_minus_one j) X
- | xI j => Pinj (xO j) X
- end.
+ | PEopp : PExpr -> PExpr
+ | PEpow : PExpr -> N -> PExpr.
- Fixpoint norm (pe:PExpr) : Pol :=
- match pe with
- | PEc c => Pc c
- | PEX j => mkX j
- | PEadd pe1 (PEopp pe2) => Psub (norm pe1) (norm pe2)
- | PEadd (PEopp pe1) pe2 => Psub (norm pe2) (norm pe1)
- | PEadd pe1 pe2 => Padd (norm pe1) (norm pe2)
- | PEsub pe1 pe2 => Psub (norm pe1) (norm pe2)
- | PEmul pe1 pe2 => Pmul (norm pe1) (norm pe2)
- | PEopp pe1 => Popp (norm pe1)
- end.
+ (** evaluation of polynomial expressions towards R *)
+ Definition mk_X j := mkPinj_pred j mkX.
(** evaluation of polynomial expressions towards R *)
-
+
Fixpoint PEeval (l:list R) (pe:PExpr) {struct pe} : R :=
- match pe with
- | PEc c => phi c
- | PEX j => nth 0 j l
- | PEadd pe1 pe2 => (PEeval l pe1) + (PEeval l pe2)
- | PEsub pe1 pe2 => (PEeval l pe1) - (PEeval l pe2)
- | PEmul pe1 pe2 => (PEeval l pe1) * (PEeval l pe2)
- | PEopp pe1 => - (PEeval l pe1)
- end.
+ match pe with
+ | PEc c => phi c
+ | PEX j => nth 0 j l
+ | PEadd pe1 pe2 => (PEeval l pe1) + (PEeval l pe2)
+ | PEsub pe1 pe2 => (PEeval l pe1) - (PEeval l pe2)
+ | PEmul pe1 pe2 => (PEeval l pe1) * (PEeval l pe2)
+ | PEopp pe1 => - (PEeval l pe1)
+ | PEpow pe1 n => rpow (PEeval l pe1) (Cp_phi n)
+ end.
(** Correctness proofs *)
-
- Lemma mkX_ok : forall p l, nth 0 p l == (mkX p) @ l.
+ Lemma mkX_ok : forall p l, nth 0 p l == (mk_X p) @ l.
Proof.
destruct p;simpl;intros;Esimpl;trivial.
rewrite <-jump_tl;rewrite nth_jump;rrefl.
@@ -995,238 +1118,579 @@ Section MakeRingPol.
rewrite nth_Pdouble_minus_one;rrefl.
Qed.
- Lemma norm_PEopp : forall l pe, (norm (PEopp pe))@l == -(norm pe)@l.
- Proof.
- intros;simpl;apply Popp_ok.
- Qed.
-
Ltac Esimpl3 :=
repeat match goal with
| |- context [(?P1 ++ ?P2)@?l] => rewrite (Padd_ok P2 P1 l)
| |- context [(?P1 -- ?P2)@?l] => rewrite (Psub_ok P2 P1 l)
- | |- context [(norm (PEopp ?pe))@?l] => rewrite (norm_PEopp l pe)
- end;Esimpl2;try rrefl;try apply (ARadd_comm ARth).
+ end;Esimpl2;try rrefl;try apply (ARadd_comm ARth).
+
+(* Power using the chinise algorithm *)
+(*Section POWER.
+ Variable subst_l : Pol -> Pol.
+ Fixpoint Ppow_pos (P:Pol) (p:positive){struct p} : Pol :=
+ match p with
+ | xH => P
+ | xO p => subst_l (Psquare (Ppow_pos P p))
+ | xI p => subst_l (Pmul P (Psquare (Ppow_pos P p)))
+ end.
+
+ Definition Ppow_N P n :=
+ match n with
+ | N0 => P1
+ | Npos p => Ppow_pos P p
+ end.
+
+ Lemma Ppow_pos_ok : forall l, (forall P, subst_l P@l == P@l) ->
+ forall P p, (Ppow_pos P p)@l == (pow_pos Pmul P p)@l.
+ Proof.
+ intros l subst_l_ok P.
+ induction p;simpl;intros;try rrefl;try rewrite subst_l_ok.
+ repeat rewrite Pmul_ok;rewrite Psquare_ok;rewrite IHp;rrefl.
+ repeat rewrite Pmul_ok;rewrite Psquare_ok;rewrite IHp;rrefl.
+ Qed.
+
+ Lemma Ppow_N_ok : forall l, (forall P, subst_l P@l == P@l) ->
+ forall P n, (Ppow_N P n)@l == (pow_N P1 Pmul P n)@l.
+ Proof. destruct n;simpl. rrefl. apply Ppow_pos_ok. trivial. Qed.
+
+ End POWER. *)
+
+Section POWER.
+ Variable subst_l : Pol -> Pol.
+ Fixpoint Ppow_pos (res P:Pol) (p:positive){struct p} : Pol :=
+ match p with
+ | xH => subst_l (Pmul res P)
+ | xO p => Ppow_pos (Ppow_pos res P p) P p
+ | xI p => subst_l (Pmul (Ppow_pos (Ppow_pos res P p) P p) P)
+ end.
+
+ Definition Ppow_N P n :=
+ match n with
+ | N0 => P1
+ | Npos p => Ppow_pos P1 P p
+ end.
+
+ Lemma Ppow_pos_ok : forall l, (forall P, subst_l P@l == P@l) ->
+ forall res P p, (Ppow_pos res P p)@l == res@l * (pow_pos Pmul P p)@l.
+ Proof.
+ intros l subst_l_ok res P p. generalize res;clear res.
+ induction p;simpl;intros;try rewrite subst_l_ok; repeat rewrite Pmul_ok;repeat rewrite IHp.
+ rsimpl. mul_push (P@l);rsimpl. rsimpl. rrefl.
+ Qed.
+
+ Lemma Ppow_N_ok : forall l, (forall P, subst_l P@l == P@l) ->
+ forall P n, (Ppow_N P n)@l == (pow_N P1 Pmul P n)@l.
+ Proof. destruct n;simpl. rrefl. rewrite Ppow_pos_ok. trivial. Esimpl. Qed.
+
+ End POWER.
+
+ (** Normalization and rewriting *)
+
+ Section NORM_SUBST_REC.
+ Variable n : nat.
+ Variable lmp:list (Mon*Pol).
+ Let subst_l P := PNSubstL P lmp n n.
+ Let Pmul_subst P1 P2 := subst_l (Pmul P1 P2).
+ Let Ppow_subst := Ppow_N subst_l.
+
+ Fixpoint norm_aux (pe:PExpr) : Pol :=
+ match pe with
+ | PEc c => Pc c
+ | PEX j => mk_X j
+ | PEadd (PEopp pe1) pe2 => Psub (norm_aux pe2) (norm_aux pe1)
+ | PEadd pe1 (PEopp pe2) =>
+ Psub (norm_aux pe1) (norm_aux pe2)
+ | PEadd pe1 pe2 => Padd (norm_aux pe1) (norm_aux pe2)
+ | PEsub pe1 pe2 => Psub (norm_aux pe1) (norm_aux pe2)
+ | PEmul pe1 pe2 => Pmul (norm_aux pe1) (norm_aux pe2)
+ | PEopp pe1 => Popp (norm_aux pe1)
+ | PEpow pe1 n => Ppow_N (fun p => p) (norm_aux pe1) n
+ end.
- Lemma norm_ok : forall l pe, PEeval l pe == (norm pe)@l.
- Proof.
- induction pe;simpl;Esimpl3.
- apply mkX_ok.
- rewrite IHpe1;rewrite IHpe2; destruct pe1;destruct pe2;Esimpl3.
- rewrite IHpe1;rewrite IHpe2;rrefl.
- rewrite Pmul_ok;rewrite IHpe1;rewrite IHpe2;rrefl.
- rewrite IHpe;rrefl.
- Qed.
+ Definition norm_subst pe := subst_l (norm_aux pe).
+
+ (*
+ Fixpoint norm_subst (pe:PExpr) : Pol :=
+ match pe with
+ | PEc c => Pc c
+ | PEX j => subst_l (mk_X j)
+ | PEadd (PEopp pe1) pe2 => Psub (norm_subst pe2) (norm_subst pe1)
+ | PEadd pe1 (PEopp pe2) =>
+ Psub (norm_subst pe1) (norm_subst pe2)
+ | PEadd pe1 pe2 => Padd (norm_subst pe1) (norm_subst pe2)
+ | PEsub pe1 pe2 => Psub (norm_subst pe1) (norm_subst pe2)
+ | PEmul pe1 pe2 => Pmul_subst (norm_subst pe1) (norm_subst pe2)
+ | PEopp pe1 => Popp (norm_subst pe1)
+ | PEpow pe1 n => Ppow_subst (norm_subst pe1) n
+ end.
- Lemma ring_correct : forall l pe1 pe2,
- ((norm pe1) ?== (norm pe2)) = true -> (PEeval l pe1) == (PEeval l pe2).
+ Lemma norm_subst_spec :
+ forall l pe, MPcond lmp l ->
+ PEeval l pe == (norm_subst pe)@l.
+ Proof.
+ intros;assert (subst_l_ok:forall P, (subst_l P)@l == P@l).
+ unfold subst_l;intros.
+ rewrite <- PNSubstL_ok;trivial. rrefl.
+ assert (Pms_ok:forall P1 P2, (Pmul_subst P1 P2)@l == P1@l*P2@l).
+ intros;unfold Pmul_subst;rewrite subst_l_ok;rewrite Pmul_ok;rrefl.
+ induction pe;simpl;Esimpl3.
+ rewrite subst_l_ok;apply mkX_ok.
+ rewrite IHpe1;rewrite IHpe2;destruct pe1;destruct pe2;Esimpl3.
+ rewrite IHpe1;rewrite IHpe2;rrefl.
+ rewrite Pms_ok;rewrite IHpe1;rewrite IHpe2;rrefl.
+ rewrite IHpe;rrefl.
+ unfold Ppow_subst. rewrite Ppow_N_ok. trivial.
+ rewrite pow_th.(rpow_pow_N). destruct n0;Esimpl3.
+ induction p;simpl;try rewrite IHp;try rewrite IHpe;repeat rewrite Pms_ok;
+ repeat rewrite Pmul_ok;rrefl.
+ Qed.
+*)
+ Lemma norm_aux_spec :
+ forall l pe, MPcond lmp l ->
+ PEeval l pe == (norm_aux pe)@l.
+ Proof.
+ intros.
+ induction pe;simpl;Esimpl3.
+ apply mkX_ok.
+ rewrite IHpe1;rewrite IHpe2;destruct pe1;destruct pe2;Esimpl3.
+ rewrite IHpe1;rewrite IHpe2;rrefl.
+ rewrite IHpe1;rewrite IHpe2. rewrite Pmul_ok. rrefl.
+ rewrite IHpe;rrefl.
+ rewrite Ppow_N_ok. intros;rrefl.
+ rewrite pow_th.(rpow_pow_N). destruct n0;Esimpl3.
+ induction p;simpl;try rewrite IHp;try rewrite IHpe;repeat rewrite Pms_ok;
+ repeat rewrite Pmul_ok;rrefl.
+ Qed.
+
+ Lemma norm_subst_spec :
+ forall l pe, MPcond lmp l ->
+ PEeval l pe == (norm_subst pe)@l.
Proof.
- intros l pe1 pe2 H.
- repeat rewrite norm_ok.
- apply (Peq_ok (norm pe1) (norm pe2) H l).
- Qed.
-
-(** Evaluation function avoiding parentheses *)
- Fixpoint mkmult (r:R) (lm:list R) {struct lm}: R :=
- match lm with
- | nil => r
- | cons h t => mkmult (r*h) t
- end.
-
- Definition mkadd_mult rP lm :=
- match lm with
- | nil => rP + 1
- | cons h t => rP + mkmult h t
+ intros;unfold norm_subst.
+ unfold subst_l;rewrite <- PNSubstL_ok;trivial. apply norm_aux_spec. trivial.
+ Qed.
+
+ End NORM_SUBST_REC.
+
+ Fixpoint interp_PElist (l:list R) (lpe:list (PExpr*PExpr)) {struct lpe} : Prop :=
+ match lpe with
+ | nil => True
+ | (me,pe)::lpe =>
+ match lpe with
+ | nil => PEeval l me == PEeval l pe
+ | _ => PEeval l me == PEeval l pe /\ interp_PElist l lpe
+ end
end.
- Fixpoint powl (i:positive) (x:R) (l:list R) {struct i}: list R :=
- match i with
- | xH => cons x l
- | xO i => powl i x (powl i x l)
- | xI i => powl i x (powl i x (cons x l))
- end.
-
- Fixpoint add_mult_dev (rP:R) (P:Pol) (fv lm:list R) {struct P} : R :=
- (* rP + P@l * lm *)
+ Fixpoint mon_of_pol (P:Pol) : option Mon :=
match P with
- | Pc c => if c ?=! cI then mkadd_mult rP (rev' lm)
- else mkadd_mult rP (cons [c] (rev' lm))
- | Pinj j Q => add_mult_dev rP Q (jump j fv) lm
- | PX P i Q =>
- let rP := add_mult_dev rP P fv (powl i (hd 0 fv) lm) in
- if Q ?== P0 then rP else add_mult_dev rP Q (tail fv) lm
+ | Pc c => if (c ?=! cI) then Some mon0 else None
+ | Pinj j P =>
+ match mon_of_pol P with
+ | None => None
+ | Some m => Some (mkZmon j m)
+ end
+ | PX P i Q =>
+ if Peq Q P0 then
+ match mon_of_pol P with
+ | None => None
+ | Some m => Some (mkVmon i m)
+ end
+ else None
end.
-
- Definition mkmult1 lm :=
- match lm with
- | nil => rI
- | cons h t => mkmult h t
+
+ Fixpoint mk_monpol_list (lpe:list (PExpr * PExpr)) : list (Mon*Pol) :=
+ match lpe with
+ | nil => nil
+ | (me,pe)::lpe =>
+ match mon_of_pol (norm_subst 0 nil me) with
+ | None => mk_monpol_list lpe
+ | Some m => (m,norm_subst 0 nil pe):: mk_monpol_list lpe
+ end
end.
+
+ Lemma mon_of_pol_ok : forall P m, mon_of_pol P = Some m ->
+ forall l, Mphi l m == P@l.
+ Proof.
+ induction P;simpl;intros;Esimpl.
+ assert (H1 := (morph_eq CRmorph) c cI).
+ destruct (c ?=! cI).
+ inversion H;rewrite H1;trivial;Esimpl.
+ discriminate.
+ generalize H;clear H;case_eq (mon_of_pol P);intros;try discriminate.
+ inversion H0.
+ rewrite mkZmon_ok;simpl;auto.
+ generalize H;clear H;change match P3 with
+ | Pc c => c ?=! cO
+ | Pinj _ _ => false
+ | PX _ _ _ => false
+ end with (P3 ?== P0).
+ assert (H := Peq_ok P3 P0).
+ destruct (P3 ?== P0).
+ case_eq (mon_of_pol P2);intros.
+ inversion H1.
+ rewrite mkVmon_ok;simpl.
+ rewrite H;trivial;Esimpl. rewrite IHP1;trivial;Esimpl. discriminate.
+ intros;discriminate.
+ Qed.
+
+ Lemma interp_PElist_ok : forall l lpe,
+ interp_PElist l lpe -> MPcond (mk_monpol_list lpe) l.
+ Proof.
+ induction lpe;simpl. trivial.
+ destruct a;simpl;intros.
+ assert (HH:=mon_of_pol_ok (norm_subst 0 nil p));
+ destruct (mon_of_pol (norm_subst 0 nil p)).
+ split.
+ rewrite <- norm_subst_spec. exact I.
+ destruct lpe;try destruct H;rewrite <- H;
+ rewrite (norm_subst_spec 0 nil); try exact I;apply HH;trivial.
+ apply IHlpe. destruct lpe;simpl;trivial. destruct H. exact H0.
+ apply IHlpe. destruct lpe;simpl;trivial. destruct H. exact H0.
+ Qed.
+
+ Lemma norm_subst_ok : forall n l lpe pe,
+ interp_PElist l lpe ->
+ PEeval l pe == (norm_subst n (mk_monpol_list lpe) pe)@l.
+ Proof.
+ intros;apply norm_subst_spec. apply interp_PElist_ok;trivial.
+ Qed.
+
+ Lemma ring_correct : forall n l lpe pe1 pe2,
+ interp_PElist l lpe ->
+ (let lmp := mk_monpol_list lpe in
+ norm_subst n lmp pe1 ?== norm_subst n lmp pe2) = true ->
+ PEeval l pe1 == PEeval l pe2.
+ Proof.
+ simpl;intros.
+ do 2 (rewrite (norm_subst_ok n l lpe);trivial).
+ apply Peq_ok;trivial.
+ Qed.
+
+
+
+ (** Generic evaluation of polynomial towards R avoiding parenthesis *)
+ Variable get_sign : C -> option C.
+ Variable get_sign_spec : sign_theory ropp req phi get_sign.
+
+
+ Section EVALUATION.
+
+ (* [mkpow x p] = x^p *)
+ Variable mkpow : R -> positive -> R.
+ (* [mkpow x p] = -(x^p) *)
+ Variable mkopp_pow : R -> positive -> R.
+ (* [mkmult_pow r x p] = r * x^p *)
+ Variable mkmult_pow : R -> R -> positive -> R.
- Fixpoint mult_dev (P:Pol) (fv lm : list R) {struct P} : R :=
- (* P@l * lm *)
+ Fixpoint mkmult_rec (r:R) (lm:list (R*positive)) {struct lm}: R :=
+ match lm with
+ | nil => r
+ | cons (x,p) t => mkmult_rec (mkmult_pow r x p) t
+ end.
+
+ Definition mkmult1 lm :=
+ match lm with
+ | nil => 1
+ | cons (x,p) t => mkmult_rec (mkpow x p) t
+ end.
+
+ Definition mkmultm1 lm :=
+ match lm with
+ | nil => ropp rI
+ | cons (x,p) t => mkmult_rec (mkopp_pow x p) t
+ end.
+
+ Definition mkmult_c_pos c lm :=
+ if c ?=! cI then mkmult1 (rev' lm)
+ else mkmult_rec [c] (rev' lm).
+
+ Definition mkmult_c c lm :=
+ match get_sign c with
+ | None => mkmult_c_pos c lm
+ | Some c' =>
+ if c' ?=! cI then mkmultm1 (rev' lm)
+ else mkmult_rec [c] (rev' lm)
+ end.
+
+ Definition mkadd_mult rP c lm :=
+ match get_sign c with
+ | None => rP + mkmult_c_pos c lm
+ | Some c' => rP - mkmult_c_pos c' lm
+ end.
+
+ Definition add_pow_list (r:R) n l :=
+ match n with
+ | N0 => l
+ | Npos p => (r,p)::l
+ end.
+
+ Fixpoint add_mult_dev
+ (rP:R) (P:Pol) (fv:list R) (n:N) (lm:list (R*positive)) {struct P} : R :=
+ match P with
+ | Pc c =>
+ let lm := add_pow_list (hd 0 fv) n lm in
+ mkadd_mult rP c lm
+ | Pinj j Q =>
+ add_mult_dev rP Q (jump j fv) N0 (add_pow_list (hd 0 fv) n lm)
+ | PX P i Q =>
+ let rP := add_mult_dev rP P fv (Nplus (Npos i) n) lm in
+ if Q ?== P0 then rP
+ else add_mult_dev rP Q (tail fv) N0 (add_pow_list (hd 0 fv) n lm)
+ end.
+
+ Fixpoint mult_dev (P:Pol) (fv : list R) (n:N)
+ (lm:list (R*positive)) {struct P} : R :=
+ (* P@l * (hd 0 l)^n * lm *)
match P with
- | Pc c => if c ?=! cI then mkmult1 (rev' lm) else mkmult [c] (rev' lm)
- | Pinj j Q => mult_dev Q (jump j fv) lm
+ | Pc c => mkmult_c c (add_pow_list (hd 0 fv) n lm)
+ | Pinj j Q => mult_dev Q (jump j fv) N0 (add_pow_list (hd 0 fv) n lm)
| PX P i Q =>
- let rP := mult_dev P fv (powl i (hd 0 fv) lm) in
- if Q ?== P0 then rP else add_mult_dev rP Q (tail fv) lm
+ let rP := mult_dev P fv (Nplus (Npos i) n) lm in
+ if Q ?== P0 then rP
+ else
+ let lmq := add_pow_list (hd 0 fv) n lm in
+ add_mult_dev rP Q (tail fv) N0 lmq
end.
- Definition Pphi_dev fv P := mult_dev P fv nil.
+ Definition Pphi_avoid fv P := mult_dev P fv N0 nil.
+
+ Fixpoint r_list_pow (l:list (R*positive)) : R :=
+ match l with
+ | nil => rI
+ | cons (r,p) l => pow_pos rmul r p * r_list_pow l
+ end.
- Add Morphism mkmult : mkmult_ext.
- intros r r0 eqr l;generalize l r r0 eqr;clear l r r0 eqr;
- induction l;simpl;intros.
- trivial. apply IHl; rewrite eqr;rrefl.
- Qed.
+ Hypothesis mkpow_spec : forall r p, mkpow r p == pow_pos rmul r p.
+ Hypothesis mkopp_pow_spec : forall r p, mkopp_pow r p == - (pow_pos rmul r p).
+ Hypothesis mkmult_pow_spec : forall r x p, mkmult_pow r x p == r * pow_pos rmul x p.
- Lemma mul_mkmult : forall lm r1 r2, r1 * mkmult r2 lm == mkmult (r1*r2) lm.
+ Lemma mkmult_rec_ok : forall lm r, mkmult_rec r lm == r * r_list_pow lm.
Proof.
- induction lm;simpl;intros;try rrefl.
- rewrite IHlm.
- setoid_replace (r1 * (r2 * a)) with (r1 * r2 * a);Esimpl.
- Qed.
+ induction lm;intros;simpl;Esimpl.
+ destruct a as (x,p);Esimpl.
+ rewrite IHlm. rewrite mkmult_pow_spec. Esimpl.
+ Qed.
- Lemma mkmult1_mkmult : forall lm r, r * mkmult1 lm == mkmult r lm.
+ Lemma mkmult1_ok : forall lm, mkmult1 lm == r_list_pow lm.
Proof.
- destruct lm;simpl;intros. Esimpl.
- apply mul_mkmult.
+ destruct lm;simpl;Esimpl.
+ destruct p. rewrite mkmult_rec_ok;rewrite mkpow_spec;Esimpl.
Qed.
-
- Lemma mkmult1_mkmult_1 : forall lm, mkmult1 lm == mkmult 1 lm.
+
+ Lemma mkmultm1_ok : forall lm, mkmultm1 lm == - r_list_pow lm.
Proof.
- intros;rewrite <- mkmult1_mkmult;Esimpl.
+ destruct lm;simpl;Esimpl.
+ destruct p;rewrite mkmult_rec_ok. rewrite mkopp_pow_spec;Esimpl.
Qed.
- Lemma mkmult_rev_append : forall lm l r,
- mkmult r (rev_append lm l) == mkmult (mkmult r l) lm.
+ Lemma r_list_pow_rev : forall l, r_list_pow (rev' l) == r_list_pow l.
+ Proof.
+ assert
+ (forall l lr : list (R * positive), r_list_pow (rev_append l lr) == r_list_pow lr * r_list_pow l).
+ induction l;intros;simpl;Esimpl.
+ destruct a;rewrite IHl;Esimpl.
+ rewrite (ARmul_comm ARth (pow_pos rmul r p)). rrefl.
+ intros;unfold rev'. rewrite H;simpl;Esimpl.
+ Qed.
+
+ Lemma mkmult_c_pos_ok : forall c lm, mkmult_c_pos c lm == [c]* r_list_pow lm.
Proof.
- induction lm; simpl in |- *; intros.
- rrefl.
- rewrite IHlm; simpl in |- *.
- repeat rewrite <- (ARmul_comm ARth a); rewrite <- mul_mkmult.
- rrefl.
+ intros;unfold mkmult_c_pos;simpl.
+ assert (H := (morph_eq CRmorph) c cI).
+ rewrite <- r_list_pow_rev; destruct (c ?=! cI).
+ rewrite H;trivial;Esimpl.
+ apply mkmult1_ok. apply mkmult_rec_ok.
Qed.
- Lemma powl_mkmult_rev : forall p r x lm,
- mkmult r (rev' (powl p x lm)) == mkmult (pow x p * r) (rev' lm).
+ Lemma mkmult_c_ok : forall c lm, mkmult_c c lm == [c] * r_list_pow lm.
+ Proof.
+ intros;unfold mkmult_c;simpl.
+ case_eq (get_sign c);intros.
+ assert (H1 := (morph_eq CRmorph) c0 cI).
+ destruct (c0 ?=! cI).
+ rewrite (get_sign_spec.(sign_spec) _ H). rewrite H1;trivial.
+ rewrite <- r_list_pow_rev;trivial;Esimpl.
+ apply mkmultm1_ok.
+ rewrite <- r_list_pow_rev; apply mkmult_rec_ok.
+ apply mkmult_c_pos_ok.
+Qed.
+
+ Lemma mkadd_mult_ok : forall rP c lm, mkadd_mult rP c lm == rP + [c]*r_list_pow lm.
Proof.
- induction p;simpl;intros.
- repeat rewrite IHp.
- unfold rev';simpl.
- repeat rewrite mkmult_rev_append.
- simpl.
- setoid_replace (pow x p * (pow x p * r) * x)
- with (x * pow x p * pow x p * r);Esimpl.
- mul_push x;rrefl.
- repeat rewrite IHp.
- setoid_replace (pow x p * (pow x p * r) )
- with (pow x p * pow x p * r);Esimpl.
- unfold rev';simpl. repeat rewrite mkmult_rev_append;simpl.
- rewrite (ARmul_comm ARth);rrefl.
+ intros;unfold mkadd_mult.
+ case_eq (get_sign c);intros.
+ rewrite (get_sign_spec.(sign_spec) _ H).
+ rewrite mkmult_c_pos_ok;Esimpl.
+ rewrite mkmult_c_pos_ok;Esimpl.
Qed.
- Lemma Pphi_add_mult_dev : forall P rP fv lm,
- rP + P@fv * mkmult1 (rev' lm) == add_mult_dev rP P fv lm.
+ Lemma add_pow_list_ok :
+ forall r n l, r_list_pow (add_pow_list r n l) == pow_N rI rmul r n * r_list_pow l.
Proof.
- induction P;simpl;intros.
- assert (H := (morph_eq CRmorph) c cI).
- destruct (c ?=! cI).
- rewrite (H (refl_equal true));rewrite (morph1 CRmorph);Esimpl.
- destruct (rev' lm);Esimpl;rrefl.
- rewrite mkmult1_mkmult;rrefl.
- apply IHP.
- replace (match P3 with
+ destruct n;simpl;intros;Esimpl.
+ Qed.
+
+ Lemma add_mult_dev_ok : forall P rP fv n lm,
+ add_mult_dev rP P fv n lm == rP + P@fv*pow_N rI rmul (hd 0 fv) n * r_list_pow lm.
+ Proof.
+ induction P;simpl;intros.
+ rewrite mkadd_mult_ok. rewrite add_pow_list_ok; Esimpl.
+ rewrite IHP. simpl. rewrite add_pow_list_ok; Esimpl.
+ change (match P3 with
| Pc c => c ?=! cO
| Pinj _ _ => false
| PX _ _ _ => false
- end) with (Peq P3 P0);trivial.
+ end) with (Peq P3 P0).
+ change match n with
+ | N0 => Npos p
+ | Npos q => Npos (p + q)
+ end with (Nplus (Npos p) n);trivial.
assert (H := Peq_ok P3 P0).
destruct (P3 ?== P0).
- rewrite (H (refl_equal true));simpl;Esimpl.
- rewrite <- IHP1.
- repeat rewrite mkmult1_mkmult_1.
- rewrite powl_mkmult_rev.
- rewrite <- mul_mkmult;Esimpl.
- rewrite <- IHP2.
- rewrite <- IHP1.
- repeat rewrite mkmult1_mkmult_1.
- rewrite powl_mkmult_rev.
- rewrite <- mul_mkmult;Esimpl.
+ rewrite (H (refl_equal true)).
+ rewrite IHP1. destruct n;simpl;Esimpl;rewrite pow_pos_Pplus;Esimpl.
+ rewrite IHP2.
+ rewrite IHP1. destruct n;simpl;Esimpl;rewrite pow_pos_Pplus;Esimpl.
Qed.
-
- Lemma Pphi_mult_dev : forall P fv lm,
- P@fv * mkmult1 (rev' lm) == mult_dev P fv lm.
+
+ Lemma mult_dev_ok : forall P fv n lm,
+ mult_dev P fv n lm == P@fv * pow_N rI rmul (hd 0 fv) n * r_list_pow lm.
Proof.
- induction P;simpl;intros.
- assert (H := (morph_eq CRmorph) c cI).
- destruct (c ?=! cI).
- rewrite (H (refl_equal true));rewrite (morph1 CRmorph);Esimpl.
- apply mkmult1_mkmult.
- apply IHP.
- replace (match P3 with
+ induction P;simpl;intros;Esimpl.
+ rewrite mkmult_c_ok;rewrite add_pow_list_ok;Esimpl.
+ rewrite IHP. simpl;rewrite add_pow_list_ok;Esimpl.
+ change (match P3 with
| Pc c => c ?=! cO
| Pinj _ _ => false
| PX _ _ _ => false
- end) with (Peq P3 P0);trivial.
+ end) with (Peq P3 P0).
+ change match n with
+ | N0 => Npos p
+ | Npos q => Npos (p + q)
+ end with (Nplus (Npos p) n);trivial.
assert (H := Peq_ok P3 P0).
- destruct (P3 ?== P0).
- rewrite (H (refl_equal true));simpl;Esimpl.
- rewrite <- IHP1.
- repeat rewrite mkmult1_mkmult_1.
- rewrite powl_mkmult_rev.
- rewrite <- mul_mkmult;Esimpl.
- rewrite <- Pphi_add_mult_dev.
- rewrite <- IHP1.
- repeat rewrite mkmult1_mkmult_1.
- rewrite powl_mkmult_rev.
- rewrite <- mul_mkmult;Esimpl.
- Qed.
+ destruct (P3 ?== P0).
+ rewrite (H (refl_equal true)).
+ rewrite IHP1. destruct n;simpl;Esimpl;rewrite pow_pos_Pplus;Esimpl.
+ rewrite add_mult_dev_ok. rewrite IHP1; rewrite add_pow_list_ok.
+ destruct n;simpl;Esimpl;rewrite pow_pos_Pplus;Esimpl.
+ Qed.
- Lemma Pphi_Pphi_dev : forall P l, P@l == Pphi_dev l P.
- Proof.
- unfold Pphi_dev;intros.
- rewrite <- Pphi_mult_dev;simpl;Esimpl.
+ Lemma Pphi_avoid_ok : forall P fv, Pphi_avoid fv P == P@fv.
+ Proof.
+ unfold Pphi_avoid;intros;rewrite mult_dev_ok;simpl;Esimpl.
Qed.
- Lemma Pphi_dev_gen_ok : forall l pe, PEeval l pe == Pphi_dev l (norm pe).
+ End EVALUATION.
+
+ Definition Pphi_pow :=
+ let mkpow x p :=
+ match p with xH => x | _ => rpow x (Cp_phi (Npos p)) end in
+ let mkopp_pow x p := ropp (mkpow x p) in
+ let mkmult_pow r x p := rmul r (mkpow x p) in
+ Pphi_avoid mkpow mkopp_pow mkmult_pow.
+
+ Lemma local_mkpow_ok :
+ forall (r : R) (p : positive),
+ match p with
+ | xI _ => rpow r (Cp_phi (Npos p))
+ | xO _ => rpow r (Cp_phi (Npos p))
+ | 1 => r
+ end == pow_pos rmul r p.
+ Proof. intros r p;destruct p;try rewrite pow_th.(rpow_pow_N);reflexivity. Qed.
+
+ Lemma Pphi_pow_ok : forall P fv, Pphi_pow fv P == P@fv.
Proof.
- intros l pe;rewrite <- Pphi_Pphi_dev;apply norm_ok.
+ unfold Pphi_pow;intros;apply Pphi_avoid_ok;intros;try rewrite local_mkpow_ok;rrefl.
Qed.
- Lemma Pphi_dev_ok :
- forall l pe npe, norm pe = npe -> PEeval l pe == Pphi_dev l npe.
+ Lemma ring_rw_pow_correct : forall n lH l,
+ interp_PElist l lH ->
+ forall lmp, mk_monpol_list lH = lmp ->
+ forall pe npe, norm_subst n lmp pe = npe ->
+ PEeval l pe == Pphi_pow l npe.
Proof.
- intros l pe npe npe_eq; subst npe; apply Pphi_dev_gen_ok.
- Qed.
+ intros n lH l H1 lmp Heq1 pe npe Heq2.
+ rewrite Pphi_pow_ok. rewrite <- Heq2;rewrite <- Heq1.
+ apply norm_subst_ok. trivial.
+ Qed.
- Fixpoint MPcond_dev (LM1: list (Mon * Pol)) (l: list R) {struct LM1} : Prop :=
- match LM1 with
- cons (M1,P2) LM2 => (Mphi l M1 == Pphi_dev l P2) /\ (MPcond_dev LM2 l)
- | _ => True
+ Fixpoint mkmult_pow (r x:R) (p: positive) {struct p} : R :=
+ match p with
+ | xH => r*x
+ | xO p => mkmult_pow (mkmult_pow r x p) x p
+ | xI p => mkmult_pow (mkmult_pow (r*x) x p) x p
+ end.
+
+ Definition mkpow x p :=
+ match p with
+ | xH => x
+ | xO p => mkmult_pow x x (Pdouble_minus_one p)
+ | xI p => mkmult_pow x x (xO p)
end.
-
- Fixpoint MPcond_map (LM1: list (Mon * PExpr)): list (Mon * Pol) :=
- match LM1 with
- cons (M1,P2) LM2 => cons (M1, norm P2) (MPcond_map LM2)
- | _ => nil
+
+ Definition mkopp_pow x p :=
+ match p with
+ | xH => -x
+ | xO p => mkmult_pow (-x) x (Pdouble_minus_one p)
+ | xI p => mkmult_pow (-x) x (xO p)
end.
- Lemma MP_cond_dev_imp_MP_cond: forall LM1 l,
- MPcond_dev LM1 l -> MPcond LM1 l.
+ Definition Pphi_dev := Pphi_avoid mkpow mkopp_pow mkmult_pow.
+
+ Lemma mkmult_pow_ok : forall p r x, mkmult_pow r x p == r*pow_pos rmul x p.
+ Proof.
+ induction p;intros;simpl;Esimpl.
+ repeat rewrite IHp;Esimpl.
+ repeat rewrite IHp;Esimpl.
+ Qed.
+
+ Lemma mkpow_ok : forall p x, mkpow x p == pow_pos rmul x p.
+ Proof.
+ destruct p;simpl;intros;Esimpl.
+ repeat rewrite mkmult_pow_ok;Esimpl.
+ rewrite mkmult_pow_ok;Esimpl.
+ pattern x at 1;replace x with (pow_pos rmul x 1).
+ rewrite <- pow_pos_Pplus.
+ rewrite <- Pplus_one_succ_l.
+ rewrite Psucc_o_double_minus_one_eq_xO.
+ simpl;Esimpl.
+ trivial.
+ Qed.
+
+ Lemma mkopp_pow_ok : forall p x, mkopp_pow x p == - pow_pos rmul x p.
+ Proof.
+ destruct p;simpl;intros;Esimpl.
+ repeat rewrite mkmult_pow_ok;Esimpl.
+ rewrite mkmult_pow_ok;Esimpl.
+ pattern x at 1;replace x with (pow_pos rmul x 1).
+ rewrite <- pow_pos_Pplus.
+ rewrite <- Pplus_one_succ_l.
+ rewrite Psucc_o_double_minus_one_eq_xO.
+ simpl;Esimpl.
+ trivial.
+ Qed.
+
+ Lemma Pphi_dev_ok : forall P fv, Pphi_dev fv P == P@fv.
+ Proof.
+ unfold Pphi_dev;intros;apply Pphi_avoid_ok.
+ intros;apply mkpow_ok.
+ intros;apply mkopp_pow_ok.
+ intros;apply mkmult_pow_ok.
+ Qed.
+
+ Lemma ring_rw_correct : forall n lH l,
+ interp_PElist l lH ->
+ forall lmp, mk_monpol_list lH = lmp ->
+ forall pe npe, norm_subst n lmp pe = npe ->
+ PEeval l pe == Pphi_dev l npe.
Proof.
- intros LM1; elim LM1; simpl; auto.
- intros (M2,P2) LM2 Hrec l [H1 H2]; split; auto.
- rewrite H1; rewrite Pphi_Pphi_dev; rsimpl.
+ intros n lH l H1 lmp Heq1 pe npe Heq2.
+ rewrite Pphi_dev_ok. rewrite <- Heq2;rewrite <- Heq1.
+ apply norm_subst_ok. trivial.
Qed.
- Lemma PNSubstL_dev_ok: forall m n lm pe l,
- let LM := MPcond_map lm in
- MPcond_dev LM l -> PEeval l pe == Pphi_dev l (PNSubstL (norm pe) LM m n).
- intros m n lm p3 l LM H.
- rewrite <- Pphi_Pphi_dev; rewrite <- PNSubstL_ok; auto.
- apply MP_cond_dev_imp_MP_cond; auto.
- rewrite Pphi_Pphi_dev; apply Pphi_dev_ok; auto.
- Qed.
-End MakeRingPol.
+End MakeRingPol.
+
diff --git a/contrib/setoid_ring/Ring_tac.v b/contrib/setoid_ring/Ring_tac.v
index 95efde7f..7419f184 100644
--- a/contrib/setoid_ring/Ring_tac.v
+++ b/contrib/setoid_ring/Ring_tac.v
@@ -3,16 +3,23 @@ Require Import Setoid.
Require Import BinPos.
Require Import Ring_polynom.
Require Import BinList.
+Require Import InitialRing.
Declare ML Module "newring".
-
+
(* adds a definition id' on the normal form of t and an hypothesis id
stating that t = id' (tries to produces a proof as small as possible) *)
Ltac compute_assertion id id' t :=
let t' := eval vm_compute in t in
- (pose (id' := t');
- assert (id : t = id');
- [exact_no_check (refl_equal id')|idtac]).
+ pose (id' := t');
+ assert (id : t = id');
+ [vm_cast_no_check (refl_equal id')|idtac].
+(* [exact_no_check (refl_equal id'<: t = id')|idtac]). *)
+
+Ltac getGoal :=
+ match goal with
+ | |- ?G => G
+ end.
(********************************************************************)
(* Tacticals to build reflexive tactics *)
@@ -23,7 +30,6 @@ Ltac OnEquation req :=
| _ => fail 1 "Goal is not an equation (of expected equality)"
end.
-
Ltac OnMainSubgoal H ty :=
match ty with
| _ -> ?ty' =>
@@ -32,43 +38,54 @@ Ltac OnMainSubgoal H ty :=
| _ => (fun tac => tac)
end.
-Ltac ApplyLemmaAndSimpl tac lemma pe:=
- let npe := fresh "ast_nf" in
+Ltac ApplyLemmaThen lemma expr tac :=
+ let nexpr := fresh "expr_nf" in
+ let H := fresh "eq_nf" in
+ let Heq := fresh "thm" in
+ let nf_spec :=
+ match type of (lemma expr) with
+ forall x, ?nf_spec = x -> _ => nf_spec
+ | _ => fail 1 "ApplyLemmaThen: cannot find norm expression"
+ end in
+ (compute_assertion H nexpr nf_spec;
+ (assert (Heq:=lemma _ _ H) || fail "anomaly: failed to apply lemma");
+ clear H;
+ OnMainSubgoal Heq ltac:(type of Heq) ltac:(tac Heq; clear Heq nexpr)).
+
+Ltac ApplyLemmaThenAndCont lemma expr tac CONT_tac cont_arg :=
+ let npe := fresh "expr_nf" in
let H := fresh "eq_nf" in
let Heq := fresh "thm" in
let npe_spec :=
- match type of (lemma pe) with
+ match type of (lemma expr) with
forall npe, ?npe_spec = npe -> _ => npe_spec
- | _ => fail 1 "ApplyLemmaAndSimpl: cannot find norm expression"
+ | _ => fail 1 "ApplyLemmaThenAndCont: cannot find norm expression"
end in
(compute_assertion H npe npe_spec;
(assert (Heq:=lemma _ _ H) || fail "anomaly: failed to apply lemma");
clear H;
OnMainSubgoal Heq ltac:(type of Heq)
- ltac:(tac Heq; rewrite Heq; clear Heq npe)).
+ ltac:(try tac Heq; clear Heq npe;CONT_tac cont_arg)).
(* General scheme of reflexive tactics using of correctness lemma
that involves normalisation of one expression *)
-Ltac ReflexiveRewriteTactic FV_tac SYN_tac SIMPL_tac lemma2 req rl :=
- let R := match type of req with ?R -> _ => R end in
- (* build the atom list *)
- let fv := list_fold_left FV_tac (@List.nil R) rl in
- (* some type-checking to avoid late errors *)
- (check_fv fv;
- (* rewrite steps *)
- list_iter
- ltac:(fun r =>
- let ast := SYN_tac r fv in
- try ApplyLemmaAndSimpl SIMPL_tac (lemma2 fv) ast)
- rl).
+
+Ltac ReflexiveRewriteTactic FV_tac SYN_tac MAIN_tac LEMMA_tac fv terms :=
+ (* extend the atom list *)
+ let fv := list_fold_left FV_tac fv terms in
+ let RW_tac lemma :=
+ let fcons term CONT_tac cont_arg :=
+ let expr := SYN_tac term fv in
+ (ApplyLemmaThenAndCont lemma expr MAIN_tac CONT_tac cont_arg) in
+ (* rewrite steps *)
+ lazy_list_fold_right fcons ltac:(idtac) terms in
+ LEMMA_tac fv RW_tac.
(********************************************************)
-(* An object to return when an expression is not recognized as a constant *)
-Definition NotConstant := false.
-
+
(* Building the atom list of a ring expression *)
-Ltac FV Cst add mul sub opp t fv :=
+Ltac FV Cst CstPow add mul sub opp pow t fv :=
let rec TFV t fv :=
match Cst t with
| NotConstant =>
@@ -77,6 +94,11 @@ Ltac FV Cst add mul sub opp t fv :=
| (mul ?t1 ?t2) => TFV t2 ltac:(TFV t1 fv)
| (sub ?t1 ?t2) => TFV t2 ltac:(TFV t1 fv)
| (opp ?t1) => TFV t1 fv
+ | (pow ?t1 ?n) =>
+ match CstPow n with
+ | InitialRing.NotConstant => AddFvTail t fv
+ | _ => TFV t1 fv
+ end
| _ => AddFvTail t fv
end
| _ => fv
@@ -84,10 +106,10 @@ Ltac FV Cst add mul sub opp t fv :=
in TFV t fv.
(* syntaxification of ring expressions *)
- Ltac mkPolexpr C Cst radd rmul rsub ropp t fv :=
+Ltac mkPolexpr C Cst CstPow radd rmul rsub ropp rpow t fv :=
let rec mkP t :=
match Cst t with
- | NotConstant =>
+ | InitialRing.NotConstant =>
match t with
| (radd ?t1 ?t2) =>
let e1 := mkP t1 in
@@ -100,6 +122,12 @@ Ltac FV Cst add mul sub opp t fv :=
let e2 := mkP t2 in constr:(PEsub e1 e2)
| (ropp ?t1) =>
let e1 := mkP t1 in constr:(PEopp e1)
+ | (rpow ?t1 ?n) =>
+ match CstPow n with
+ | InitialRing.NotConstant =>
+ let p := Find_at t fv in constr:(PEX C p)
+ | ?c => let e1 := mkP t1 in constr:(PEpow e1 c)
+ end
| _ =>
let p := Find_at t fv in constr:(PEX C p)
end
@@ -107,54 +135,222 @@ Ltac FV Cst add mul sub opp t fv :=
end
in mkP t.
+Ltac ParseRingComponents lemma :=
+ match type of lemma with
+ | context
+ [@PEeval ?R ?rO ?add ?mul ?sub ?opp ?C ?phi ?Cpow ?powphi ?pow _ _] =>
+ (fun f => f R add mul sub opp pow C)
+ | _ => fail 1 "ring anomaly: bad correctness lemma (parse)"
+ end.
+
+
(* ring tactics *)
- Ltac Ring Cst_tac lemma1 req :=
- let Make_tac :=
- match type of lemma1 with
- | forall (l:list ?R) (pe1 pe2:PExpr ?C),
- _ = true ->
- req (PEeval ?rO ?add ?mul ?sub ?opp ?phi l pe1) _ =>
- let mkFV := FV Cst_tac add mul sub opp in
- let mkPol := mkPolexpr C Cst_tac add mul sub opp in
- fun f => f R mkFV mkPol
- | _ => fail 1 "ring anomaly: bad correctness lemma"
+Ltac FV_hypo_tac mkFV req lH :=
+ let R := match type of req with ?R -> _ => R end in
+ let FV_hypo_l_tac h :=
+ match h with @mkhypo (req ?pe _) _ => mkFV pe end in
+ let FV_hypo_r_tac h :=
+ match h with @mkhypo (req _ ?pe) _ => mkFV pe end in
+ let fv := list_fold_right FV_hypo_l_tac (@nil R) lH in
+ list_fold_right FV_hypo_r_tac fv lH.
+
+Ltac mkHyp_tac C req mkPE lH :=
+ let mkHyp h res :=
+ match h with
+ | @mkhypo (req ?r1 ?r2) _ =>
+ let pe1 := mkPE r1 in
+ let pe2 := mkPE r2 in
+ constr:(cons (pe1,pe2) res)
+ | _ => fail "hypothesis is not a ring equality"
+ end in
+ list_fold_right mkHyp (@nil (PExpr C * PExpr C)) lH.
+
+Ltac proofHyp_tac lH :=
+ let get_proof h :=
+ match h with
+ | @mkhypo _ ?p => p
end in
- let Main r1 r2 R mkFV mkPol :=
- let fv := mkFV r1 (@List.nil R) in
- let fv := mkFV r2 fv in
- check_fv fv;
- (let pe1 := mkPol r1 fv in
- let pe2 := mkPol r2 fv in
- apply (lemma1 fv pe1 pe2) || fail "typing error while applying ring";
- vm_compute;
- exact (refl_equal true) || fail "not a valid ring equation") in
- Make_tac ltac:(OnEquation req Main).
-
-Ltac Ring_simplify Cst_tac lemma2 req rl :=
- let Make_tac :=
- match type of lemma2 with
- forall (l:list ?R) (pe:PExpr ?C) (npe:Pol ?C),
- _ = npe ->
- req (PEeval ?rO ?add ?mul ?sub ?opp ?phi l pe) _ =>
- let mkFV := FV Cst_tac add mul sub opp in
- let mkPol := mkPolexpr C Cst_tac add mul sub opp in
- let simpl_ring H := protect_fv "ring" in H in
- (fun tac => tac mkFV mkPol simpl_ring lemma2 req rl)
- | _ => fail 1 "ring anomaly: bad correctness lemma"
+ let rec bh l :=
+ match l with
+ | nil => constr:(I)
+ | cons ?h nil => get_proof h
+ | cons ?h ?tl =>
+ let l := get_proof h in
+ let r := bh tl in
+ constr:(conj l r)
end in
- Make_tac ReflexiveRewriteTactic.
+ bh lH.
+
+Definition ring_subst_niter := (10*10*10)%nat.
+
+Ltac Ring Cst_tac CstPow_tac lemma1 req n lH :=
+ let Main lhs rhs R radd rmul rsub ropp rpow C :=
+ let mkFV := FV Cst_tac CstPow_tac radd rmul rsub ropp rpow in
+ let mkPol := mkPolexpr C Cst_tac CstPow_tac radd rmul rsub ropp rpow in
+ let fv := FV_hypo_tac mkFV req lH in
+ let fv := mkFV lhs fv in
+ let fv := mkFV rhs fv in
+ check_fv fv;
+ let pe1 := mkPol lhs fv in
+ let pe2 := mkPol rhs fv in
+ let lpe := mkHyp_tac C req ltac:(fun t => mkPol t fv) lH in
+ let vlpe := fresh "hyp_list" in
+ let vfv := fresh "fv_list" in
+ pose (vlpe := lpe);
+ pose (vfv := fv);
+ (apply (lemma1 n vfv vlpe pe1 pe2)
+ || fail "typing error while applying ring");
+ [ ((let prh := proofHyp_tac lH in exact prh)
+ || idtac "can not automatically proof hypothesis : maybe a left member of a hypothesis is not a monomial")
+ | vm_compute;
+ (exact (refl_equal true) || fail "not a valid ring equation")] in
+ ParseRingComponents lemma1 ltac:(OnEquation req Main).
+
+Ltac Ring_norm_gen f Cst_tac CstPow_tac lemma2 req n lH rl :=
+ let Main R add mul sub opp pow C :=
+ let mkFV := FV Cst_tac CstPow_tac add mul sub opp pow in
+ let mkPol := mkPolexpr C Cst_tac CstPow_tac add mul sub opp pow in
+ let fv := FV_hypo_tac mkFV req lH in
+ let simpl_ring H := (protect_fv "ring" in H; f H) in
+ let Coeffs :=
+ match type of lemma2 with
+ | context [mk_monpol_list ?cO ?cI ?cadd ?cmul ?csub ?copp ?ceqb _] =>
+ (fun f => f cO cI cadd cmul csub copp ceqb)
+ | _ => fail 1 "ring_simplify anomaly: bad correctness lemma"
+ end in
+ let lemma_tac fv RW_tac :=
+ let rr_lemma := fresh "r_rw_lemma" in
+ let lpe := mkHyp_tac C req ltac:(fun t => mkPol t fv) lH in
+ let vlpe := fresh "list_hyp" in
+ let vlmp := fresh "list_hyp_norm" in
+ let vlmp_eq := fresh "list_hyp_norm_eq" in
+ let prh := proofHyp_tac lH in
+ pose (vlpe := lpe);
+ Coeffs ltac:(fun cO cI cadd cmul csub copp ceqb =>
+ compute_assertion vlmp_eq vlmp
+ (mk_monpol_list cO cI cadd cmul csub copp ceqb vlpe);
+ assert (rr_lemma := lemma2 n vlpe fv prh vlmp vlmp_eq)
+ || fail "type error when build the rewriting lemma";
+ RW_tac rr_lemma;
+ try clear rr_lemma vlmp_eq vlmp vlpe) in
+ ReflexiveRewriteTactic mkFV mkPol simpl_ring lemma_tac fv rl in
+ ParseRingComponents lemma2 Main.
+Ltac Ring_gen
+ req sth ext morph arth cst_tac pow_tac lemma1 lemma2 pre post lH rl :=
+ pre();Ring cst_tac pow_tac lemma1 req ring_subst_niter lH.
Tactic Notation (at level 0) "ring" :=
- ring_lookup
- (fun req sth ext morph arth cst_tac lemma1 lemma2 pre post rl =>
- pre(); Ring cst_tac lemma1 req).
+ let G := getGoal in ring_lookup Ring_gen [] [G].
+
+Tactic Notation (at level 0) "ring" "[" constr_list(lH) "]" :=
+ let G := getGoal in ring_lookup Ring_gen [lH] [G].
+
+(* Simplification *)
+
+Ltac Ring_simplify_gen f :=
+ fun req sth ext morph arth cst_tac pow_tac lemma1 lemma2 pre post lH rl =>
+ let l := fresh "to_rewrite" in
+ pose (l:= rl);
+ generalize (refl_equal l);
+ unfold l at 2;
+ pre();
+ match goal with
+ | [|- l = ?RL -> _ ] =>
+ let Heq := fresh "Heq" in
+ intros Heq;clear Heq l;
+ Ring_norm_gen f cst_tac pow_tac lemma2 req ring_subst_niter lH RL;
+ post()
+ | _ => fail 1 "ring_simplify anomaly: bad goal after pre"
+ end.
+
+Ltac Ring_simplify := Ring_simplify_gen ltac:(fun H => rewrite H).
+
+Ltac Ring_nf Cst_tac lemma2 req rl f :=
+ let on_rhs H :=
+ match type of H with
+ | req _ ?rhs => clear H; f rhs
+ end in
+ Ring_norm_gen on_rhs Cst_tac lemma2 req rl.
+
+
+Tactic Notation (at level 0)
+ "ring_simplify" "[" constr_list(lH) "]" constr_list(rl) :=
+ let G := getGoal in ring_lookup Ring_simplify [lH] rl [G].
+
+Tactic Notation (at level 0)
+ "ring_simplify" constr_list(rl) :=
+ let G := getGoal in ring_lookup Ring_simplify [] rl [G].
+
+
+Tactic Notation "ring_simplify" constr_list(rl) "in" hyp(H):=
+ let G := getGoal in
+ let t := type of H in
+ let g := fresh "goal" in
+ set (g:= G);
+ generalize H;clear H;
+ ring_lookup Ring_simplify [] rl [t];
+ intro H;
+ unfold g;clear g.
+
+Tactic Notation "ring_simplify" "["constr_list(lH)"]" constr_list(rl) "in" hyp(H):=
+ let G := getGoal in
+ let t := type of H in
+ let g := fresh "goal" in
+ set (g:= G);
+ generalize H;clear H;
+ ring_lookup Ring_simplify [lH] rl [t];
+ intro H;
+ unfold g;clear g.
+
+
+(*
+
+Ltac Ring_simplify_in hyp:= Ring_simplify_gen ltac:(fun H => rewrite H in hyp).
+
+
+Tactic Notation (at level 0)
+ "ring_simplify" "[" constr_list(lH) "]" constr_list(rl) :=
+ match goal with [|- ?G] => ring_lookup Ring_simplify [lH] rl [G] end.
+
+Tactic Notation (at level 0)
+ "ring_simplify" constr_list(rl) :=
+ match goal with [|- ?G] => ring_lookup Ring_simplify [] rl [G] end.
+
+Tactic Notation (at level 0)
+ "ring_simplify" "[" constr_list(lH) "]" constr_list(rl) "in" hyp(h):=
+ let t := type of h in
+ ring_lookup
+ (fun req sth ext morph arth cst_tac pow_tac lemma1 lemma2 pre post lH rl =>
+ pre();
+ Ring_norm_gen ltac:(fun EQ => rewrite EQ in h) cst_tac pow_tac lemma2 req ring_subst_niter lH rl;
+ post())
+ [lH] rl [t].
+(* ring_lookup ltac:(Ring_simplify_in h) [lH] rl [t]. NE MARCHE PAS ??? *)
+
+Ltac Ring_simpl_in hyp := Ring_norm_gen ltac:(fun H => rewrite H in hyp).
+
+Tactic Notation (at level 0)
+ "ring_simplify" constr_list(rl) "in" constr(h):=
+ let t := type of h in
+ ring_lookup
+ (fun req sth ext morph arth cst_tac pow_tac lemma1 lemma2 pre post lH rl =>
+ pre();
+ Ring_simpl_in h cst_tac pow_tac lemma2 req ring_subst_niter lH rl;
+ post())
+ [] rl [t].
+
+Ltac rw_in H Heq := rewrite Heq in H.
+
+Ltac simpl_in H :=
+ let t := type of H in
+ ring_lookup
+ (fun req sth ext morph arth cst_tac pow_tac lemma1 lemma2 pre post lH rl =>
+ pre();
+ Ring_norm_gen ltac:(fun Heq => rewrite Heq in H) cst_tac pow_tac lemma2 req ring_subst_niter lH rl;
+ post())
+ [] [t].
-Tactic Notation (at level 0) "ring_simplify" constr_list(rl) :=
- ring_lookup
- (fun req sth ext morph arth cst_tac lemma1 lemma2 pre post rl =>
- pre(); Ring_simplify cst_tac lemma2 req rl; post()) rl.
-(* A simple macro tactic to be prefered to ring_simplify *)
-Ltac ring_replace t1 t2 := replace t1 with t2 by ring.
+*)
diff --git a/contrib/setoid_ring/Ring_theory.v b/contrib/setoid_ring/Ring_theory.v
index 2f7378eb..5498911d 100644
--- a/contrib/setoid_ring/Ring_theory.v
+++ b/contrib/setoid_ring/Ring_theory.v
@@ -7,6 +7,9 @@
(************************************************************************)
Require Import Setoid.
+Require Import BinPos.
+Require Import BinNat.
+
Set Implicit Arguments.
Module RingSyntax.
@@ -27,6 +30,71 @@ Reserved Notation "x == y" (at level 70, no associativity).
End RingSyntax.
Import RingSyntax.
+Section Power.
+ Variable R:Type.
+ Variable rI : R.
+ Variable rmul : R -> R -> R.
+ Variable req : R -> R -> Prop.
+ Variable Rsth : Setoid_Theory R req.
+ Notation "x * y " := (rmul x y).
+ Notation "x == y" := (req x y).
+
+ Hypothesis mul_ext :
+ forall x1 x2, x1 == x2 -> forall y1 y2, y1 == y2 -> x1 * y1 == x2 * y2.
+ Hypothesis mul_comm : forall x y, x * y == y * x.
+ Hypothesis mul_assoc : forall x y z, x * (y * z) == (x * y) * z.
+ Add Setoid R req Rsth as R_set_Power.
+ Add Morphism rmul : rmul_ext_Power. exact mul_ext. Qed.
+
+
+ Fixpoint pow_pos (x:R) (i:positive) {struct i}: R :=
+ match i with
+ | xH => x
+ | xO i => let p := pow_pos x i in rmul p p
+ | xI i => let p := pow_pos x i in rmul x (rmul p p)
+ end.
+
+ Lemma pow_pos_Psucc : forall x j, pow_pos x (Psucc j) == x * pow_pos x j.
+ Proof.
+ induction j;simpl.
+ rewrite IHj.
+ rewrite (mul_comm x (pow_pos x j *pow_pos x j)).
+ set (w:= x*pow_pos x j);unfold w at 2.
+ rewrite (mul_comm x (pow_pos x j));unfold w.
+ repeat rewrite mul_assoc. apply (Seq_refl _ _ Rsth).
+ repeat rewrite mul_assoc. apply (Seq_refl _ _ Rsth).
+ apply (Seq_refl _ _ Rsth).
+ Qed.
+
+ Lemma pow_pos_Pplus : forall x i j, pow_pos x (i + j) == pow_pos x i * pow_pos x j.
+ Proof.
+ intro x;induction i;intros.
+ rewrite xI_succ_xO;rewrite Pplus_one_succ_r.
+ rewrite <- Pplus_diag;repeat rewrite <- Pplus_assoc.
+ repeat rewrite IHi.
+ rewrite Pplus_comm;rewrite <- Pplus_one_succ_r;rewrite pow_pos_Psucc.
+ simpl;repeat rewrite mul_assoc. apply (Seq_refl _ _ Rsth).
+ rewrite <- Pplus_diag;repeat rewrite <- Pplus_assoc.
+ repeat rewrite IHi;rewrite mul_assoc. apply (Seq_refl _ _ Rsth).
+ rewrite Pplus_comm;rewrite <- Pplus_one_succ_r;rewrite pow_pos_Psucc;
+ simpl. apply (Seq_refl _ _ Rsth).
+ Qed.
+
+ Definition pow_N (x:R) (p:N) :=
+ match p with
+ | N0 => rI
+ | Npos p => pow_pos x p
+ end.
+
+ Definition id_phi_N (x:N) : N := x.
+
+ Lemma pow_N_pow_N : forall x n, pow_N x (id_phi_N n) == pow_N x n.
+ Proof.
+ intros; apply (Seq_refl _ _ Rsth).
+ Qed.
+
+End Power.
+
Section DEFINITIONS.
Variable R : Type.
Variable (rO rI : R) (radd rmul rsub: R->R->R) (ropp : R -> R).
@@ -126,6 +194,19 @@ Section DEFINITIONS.
morph_opp : forall x, [-!x] == -[x];
morph_eq : forall x y, x?=!y = true -> [x] == [y]
}.
+
+ Section SIGN.
+ Variable get_sign : C -> option C.
+ Record sign_theory : Prop := mksign_th {
+ sign_spec : forall c c', get_sign c = Some c' -> [c] == - [c']
+ }.
+ End SIGN.
+
+ Definition get_sign_None (c:C) := @None C.
+
+ Lemma get_sign_None_th : sign_theory get_sign_None.
+ Proof. constructor;intros;discriminate. Qed.
+
End MORPHISM.
(** Identity is a morphism *)
@@ -140,6 +221,20 @@ Section DEFINITIONS.
try apply (Seq_refl _ _ Rsth);auto.
Qed.
+ (** Specification of the power function *)
+ Section POWER.
+ Variable Cpow : Set.
+ Variable Cp_phi : N -> Cpow.
+ Variable rpow : R -> Cpow -> R.
+
+ Record power_theory : Prop := mkpow_th {
+ rpow_pow_N : forall r n, req (rpow r (Cp_phi n)) (pow_N rI rmul r n)
+ }.
+
+ End POWER.
+
+ Definition pow_N_th := mkpow_th id_phi_N (pow_N rI rmul) (pow_N_pow_N rI rmul Rsth).
+
End DEFINITIONS.
@@ -437,11 +532,12 @@ Qed.
End ALMOST_RING.
+
Section AddRing.
- Variable R : Type.
+(* Variable R : Type.
Variable (rO rI : R) (radd rmul rsub: R->R->R) (ropp : R -> R).
- Variable req : R -> R -> Prop.
+ Variable req : R -> R -> Prop. *)
Inductive ring_kind : Type :=
| Abstract
@@ -461,6 +557,7 @@ Inductive ring_kind : Type :=
(_ : ring_morph rO rI radd rmul rsub ropp req
cO cI cadd cmul csub copp ceqb phi).
+
End AddRing.
diff --git a/contrib/setoid_ring/ZArithRing.v b/contrib/setoid_ring/ZArithRing.v
index 4f47fff0..8de7021e 100644
--- a/contrib/setoid_ring/ZArithRing.v
+++ b/contrib/setoid_ring/ZArithRing.v
@@ -8,26 +8,49 @@
Require Export Ring.
Require Import ZArith_base.
+Require Import Zpow_def.
+
Import InitialRing.
Set Implicit Arguments.
-Ltac isZcst t :=
- let t := eval hnf in t in
- match t with
- Z0 => constr:true
- | Zpos ?p => isZcst p
- | Zneg ?p => isZcst p
- | xI ?p => isZcst p
- | xO ?p => isZcst p
- | xH => constr:true
- | _ => constr:false
- end.
Ltac Zcst t :=
match isZcst t with
true => t
| _ => NotConstant
end.
+Ltac isZpow_coef t :=
+ match t with
+ | Zpos ?p => isPcst p
+ | Z0 => true
+ | _ => false
+ end.
+
+Definition N_of_Z x :=
+ match x with
+ | Zpos p => Npos p
+ | _ => N0
+ end.
+
+Ltac Zpow_tac t :=
+ match isZpow_coef t with
+ | true => constr:(N_of_Z t)
+ | _ => constr:(NotConstant)
+ end.
+
+Ltac Zpower_neg :=
+ repeat match goal with
+ | [|- ?G] =>
+ match G with
+ | context c [Zpower _ (Zneg _)] =>
+ let t := context c [Z0] in
+ change t
+ end
+ end.
+
+
Add Ring Zr : Zth
- (decidable Zeqb_ok, constants [Zcst], preprocess [unfold Zsucc]).
+ (decidable Zeqb_ok, constants [Zcst], preprocess [Zpower_neg;unfold Zsucc],
+ power_tac Zpower_theory [Zpow_tac]).
+
diff --git a/contrib/setoid_ring/newring.ml4 b/contrib/setoid_ring/newring.ml4
index daa2fedb..8b2ce26b 100644
--- a/contrib/setoid_ring/newring.ml4
+++ b/contrib/setoid_ring/newring.ml4
@@ -8,7 +8,7 @@
(*i camlp4deps: "parsing/grammar.cma" i*)
-(*i $Id: newring.ml4 9302 2006-10-27 21:21:17Z barras $ i*)
+(*i $Id: newring.ml4 9603 2007-02-07 00:41:16Z barras $ i*)
open Pp
open Util
@@ -127,6 +127,12 @@ TACTIC EXTEND closed_term
[ closed_term t l ]
END
;;
+
+TACTIC EXTEND echo
+| [ "echo" constr(t) ] ->
+ [ Pp.msg (Termops.print_constr t); Tacinterp.eval_tactic (TacId []) ]
+END;;
+
(*
let closed_term_ast l =
TacFun([Some(id_of_string"t")],
@@ -196,7 +202,8 @@ let constr_of = function
let stdlib_modules =
[["Coq";"Setoids";"Setoid"];
- ["Coq";"Lists";"List"]
+ ["Coq";"Lists";"List"];
+ ["Coq";"Init";"Datatypes"]
]
let coq_constant c =
@@ -205,18 +212,24 @@ let coq_constant c =
let coq_mk_Setoid = coq_constant "Build_Setoid_Theory"
let coq_cons = coq_constant "cons"
let coq_nil = coq_constant "nil"
+let coq_None = coq_constant "None"
+let coq_Some = coq_constant "Some"
let lapp f args = mkApp(Lazy.force f,args)
+let dest_rel0 t =
+ match kind_of_term t with
+ | App(f,args) when Array.length args >= 2 ->
+ let rel = mkApp(f,Array.sub args 0 (Array.length args - 2)) in
+ if closed0 rel then
+ (rel,args.(Array.length args - 2),args.(Array.length args - 1))
+ else error "ring: cannot find relation (not closed)"
+ | _ -> error "ring: cannot find relation"
+
let rec dest_rel t =
match kind_of_term t with
- App(f,args) when Array.length args >= 2 ->
- let rel = mkApp(f,Array.sub args 0 (Array.length args - 2)) in
- if closed0 rel then
- (rel,args.(Array.length args - 2),args.(Array.length args - 1))
- else error "ring: cannot find relation (not closed)"
- | Prod(_,_,c) -> dest_rel c
- | _ -> error "ring: cannot find relation"
+ | Prod(_,_,c) -> dest_rel c
+ | _ -> dest_rel0 t
(****************************************************************************)
(* Library linking *)
@@ -265,11 +278,18 @@ let coq_mk_seqe = my_constant "mk_seqe"
let ltac_inv_morphZ = zltac"inv_gen_phiZ"
let ltac_inv_morphN = zltac"inv_gen_phiN"
-
let coq_abstract = my_constant"Abstract"
let coq_comp = my_constant"Computational"
let coq_morph = my_constant"Morphism"
+(* power function *)
+let ltac_inv_morph_nothing = zltac"inv_morph_nothing"
+let coq_pow_N_pow_N = my_constant "pow_N_pow_N"
+
+(* hypothesis *)
+let coq_mkhypo = my_constant "mkhypo"
+let coq_hypo = my_constant "hypo"
+
(* Equality: do not evaluate but make recursive call on both sides *)
let map_with_eq arg_map c =
let (req,_,_) = dest_rel c in
@@ -283,10 +303,12 @@ let _ = add_map "ring"
coq_nil, (function -1->Eval|_ -> Prot);
(* Pphi_dev: evaluate polynomial and coef operations, protect
ring operations and make recursive call on the var map *)
- pol_cst "Pphi_dev", (function -1|6|7|8|9|11->Eval|10->Rec|_->Prot);
+ pol_cst "Pphi_dev", (function -1|8|9|10|11|12|14->Eval|13->Rec|_->Prot);
+ pol_cst "Pphi_pow",
+ (function -1|8|9|10|11|13|15|17->Eval|16->Rec|_->Prot);
(* PEeval: evaluate morphism and polynomial, protect ring
operations and make recursive call on the var map *)
- pol_cst "PEeval", (function -1|7|9->Eval|8->Rec|_->Prot)])
+ pol_cst "PEeval", (function -1|7|9|12->Eval|11->Rec|_->Prot)])
(****************************************************************************)
(* Ring database *)
@@ -299,6 +321,7 @@ type ring_info =
ring_morph : constr;
ring_th : constr;
ring_cst_tac : glob_tactic_expr;
+ ring_pow_tac : glob_tactic_expr;
ring_lemma1 : constr;
ring_lemma2 : constr;
ring_pre_tac : glob_tactic_expr;
@@ -316,7 +339,7 @@ let ring_lookup_by_name ref =
Spmap.find (Nametab.locate_obj (snd(qualid_of_reference ref))) !from_name
-let find_ring_structure env sigma l cl oname =
+let find_ring_structure env sigma l oname =
match oname, l with
Some rf, _ ->
(try ring_lookup_by_name rf
@@ -337,13 +360,14 @@ let find_ring_structure env sigma l cl oname =
errorlabstrm "ring"
(str"cannot find a declared ring structure over"++
spc()++str"\""++pr_constr ty++str"\""))
- | None, [] ->
+ | None, [] -> assert false
+(*
let (req,_,_) = dest_rel cl in
(try ring_for_relation req
with Not_found ->
errorlabstrm "ring"
(str"cannot find a declared ring structure for equality"++
- spc()++str"\""++pr_constr req++str"\""))
+ spc()++str"\""++pr_constr req++str"\"")) *)
let _ =
Summary.declare_summary "tactic-new-ring-table"
@@ -378,6 +402,7 @@ let subst_th (_,subst,th) =
let thm1' = subst_mps subst th.ring_lemma1 in
let thm2' = subst_mps subst th.ring_lemma2 in
let tac'= subst_tactic subst th.ring_cst_tac in
+ let pow_tac'= subst_tactic subst th.ring_pow_tac in
let pretac'= subst_tactic subst th.ring_pre_tac in
let posttac'= subst_tactic subst th.ring_post_tac in
if c' == th.ring_carrier &&
@@ -389,6 +414,7 @@ let subst_th (_,subst,th) =
thm1' == th.ring_lemma1 &&
thm2' == th.ring_lemma2 &&
tac' == th.ring_cst_tac &&
+ pow_tac' == th.ring_pow_tac &&
pretac' == th.ring_pre_tac &&
posttac' == th.ring_post_tac then th
else
@@ -399,6 +425,7 @@ let subst_th (_,subst,th) =
ring_morph = morph';
ring_th = th';
ring_cst_tac = tac';
+ ring_pow_tac = pow_tac';
ring_lemma1 = thm1';
ring_lemma2 = thm2';
ring_pre_tac = pretac';
@@ -532,14 +559,50 @@ let interp_cst_tac kind (zero,one,add,mul,opp) cst_tac =
TacArg(TacCall(dummy_loc,t,List.map carg [zero;one;add;mul;opp]))
| _ -> error"a tactic must be specified for an almost_ring")
-let add_theory name rth eqth morphth cst_tac (pre,post) =
+let make_hyp env c =
+ let t = (Typeops.typing env c).uj_type in
+ lapp coq_mkhypo [|t;c|]
+
+let make_hyp_list env lH =
+ let carrier = Lazy.force coq_hypo in
+ List.fold_right
+ (fun c l -> lapp coq_cons [|carrier; (make_hyp env c); l|]) lH
+ (lapp coq_nil [|carrier|])
+
+let interp_power env pow =
+ let carrier = Lazy.force coq_hypo in
+ match pow with
+ | None ->
+ let t = ArgArg(dummy_loc, Lazy.force ltac_inv_morph_nothing) in
+ (TacArg(TacCall(dummy_loc,t,[])), lapp coq_None [|carrier|])
+ | Some (tac, spec) ->
+ let tac =
+ match tac with
+ | CstTac t -> Tacinterp.glob_tactic t
+ | Closed lc -> closed_term_ast (List.map Nametab.global lc) in
+ let spec = make_hyp env (ic spec) in
+ (tac, lapp coq_Some [|carrier; spec|])
+
+let interp_sign env sign =
+ let carrier = Lazy.force coq_hypo in
+ match sign with
+ | None -> lapp coq_None [|carrier|]
+ | Some spec ->
+ let spec = make_hyp env (ic spec) in
+ lapp coq_Some [|carrier;spec|]
+ (* Same remark on ill-typed terms ... *)
+
+let add_theory name rth eqth morphth cst_tac (pre,post) power sign =
let env = Global.env() in
let sigma = Evd.empty in
let (kind,r,zero,one,add,mul,sub,opp,req) = dest_ring env sigma rth in
let (sth,ext) = build_setoid_params r add mul opp req eqth in
+ let (pow_tac, pspec) = interp_power env power in
+ let sspec = interp_sign env sign in
let rk = reflect_coeff morphth in
let params =
- exec_tactic env 5 (zltac"ring_lemmas") (List.map carg[sth;ext;rth;rk]) in
+ exec_tactic env 5 (zltac "ring_lemmas")
+ (List.map carg[sth;ext;rth;pspec;sspec;rk]) in
let lemma1 = constr_of params.(3) in
let lemma2 = constr_of params.(4) in
@@ -564,6 +627,7 @@ let add_theory name rth eqth morphth cst_tac (pre,post) =
ring_morph = constr_of params.(2);
ring_th = constr_of params.(0);
ring_cst_tac = cst_tac;
+ ring_pow_tac = pow_tac;
ring_lemma1 = lemma1;
ring_lemma2 = lemma2;
ring_pre_tac = pretac;
@@ -576,6 +640,10 @@ type ring_mod =
| Pre_tac of raw_tactic_expr
| Post_tac of raw_tactic_expr
| Setoid of Topconstr.constr_expr * Topconstr.constr_expr
+ | Pow_spec of cst_tac_spec * Topconstr.constr_expr
+ (* Syntaxification tactic , correctness lemma *)
+ | Sign_spec of Topconstr.constr_expr
+
VERNAC ARGUMENT EXTEND ring_mod
| [ "decidable" constr(eq_test) ] -> [ Ring_kind(Computational (ic eq_test)) ]
@@ -586,6 +654,11 @@ VERNAC ARGUMENT EXTEND ring_mod
| [ "preprocess" "[" tactic(pre) "]" ] -> [ Pre_tac pre ]
| [ "postprocess" "[" tactic(post) "]" ] -> [ Post_tac post ]
| [ "setoid" constr(sth) constr(ext) ] -> [ Setoid(sth,ext) ]
+ | [ "sign" constr(sign_spec) ] -> [ Sign_spec sign_spec ]
+ | [ "power" constr(pow_spec) "[" ne_global_list(l) "]" ] ->
+ [ Pow_spec (Closed l, pow_spec) ]
+ | [ "power_tac" constr(pow_spec) "[" tactic(cst_tac) "]" ] ->
+ [ Pow_spec (CstTac cst_tac, pow_spec) ]
END
let set_once s r v =
@@ -597,45 +670,54 @@ let process_ring_mods l =
let cst_tac = ref None in
let pre = ref None in
let post = ref None in
+ let sign = ref None in
+ let power = ref None in
List.iter(function
Ring_kind k -> set_once "ring kind" kind k
| Const_tac t -> set_once "tactic recognizing constants" cst_tac t
| Pre_tac t -> set_once "preprocess tactic" pre t
| Post_tac t -> set_once "postprocess tactic" post t
- | Setoid(sth,ext) -> set_once "setoid" set (ic sth,ic ext)) l;
+ | Setoid(sth,ext) -> set_once "setoid" set (ic sth,ic ext)
+ | Pow_spec(t,spec) -> set_once "power" power (t,spec)
+ | Sign_spec t -> set_once "sign" sign t) l;
let k = match !kind with Some k -> k | None -> Abstract in
- (k, !set, !cst_tac, !pre, !post)
+ (k, !set, !cst_tac, !pre, !post, !power, !sign)
VERNAC COMMAND EXTEND AddSetoidRing
| [ "Add" "Ring" ident(id) ":" constr(t) ring_mods(l) ] ->
- [ let (k,set,cst,pre,post) = process_ring_mods l in
- add_theory id (ic t) set k cst (pre,post) ]
+ [ let (k,set,cst,pre,post,power,sign) = process_ring_mods l in
+ add_theory id (ic t) set k cst (pre,post) power sign ]
END
(*****************************************************************************)
(* The tactics consist then only in a lookup in the ring database and
call the appropriate ltac. *)
-let make_term_list carrier rl gl =
- let rl =
- match rl with
- [] -> let (_,t1,t2) = dest_rel (pf_concl gl) in [t1;t2]
- | _ -> rl in
+let make_args_list rl t =
+ match rl with
+ | [] -> let (_,t1,t2) = dest_rel0 t in [t1;t2]
+ | _ -> rl
+
+let make_term_list carrier rl =
List.fold_right
(fun x l -> lapp coq_cons [|carrier;x;l|]) rl
(lapp coq_nil [|carrier|])
-let ring_lookup (f:glob_tactic_expr) rl gl =
+
+let ring_lookup (f:glob_tactic_expr) lH rl t gl =
let env = pf_env gl in
let sigma = project gl in
- let e = find_ring_structure env sigma rl (pf_concl gl) None in
- let rl = carg (make_term_list e.ring_carrier rl gl) in
+ let rl = make_args_list rl t in
+ let e = find_ring_structure env sigma rl None in
+ let rl = carg (make_term_list e.ring_carrier rl) in
+ let lH = carg (make_hyp_list env lH) in
let req = carg e.ring_req in
let sth = carg e.ring_setoid in
let ext = carg e.ring_ext in
let morph = carg e.ring_morph in
let th = carg e.ring_th in
let cst_tac = Tacexp e.ring_cst_tac in
+ let pow_tac = Tacexp e.ring_pow_tac in
let lemma1 = carg e.ring_lemma1 in
let lemma2 = carg e.ring_lemma2 in
let pretac = Tacexp(TacFun([None],e.ring_pre_tac)) in
@@ -644,12 +726,17 @@ let ring_lookup (f:glob_tactic_expr) rl gl =
(TacLetIn
([(dummy_loc,id_of_string"f"),None,Tacexp f],
ltac_lcall "f"
- [req;sth;ext;morph;th;cst_tac;lemma1;lemma2;pretac;posttac;rl])) gl
+ [req;sth;ext;morph;th;cst_tac;pow_tac;
+ lemma1;lemma2;pretac;posttac;lH;rl])) gl
TACTIC EXTEND ring_lookup
-| [ "ring_lookup" tactic(f) constr_list(l) ] -> [ ring_lookup (fst f) l ]
+| [ "ring_lookup" tactic(f) "[" constr_list(lH) "]" constr_list(lr)
+ "[" constr(t) "]" ] ->
+ [ring_lookup (fst f) lH lr t]
END
+
+
(***********************************************************************)
let new_field_path =
@@ -666,14 +753,20 @@ let _ = add_map "field"
(* display_linear: evaluate polynomials and coef operations, protect
field operations and make recursive call on the var map *)
my_constant "display_linear",
- (function -1|7|8|9|10|12|13->Eval|11->Rec|_->Prot);
- (* Pphi_dev: evaluate polynomial and coef operations, protect
+ (function -1|9|10|11|12|13|15|16->Eval|14->Rec|_->Prot);
+ my_constant "display_pow_linear",
+ (function -1|9|10|11|12|13|14|16|18|19->Eval|17->Rec|_->Prot);
+ (* Pphi_dev: evaluate polynomial and coef operations, protect
ring operations and make recursive call on the var map *)
- my_constant "Pphi_dev", (function -1|6|7|8|9|11->Eval|10->Rec|_->Prot);
+ pol_cst "Pphi_dev", (function -1|8|9|10|11|12|14->Eval|13->Rec|_->Prot);
+ pol_cst "Pphi_pow",
+ (function -1|8|9|10|11|13|15|17->Eval|16->Rec|_->Prot);
(* PEeval: evaluate morphism and polynomial, protect ring
operations and make recursive call on the var map *)
- my_constant "FEeval", (function -1|9|11->Eval|10->Rec|_->Prot)]);;
-
+ pol_cst "PEeval", (function -1|7|9|12->Eval|11->Rec|_->Prot);
+ (* FEeval: evaluate morphism, protect field
+ operations and make recursive call on the var map *)
+ my_constant "FEeval", (function -1|8|9|10|11|14->Eval|13->Rec|_->Prot)]);;
let _ = add_map "field_cond"
(map_with_eq
@@ -681,7 +774,8 @@ let _ = add_map "field_cond"
coq_nil, (function -1->Eval|_ -> Prot);
(* PCond: evaluate morphism and denum list, protect ring
operations and make recursive call on the var map *)
- my_constant "PCond", (function -1|8|10->Eval|9->Rec|_->Prot)]);;
+ my_constant "PCond", (function -1|8|10|13->Eval|12->Rec|_->Prot)]);;
+(* (function -1|8|10->Eval|9->Rec|_->Prot)]);;*)
let afield_theory = my_constant "almost_field_theory"
@@ -715,9 +809,11 @@ type field_info =
{ field_carrier : types;
field_req : constr;
field_cst_tac : glob_tactic_expr;
+ field_pow_tac : glob_tactic_expr;
field_ok : constr;
field_simpl_eq_ok : constr;
field_simpl_ok : constr;
+ field_simpl_eq_in_ok : constr;
field_cond : constr;
field_pre_tac : glob_tactic_expr;
field_post_tac : glob_tactic_expr }
@@ -734,7 +830,7 @@ let field_lookup_by_name ref =
!field_from_name
-let find_field_structure env sigma l cl oname =
+let find_field_structure env sigma l oname =
check_required_library (cdir@["Field_tac"]);
match oname, l with
Some rf, _ ->
@@ -756,13 +852,13 @@ let find_field_structure env sigma l cl oname =
errorlabstrm "field"
(str"cannot find a declared field structure over"++
spc()++str"\""++pr_constr ty++str"\""))
- | None, [] ->
- let (req,_,_) = dest_rel cl in
+ | None, [] -> assert false
+(* let (req,_,_) = dest_rel cl in
(try field_for_relation req
with Not_found ->
errorlabstrm "field"
(str"cannot find a declared field structure for equality"++
- spc()++str"\""++pr_constr req++str"\""))
+ spc()++str"\""++pr_constr req++str"\"")) *)
let _ =
Summary.declare_summary "tactic-new-field-table"
@@ -796,8 +892,10 @@ let subst_th (_,subst,th) =
let thm1' = subst_mps subst th.field_ok in
let thm2' = subst_mps subst th.field_simpl_eq_ok in
let thm3' = subst_mps subst th.field_simpl_ok in
- let thm4' = subst_mps subst th.field_cond in
+ let thm4' = subst_mps subst th.field_simpl_eq_in_ok in
+ let thm5' = subst_mps subst th.field_cond in
let tac'= subst_tactic subst th.field_cst_tac in
+ let pow_tac' = subst_tactic subst th.field_pow_tac in
let pretac'= subst_tactic subst th.field_pre_tac in
let posttac'= subst_tactic subst th.field_post_tac in
if c' == th.field_carrier &&
@@ -805,18 +903,22 @@ let subst_th (_,subst,th) =
thm1' == th.field_ok &&
thm2' == th.field_simpl_eq_ok &&
thm3' == th.field_simpl_ok &&
- thm4' == th.field_cond &&
+ thm4' == th.field_simpl_eq_in_ok &&
+ thm5' == th.field_cond &&
tac' == th.field_cst_tac &&
+ pow_tac' == th.field_pow_tac &&
pretac' == th.field_pre_tac &&
posttac' == th.field_post_tac then th
else
{ field_carrier = c';
field_req = eq';
field_cst_tac = tac';
+ field_pow_tac = pow_tac';
field_ok = thm1';
field_simpl_eq_ok = thm2';
field_simpl_ok = thm3';
- field_cond = thm4';
+ field_simpl_eq_in_ok = thm4';
+ field_cond = thm5';
field_pre_tac = pretac';
field_post_tac = posttac' }
@@ -850,30 +952,34 @@ let default_field_equality r inv req =
error "field inverse should be declared as a morphism" in
inv_m.lem
-let add_field_theory name fth eqth morphth cst_tac inj (pre,post) =
+let add_field_theory name fth eqth morphth cst_tac inj (pre,post) power sign =
let env = Global.env() in
let sigma = Evd.empty in
let (kind,r,zero,one,add,mul,sub,opp,div,inv,req,rth) =
dest_field env sigma fth in
let (sth,ext) = build_setoid_params r add mul opp req eqth in
let eqth = Some(sth,ext) in
- let _ = add_theory name rth eqth morphth cst_tac (None,None) in
+ let _ = add_theory name rth eqth morphth cst_tac (None,None) power sign in
+ let (pow_tac, pspec) = interp_power env power in
+ let sspec = interp_sign env sign in
let inv_m = default_field_equality r inv req in
let rk = reflect_coeff morphth in
let params =
- exec_tactic env 8 (field_ltac"field_lemmas")
- (List.map carg[sth;ext;inv_m;fth;rk]) in
+ exec_tactic env 9 (field_ltac"field_lemmas")
+ (List.map carg[sth;ext;inv_m;fth;pspec;sspec;rk]) in
let lemma1 = constr_of params.(3) in
let lemma2 = constr_of params.(4) in
let lemma3 = constr_of params.(5) in
+ let lemma4 = constr_of params.(6) in
let cond_lemma =
match inj with
- | Some thm -> mkApp(constr_of params.(7),[|thm|])
- | None -> constr_of params.(6) in
+ | Some thm -> mkApp(constr_of params.(8),[|thm|])
+ | None -> constr_of params.(7) in
let lemma1 = decl_constant (string_of_id name^"_field_lemma1") lemma1 in
let lemma2 = decl_constant (string_of_id name^"_field_lemma2") lemma2 in
let lemma3 = decl_constant (string_of_id name^"_field_lemma3") lemma3 in
- let cond_lemma = decl_constant (string_of_id name^"_lemma4") cond_lemma in
+ let lemma4 = decl_constant (string_of_id name^"_field_lemma4") lemma4 in
+ let cond_lemma = decl_constant (string_of_id name^"_lemma5") cond_lemma in
let cst_tac = interp_cst_tac kind (zero,one,add,mul,opp) cst_tac in
let pretac =
match pre with
@@ -889,9 +995,11 @@ let add_field_theory name fth eqth morphth cst_tac inj (pre,post) =
{ field_carrier = r;
field_req = req;
field_cst_tac = cst_tac;
+ field_pow_tac = pow_tac;
field_ok = lemma1;
field_simpl_eq_ok = lemma2;
field_simpl_ok = lemma3;
+ field_simpl_eq_in_ok = lemma4;
field_cond = cond_lemma;
field_pre_tac = pretac;
field_post_tac = posttac }) in ()
@@ -902,7 +1010,7 @@ type field_mod =
VERNAC ARGUMENT EXTEND field_mod
| [ ring_mod(m) ] -> [ Ring_mod m ]
- | [ "infinite" constr(inj) ] -> [ Inject inj ]
+ | [ "completeness" constr(inj) ] -> [ Inject inj ]
END
let process_field_mods l =
@@ -911,7 +1019,9 @@ let process_field_mods l =
let cst_tac = ref None in
let pre = ref None in
let post = ref None in
- let inj = ref None in
+ let inj = ref None in
+ let sign = ref None in
+ let power = ref None in
List.iter(function
Ring_mod(Ring_kind k) -> set_once "field kind" kind k
| Ring_mod(Const_tac t) ->
@@ -919,26 +1029,32 @@ let process_field_mods l =
| Ring_mod(Pre_tac t) -> set_once "preprocess tactic" pre t
| Ring_mod(Post_tac t) -> set_once "postprocess tactic" post t
| Ring_mod(Setoid(sth,ext)) -> set_once "setoid" set (ic sth,ic ext)
+ | Ring_mod(Pow_spec(t,spec)) -> set_once "power" power (t,spec)
+ | Ring_mod(Sign_spec t) -> set_once "sign" sign t
| Inject i -> set_once "infinite property" inj (ic i)) l;
let k = match !kind with Some k -> k | None -> Abstract in
- (k, !set, !inj, !cst_tac, !pre, !post)
+ (k, !set, !inj, !cst_tac, !pre, !post, !power, !sign)
VERNAC COMMAND EXTEND AddSetoidField
| [ "Add" "Field" ident(id) ":" constr(t) field_mods(l) ] ->
- [ let (k,set,inj,cst_tac,pre,post) = process_field_mods l in
- add_field_theory id (ic t) set k cst_tac inj (pre,post) ]
+ [ let (k,set,inj,cst_tac,pre,post,power,sign) = process_field_mods l in
+ add_field_theory id (ic t) set k cst_tac inj (pre,post) power sign]
END
-let field_lookup (f:glob_tactic_expr) rl gl =
+let field_lookup (f:glob_tactic_expr) lH rl t gl =
let env = pf_env gl in
let sigma = project gl in
- let e = find_field_structure env sigma rl (pf_concl gl) None in
- let rl = carg (make_term_list e.field_carrier rl gl) in
+ let rl = make_args_list rl t in
+ let e = find_field_structure env sigma rl None in
+ let rl = carg (make_term_list e.field_carrier rl) in
+ let lH = carg (make_hyp_list env lH) in
let req = carg e.field_req in
let cst_tac = Tacexp e.field_cst_tac in
+ let pow_tac = Tacexp e.field_pow_tac in
let field_ok = carg e.field_ok in
let field_simpl_ok = carg e.field_simpl_ok in
let field_simpl_eq_ok = carg e.field_simpl_eq_ok in
+ let field_simpl_eq_in_ok = carg e.field_simpl_eq_in_ok in
let cond_ok = carg e.field_cond in
let pretac = Tacexp(TacFun([None],e.field_pre_tac)) in
let posttac = Tacexp(TacFun([None],e.field_post_tac)) in
@@ -946,9 +1062,11 @@ let field_lookup (f:glob_tactic_expr) rl gl =
(TacLetIn
([(dummy_loc,id_of_string"f"),None,Tacexp f],
ltac_lcall "f"
- [req;cst_tac;field_ok;field_simpl_ok;field_simpl_eq_ok;cond_ok;
- pretac;posttac;rl])) gl
+ [req;cst_tac;pow_tac;field_ok;field_simpl_ok;field_simpl_eq_ok;
+ field_simpl_eq_in_ok;cond_ok;pretac;posttac;lH;rl])) gl
TACTIC EXTEND field_lookup
-| [ "field_lookup" tactic(f) constr_list(l) ] -> [ field_lookup (fst f) l ]
+| [ "field_lookup" tactic(f) "[" constr_list(lH) "]" constr_list(l)
+ "[" constr(t) "]" ] ->
+ [ field_lookup (fst f) lH l t ]
END
diff --git a/contrib/subtac/FixSub.v b/contrib/subtac/FixSub.v
index ded069bf..46121ff1 100644
--- a/contrib/subtac/FixSub.v
+++ b/contrib/subtac/FixSub.v
@@ -1,37 +1,87 @@
Require Import Wf.
+Require Import Coq.subtac.Utils.
Section Well_founded.
-Variable A : Set.
-Variable R : A -> A -> Prop.
-Hypothesis Rwf : well_founded R.
+ Variable A : Type.
+ Variable R : A -> A -> Prop.
+ Hypothesis Rwf : well_founded R.
+
+ Section Acc.
+
+ Variable P : A -> Type.
+
+ Variable F_sub : forall x:A, (forall y: { y : A | R y x }, P (proj1_sig y)) -> P x.
+
+ Fixpoint Fix_F_sub (x : A) (r : Acc R x) {struct r} : P x :=
+ F_sub x (fun y: { y : A | R y x} => Fix_F_sub (proj1_sig y)
+ (Acc_inv r (proj1_sig y) (proj2_sig y))).
+
+ Definition Fix_sub (x : A) := Fix_F_sub x (Rwf x).
+ End Acc.
+
+ Section FixPoint.
+ Variable P : A -> Type.
+
+ Variable F_sub : forall x:A, (forall y: { y : A | R y x }, P (proj1_sig y)) -> P x.
+
+ Notation Fix_F := (Fix_F_sub P F_sub) (only parsing). (* alias *)
+
+ Definition Fix (x:A) := Fix_F_sub P F_sub x (Rwf x).
+
+ Hypothesis
+ F_ext :
+ forall (x:A) (f g:forall y:{y:A | R y x}, P (`y)),
+ (forall y:{ y:A | R y x}, f y = g y) -> F_sub x f = F_sub x g.
-Section FixPoint.
-
-Variable P : A -> Set.
+ Lemma Fix_F_eq :
+ forall (x:A) (r:Acc R x),
+ F_sub x (fun (y:{y:A|R y x}) => Fix_F (`y) (Acc_inv r (proj1_sig y) (proj2_sig y))) = Fix_F x r.
+ Proof.
+ destruct r using Acc_inv_dep; auto.
+ Qed.
+
+ Lemma Fix_F_inv : forall (x:A) (r s:Acc R x), Fix_F x r = Fix_F x s.
+ Proof.
+ intro x; induction (Rwf x); intros.
+ rewrite <- (Fix_F_eq x r); rewrite <- (Fix_F_eq x s); intros.
+ apply F_ext; auto.
+ intros.
+ rewrite (proof_irrelevance (Acc R x) r s) ; auto.
+ Qed.
-Variable F_sub : forall x:A, (forall y: { y : A | R y x }, P (proj1_sig y)) -> P x.
-
-Fixpoint Fix_F_sub (x : A) (r : Acc R x) {struct r} : P x :=
- F_sub x (fun y: { y : A | R y x} => Fix_F_sub (proj1_sig y)
- (Acc_inv r (proj1_sig y) (proj2_sig y))).
+ Lemma Fix_eq : forall x:A, Fix x = F_sub x (fun (y:{y:A|R y x}) => Fix (proj1_sig y)).
+ Proof.
+ intro x; unfold Fix in |- *.
+ rewrite <- (Fix_F_eq ).
+ apply F_ext; intros.
+ apply Fix_F_inv.
+ Qed.
-Definition Fix_sub (x : A) := Fix_F_sub x (Rwf x).
+ Lemma fix_sub_eq :
+ forall x : A,
+ Fix_sub P F_sub x =
+ let f_sub := F_sub in
+ f_sub x (fun {y : A | R y x}=> Fix (`y)).
+ exact Fix_eq.
+ Qed.
-End FixPoint.
+ End FixPoint.
End Well_founded.
+Extraction Inline Fix_F_sub Fix_sub.
+
Require Import Wf_nat.
Require Import Lt.
Section Well_founded_measure.
-Variable A : Set.
+Variable A : Type.
Variable f : A -> nat.
Definition R := fun x y => f x < f y.
Section FixPoint.
-Variable P : A -> Set.
+Variable P : A -> Type.
Variable F_sub : forall x:A, (forall y: { y : A | f y < f x }, P (proj1_sig y)) -> P x.
@@ -44,3 +94,5 @@ Definition Fix_measure_sub (x : A) := Fix_measure_F_sub x (lt_wf (f x)).
End FixPoint.
End Well_founded_measure.
+
+Extraction Inline Fix_measure_F_sub Fix_measure_sub.
diff --git a/contrib/subtac/FunctionalExtensionality.v b/contrib/subtac/FunctionalExtensionality.v
new file mode 100644
index 00000000..1a12ac82
--- /dev/null
+++ b/contrib/subtac/FunctionalExtensionality.v
@@ -0,0 +1,25 @@
+Axiom fun_extensionality : forall A B (f g : A -> B),
+ (forall x, f x = g x) -> f = g.
+
+Axiom fun_extensionality_dep : forall A, forall B : (A -> Type), forall (f g : forall x : A, B x),
+ (forall x, f x = g x) -> f = g.
+
+Hint Resolve fun_extensionality fun_extensionality_dep : subtac.
+
+Require Import Coq.subtac.Utils.
+Require Import Coq.subtac.FixSub.
+
+Lemma fix_sub_eq_ext :
+ forall (A : Set) (R : A -> A -> Prop) (Rwf : well_founded R)
+ (P : A -> Set)
+ (F_sub : forall x : A, (forall {y : A | R y x}, P (`y)) -> P x),
+ forall x : A,
+ Fix_sub A R Rwf P F_sub x =
+ F_sub x (fun {y : A | R y x}=> Fix A R Rwf P F_sub (`y)).
+Proof.
+ intros ; apply Fix_eq ; auto.
+ intros.
+ assert(f = g).
+ apply (fun_extensionality_dep _ _ _ _ H).
+ rewrite H0 ; auto.
+Qed.
diff --git a/contrib/subtac/Subtac.v b/contrib/subtac/Subtac.v
new file mode 100644
index 00000000..9912cd24
--- /dev/null
+++ b/contrib/subtac/Subtac.v
@@ -0,0 +1,2 @@
+Require Export Coq.subtac.Utils.
+Require Export Coq.subtac.FixSub. \ No newline at end of file
diff --git a/contrib/subtac/Utils.v b/contrib/subtac/Utils.v
index 219cd75b..4a2208ce 100644
--- a/contrib/subtac/Utils.v
+++ b/contrib/subtac/Utils.v
@@ -6,6 +6,8 @@ Notation "'fun' { x : A | P } => Q" :=
Notation "( x & ? )" := (@exist _ _ x _) : core_scope.
+Notation " ! " := (False_rect _ _).
+
Definition ex_pi1 (A : Prop) (P : A -> Prop) (t : ex P) : A.
intros.
induction t.
@@ -44,4 +46,30 @@ end.
Ltac destruct_exists := repeat (destruct_one_pair) .
+Ltac subtac_simpl := simpl ; intros ; destruct_exists ; simpl in * ; try subst ; auto with arith.
+
+(* Destructs calls to f in hypothesis or conclusion, useful if f creates a subset object *)
+Ltac destruct_call f :=
+ match goal with
+ | H : ?T |- _ =>
+ match T with
+ context [f ?x ?y ?z] => destruct (f x y z)
+ | context [f ?x ?y] => destruct (f x y)
+ | context [f ?x] => destruct (f x)
+ end
+ | |- ?T =>
+ match T with
+ context [f ?x ?y ?z] => let n := fresh "H" in set (n:=f x y z); destruct n
+ | context [f ?x ?y] => let n := fresh "H" in set (n:=f x y); destruct n
+ | context [f ?x] => let n := fresh "H" in set (n:=f x); destruct n
+ end
+ end.
+
Extraction Inline proj1_sig.
+Extract Inductive unit => "unit" [ "()" ].
+Extract Inductive bool => "bool" [ "true" "false" ].
+Extract Inductive sumbool => "bool" [ "true" "false" ].
+Extract Inductive prod => "pair" [ "" ].
+Extract Inductive sigT => "pair" [ "" ].
+
+Require Export ProofIrrelevance.
diff --git a/contrib/subtac/eterm.ml b/contrib/subtac/eterm.ml
index 790e61a0..1844fea5 100644
--- a/contrib/subtac/eterm.ml
+++ b/contrib/subtac/eterm.ml
@@ -52,8 +52,8 @@ let subst_evar_constr evs n t =
anomaly ("eterm: existential variable " ^ string_of_int k ^ " not found")
in
seen := Intset.add id !seen;
- (try trace (str "Evar " ++ int k ++ str " found, applied to " ++ int (Array.length args) ++ str "arguments," ++
- int (List.length hyps) ++ str " hypotheses"); with _ -> () );
+(* (try trace (str "Evar " ++ int k ++ str " found, applied to " ++ int (Array.length args) ++ str "arguments," ++ *)
+(* int (List.length hyps) ++ str " hypotheses"); with _ -> () ); *)
(* Evar arguments are created in inverse order,
and we must not apply to defined ones (i.e. LetIn's)
*)
@@ -126,7 +126,6 @@ let eterm_obligations name nclen evm t tycon =
(* 'Serialize' the evars, we assume that the types of the existentials
refer to previous existentials in the list only *)
let evl = List.rev (to_list evm) in
- trace (str "Eterm, transformed to list");
let evn =
let i = ref (-1) in
List.rev_map (fun (id, ev) -> incr i;
@@ -136,12 +135,9 @@ let eterm_obligations name nclen evm t tycon =
(* Remove existential variables in types and build the corresponding products *)
fold_right
(fun (id, (n, nstr), ev) l ->
- trace (str "Eterm: " ++ str "treating evar: " ++ int id);
let hyps = Environ.named_context_of_val ev.evar_hyps in
let hyps = trunc_named_context nclen hyps in
- trace (str "Named context is: " ++ Printer.pr_named_context (Global.env ()) hyps);
let evtyp, deps = etype_of_evar l ev hyps in
- trace (str "Evar " ++ str (string_of_int n) ++ str "'s type is: " ++ Termops.print_constr_env (Global.env ()) evtyp);
let y' = (id, ((n, nstr), hyps, evtyp, deps)) in
y' :: l)
evn []
@@ -152,17 +148,17 @@ let eterm_obligations name nclen evm t tycon =
let evars =
List.map (fun (_, ((_, name), _, typ, deps)) -> name, typ, deps) evts
in
- (try
- trace (str "Term given to eterm" ++ spc () ++
- Termops.print_constr_env (Global.env ()) t);
- trace (str "Term constructed in eterm" ++ spc () ++
- Termops.print_constr_env (Global.env ()) t');
- ignore(iter
- (fun (name, typ, deps) ->
- trace (str "Evar :" ++ spc () ++ str (string_of_id name) ++
- Termops.print_constr_env (Global.env ()) typ))
- evars);
- with _ -> ());
+(* (try *)
+(* trace (str "Term given to eterm" ++ spc () ++ *)
+(* Termops.print_constr_env (Global.env ()) t); *)
+(* trace (str "Term constructed in eterm" ++ spc () ++ *)
+(* Termops.print_constr_env (Global.env ()) t'); *)
+(* ignore(iter *)
+(* (fun (name, typ, deps) -> *)
+(* trace (str "Evar :" ++ spc () ++ str (string_of_id name) ++ *)
+(* Termops.print_constr_env (Global.env ()) typ)) *)
+(* evars); *)
+(* with _ -> ()); *)
Array.of_list (List.rev evars), t'
let mkMetas n =
diff --git a/contrib/subtac/g_subtac.ml4 b/contrib/subtac/g_subtac.ml4
index 243cb191..e31326e9 100644
--- a/contrib/subtac/g_subtac.ml4
+++ b/contrib/subtac/g_subtac.ml4
@@ -10,7 +10,7 @@
Syntax for the subtac terms and types.
Elaborated from correctness/psyntax.ml4 by Jean-Christophe Filliâtre *)
-(* $Id: g_subtac.ml4 9326 2006-10-31 12:57:26Z msozeau $ *)
+(* $Id: g_subtac.ml4 9588 2007-02-02 16:17:13Z herbelin $ *)
(*i camlp4deps: "parsing/grammar.cma" i*)
@@ -37,6 +37,8 @@ struct
let gec s = Gram.Entry.create ("Subtac."^s)
(* types *)
let subtac_gallina_loc : Vernacexpr.vernac_expr located Gram.Entry.e = gec "subtac_gallina_loc"
+
+ let subtac_nameopt : identifier option Gram.Entry.e = gec "subtac_nameopt"
end
open SubtacGram
@@ -46,12 +48,17 @@ open Pcoq
let sigref = mkRefC (Qualid (dummy_loc, Libnames.qualid_of_string "Coq.Init.Specif.sig"))
GEXTEND Gram
- GLOBAL: subtac_gallina_loc Constr.binder_let Constr.binder;
+ GLOBAL: subtac_gallina_loc Constr.binder_let Constr.binder subtac_nameopt;
subtac_gallina_loc:
[ [ g = Vernac.gallina -> loc, g ] ]
;
+ subtac_nameopt:
+ [ [ "ofb"; id=Prim.ident -> Some (id)
+ | -> None ] ]
+ ;
+
Constr.binder_let:
[ [ "("; id=Prim.name; ":"; t=Constr.lconstr; "|"; c=Constr.lconstr; ")" ->
let typ = mkAppC (sigref, [mkLambdaC ([id], t, c)]) in
@@ -60,8 +67,12 @@ GEXTEND Gram
Constr.binder:
[ [ "("; id=Prim.name; ":"; c=Constr.lconstr; "|"; p=Constr.lconstr; ")" ->
- let typ = mkAppC (sigref, [mkLambdaC ([id], c, p)]) in
- ([id], typ) ] ];
+ ([id],mkAppC (sigref, [mkLambdaC ([id], c, p)]))
+ | "("; id=Prim.name; ":"; c=Constr.lconstr; ")" ->
+ ([id],c)
+ | "("; id=Prim.name; lid=LIST1 Prim.name; ":"; c=Constr.lconstr; ")" ->
+ (id::lid,c)
+ ] ];
END
@@ -69,16 +80,42 @@ GEXTEND Gram
type ('a,'b) gallina_loc_argtype = (Vernacexpr.vernac_expr located, 'a, 'b) Genarg.abstract_argument_type
let (wit_subtac_gallina_loc : (Genarg.tlevel, Proof_type.tactic) gallina_loc_argtype),
- (globwit_subtac_gallina_loc : (Genarg.glevel, Tacexpr.glob_tactic_expr) gallina_loc_argtype),
+ (globwit_subtac_gallina_loc : (Genarg.glevel, Tacexpr.glob_tactic_expr ) gallina_loc_argtype),
(rawwit_subtac_gallina_loc : (Genarg.rlevel, Tacexpr.raw_tactic_expr) gallina_loc_argtype) =
Genarg.create_arg "subtac_gallina_loc"
+type 'a nameopt_argtype = (identifier option, 'a, 'a) Genarg.abstract_argument_type
+
+let (wit_subtac_nameopt : Genarg.tlevel nameopt_argtype),
+ (globwit_subtac_nameopt : Genarg.glevel nameopt_argtype),
+ (rawwit_subtac_nameopt : Genarg.rlevel nameopt_argtype) =
+ Genarg.create_arg "subtac_nameopt"
+
VERNAC COMMAND EXTEND Subtac
[ "Program" subtac_gallina_loc(g) ] -> [ Subtac.subtac g ]
-| [ "Obligation" integer(num) "of" ident(name) ] -> [ Subtac_obligations.subtac_obligation (num, Some name) ]
-| [ "Obligation" integer(num) ] -> [ Subtac_obligations.subtac_obligation (num, None) ]
+ END
+
+VERNAC COMMAND EXTEND Subtac_Obligations
+| [ "Obligation" integer(num) "of" ident(name) ":" lconstr(t) ] -> [ Subtac_obligations.subtac_obligation (num, Some name, Some t) ]
+| [ "Obligation" integer(num) "of" ident(name) ] -> [ Subtac_obligations.subtac_obligation (num, Some name, None) ]
+| [ "Obligation" integer(num) ":" lconstr(t) ] -> [ Subtac_obligations.subtac_obligation (num, None, Some t) ]
+| [ "Obligation" integer(num) ] -> [ Subtac_obligations.subtac_obligation (num, None, None) ]
+| [ "Next" "Obligation" "of" ident(name) ] -> [ Subtac_obligations.next_obligation (Some name) ]
+| [ "Next" "Obligation" ] -> [ Subtac_obligations.next_obligation None ]
+END
+
+VERNAC COMMAND EXTEND Subtac_Solve_Obligations
| [ "Solve" "Obligations" "of" ident(name) "using" tactic(t) ] -> [ Subtac_obligations.solve_obligations (Some name) (Tacinterp.interp t) ]
| [ "Solve" "Obligations" "using" tactic(t) ] -> [ Subtac_obligations.solve_obligations None (Tacinterp.interp t) ]
+| [ "Admit" "Obligations" "of" ident(name) ] -> [ Subtac_obligations.admit_obligations (Some name) ]
+| [ "Admit" "Obligations" ] -> [ Subtac_obligations.admit_obligations None ]
+ END
+
+VERNAC COMMAND EXTEND Subtac_Set_Solver
+| [ "Obligations" "Tactic" ":=" tactic(t) ] -> [ Subtac_obligations.set_default_tactic (Tacinterp.interp t) ]
+END
+
+VERNAC COMMAND EXTEND Subtac_Show_Obligations
| [ "Obligations" "of" ident(name) ] -> [ Subtac_obligations.show_obligations (Some name) ]
| [ "Obligations" ] -> [ Subtac_obligations.show_obligations None ]
END
diff --git a/contrib/subtac/subtac.ml b/contrib/subtac/subtac.ml
index 26e8f715..5e46bead 100644
--- a/contrib/subtac/subtac.ml
+++ b/contrib/subtac/subtac.ml
@@ -6,7 +6,7 @@
(* * GNU Lesser General Public License Version 2.1 *)
(************************************************************************)
-(* $Id: subtac.ml 9284 2006-10-26 12:06:57Z msozeau $ *)
+(* $Id: subtac.ml 9563 2007-01-31 09:37:18Z msozeau $ *)
open Global
open Pp
@@ -120,6 +120,8 @@ let subtac_end_proof = function
open Pp
open Ppconstr
open Decl_kinds
+open Tacinterp
+open Tacexpr
let start_proof_com env isevars sopt kind (bl,t) hook =
let id = match sopt with
@@ -140,14 +142,27 @@ let start_proof_com env isevars sopt kind (bl,t) hook =
let print_subgoals () = Options.if_verbose (fun () -> msg (Printer.pr_open_subgoals ())) ()
+let subtac_utils_path =
+ make_dirpath (List.map id_of_string ["Utils";contrib_name;"Coq"])
+let utils_tac s =
+ lazy(make_kn (MPfile subtac_utils_path) (make_dirpath []) (mk_label s))
+
+let utils_call tac args =
+ TacArg(TacCall(dummy_loc, ArgArg(dummy_loc, Lazy.force (utils_tac tac)),args))
+
let start_proof_and_print env isevars idopt k t hook =
start_proof_com env isevars idopt k t hook;
print_subgoals ()
(*if !pcoq <> None then (out_some !pcoq).start_proof ()*)
+let _ = Subtac_obligations.set_default_tactic
+ (Tacinterp.eval_tactic (utils_call "subtac_simpl" []))
+
+
let subtac (loc, command) =
check_required_library ["Coq";"Init";"Datatypes"];
check_required_library ["Coq";"Init";"Specif"];
+ (* check_required_library ["Coq";"Logic";"JMeq"]; *)
require_library "Coq.subtac.FixSub";
require_library "Coq.subtac.Utils";
let env = Global.env () in
diff --git a/contrib/subtac/subtac_cases.ml b/contrib/subtac/subtac_cases.ml
new file mode 100644
index 00000000..fbe1ac37
--- /dev/null
+++ b/contrib/subtac/subtac_cases.ml
@@ -0,0 +1,1925 @@
+(************************************************************************)
+(* v * The Coq Proof Assistant / The Coq Development Team *)
+(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(************************************************************************)
+
+(* $Id: cases.ml 9399 2006-11-22 16:11:53Z herbelin $ *)
+
+open Util
+open Names
+open Nameops
+open Term
+open Termops
+open Declarations
+open Inductiveops
+open Environ
+open Sign
+open Reductionops
+open Typeops
+open Type_errors
+
+open Rawterm
+open Retyping
+open Pretype_errors
+open Evarutil
+open Evarconv
+
+open Subtac_utils
+
+(* Pattern-matching errors *)
+
+type pattern_matching_error =
+ | BadPattern of constructor * constr
+ | BadConstructor of constructor * inductive
+ | WrongNumargConstructor of constructor * int
+ | WrongNumargInductive of inductive * int
+ | WrongPredicateArity of constr * constr * constr
+ | NeedsInversion of constr * constr
+ | UnusedClause of cases_pattern list
+ | NonExhaustive of cases_pattern list
+ | CannotInferPredicate of (constr * types) array
+
+exception PatternMatchingError of env * pattern_matching_error
+
+let raise_pattern_matching_error (loc,ctx,te) =
+ Stdpp.raise_with_loc loc (PatternMatchingError(ctx,te))
+
+let error_bad_pattern_loc loc cstr ind =
+ raise_pattern_matching_error (loc, Global.env(), BadPattern (cstr,ind))
+
+let error_bad_constructor_loc loc cstr ind =
+ raise_pattern_matching_error (loc, Global.env(), BadConstructor (cstr,ind))
+
+let error_wrong_numarg_constructor_loc loc env c n =
+ raise_pattern_matching_error (loc, env, WrongNumargConstructor(c,n))
+
+let error_wrong_numarg_inductive_loc loc env c n =
+ raise_pattern_matching_error (loc, env, WrongNumargInductive(c,n))
+
+let error_wrong_predicate_arity_loc loc env c n1 n2 =
+ raise_pattern_matching_error (loc, env, WrongPredicateArity (c,n1,n2))
+
+let error_needs_inversion env x t =
+ raise (PatternMatchingError (env, NeedsInversion (x,t)))
+
+module type S = sig
+ val compile_cases :
+ loc ->
+ (type_constraint -> env -> rawconstr -> unsafe_judgment) *
+ Evd.evar_defs ref ->
+ type_constraint ->
+ env -> rawconstr option * tomatch_tuple * cases_clauses ->
+ unsafe_judgment
+end
+
+(************************************************************************)
+(* Pattern-matching compilation (Cases) *)
+(************************************************************************)
+
+(************************************************************************)
+(* Configuration, errors and warnings *)
+
+open Pp
+
+let mssg_may_need_inversion () =
+ str "Found a matching with no clauses on a term unknown to have an empty inductive type"
+
+(* Utils *)
+let make_anonymous_patvars =
+ list_tabulate (fun _ -> PatVar (dummy_loc,Anonymous))
+
+(* Environment management *)
+let push_rels vars env = List.fold_right push_rel vars env
+
+let push_rel_defs =
+ List.fold_right (fun (x,d,t) e -> push_rel (x,Some d,t) e)
+
+(* We have x1:t1...xn:tn,xi':ti,y1..yk |- c and re-generalize
+ over xi:ti to get x1:t1...xn:tn,xi':ti,y1..yk |- c[xi:=xi'] *)
+
+let regeneralize_rel i k j = if j = i+k then k else if j < i+k then j else j
+
+let rec regeneralize_index i k t = match kind_of_term t with
+ | Rel j when j = i+k -> mkRel (k+1)
+ | Rel j when j < i+k -> t
+ | Rel j when j > i+k -> t
+ | _ -> map_constr_with_binders succ (regeneralize_index i) k t
+
+type alias_constr =
+ | DepAlias
+ | NonDepAlias
+
+let mkSpecialLetInJudge j (na,(deppat,nondeppat,d,t)) =
+ { uj_val =
+ (match d with
+ | DepAlias -> mkLetIn (na,deppat,t,j.uj_val)
+ | NonDepAlias ->
+ if (not (dependent (mkRel 1) j.uj_type))
+ or (* A leaf: *) isRel deppat
+ then
+ (* The body of pat is not needed to type j - see *)
+ (* insert_aliases - and both deppat and nondeppat have the *)
+ (* same type, then one can freely substitute one by the other *)
+ subst1 nondeppat j.uj_val
+ else
+ (* The body of pat is not needed to type j but its value *)
+ (* is dependent in the type of j; our choice is to *)
+ (* enforce this dependency *)
+ mkLetIn (na,deppat,t,j.uj_val));
+ uj_type = subst1 deppat j.uj_type }
+
+(**********************************************************************)
+(* Structures used in compiling pattern-matching *)
+
+type rhs =
+ { rhs_env : env;
+ avoid_ids : identifier list;
+ it : rawconstr;
+ }
+
+type equation =
+ { patterns : cases_pattern list;
+ rhs : rhs;
+ alias_stack : name list;
+ eqn_loc : loc;
+ used : bool ref;
+ tag : pattern_source }
+
+type matrix = equation list
+
+(* 1st argument of IsInd is the original ind before extracting the summary *)
+type tomatch_type =
+ | IsInd of types * inductive_type
+ | NotInd of constr option * types
+
+type tomatch_status =
+ | Pushed of ((constr * tomatch_type) * int list)
+ | Alias of (constr * constr * alias_constr * constr)
+ | Abstract of rel_declaration
+
+type tomatch_stack = tomatch_status list
+
+(* The type [predicate_signature] types the terms to match and the rhs:
+
+ - [PrLetIn (names,dep,pred)] types a pushed term ([Pushed]),
+ if dep<>Anonymous, the term is dependent, let n=|names|, if
+ n<>0 then the type of the pushed term is necessarily an
+ inductive with n real arguments. Otherwise, it may be
+ non inductive, or inductive without real arguments, or inductive
+ originating from a subterm in which case real args are not dependent;
+ it accounts for n+1 binders if dep or n binders if not dep
+ - [PrProd] types abstracted term ([Abstract]); it accounts for one binder
+ - [PrCcl] types the right-hand-side
+ - Aliases [Alias] have no trace in [predicate_signature]
+*)
+
+type predicate_signature =
+ | PrLetIn of (name list * name) * predicate_signature
+ | PrProd of predicate_signature
+ | PrCcl of constr
+
+(* We keep a constr for aliases and a cases_pattern for error message *)
+
+type alias_builder =
+ | AliasLeaf
+ | AliasConstructor of constructor
+
+type pattern_history =
+ | Top
+ | MakeAlias of alias_builder * pattern_continuation
+
+and pattern_continuation =
+ | Continuation of int * cases_pattern list * pattern_history
+ | Result of cases_pattern list
+
+let start_history n = Continuation (n, [], Top)
+
+let initial_history = function Continuation (_,[],Top) -> true | _ -> false
+
+let feed_history arg = function
+ | Continuation (n, l, h) when n>=1 ->
+ Continuation (n-1, arg :: l, h)
+ | Continuation (n, _, _) ->
+ anomaly ("Bad number of expected remaining patterns: "^(string_of_int n))
+ | Result _ ->
+ anomaly "Exhausted pattern history"
+
+(* This is for non exhaustive error message *)
+
+let rec rawpattern_of_partial_history args2 = function
+ | Continuation (n, args1, h) ->
+ let args3 = make_anonymous_patvars (n - (List.length args2)) in
+ build_rawpattern (List.rev_append args1 (args2@args3)) h
+ | Result pl -> pl
+
+and build_rawpattern args = function
+ | Top -> args
+ | MakeAlias (AliasLeaf, rh) ->
+ assert (args = []);
+ rawpattern_of_partial_history [PatVar (dummy_loc, Anonymous)] rh
+ | MakeAlias (AliasConstructor pci, rh) ->
+ rawpattern_of_partial_history
+ [PatCstr (dummy_loc, pci, args, Anonymous)] rh
+
+let complete_history = rawpattern_of_partial_history []
+
+(* This is to build glued pattern-matching history and alias bodies *)
+
+let rec simplify_history = function
+ | Continuation (0, l, Top) -> Result (List.rev l)
+ | Continuation (0, l, MakeAlias (f, rh)) ->
+ let pargs = List.rev l in
+ let pat = match f with
+ | AliasConstructor pci ->
+ PatCstr (dummy_loc,pci,pargs,Anonymous)
+ | AliasLeaf ->
+ assert (l = []);
+ PatVar (dummy_loc, Anonymous) in
+ feed_history pat rh
+ | h -> h
+
+(* Builds a continuation expecting [n] arguments and building [ci] applied
+ to this [n] arguments *)
+
+let push_history_pattern n current cont =
+ Continuation (n, [], MakeAlias (current, cont))
+
+(* A pattern-matching problem has the following form:
+
+ env, isevars |- <pred> Cases tomatch of mat end
+
+ where tomatch is some sequence of "instructions" (t1 ... tn)
+
+ and mat is some matrix
+ (p11 ... p1n -> rhs1)
+ ( ... )
+ (pm1 ... pmn -> rhsm)
+
+ Terms to match: there are 3 kinds of instructions
+
+ - "Pushed" terms to match are typed in [env]; these are usually just
+ Rel(n) except for the initial terms given by user and typed in [env]
+ - "Abstract" instructions means an abstraction has to be inserted in the
+ current branch to build (this means a pattern has been detected dependent
+ in another one and generalisation is necessary to ensure well-typing)
+ - "Alias" instructions means an alias has to be inserted (this alias
+ is usually removed at the end, except when its type is not the
+ same as the type of the matched term from which it comes -
+ typically because the inductive types are "real" parameters)
+
+ Right-hand-sides:
+
+ They consist of a raw term to type in an environment specific to the
+ clause they belong to: the names of declarations are those of the
+ variables present in the patterns. Therefore, they come with their
+ own [rhs_env] (actually it is the same as [env] except for the names
+ of variables).
+
+*)
+type pattern_matching_problem =
+ { env : env;
+ isevars : Evd.evar_defs ref;
+ pred : predicate_signature option;
+ tomatch : tomatch_stack;
+ history : pattern_continuation;
+ mat : matrix;
+ caseloc : loc;
+ typing_function: type_constraint -> env -> rawconstr -> unsafe_judgment }
+
+(*--------------------------------------------------------------------------*
+ * A few functions to infer the inductive type from the patterns instead of *
+ * checking that the patterns correspond to the ind. type of the *
+ * destructurated object. Allows type inference of examples like *
+ * match n with O => true | _ => false end *
+ * match x in I with C => true | _ => false end *
+ *--------------------------------------------------------------------------*)
+
+(* Computing the inductive type from the matrix of patterns *)
+
+(* We use the "in I" clause to coerce the terms to match and otherwise
+ use the constructor to know in which type is the matching problem
+
+ Note that insertion of coercions inside nested patterns is done
+ each time the matrix is expanded *)
+
+let rec find_row_ind = function
+ [] -> None
+ | PatVar _ :: l -> find_row_ind l
+ | PatCstr(loc,c,_,_) :: _ -> Some (loc,c)
+
+let inductive_template isevars env tmloc ind =
+ let arsign = get_full_arity_sign env ind in
+ let hole_source = match tmloc with
+ | Some loc -> fun i -> (loc, Evd.TomatchTypeParameter (ind,i))
+ | None -> fun _ -> (dummy_loc, Evd.InternalHole) in
+ let (_,evarl,_) =
+ List.fold_right
+ (fun (na,b,ty) (subst,evarl,n) ->
+ match b with
+ | None ->
+ let ty' = substl subst ty in
+ let e = e_new_evar isevars env ~src:(hole_source n) ty' in
+ (e::subst,e::evarl,n+1)
+ | Some b ->
+ (b::subst,evarl,n+1))
+ arsign ([],[],1) in
+ applist (mkInd ind,List.rev evarl)
+
+
+(************************************************************************)
+(* Utils *)
+
+let mkExistential env ?(src=(dummy_loc,Evd.InternalHole)) isevars =
+ e_new_evar isevars env ~src:src (new_Type ())
+
+let evd_comb2 f isevars x y =
+ let (evd',y) = f !isevars x y in
+ isevars := evd';
+ y
+
+
+module Cases_F(Coercion : Coercion.S) : S = struct
+
+let inh_coerce_to_ind isevars env ty tyi =
+ let expected_typ = inductive_template isevars env None tyi in
+ (* devrait être indifférent d'exiger leq ou pas puisque pour
+ un inductif cela doit être égal *)
+ let _ = e_cumul env isevars expected_typ ty in ()
+
+let unify_tomatch_with_patterns isevars env loc typ pats =
+ match find_row_ind pats with
+ | None -> NotInd (None,typ)
+ | Some (_,(ind,_)) ->
+ inh_coerce_to_ind isevars env typ ind;
+ try IsInd (typ,find_rectype env (Evd.evars_of !isevars) typ)
+ with Not_found -> NotInd (None,typ)
+
+let find_tomatch_tycon isevars env loc = function
+ (* Try if some 'in I ...' is present and can be used as a constraint *)
+ | Some (_,ind,_,_) -> mk_tycon (inductive_template isevars env loc ind)
+ | None -> empty_tycon
+
+let coerce_row typing_fun isevars env pats (tomatch,(_,indopt)) =
+ let loc = Some (loc_of_rawconstr tomatch) in
+ let tycon = find_tomatch_tycon isevars env loc indopt in
+ let j = typing_fun tycon env tomatch in
+ let evd, j = Coercion.inh_coerce_to_base (loc_of_rawconstr tomatch) env !isevars j in
+ isevars := evd;
+ let typ = nf_evar (Evd.evars_of !isevars) j.uj_type in
+ let t =
+ try IsInd (typ,find_rectype env (Evd.evars_of !isevars) typ)
+ with Not_found ->
+ unify_tomatch_with_patterns isevars env loc typ pats in
+ (j.uj_val,t)
+
+let coerce_to_indtype typing_fun isevars env matx tomatchl =
+ let pats = List.map (fun r -> r.patterns) matx in
+ let matx' = match matrix_transpose pats with
+ | [] -> List.map (fun _ -> []) tomatchl (* no patterns at all *)
+ | m -> m in
+ List.map2 (coerce_row typing_fun isevars env) matx' tomatchl
+
+
+
+let adjust_tomatch_to_pattern pb ((current,typ),deps) =
+ (* Ideally, we could find a common inductive type to which both the
+ term to match and the patterns coerce *)
+ (* In practice, we coerce the term to match if it is not already an
+ inductive type and it is not dependent; moreover, we use only
+ the first pattern type and forget about the others *)
+ let typ = match typ with IsInd (t,_) -> t | NotInd (_,t) -> t in
+ let typ =
+ try IsInd (typ,find_rectype pb.env (Evd.evars_of !(pb.isevars)) typ)
+ with Not_found -> NotInd (None,typ) in
+ let tomatch = ((current,typ),deps) in
+ match typ with
+ | NotInd (None,typ) ->
+ let tm1 = List.map (fun eqn -> List.hd eqn.patterns) pb.mat in
+ (match find_row_ind tm1 with
+ | None -> tomatch
+ | Some (_,(ind,_)) ->
+ let indt = inductive_template pb.isevars pb.env None ind in
+ let current =
+ if deps = [] & isEvar typ then
+ (* Don't insert coercions if dependent; only solve evars *)
+ let _ = e_cumul pb.env pb.isevars indt typ in
+ current
+ else
+ (evd_comb2 (Coercion.inh_conv_coerce_to dummy_loc pb.env)
+ pb.isevars (make_judge current typ) (mk_tycon_type indt)).uj_val in
+ let sigma = Evd.evars_of !(pb.isevars) in
+ let typ = IsInd (indt,find_rectype pb.env sigma indt) in
+ ((current,typ),deps))
+ | _ -> tomatch
+
+ (* extract some ind from [t], possibly coercing from constructors in [tm] *)
+let to_mutind env isevars tm c t =
+(* match c with
+ | Some body -> *) NotInd (c,t)
+(* | None -> unify_tomatch_with_patterns isevars env t tm*)
+
+let type_of_tomatch = function
+ | IsInd (t,_) -> t
+ | NotInd (_,t) -> t
+
+let mkDeclTomatch na = function
+ | IsInd (t,_) -> (na,None,t)
+ | NotInd (c,t) -> (na,c,t)
+
+let map_tomatch_type f = function
+ | IsInd (t,ind) -> IsInd (f t,map_inductive_type f ind)
+ | NotInd (c,t) -> NotInd (option_map f c, f t)
+
+let liftn_tomatch_type n depth = map_tomatch_type (liftn n depth)
+let lift_tomatch_type n = liftn_tomatch_type n 1
+
+let lift_tomatch n ((current,typ),info) =
+ ((lift n current,lift_tomatch_type n typ),info)
+
+(**********************************************************************)
+(* Utilities on patterns *)
+
+let current_pattern eqn =
+ match eqn.patterns with
+ | pat::_ -> pat
+ | [] -> anomaly "Empty list of patterns"
+
+let alias_of_pat = function
+ | PatVar (_,name) -> name
+ | PatCstr(_,_,_,name) -> name
+
+let unalias_pat = function
+ | PatVar (c,name) as p ->
+ if name = Anonymous then p else PatVar (c,Anonymous)
+ | PatCstr(a,b,c,name) as p ->
+ if name = Anonymous then p else PatCstr (a,b,c,Anonymous)
+
+let remove_current_pattern eqn =
+ match eqn.patterns with
+ | pat::pats ->
+ { eqn with
+ patterns = pats;
+ alias_stack = alias_of_pat pat :: eqn.alias_stack }
+ | [] -> anomaly "Empty list of patterns"
+
+let prepend_pattern tms eqn = {eqn with patterns = tms@eqn.patterns }
+
+(**********************************************************************)
+(* Dealing with regular and default patterns *)
+let is_regular eqn = eqn.tag = RegularPat
+
+let lower_pattern_status = function
+ | RegularPat -> DefaultPat 0
+ | DefaultPat n -> DefaultPat (n+1)
+
+let pattern_status pats =
+ if array_exists ((=) RegularPat) pats then RegularPat
+ else
+ let min =
+ Array.fold_right
+ (fun pat n -> match pat with
+ | DefaultPat i when i<n -> i
+ | _ -> n)
+ pats 0 in
+ DefaultPat min
+
+(**********************************************************************)
+(* Well-formedness tests *)
+(* Partial check on patterns *)
+
+exception NotAdjustable
+
+let rec adjust_local_defs loc = function
+ | (pat :: pats, (_,None,_) :: decls) ->
+ pat :: adjust_local_defs loc (pats,decls)
+ | (pats, (_,Some _,_) :: decls) ->
+ PatVar (loc, Anonymous) :: adjust_local_defs loc (pats,decls)
+ | [], [] -> []
+ | _ -> raise NotAdjustable
+
+let check_and_adjust_constructor env ind cstrs = function
+ | PatVar _ as pat -> pat
+ | PatCstr (loc,((_,i) as cstr),args,alias) as pat ->
+ (* Check it is constructor of the right type *)
+ let ind' = inductive_of_constructor cstr in
+ if Closure.mind_equiv env ind' ind then
+ (* Check the constructor has the right number of args *)
+ let ci = cstrs.(i-1) in
+ let nb_args_constr = ci.cs_nargs in
+ if List.length args = nb_args_constr then pat
+ else
+ try
+ let args' = adjust_local_defs loc (args, List.rev ci.cs_args)
+ in PatCstr (loc, cstr, args', alias)
+ with NotAdjustable ->
+ error_wrong_numarg_constructor_loc loc (Global.env())
+ cstr nb_args_constr
+ else
+ (* Try to insert a coercion *)
+ try
+ Coercion.inh_pattern_coerce_to loc pat ind' ind
+ with Not_found ->
+ error_bad_constructor_loc loc cstr ind
+
+let check_all_variables typ mat =
+ List.iter
+ (fun eqn -> match current_pattern eqn with
+ | PatVar (_,id) -> ()
+ | PatCstr (loc,cstr_sp,_,_) ->
+ error_bad_pattern_loc loc cstr_sp typ)
+ mat
+
+let check_unused_pattern env eqn =
+ if not !(eqn.used) then
+ raise_pattern_matching_error
+ (eqn.eqn_loc, env, UnusedClause eqn.patterns)
+
+let set_used_pattern eqn = eqn.used := true
+
+let extract_rhs pb =
+ match pb.mat with
+ | [] -> errorlabstrm "build_leaf" (mssg_may_need_inversion())
+ | eqn::_ ->
+ set_used_pattern eqn;
+ eqn.tag, eqn.rhs
+
+(**********************************************************************)
+(* Functions to deal with matrix factorization *)
+
+let occur_in_rhs na rhs =
+ match na with
+ | Anonymous -> false
+ | Name id -> occur_rawconstr id rhs.it
+
+let is_dep_patt eqn = function
+ | PatVar (_,name) -> occur_in_rhs name eqn.rhs
+ | PatCstr _ -> true
+
+let dependencies_in_rhs nargs eqns =
+ if eqns = [] then list_tabulate (fun _ -> false) nargs (* Only "_" patts *)
+ else
+ let deps = List.map (fun (tms,eqn) -> List.map (is_dep_patt eqn) tms) eqns in
+ let columns = matrix_transpose deps in
+ List.map (List.exists ((=) true)) columns
+
+let dependent_decl a = function
+ | (na,None,t) -> dependent a t
+ | (na,Some c,t) -> dependent a t || dependent a c
+
+(* Computing the matrix of dependencies *)
+
+(* We are in context d1...dn |- and [find_dependencies k 1 nextlist]
+ computes for declaration [k+1] in which of declarations in
+ [nextlist] (which corresponds to d(k+2)...dn) it depends;
+ declarations are expressed by index, e.g. in dependency list
+ [n-2;1], [1] points to [dn] and [n-2] to [d3] *)
+
+let rec find_dependency_list k n = function
+ | [] -> []
+ | (used,tdeps,d)::rest ->
+ let deps = find_dependency_list k (n+1) rest in
+ if used && dependent_decl (mkRel n) d
+ then list_add_set (List.length rest + 1) (list_union deps tdeps)
+ else deps
+
+let find_dependencies is_dep_or_cstr_in_rhs d (k,nextlist) =
+ let deps = find_dependency_list k 1 nextlist in
+ if is_dep_or_cstr_in_rhs || deps <> []
+ then (k-1,(true ,deps,d)::nextlist)
+ else (k-1,(false,[] ,d)::nextlist)
+
+let find_dependencies_signature deps_in_rhs typs =
+ let k = List.length deps_in_rhs in
+ let _,l = List.fold_right2 find_dependencies deps_in_rhs typs (k,[]) in
+ List.map (fun (_,deps,_) -> deps) l
+
+(******)
+
+(* A Pushed term to match has just been substituted by some
+ constructor t = (ci x1...xn) and the terms x1 ... xn have been added to
+ match
+
+ - all terms to match and to push (dependent on t by definition)
+ must have (Rel depth) substituted by t and Rel's>depth lifted by n
+ - all pushed terms to match (non dependent on t by definition) must
+ be lifted by n
+
+ We start with depth=1
+*)
+
+let regeneralize_index_tomatch n =
+ let rec genrec depth = function
+ | [] -> []
+ | Pushed ((c,tm),l)::rest ->
+ let c = regeneralize_index n depth c in
+ let tm = map_tomatch_type (regeneralize_index n depth) tm in
+ let l = List.map (regeneralize_rel n depth) l in
+ Pushed ((c,tm),l)::(genrec depth rest)
+ | Alias (c1,c2,d,t)::rest ->
+ Alias (regeneralize_index n depth c1,c2,d,t)::(genrec depth rest)
+ | Abstract d::rest ->
+ Abstract (map_rel_declaration (regeneralize_index n depth) d)
+ ::(genrec (depth+1) rest) in
+ genrec 0
+
+let rec replace_term n c k t =
+ if t = mkRel (n+k) then lift k c
+ else map_constr_with_binders succ (replace_term n c) k t
+
+let replace_tomatch n c =
+ let rec replrec depth = function
+ | [] -> []
+ | Pushed ((b,tm),l)::rest ->
+ let b = replace_term n c depth b in
+ let tm = map_tomatch_type (replace_term n c depth) tm in
+ List.iter (fun i -> if i=n+depth then anomaly "replace_tomatch") l;
+ Pushed ((b,tm),l)::(replrec depth rest)
+ | Alias (c1,c2,d,t)::rest ->
+ Alias (replace_term n c depth c1,c2,d,t)::(replrec depth rest)
+ | Abstract d::rest ->
+ Abstract (map_rel_declaration (replace_term n c depth) d)
+ ::(replrec (depth+1) rest) in
+ replrec 0
+
+let liftn_rel_declaration n k = map_rel_declaration (liftn n k)
+let substnl_rel_declaration sigma k = map_rel_declaration (substnl sigma k)
+
+let rec liftn_tomatch_stack n depth = function
+ | [] -> []
+ | Pushed ((c,tm),l)::rest ->
+ let c = liftn n depth c in
+ let tm = liftn_tomatch_type n depth tm in
+ let l = List.map (fun i -> if i<depth then i else i+n) l in
+ Pushed ((c,tm),l)::(liftn_tomatch_stack n depth rest)
+ | Alias (c1,c2,d,t)::rest ->
+ Alias (liftn n depth c1,liftn n depth c2,d,liftn n depth t)
+ ::(liftn_tomatch_stack n depth rest)
+ | Abstract d::rest ->
+ Abstract (map_rel_declaration (liftn n depth) d)
+ ::(liftn_tomatch_stack n (depth+1) rest)
+
+
+let lift_tomatch_stack n = liftn_tomatch_stack n 1
+
+(* if [current] has type [I(p1...pn u1...um)] and we consider the case
+ of constructor [ci] of type [I(p1...pn u'1...u'm)], then the
+ default variable [name] is expected to have which type?
+ Rem: [current] is [(Rel i)] except perhaps for initial terms to match *)
+
+(************************************************************************)
+(* Some heuristics to get names for variables pushed in pb environment *)
+(* Typical requirement:
+
+ [match y with (S (S x)) => x | x => x end] should be compiled into
+ [match y with O => y | (S n) => match n with O => y | (S x) => x end end]
+
+ and [match y with (S (S n)) => n | n => n end] into
+ [match y with O => y | (S n0) => match n0 with O => y | (S n) => n end end]
+
+ i.e. user names should be preserved and created names should not
+ interfere with user names *)
+
+let merge_name get_name obj = function
+ | Anonymous -> get_name obj
+ | na -> na
+
+let merge_names get_name = List.map2 (merge_name get_name)
+
+let get_names env sign eqns =
+ let names1 = list_tabulate (fun _ -> Anonymous) (List.length sign) in
+ (* If any, we prefer names used in pats, from top to bottom *)
+ let names2 =
+ List.fold_right
+ (fun (pats,eqn) names -> merge_names alias_of_pat pats names)
+ eqns names1 in
+ (* Otherwise, we take names from the parameters of the constructor but
+ avoiding conflicts with user ids *)
+ let allvars =
+ List.fold_left (fun l (_,eqn) -> list_union l eqn.rhs.avoid_ids) [] eqns in
+ let names4,_ =
+ List.fold_left2
+ (fun (l,avoid) d na ->
+ let na =
+ merge_name
+ (fun (na,_,t) -> Name (next_name_away (named_hd env t na) avoid))
+ d na
+ in
+ (na::l,(out_name na)::avoid))
+ ([],allvars) (List.rev sign) names2 in
+ names4
+
+(************************************************************************)
+(* Recovering names for variables pushed to the rhs' environment *)
+
+let recover_alias_names get_name = List.map2 (fun x (_,c,t) ->(get_name x,c,t))
+
+let all_name sign = List.map (fun (n, b, t) -> let n = match n with Name _ -> n | Anonymous -> Name (id_of_string "Anonymous") in
+ (n, b, t)) sign
+
+let push_rels_eqn sign eqn =
+ let sign = all_name sign in
+(* trace (str "push_rels_eqn: " ++ my_print_rel_context eqn.rhs.rhs_env sign ++ str "end"); *)
+(* str " branch is " ++ my_print_constr (fst eqn.rhs.c_orig) (snd eqn.rhs.c_orig)); *)
+(* let rhs = eqn.rhs in *)
+(* let l, c, s, e = *)
+(* List.fold_right *)
+(* (fun (na, c, t) (itlift, it, sign, env) -> *)
+(* (try trace (str "Pushing decl: " ++ pr_rel_decl env (na, c, t) ++ *)
+(* str " lift is " ++ int itlift); *)
+(* with _ -> trace (str "error in push_rels_eqn")); *)
+(* let env' = push_rel (na, c, t) env in *)
+(* match sign with *)
+(* [] -> (itlift, lift 1 it, sign, env') *)
+(* | (na', c, t) :: sign' -> *)
+(* if na' = na then *)
+(* (pred itlift, it, sign', env') *)
+(* else ( *)
+(* trace (str "skipping it"); *)
+(* (itlift, liftn 1 itlift it, sign, env'))) *)
+(* sign (rhs.rhs_lift, rhs.c_it, eqn.rhs.rhs_sign, eqn.rhs.rhs_env) *)
+(* in *)
+ {eqn with rhs = {eqn.rhs with rhs_env = push_rels sign eqn.rhs.rhs_env; } }
+
+let push_rels_eqn_with_names sign eqn =
+ let pats = List.rev (list_firstn (List.length sign) eqn.patterns) in
+ let sign = recover_alias_names alias_of_pat pats sign in
+ push_rels_eqn sign eqn
+
+let build_aliases_context env sigma names allpats pats =
+ (* pats is the list of bodies to push as an alias *)
+ (* They all are defined in env and we turn them into a sign *)
+ (* cuts in sign need to be done in allpats *)
+ let rec insert env sign1 sign2 n newallpats oldallpats = function
+ | (deppat,_,_,_)::pats, Anonymous::names when not (isRel deppat) ->
+ (* Anonymous leaves must be considered named and treated in the *)
+ (* next clause because they may occur in implicit arguments *)
+ insert env sign1 sign2
+ n newallpats (List.map List.tl oldallpats) (pats,names)
+ | (deppat,nondeppat,d,t)::pats, na::names ->
+ let nondeppat = lift n nondeppat in
+ let deppat = lift n deppat in
+ let newallpats =
+ List.map2 (fun l1 l2 -> List.hd l2::l1) newallpats oldallpats in
+ let oldallpats = List.map List.tl oldallpats in
+ let decl = (na,Some deppat,t) in
+ let a = (deppat,nondeppat,d,t) in
+ insert (push_rel decl env) (decl::sign1) ((na,a)::sign2) (n+1)
+ newallpats oldallpats (pats,names)
+ | [], [] -> newallpats, sign1, sign2, env
+ | _ -> anomaly "Inconsistent alias and name lists" in
+ let allpats = List.map (fun x -> [x]) allpats
+ in insert env [] [] 0 (List.map (fun _ -> []) allpats) allpats (pats, names)
+
+let insert_aliases_eqn sign eqnnames alias_rest eqn =
+ let thissign = List.map2 (fun na (_,c,t) -> (na,c,t)) eqnnames sign in
+ push_rels_eqn thissign { eqn with alias_stack = alias_rest; }
+
+
+let insert_aliases env sigma alias eqns =
+ (* Là, y a une faiblesse, si un alias est utilisé dans un cas par *)
+ (* défaut présent mais inutile, ce qui est le cas général, l'alias *)
+ (* est introduit même s'il n'est pas utilisé dans les cas réguliers *)
+ let eqnsnames = List.map (fun eqn -> List.hd eqn.alias_stack) eqns in
+ let alias_rests = List.map (fun eqn -> List.tl eqn.alias_stack) eqns in
+ (* names2 takes the meet of all needed aliases *)
+ let names2 =
+ List.fold_right (merge_name (fun x -> x)) eqnsnames Anonymous in
+ (* Only needed aliases are kept by build_aliases_context *)
+ let eqnsnames, sign1, sign2, env =
+ build_aliases_context env sigma [names2] eqnsnames [alias] in
+ let eqns = list_map3 (insert_aliases_eqn sign1) eqnsnames alias_rests eqns in
+ sign2, env, eqns
+
+(**********************************************************************)
+(* Functions to deal with elimination predicate *)
+
+exception Occur
+let noccur_between_without_evar n m term =
+ let rec occur_rec n c = match kind_of_term c with
+ | Rel p -> if n<=p && p<n+m then raise Occur
+ | Evar (_,cl) -> ()
+ | _ -> iter_constr_with_binders succ occur_rec n c
+ in
+ try occur_rec n term; true with Occur -> false
+
+(* Inferring the predicate *)
+let prepare_unif_pb typ cs =
+ let n = List.length (assums_of_rel_context cs.cs_args) in
+
+ (* We may need to invert ci if its parameters occur in typ *)
+ let typ' =
+ if noccur_between_without_evar 1 n typ then lift (-n) typ
+ else (* TODO4-1 *)
+ error "Unable to infer return clause of this pattern-matching problem" in
+ let args = extended_rel_list (-n) cs.cs_args in
+ let ci = applist (mkConstruct cs.cs_cstr, cs.cs_params@args) in
+
+ (* This is the problem: finding P s.t. cs_args |- (P realargs ci) = typ' *)
+ (Array.map (lift (-n)) cs.cs_concl_realargs, ci, typ')
+
+
+(* Infering the predicate *)
+(*
+The problem to solve is the following:
+
+We match Gamma |- t : I(u01..u0q) against the following constructors:
+
+ Gamma, x11...x1p1 |- C1(x11..x1p1) : I(u11..u1q)
+ ...
+ Gamma, xn1...xnpn |- Cn(xn1..xnp1) : I(un1..unq)
+
+Assume the types in the branches are the following
+
+ Gamma, x11...x1p1 |- branch1 : T1
+ ...
+ Gamma, xn1...xnpn |- branchn : Tn
+
+Assume the type of the global case expression is Gamma |- T
+
+The predicate has the form phi = [y1..yq][z:I(y1..yq)]? and must satisfy
+the following n+1 equations:
+
+ Gamma, x11...x1p1 |- (phi u11..u1q (C1 x11..x1p1)) = T1
+ ...
+ Gamma, xn1...xnpn |- (phi un1..unq (Cn xn1..xnpn)) = Tn
+ Gamma |- (phi u01..u0q t) = T
+
+Some hints:
+
+- Clearly, if xij occurs in Ti, then, a "match z with (Ci xi1..xipi) => ..."
+ should be inserted somewhere in Ti.
+
+- If T is undefined, an easy solution is to insert a "match z with (Ci
+ xi1..xipi) => ..." in front of each Ti
+
+- Otherwise, T1..Tn and T must be step by step unified, if some of them
+ diverge, then try to replace the diverging subterm by one of y1..yq or z.
+
+- The main problem is what to do when an existential variables is encountered
+
+let prepare_unif_pb typ cs =
+ let n = cs.cs_nargs in
+ let _,p = decompose_prod_n n typ in
+ let ci = build_dependent_constructor cs in
+ (* This is the problem: finding P s.t. cs_args |- (P realargs ci) = p *)
+ (n, cs.cs_concl_realargs, ci, p)
+
+let eq_operator_lift k (n,n') = function
+ | OpRel p, OpRel p' when p > k & p' > k ->
+ if p < k+n or p' < k+n' then false else p - n = p' - n'
+ | op, op' -> op = op'
+
+let rec transpose_args n =
+ if n=0 then []
+ else
+ (Array.map (fun l -> List.hd l) lv)::
+ (transpose_args (m-1) (Array.init (fun l -> List.tl l)))
+
+let shift_operator k = function OpLambda _ | OpProd _ -> k+1 | _ -> k
+
+let reloc_operator (k,n) = function OpRel p when p > k ->
+let rec unify_clauses k pv =
+ let pv'= Array.map (fun (n,sign,_,p) -> n,splay_constr (whd_betaiotaevar (push_rels (List.rev sign) env) (Evd.evars_of isevars)) p) pv in
+ let n1,op1 = let (n1,(op1,args1)) = pv'.(0) in n1,op1 in
+ if Array.for_all (fun (ni,(opi,_)) -> eq_operator_lift k (n1,ni) (op1,opi)) pv'
+ then
+ let argvl = transpose_args (List.length args1) pv' in
+ let k' = shift_operator k op1 in
+ let argl = List.map (unify_clauses k') argvl in
+ gather_constr (reloc_operator (k,n1) op1) argl
+*)
+
+let abstract_conclusion typ cs =
+ let n = List.length (assums_of_rel_context cs.cs_args) in
+ let (sign,p) = decompose_prod_n n typ in
+ lam_it p sign
+
+let infer_predicate loc env isevars typs cstrs indf =
+ (* Il faudra substituer les isevars a un certain moment *)
+ if Array.length cstrs = 0 then (* "TODO4-3" *)
+ error "Inference of annotation for empty inductive types not implemented"
+ else
+ (* Empiric normalization: p may depend in a irrelevant way on args of the*)
+ (* cstr as in [c:{_:Alpha & Beta}] match c with (existS a b)=>(a,b) end *)
+ let typs =
+ Array.map (local_strong (whd_betaevar empty_env (Evd.evars_of !isevars))) typs
+ in
+ let eqns = array_map2 prepare_unif_pb typs cstrs in
+ (* First strategy: no dependencies at all *)
+(*
+ let (mis,_) = dest_ind_family indf in
+ let (cclargs,_,typn) = eqns.(mis_nconstr mis -1) in
+*)
+ let (sign,_) = get_arity env indf in
+ let mtyp =
+ if array_exists is_Type typs then
+ (* Heuristic to avoid comparison between non-variables algebric univs*)
+ new_Type ()
+ else
+ mkExistential env ~src:(loc, Evd.CasesType) isevars
+ in
+ if array_for_all (fun (_,_,typ) -> e_cumul env isevars typ mtyp) eqns
+ then
+ (* Non dependent case -> turn it into a (dummy) dependent one *)
+ let sign = (Anonymous,None,build_dependent_inductive env indf)::sign in
+ let pred = it_mkLambda_or_LetIn (lift (List.length sign) mtyp) sign in
+ (true,pred) (* true = dependent -- par défaut *)
+ else
+(*
+ let s = get_sort_of env (evars_of isevars) typs.(0) in
+ let predpred = it_mkLambda_or_LetIn (mkSort s) sign in
+ let caseinfo = make_default_case_info mis in
+ let brs = array_map2 abstract_conclusion typs cstrs in
+ let predbody = mkCase (caseinfo, (nf_betaiota predpred), mkRel 1, brs) in
+ let pred = it_mkLambda_or_LetIn (lift (List.length sign) mtyp) sign in
+*)
+ (* "TODO4-2" *)
+ (* We skip parameters *)
+ let cis =
+ Array.map
+ (fun cs ->
+ applist (mkConstruct cs.cs_cstr, extended_rel_list 0 cs.cs_args))
+ cstrs in
+ let ct = array_map2 (fun ci (_,_,t) -> (ci,t)) cis eqns in
+ raise_pattern_matching_error (loc,env, CannotInferPredicate ct)
+(*
+ (true,pred)
+*)
+
+(* Propagation of user-provided predicate through compilation steps *)
+
+let rec map_predicate f k = function
+ | PrCcl ccl -> PrCcl (f k ccl)
+ | PrProd pred ->
+ PrProd (map_predicate f (k+1) pred)
+ | PrLetIn ((names,dep as tm),pred) ->
+ let k' = List.length names + (if dep<>Anonymous then 1 else 0) in
+ PrLetIn (tm, map_predicate f (k+k') pred)
+
+let rec noccurn_predicate k = function
+ | PrCcl ccl -> noccurn k ccl
+ | PrProd pred -> noccurn_predicate (k+1) pred
+ | PrLetIn ((names,dep),pred) ->
+ let k' = List.length names + (if dep<>Anonymous then 1 else 0) in
+ noccurn_predicate (k+k') pred
+
+let liftn_predicate n = map_predicate (liftn n)
+
+let lift_predicate n = liftn_predicate n 1
+
+let regeneralize_index_predicate n = map_predicate (regeneralize_index n) 0
+
+let substnl_predicate sigma = map_predicate (substnl sigma)
+
+(* This is parallel bindings *)
+let subst_predicate (args,copt) pred =
+ let sigma = match copt with
+ | None -> List.rev args
+ | Some c -> c::(List.rev args) in
+ substnl_predicate sigma 0 pred
+
+let specialize_predicate_var (cur,typ) = function
+ | PrProd _ | PrCcl _ ->
+ anomaly "specialize_predicate_var: a pattern-variable must be pushed"
+ | PrLetIn (([],dep),pred) ->
+ subst_predicate ([],if dep<>Anonymous then Some cur else None) pred
+ | PrLetIn ((_,dep),pred) ->
+ (match typ with
+ | IsInd (_,IndType (_,realargs)) ->
+ subst_predicate (realargs,if dep<>Anonymous then Some cur else None) pred
+ | _ -> anomaly "specialize_predicate_var")
+
+let ungeneralize_predicate = function
+ | PrLetIn _ | PrCcl _ -> anomaly "ungeneralize_predicate: expects a product"
+ | PrProd pred -> pred
+
+(*****************************************************************************)
+(* We have pred = [X:=realargs;x:=c]P typed in Gamma1, x:I(realargs), Gamma2 *)
+(* and we want to abstract P over y:t(x) typed in the same context to get *)
+(* *)
+(* pred' = [X:=realargs;x':=c](y':t(x'))P[y:=y'] *)
+(* *)
+(* We first need to lift t(x) s.t. it is typed in Gamma, X:=rargs, x' *)
+(* then we have to replace x by x' in t(x) and y by y' in P *)
+(*****************************************************************************)
+let generalize_predicate ny d = function
+ | PrLetIn ((names,dep as tm),pred) ->
+ if dep=Anonymous then anomaly "Undetected dependency";
+ let p = List.length names + 1 in
+ let pred = lift_predicate 1 pred in
+ let pred = regeneralize_index_predicate (ny+p+1) pred in
+ PrLetIn (tm, PrProd pred)
+ | PrProd _ | PrCcl _ ->
+ anomaly "generalize_predicate: expects a non trivial pattern"
+
+let rec extract_predicate l = function
+ | pred, Alias (deppat,nondeppat,_,_)::tms ->
+ let tms' = match kind_of_term nondeppat with
+ | Rel i -> replace_tomatch i deppat tms
+ | _ -> (* initial terms are not dependent *) tms in
+ extract_predicate l (pred,tms')
+ | PrProd pred, Abstract d'::tms ->
+ let d' = map_rel_declaration (lift (List.length l)) d' in
+ substl l (mkProd_or_LetIn d' (extract_predicate [] (pred,tms)))
+ | PrLetIn (([],dep),pred), Pushed ((cur,_),_)::tms ->
+ extract_predicate (if dep<>Anonymous then cur::l else l) (pred,tms)
+ | PrLetIn ((_,dep),pred), Pushed ((cur,IsInd (_,(IndType(_,realargs)))),_)::tms ->
+ let l = List.rev realargs@l in
+ extract_predicate (if dep<>Anonymous then cur::l else l) (pred,tms)
+ | PrCcl ccl, [] ->
+ substl l ccl
+ | _ -> anomaly"extract_predicate: predicate inconsistent with terms to match"
+
+let abstract_predicate env sigma indf cur tms = function
+ | (PrProd _ | PrCcl _) -> anomaly "abstract_predicate: must be some LetIn"
+ | PrLetIn ((names,dep),pred) ->
+ let sign = make_arity_signature env true indf in
+ (* n is the number of real args + 1 *)
+ let n = List.length sign in
+ let tms = lift_tomatch_stack n tms in
+ let tms =
+ match kind_of_term cur with
+ | Rel i -> regeneralize_index_tomatch (i+n) tms
+ | _ -> (* Initial case *) tms in
+ (* Depending on whether the predicate is dependent or not, and has real
+ args or not, we lift it to make room for [sign] *)
+ (* Even if not intrinsically dep, we move the predicate into a dep one *)
+ let sign,k =
+ if names = [] & n <> 1 then
+ (* Real args were not considered *)
+ (if dep<>Anonymous then
+ ((let (_,c,t) = List.hd sign in (dep,c,t)::List.tl sign),n-1)
+ else
+ (sign,n))
+ else
+ (* Real args are OK *)
+ (List.map2 (fun na (_,c,t) -> (na,c,t)) (dep::names) sign,
+ if dep<>Anonymous then 0 else 1) in
+ let pred = lift_predicate k pred in
+ let pred = extract_predicate [] (pred,tms) in
+ (true, it_mkLambda_or_LetIn_name env pred sign)
+
+let rec known_dependent = function
+ | None -> false
+ | Some (PrLetIn ((_,dep),_)) -> dep<>Anonymous
+ | Some (PrCcl _) -> false
+ | Some (PrProd _) ->
+ anomaly "known_dependent: can only be used when patterns remain"
+
+(* [expand_arg] is used by [specialize_predicate]
+ it replaces gamma, x1...xn, x1...xk |- pred
+ by gamma, x1...xn, x1...xk-1 |- [X=realargs,xk=xk]pred (if dep) or
+ by gamma, x1...xn, x1...xk-1 |- [X=realargs]pred (if not dep) *)
+
+let expand_arg n alreadydep (na,t) deps (k,pred) =
+ (* current can occur in pred even if the original problem is not dependent *)
+ let dep =
+ if alreadydep<>Anonymous then alreadydep
+ else if deps = [] && noccurn_predicate 1 pred then Anonymous
+ else Name (id_of_string "x") in
+ let pred = if dep<>Anonymous then pred else lift_predicate (-1) pred in
+ (* There is no dependency in realargs for subpattern *)
+ (k-1, PrLetIn (([],dep), pred))
+
+
+(*****************************************************************************)
+(* pred = [X:=realargs;x:=c]P types the following problem: *)
+(* *)
+(* Gamma |- match Pushed(c:I(realargs)) rest with...end: pred *)
+(* *)
+(* where the branch with constructor Ci:(x1:T1)...(xn:Tn)->I(realargsi) *)
+(* is considered. Assume each Ti is some Ii(argsi). *)
+(* We let e=Ci(x1,...,xn) and replace pred by *)
+(* *)
+(* pred' = [X1:=rargs1,x1:=x1']...[Xn:=rargsn,xn:=xn'](P[X:=realargsi;x:=e]) *)
+(* *)
+(* s.t Gamma,x1'..xn' |- match Pushed(x1')..Pushed(xn') rest with..end :pred'*)
+(* *)
+(*****************************************************************************)
+let specialize_predicate tomatchs deps cs = function
+ | (PrProd _ | PrCcl _) ->
+ anomaly "specialize_predicate: a matched pattern must be pushed"
+ | PrLetIn ((names,isdep),pred) ->
+ (* Assume some gamma st: gamma, (X,x:=realargs,copt) |- pred *)
+ let nrealargs = List.length names in
+ let k = nrealargs + (if isdep<>Anonymous then 1 else 0) in
+ (* We adjust pred st: gamma, x1..xn, (X,x:=realargs,copt) |- pred' *)
+ let n = cs.cs_nargs in
+ let pred' = liftn_predicate n (k+1) pred in
+ let argsi = if nrealargs <> 0 then Array.to_list cs.cs_concl_realargs else [] in
+ let copti = if isdep<>Anonymous then Some (build_dependent_constructor cs) else None in
+ (* The substituends argsi, copti are all defined in gamma, x1...xn *)
+ (* We need _parallel_ bindings to get gamma, x1...xn |- pred'' *)
+ let pred'' = subst_predicate (argsi, copti) pred' in
+ (* We adjust pred st: gamma, x1..xn, x1..xn |- pred'' *)
+ let pred''' = liftn_predicate n (n+1) pred'' in
+ (* We finally get gamma,x1..xn |- [X1,x1:=R1,x1]..[Xn,xn:=Rn,xn]pred'''*)
+ snd (List.fold_right2 (expand_arg n isdep) tomatchs deps (n,pred'''))
+
+let find_predicate loc env isevars p typs cstrs current
+ (IndType (indf,realargs)) tms =
+ let (dep,pred) =
+ match p with
+ | Some p -> abstract_predicate env (Evd.evars_of !isevars) indf current tms p
+ | None -> infer_predicate loc env isevars typs cstrs indf in
+ let typ = whd_beta (applist (pred, realargs)) in
+ if dep then
+ (pred, whd_beta (applist (typ, [current])), new_Type ())
+ else
+ (pred, typ, new_Type ())
+
+(************************************************************************)
+(* Sorting equations by constructor *)
+
+type inversion_problem =
+ (* the discriminating arg in some Ind and its order in Ind *)
+ | Incompatible of int * (int * int)
+ | Constraints of (int * constr) list
+
+let solve_constraints constr_info indt =
+ (* TODO *)
+ Constraints []
+
+let rec irrefutable env = function
+ | PatVar (_,name) -> true
+ | PatCstr (_,cstr,args,_) ->
+ let ind = inductive_of_constructor cstr in
+ let (_,mip) = Inductive.lookup_mind_specif env ind in
+ let one_constr = Array.length mip.mind_user_lc = 1 in
+ one_constr & List.for_all (irrefutable env) args
+
+let first_clause_irrefutable env = function
+ | eqn::mat -> List.for_all (irrefutable env) eqn.patterns
+ | _ -> false
+
+let group_equations pb ind current cstrs mat =
+ let mat =
+ if first_clause_irrefutable pb.env mat then [List.hd mat] else mat in
+ let brs = Array.create (Array.length cstrs) [] in
+ let only_default = ref true in
+ let _ =
+ List.fold_right (* To be sure it's from bottom to top *)
+ (fun eqn () ->
+ let rest = remove_current_pattern eqn in
+ let pat = current_pattern eqn in
+ match check_and_adjust_constructor pb.env ind cstrs pat with
+ | PatVar (_,name) ->
+ (* This is a default clause that we expand *)
+ for i=1 to Array.length cstrs do
+ let n = cstrs.(i-1).cs_nargs in
+ let args = make_anonymous_patvars n in
+ let rest = {rest with tag = lower_pattern_status rest.tag } in
+ brs.(i-1) <- (args, rest) :: brs.(i-1)
+ done
+ | PatCstr (loc,((_,i)),args,_) ->
+ (* This is a regular clause *)
+ only_default := false;
+ brs.(i-1) <- (args,rest) :: brs.(i-1)) mat () in
+ (brs,!only_default)
+
+(************************************************************************)
+(* Here starts the pattern-matching compilation algorithm *)
+
+(* Abstracting over dependent subterms to match *)
+let rec generalize_problem pb = function
+ | [] -> pb
+ | i::l ->
+ let d = map_rel_declaration (lift i) (Environ.lookup_rel i pb.env) in
+ let pb' = generalize_problem pb l in
+ let tomatch = lift_tomatch_stack 1 pb'.tomatch in
+ let tomatch = regeneralize_index_tomatch (i+1) tomatch in
+ { pb with
+ tomatch = Abstract d :: tomatch;
+ pred = option_map (generalize_predicate i d) pb'.pred }
+
+(* No more patterns: typing the right-hand-side of equations *)
+let build_leaf pb =
+ let tag, rhs = extract_rhs pb in
+ let tycon = match pb.pred with
+ | None -> anomaly "Predicate not found"
+ | Some (PrCcl typ) -> mk_tycon typ
+ | Some _ -> anomaly "not all parameters of pred have been consumed" in
+ tag, pb.typing_function tycon rhs.rhs_env rhs.it
+
+(* Building the sub-problem when all patterns are variables *)
+let shift_problem (current,t) pb =
+ {pb with
+ tomatch = Alias (current,current,NonDepAlias,type_of_tomatch t)::pb.tomatch;
+ pred = option_map (specialize_predicate_var (current,t)) pb.pred;
+ history = push_history_pattern 0 AliasLeaf pb.history;
+ mat = List.map remove_current_pattern pb.mat }
+
+(* Building the sub-pattern-matching problem for a given branch *)
+let build_branch current deps pb eqns const_info =
+ (* We remember that we descend through a constructor *)
+ let alias_type =
+ if Array.length const_info.cs_concl_realargs = 0
+ & not (known_dependent pb.pred) & deps = []
+ then
+ NonDepAlias
+ else
+ DepAlias
+ in
+ let history =
+ push_history_pattern const_info.cs_nargs
+ (AliasConstructor const_info.cs_cstr)
+ pb.history in
+
+ (* We find matching clauses *)
+ let cs_args = (*assums_of_rel_context*) const_info.cs_args in
+ let names = get_names pb.env cs_args eqns in
+ let submat = List.map (fun (tms,eqn) -> prepend_pattern tms eqn) eqns in
+ if submat = [] then
+ raise_pattern_matching_error
+ (dummy_loc, pb.env, NonExhaustive (complete_history history));
+ let typs = List.map2 (fun (_,c,t) na -> (na,c,t)) cs_args names in
+ let _,typs',_ =
+ List.fold_right
+ (fun (na,c,t as d) (env,typs,tms) ->
+ let tm1 = List.map List.hd tms in
+ let tms = List.map List.tl tms in
+ (push_rel d env, (na,to_mutind env pb.isevars tm1 c t)::typs,tms))
+ typs (pb.env,[],List.map fst eqns) in
+
+ let dep_sign =
+ find_dependencies_signature
+ (dependencies_in_rhs const_info.cs_nargs eqns) (List.rev typs) in
+
+ (* The dependent term to subst in the types of the remaining UnPushed
+ terms is relative to the current context enriched by topushs *)
+ let ci = build_dependent_constructor const_info in
+
+ (* We replace [(mkRel 1)] by its expansion [ci] *)
+ (* and context "Gamma = Gamma1, current, Gamma2" by "Gamma;typs;curalias" *)
+ (* This is done in two steps : first from "Gamma |- tms" *)
+ (* into "Gamma; typs; curalias |- tms" *)
+ let tomatch = lift_tomatch_stack const_info.cs_nargs pb.tomatch in
+
+ let currents =
+ list_map2_i
+ (fun i (na,t) deps -> Pushed ((mkRel i, lift_tomatch_type i t), deps))
+ 1 typs' (List.rev dep_sign) in
+
+ let sign = List.map (fun (na,t) -> mkDeclTomatch na t) typs' in
+ let ind =
+ appvect (
+ applist (mkInd (inductive_of_constructor const_info.cs_cstr),
+ List.map (lift const_info.cs_nargs) const_info.cs_params),
+ const_info.cs_concl_realargs) in
+
+ let cur_alias = lift (List.length sign) current in
+ let currents = Alias (ci,cur_alias,alias_type,ind) :: currents in
+ let env' = push_rels sign pb.env in
+ let pred' = option_map (specialize_predicate (List.rev typs') dep_sign const_info) pb.pred in
+ sign,
+ { pb with
+ env = env';
+ tomatch = List.rev_append currents tomatch;
+ pred = pred';
+ history = history;
+ mat = List.map (push_rels_eqn_with_names sign) submat }
+
+(**********************************************************************
+ INVARIANT:
+
+ pb = { env, subst, tomatch, mat, ...}
+ tomatch = list of Pushed (c:T) or Abstract (na:T) or Alias (c:T)
+
+ "Pushed" terms and types are relative to env
+ "Abstract" types are relative to env enriched by the previous terms to match
+
+*)
+
+(**********************************************************************)
+(* Main compiling descent *)
+let rec compile pb =
+ match pb.tomatch with
+ | (Pushed cur)::rest -> match_current { pb with tomatch = rest } cur
+ | (Alias x)::rest -> compile_alias pb x rest
+ | (Abstract d)::rest -> compile_generalization pb d rest
+ | [] -> build_leaf pb
+
+and match_current pb tomatch =
+ let ((current,typ as ct),deps) = adjust_tomatch_to_pattern pb tomatch in
+ match typ with
+ | NotInd (_,typ) ->
+ check_all_variables typ pb.mat;
+ compile (shift_problem ct pb)
+ | IsInd (_,(IndType(indf,realargs) as indt)) ->
+ let mind,_ = dest_ind_family indf in
+ let cstrs = get_constructors pb.env indf in
+ let eqns,onlydflt = group_equations pb mind current cstrs pb.mat in
+ if (Array.length cstrs <> 0 or pb.mat <> []) & onlydflt then
+ compile (shift_problem ct pb)
+ else
+ let _constraints = Array.map (solve_constraints indt) cstrs in
+
+ (* We generalize over terms depending on current term to match *)
+ let pb = generalize_problem pb deps in
+
+ (* We compile branches *)
+ let brs = array_map2 (compile_branch current deps pb) eqns cstrs in
+
+ (* We build the (elementary) case analysis *)
+ let tags = Array.map (fun (t,_,_) -> t) brs in
+ let brvals = Array.map (fun (_,v,_) -> v) brs in
+ let brtyps = Array.map (fun (_,_,t) -> t) brs in
+ let (pred,typ,s) =
+ find_predicate pb.caseloc pb.env pb.isevars
+ pb.pred brtyps cstrs current indt pb.tomatch in
+ let ci = make_case_info pb.env mind RegularStyle tags in
+ let case = mkCase (ci,nf_betaiota pred,current,brvals) in
+ let inst = List.map mkRel deps in
+ pattern_status tags,
+ { uj_val = applist (case, inst);
+ uj_type = substl inst typ }
+
+and compile_branch current deps pb eqn cstr =
+ let sign, pb = build_branch current deps pb eqn cstr in
+ let tag, j = compile pb in
+ (tag, it_mkLambda_or_LetIn j.uj_val sign, j.uj_type)
+
+and compile_generalization pb d rest =
+ let pb =
+ { pb with
+ env = push_rel d pb.env;
+ tomatch = rest;
+ pred = option_map ungeneralize_predicate pb.pred;
+ mat = List.map (push_rels_eqn [d]) pb.mat } in
+ let patstat,j = compile pb in
+ patstat,
+ { uj_val = mkLambda_or_LetIn d j.uj_val;
+ uj_type = mkProd_or_LetIn d j.uj_type }
+
+and compile_alias pb (deppat,nondeppat,d,t) rest =
+ let history = simplify_history pb.history in
+ let sign, newenv, mat =
+ insert_aliases pb.env (Evd.evars_of !(pb.isevars)) (deppat,nondeppat,d,t) pb.mat in
+ let n = List.length sign in
+
+ (* We had Gamma1; x:current; Gamma2 |- tomatch(x) and we rebind x to get *)
+ (* Gamma1; x:current; Gamma2; typs; x':=curalias |- tomatch(x') *)
+ let tomatch = lift_tomatch_stack n rest in
+ let tomatch = match kind_of_term nondeppat with
+ | Rel i ->
+ if n = 1 then regeneralize_index_tomatch (i+n) tomatch
+ else replace_tomatch i deppat tomatch
+ | _ -> (* initial terms are not dependent *) tomatch in
+
+ let pb =
+ {pb with
+ env = newenv;
+ tomatch = tomatch;
+ pred = option_map (lift_predicate n) pb.pred;
+ history = history;
+ mat = mat } in
+ let patstat,j = compile pb in
+ patstat,
+ List.fold_left mkSpecialLetInJudge j sign
+
+(* pour les alias des initiaux, enrichir les env de ce qu'il faut et
+substituer après par les initiaux *)
+
+(**************************************************************************)
+(* Preparation of the pattern-matching problem *)
+
+(* builds the matrix of equations testing that each eqn has n patterns
+ * and linearizing the _ patterns.
+ * Syntactic correctness has already been done in astterm *)
+let matx_of_eqns env eqns =
+ let build_eqn (loc,ids,lpat,rhs) =
+ let rhs =
+ { rhs_env = env;
+ avoid_ids = ids@(ids_of_named_context (named_context env));
+ it = rhs;
+ } in
+ { patterns = lpat;
+ tag = RegularPat;
+ alias_stack = [];
+ eqn_loc = loc;
+ used = ref false;
+ rhs = rhs }
+ in List.map build_eqn eqns
+
+(************************************************************************)
+(* preparing the elimination predicate if any *)
+
+let build_expected_arity env isevars isdep tomatchl =
+ let cook n = function
+ | _,IsInd (_,IndType(indf,_)) ->
+ let indf' = lift_inductive_family n indf in
+ Some (build_dependent_inductive env indf', fst (get_arity env indf'))
+ | _,NotInd _ -> None
+ in
+ let rec buildrec n env = function
+ | [] -> new_Type ()
+ | tm::ltm ->
+ match cook n tm with
+ | None -> buildrec n env ltm
+ | Some (ty1,aritysign) ->
+ let rec follow n env = function
+ | d::sign ->
+ mkProd_or_LetIn_name env
+ (follow (n+1) (push_rel d env) sign) d
+ | [] ->
+ if isdep then
+ mkProd (Anonymous, ty1,
+ buildrec (n+1)
+ (push_rel_assum (Anonymous, ty1) env)
+ ltm)
+ else buildrec n env ltm
+ in follow n env (List.rev aritysign)
+ in buildrec 0 env tomatchl
+
+let extract_predicate_conclusion isdep tomatchl pred =
+ let cook = function
+ | _,IsInd (_,IndType(_,args)) -> Some (List.length args)
+ | _,NotInd _ -> None in
+ let rec decomp_lam_force n l p =
+ if n=0 then (l,p) else
+ match kind_of_term p with
+ | Lambda (na,_,c) -> decomp_lam_force (n-1) (na::l) c
+ | _ -> (* eta-expansion *)
+ let na = Name (id_of_string "x") in
+ decomp_lam_force (n-1) (na::l) (applist (lift 1 p, [mkRel 1])) in
+ let rec buildrec allnames p = function
+ | [] -> (List.rev allnames,p)
+ | tm::ltm ->
+ match cook tm with
+ | None ->
+ let p =
+ (* adjust to a sign containing the NotInd's *)
+ if isdep then lift 1 p else p in
+ let names = if isdep then [Anonymous] else [] in
+ buildrec (names::allnames) p ltm
+ | Some n ->
+ let n = if isdep then n+1 else n in
+ let names,p = decomp_lam_force n [] p in
+ buildrec (names::allnames) p ltm
+ in buildrec [] pred tomatchl
+
+let set_arity_signature dep n arsign tomatchl pred x =
+ (* avoid is not exhaustive ! *)
+ let rec decomp_lam_force n avoid l p =
+ if n = 0 then (List.rev l,p,avoid) else
+ match p with
+ | RLambda (_,(Name id as na),_,c) ->
+ decomp_lam_force (n-1) (id::avoid) (na::l) c
+ | RLambda (_,(Anonymous as na),_,c) -> decomp_lam_force (n-1) avoid (na::l) c
+ | _ ->
+ let x = next_ident_away (id_of_string "x") avoid in
+ decomp_lam_force (n-1) (x::avoid) (Name x :: l)
+ (* eta-expansion *)
+ (let a = RVar (dummy_loc,x) in
+ match p with
+ | RApp (loc,p,l) -> RApp (loc,p,l@[a])
+ | _ -> (RApp (dummy_loc,p,[a]))) in
+ let rec decomp_block avoid p = function
+ | ([], _) -> x := Some p
+ | ((_,IsInd (_,IndType(indf,realargs)))::l),(y::l') ->
+ let (ind,params) = dest_ind_family indf in
+ let (nal,p,avoid') = decomp_lam_force (List.length realargs) avoid [] p
+ in
+ let na,p,avoid' =
+ if dep then decomp_lam_force 1 avoid' [] p else [Anonymous],p,avoid'
+ in
+ y :=
+ (List.hd na,
+ if List.for_all ((=) Anonymous) nal then
+ None
+ else
+ Some (dummy_loc, ind, (List.map (fun _ -> Anonymous) params)@nal));
+ decomp_block avoid' p (l,l')
+ | (_::l),(y::l') ->
+ y := (Anonymous,None);
+ decomp_block avoid p (l,l')
+ | _ -> anomaly "set_arity_signature"
+ in
+ decomp_block [] pred (tomatchl,arsign)
+
+let prepare_predicate_from_tycon loc dep env isevars tomatchs sign c =
+ let cook (n, l, env, signs) = function
+ | c,IsInd (_,IndType(indf,realargs)) ->
+ let indf' = lift_inductive_family n indf in
+ let sign = make_arity_signature env dep indf' in
+ let p = List.length realargs in
+ if dep then
+ (n + p + 1, c::(List.rev realargs)@l, push_rels sign env,sign::signs)
+ else
+ (n + p, (List.rev realargs)@l, push_rels sign env,sign::signs)
+ | c,NotInd _ ->
+ (n, l, env, []::signs) in
+ let n, allargs, env, signs = List.fold_left cook (0, [], env, []) tomatchs in
+ let names = List.rev (List.map (List.map pi1) signs) in
+ let allargs =
+ List.map (fun c -> lift n (nf_betadeltaiota env (Evd.evars_of !isevars) c)) allargs in
+ let rec build_skeleton env c =
+ (* Don't put into normal form, it has effects on the synthesis of evars *)
+ (* let c = whd_betadeltaiota env (evars_of isevars) c in *)
+ (* We turn all subterms possibly dependent into an evar with maximum ctxt*)
+ if isEvar c or List.exists (eq_constr c) allargs then
+ e_new_evar isevars env ~src:(loc, Evd.CasesType)
+ (Retyping.get_type_of env (Evd.evars_of !isevars) c)
+ else
+ map_constr_with_full_binders push_rel build_skeleton env c
+ in
+ names, build_skeleton env (lift n c)
+
+(* Here, [pred] is assumed to be in the context built from all *)
+(* realargs and terms to match *)
+let build_initial_predicate isdep allnames pred =
+ let nar = List.fold_left (fun n names -> List.length names + n) 0 allnames in
+ let rec buildrec n pred = function
+ | [] -> PrCcl pred
+ | names::lnames ->
+ let names' = if isdep then List.tl names else names in
+ let n' = n + List.length names' in
+ let pred, p, user_p =
+ if isdep then
+ if dependent (mkRel (nar-n')) pred then pred, 1, 1
+ else liftn (-1) (nar-n') pred, 0, 1
+ else pred, 0, 0 in
+ let na =
+ if p=1 then
+ let na = List.hd names in
+ if na = Anonymous then
+ (* peut arriver en raison des evars *)
+ Name (id_of_string "x") (*Hum*)
+ else na
+ else Anonymous in
+ PrLetIn ((names',na), buildrec (n'+user_p) pred lnames)
+ in buildrec 0 pred allnames
+
+let extract_arity_signature env0 tomatchl tmsign =
+ let get_one_sign n tm (na,t) =
+ match tm with
+ | NotInd (bo,typ) ->
+ (match t with
+ | None -> [na,option_map (lift n) bo,lift n typ]
+ | Some (loc,_,_,_) ->
+ user_err_loc (loc,"",
+ str "Unexpected type annotation for a term of non inductive type"))
+ | IsInd (_,IndType(indf,realargs)) ->
+ let indf' = lift_inductive_family n indf in
+ let (ind,params) = dest_ind_family indf' in
+ let nrealargs = List.length realargs in
+ let realnal =
+ match t with
+ | Some (loc,ind',nparams,realnal) ->
+ if ind <> ind' then
+ user_err_loc (loc,"",str "Wrong inductive type");
+ if List.length params <> nparams
+ or nrealargs <> List.length realnal then
+ anomaly "Ill-formed 'in' clause in cases";
+ List.rev realnal
+ | None -> list_tabulate (fun _ -> Anonymous) nrealargs in
+ let arsign = fst (get_arity env0 indf') in
+ (na,None,build_dependent_inductive env0 indf')
+ ::(List.map2 (fun x (_,c,t) ->(x,c,t)) realnal arsign) in
+ let rec buildrec n = function
+ | [],[] -> []
+ | (_,tm)::ltm, x::tmsign ->
+ let l = get_one_sign n tm x in
+ l :: buildrec (n + List.length l) (ltm,tmsign)
+ | _ -> assert false
+ in List.rev (buildrec 0 (tomatchl,tmsign))
+
+let inh_conv_coerce_to_tycon loc env isevars j tycon =
+ match tycon with
+ | Some p ->
+ let (evd',j) = Coercion.inh_conv_coerce_to loc env !isevars j p in
+ isevars := evd';
+ j
+ | None -> j
+
+let out_ind = function IsInd (_, IndType(x, y)) -> (x, y) | _ -> assert(false)
+
+let list_mapi f l =
+ let rec aux n = function
+ [] -> []
+ | hd :: tl -> f n hd :: aux (succ n) tl
+ in aux 0 l
+
+let constr_of_pat env isevars ty pat idents =
+ let rec typ env ty pat idents =
+ trace (str "Typing pattern " ++ Printer.pr_cases_pattern pat ++ str " in env " ++
+ print_env env ++ str" should have type: " ++ my_print_constr env ty);
+ match pat with
+ | PatVar (l,name) ->
+ let name, idents' = match name with
+ Name n -> name, idents
+ | Anonymous ->
+ let n' = next_ident_away_from (id_of_string "wildcard") idents in
+ Name n', n' :: idents
+ in
+(* trace (str "Treating pattern variable " ++ str (string_of_id (id_of_name name))); *)
+ PatVar (l, name), [name, None, ty], mkRel 1, 1, idents'
+ | PatCstr (l,((_, i) as cstr),args,alias) ->
+ let _ind = inductive_of_constructor cstr in
+ let IndType (indf, realargs) = find_rectype env (Evd.evars_of !isevars) ty in
+ let ind, params = dest_ind_family indf in
+ let cstrs = get_constructors env indf in
+ let ci = cstrs.(i-1) in
+ let nb_args_constr = ci.cs_nargs in
+ assert(nb_args_constr = List.length args);
+ let idents' = idents in
+ let patargs, args, sign, env, n, m, idents' =
+ List.fold_right2
+ (fun (na, c, t) ua (patargs, args, sign, env, n, m, idents) ->
+ let pat', sign', arg', n', idents' = typ env (lift (n - m) t) ua idents in
+ let args' = arg' :: List.map (lift n') args in
+ let env' = push_rels sign' env in
+ (pat' :: patargs, args', sign' @ sign, env', n' + n, succ m, idents'))
+ ci.cs_args (List.rev args) ([], [], [], env, 0, 0, idents')
+ in
+ let args = List.rev args in
+ let patargs = List.rev patargs in
+ let pat' = PatCstr (l, cstr, patargs, alias) in
+ let cstr = mkConstruct ci.cs_cstr in
+ let app = applistc cstr (List.map (lift (List.length sign)) params) in
+ let app = applistc app args in
+(* trace (str "New pattern: " ++ Printer.pr_cases_pattern pat'); *)
+(* let alname = if alias <> Anonymous then alias else Name (id_of_string "anon") in *)
+(* let al = alname, Some (mkRel 1), lift 1 ty in *)
+ if alias <> Anonymous then
+ pat', (alias, Some app, ty) :: sign, lift 1 app, n + 1, idents'
+ else pat', sign, app, n, idents'
+ in
+ let pat', sign, y, z, idents = typ env ty pat idents in
+ let c = it_mkProd_or_LetIn y sign in
+ trace (str "Constr_of_pat gives: " ++ my_print_constr env c);
+ pat', (sign, y), idents
+
+let mk_refl typ a = mkApp (Lazy.force eq_refl, [| typ; a |])
+
+let vars_of_ctx =
+ List.rev_map (fun (na, _, t) ->
+ match na with
+ Anonymous -> raise (Invalid_argument "vars_of_ctx")
+ | Name n -> RVar (dummy_loc, n))
+
+(*let build_ineqs eqns pats =
+ List.fold_left
+ (fun (sign, c) eqn ->
+ let acc = fold_left3
+ (fun acc prevpat (ppat_sign, ppat_c, ppat_ty) (pat, pat_c) ->
+ match acc with
+ None -> None
+ | Some (sign,len, c) ->
+ if is_included pat prevpat then
+ let lens = List.length ppat_sign in
+ let acc =
+ (lift_rels lens ppat_sign @ sign,
+ lens + len,
+ mkApp (Lazy.force eq_ind,
+ [| ppat_ty ; ppat_c ;
+ lift (lens + len) pat_c |]) :: c)
+ in Some acc
+ else None)
+ (sign, c) eqn.patterns eqn.c_patterns pats
+ in match acc with
+ None -> (sign, c)
+ | Some (sign, len, c) ->
+ it_mkProd_or_LetIn c sign
+
+ )
+ ([], []) eqns*)
+
+let constrs_of_pats typing_fun tycon env isevars eqns tomatchs =
+ let i = ref 0 in
+ List.fold_left
+ (fun (branches, eqns) eqn ->
+ let _, newpatterns, pats =
+ List.fold_right2 (fun pat (_, ty) (idents, newpatterns, pats) ->
+ let x, y, z = constr_of_pat env isevars (type_of_tomatch ty) pat idents in
+ (z, x :: newpatterns, y :: pats))
+ eqn.patterns tomatchs ([], [], [])
+ in
+ let rhs_rels, signlen =
+ List.fold_left (fun (renv, n) (sign,_) ->
+ ((lift_rel_context n sign) @ renv, List.length sign + n))
+ ([], 0) pats in
+ let eqs, _, _ = List.fold_left2
+ (fun (eqs, n, slen) (sign, c) (tm, ty) ->
+ let len = n + signlen in (* Number of already defined equations + signature *)
+ let csignlen = List.length sign in
+ let slen' = slen - csignlen in (* Lift to get pattern variables signature *)
+ let c = liftn (signlen - slen) signlen c in (* Lift to jump over previous ind signatures for pattern variables outside sign
+ in c (e.g. type arguments of constructors instanciated by variables ) *)
+ let cstr = lift (slen' + n) c in
+(* trace (str "lift " ++ my_print_constr (push_rels sign env) c ++ *)
+(* str " by " ++ int ++ str " to get " ++ *)
+(* my_print_constr (push_rels sign env) cstr); *)
+ let app =
+ mkApp (Lazy.force eq_ind,
+ [| lift len (type_of_tomatch ty); cstr; lift len tm |])
+ in app :: eqs, succ n, slen')
+ ([], 0, signlen) pats tomatchs
+ in
+ let eqs_rels = List.map (fun eq -> Name (id_of_string "H"), None, eq) eqs in
+(* let ineqs = build_ineqs eqns newpatterns in *)
+ let rhs_rels' = eqs_rels @ rhs_rels in
+ let rhs_env = push_rels rhs_rels' env in
+(* (try trace (str "branch env: " ++ print_env rhs_env) *)
+(* with _ -> trace (str "error in print branch env")); *)
+ let tycon = lift_tycon (List.length eqs + signlen) tycon in
+
+ let j = typing_fun tycon rhs_env eqn.rhs.it in
+(* (try trace (str "in env: " ++ my_print_env rhs_env ++ str"," ++ *)
+(* str "Typed branch: " ++ Prettyp.print_judgment rhs_env j); *)
+(* with _ -> *)
+(* trace (str "Error in typed branch pretty printing")); *)
+ let bbody = it_mkLambda_or_LetIn j.uj_val rhs_rels'
+ and btype = it_mkProd_or_LetIn j.uj_type rhs_rels' in
+ let branch_name = id_of_string ("branch_" ^ (string_of_int !i)) in
+ let branch_decl = (Name branch_name, Some (lift !i bbody), (lift !i btype)) in
+(* (try trace (str "Branch decl: " ++ pr_rel_decl env (Name branch_name, Some bbody, btype)) *)
+(* with _ -> trace (str "Error in branch decl pp")); *)
+ let branch =
+ let bref = RVar (dummy_loc, branch_name) in
+ match vars_of_ctx rhs_rels with
+ [] -> bref
+ | l -> RApp (dummy_loc, bref, l)
+ in
+(* let branch = *)
+(* List.fold_left (fun br (eqH, _, t) -> RLambda (dummy_loc, eqH, RHole (dummy_loc, Evd.InternalHole), br)) branch eqs_rels *)
+(* in *)
+(* (try trace (str "New branch: " ++ Printer.pr_rawconstr branch) *)
+(* with _ -> trace (str "Error in new branch pp")); *)
+ incr i;
+ let rhs = { eqn.rhs with it = branch } in
+ (branch_decl :: branches,
+ { eqn with patterns = newpatterns; rhs = rhs } :: eqns))
+ ([], []) eqns
+
+
+(* liftn_rel_declaration *)
+
+
+(* Builds the predicate. If the predicate is dependent, its context is
+ * made of 1+nrealargs assumptions for each matched term in an inductive
+ * type and 1 assumption for each term not _syntactically_ in an
+ * inductive type.
+
+ * Each matched terms are independently considered dependent or not.
+
+ * A type constraint but no annotation case: it is assumed non dependent.
+ *)
+
+let prepare_predicate_from_tycon loc typing_fun isevars env tomatchs arsign tycon =
+ (* We extract the signature of the arity *)
+(* List.iter *)
+(* (fun arsign -> *)
+(* trace (str "arity signature: " ++ my_print_rel_context env arsign)) *)
+(* arsign; *)
+(* let env = List.fold_right push_rels arsign env in *)
+ let allnames = List.rev (List.map (List.map pi1) arsign) in
+ let nar = List.fold_left (fun n names -> List.length names + n) 0 allnames in
+ let pred = out_some (valcon_of_tycon tycon) in
+ let predcclj, pred, neqs =
+ let _, _, eqs =
+ List.fold_left2
+ (fun (neqs, slift, eqs) ctx (tm,ty) ->
+ let len = List.length ctx in
+ let _name, _, _typ' = List.hd ctx in (* FixMe: Ignoring dependent inductives *)
+ let eq = mkApp (Lazy.force eq_ind,
+ [| lift (neqs + nar) (type_of_tomatch ty);
+ mkRel (neqs + slift);
+ lift (neqs + nar) tm|])
+ in
+ (succ neqs, slift - len, (Anonymous, None, eq) :: eqs))
+ (0, nar, []) (List.rev arsign) tomatchs
+ in
+ let len = List.length eqs in
+ it_mkProd_wo_LetIn (lift (nar + len) pred) eqs, pred, len
+ in
+ let predccl = nf_isevar !isevars predcclj in
+(* let env' = List.fold_right push_rel_context arsign env in *)
+(* trace (str " Env:" ++ my_print_env env' ++ str" Predicate: " ++ my_print_constr env' predccl); *)
+ build_initial_predicate true allnames predccl, pred
+
+let prepare_predicate_from_rettyp loc typing_fun isevars env tomatchs sign tycon rtntyp =
+ (* We extract the signature of the arity *)
+ let arsign = extract_arity_signature env tomatchs sign in
+ let env = List.fold_right push_rels arsign env in
+ let allnames = List.rev (List.map (List.map pi1) arsign) in
+ let predcclj = typing_fun (mk_tycon (new_Type ())) env rtntyp in
+(* let _ = *)
+(* option_map (fun tycon -> *)
+(* isevars := Coercion.inh_conv_coerces_to loc env !isevars predcclj.uj_val *)
+(* (lift_tycon_type (List.length arsign) tycon)) *)
+(* tycon *)
+(* in *)
+ let predccl = (j_nf_isevar !isevars predcclj).uj_val in
+ Some (build_initial_predicate true allnames predccl)
+
+let lift_ctx n ctx =
+ let ctx', _ =
+ List.fold_right (fun (c, t) (ctx, n') -> (liftn n n' c, liftn_tomatch_type n n' t) :: ctx, succ n') ctx ([], 0)
+ in ctx'
+
+(* Turn matched terms into variables. *)
+let abstract_tomatch env tomatchs =
+ let prev, ctx, names =
+ List.fold_left
+ (fun (prev, ctx, names) (c, t) ->
+ let lenctx = List.length ctx in
+ match kind_of_term c with
+ Rel n -> (lift lenctx c, lift_tomatch_type lenctx t) :: prev, ctx, names
+ | _ ->
+ let name = next_ident_away_from (id_of_string "filtered_var") names in
+ (mkRel 1, lift_tomatch_type 1 t) :: lift_ctx 1 prev,
+ (Name name, Some (lift lenctx c), lift lenctx $ type_of_tomatch t) :: ctx,
+ name :: names)
+ ([], [], []) tomatchs
+ in List.rev prev, ctx
+
+(**************************************************************************)
+(* Main entry of the matching compilation *)
+
+let compile_cases loc (typing_fun, isevars) (tycon : Evarutil.type_constraint) env (predopt, tomatchl, eqns)=
+ let tycon0 = tycon in
+ (* We build the matrix of patterns and right-hand-side *)
+ let matx = matx_of_eqns env eqns in
+
+ (* We build the vector of terms to match consistently with the *)
+ (* constructors found in patterns *)
+ let tomatchs = coerce_to_indtype typing_fun isevars env matx tomatchl in
+ let tomatchs, tomatchs_lets = abstract_tomatch env tomatchs in
+ let tomatchs_len = List.length tomatchs_lets in
+ let tycon = lift_tycon tomatchs_len tycon in
+ let env = push_rel_context tomatchs_lets env in
+ match predopt with
+ None ->
+ let lets, matx = constrs_of_pats typing_fun tycon env isevars matx tomatchs in
+ let matx = List.rev matx in
+ let len = List.length lets in
+ let sign =
+ let arsign = extract_arity_signature env tomatchs (List.map snd tomatchl) in
+ List.map (lift_rel_context len) arsign
+ in
+ let env = push_rels lets env in
+ let matx = List.map (fun eqn -> { eqn with rhs = { eqn.rhs with rhs_env = env } }) matx in
+ let tycon = lift_tycon len tycon in
+ let tomatchs = List.map (fun (x, y) -> lift len x, lift_tomatch_type len y) tomatchs in
+ let args = List.map (fun (tm,ty) -> mk_refl (type_of_tomatch ty) tm) tomatchs in
+
+ (* We build the elimination predicate if any and check its consistency *)
+ (* with the type of arguments to match *)
+ let pred, opred = prepare_predicate_from_tycon loc typing_fun isevars env tomatchs sign tycon in
+ (* We push the initial terms to match and push their alias to rhs' envs *)
+ (* names of aliases will be recovered from patterns (hence Anonymous here) *)
+ let initial_pushed = List.map (fun tm -> Pushed (tm,[])) tomatchs in
+
+ let pb =
+ { env = env;
+ isevars = isevars;
+ pred = Some pred;
+ tomatch = initial_pushed;
+ history = start_history (List.length initial_pushed);
+ mat = matx;
+ caseloc = loc;
+ typing_function = typing_fun } in
+
+ let _, j = compile pb in
+ (* We check for unused patterns *)
+ List.iter (check_unused_pattern env) matx;
+ let ty = out_some (valcon_of_tycon tycon0) in
+ let body = it_mkLambda_or_LetIn (applistc j.uj_val args) lets in
+ let j =
+ { uj_val = it_mkLambda_or_LetIn body tomatchs_lets;
+ uj_type = ty; }
+ in
+ inh_conv_coerce_to_tycon loc env isevars j tycon0
+
+ | Some rtntyp ->
+ (* We build the elimination predicate if any and check its consistency *)
+ (* with the type of arguments to match *)
+ let tmsign = List.map snd tomatchl in
+ let pred = prepare_predicate_from_rettyp loc typing_fun isevars env tomatchs tmsign tycon rtntyp in
+
+ (* We push the initial terms to match and push their alias to rhs' envs *)
+ (* names of aliases will be recovered from patterns (hence Anonymous here) *)
+ let initial_pushed = List.map (fun tm -> Pushed (tm,[])) tomatchs in
+
+ let pb =
+ { env = env;
+ isevars = isevars;
+ pred = pred;
+ tomatch = initial_pushed;
+ history = start_history (List.length initial_pushed);
+ mat = matx;
+ caseloc = loc;
+ typing_function = typing_fun } in
+
+ let _, j = compile pb in
+ (* We check for unused patterns *)
+ List.iter (check_unused_pattern env) matx;
+ let j = { j with uj_val = it_mkLambda_or_LetIn j.uj_val tomatchs_lets } in
+ inh_conv_coerce_to_tycon loc env isevars j tycon
+
+end
+
diff --git a/contrib/subtac/subtac_cases.mli b/contrib/subtac/subtac_cases.mli
new file mode 100644
index 00000000..9e902126
--- /dev/null
+++ b/contrib/subtac/subtac_cases.mli
@@ -0,0 +1,50 @@
+(************************************************************************)
+(* v * The Coq Proof Assistant / The Coq Development Team *)
+(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(************************************************************************)
+
+(*i $Id: cases.mli 8741 2006-04-26 22:30:32Z herbelin $ i*)
+
+(*i*)
+open Util
+open Names
+open Term
+open Evd
+open Environ
+open Inductiveops
+open Rawterm
+open Evarutil
+(*i*)
+
+type pattern_matching_error =
+ | BadPattern of constructor * constr
+ | BadConstructor of constructor * inductive
+ | WrongNumargConstructor of constructor * int
+ | WrongNumargInductive of inductive * int
+ | WrongPredicateArity of constr * constr * constr
+ | NeedsInversion of constr * constr
+ | UnusedClause of cases_pattern list
+ | NonExhaustive of cases_pattern list
+ | CannotInferPredicate of (constr * types) array
+
+exception PatternMatchingError of env * pattern_matching_error
+
+val error_wrong_numarg_constructor_loc : loc -> env -> constructor -> int -> 'a
+
+val error_wrong_numarg_inductive_loc : loc -> env -> inductive -> int -> 'a
+
+(*s Compilation of pattern-matching. *)
+
+module type S = sig
+ val compile_cases :
+ loc ->
+ (type_constraint -> env -> rawconstr -> unsafe_judgment) * evar_defs ref ->
+ type_constraint ->
+ env -> rawconstr option * tomatch_tuple * cases_clauses ->
+ unsafe_judgment
+end
+
+module Cases_F(C : Coercion.S) : S
diff --git a/contrib/subtac/subtac_coercion.ml b/contrib/subtac/subtac_coercion.ml
index da5c497c..3613ec4f 100644
--- a/contrib/subtac/subtac_coercion.ml
+++ b/contrib/subtac/subtac_coercion.ml
@@ -5,7 +5,7 @@
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(************************************************************************)
-(* $Id: subtac_coercion.ml 9284 2006-10-26 12:06:57Z msozeau $ *)
+(* $Id: subtac_coercion.ml 9563 2007-01-31 09:37:18Z msozeau $ *)
open Util
open Names
@@ -53,8 +53,6 @@ module Coercion = struct
| _ -> None
and disc_exist env x =
- (try trace (str "Disc_exist: " ++ my_print_constr env x)
- with _ -> ());
match kind_of_term x with
| App (c, l) ->
(match kind_of_term c with
@@ -67,8 +65,6 @@ module Coercion = struct
let disc_proj_exist env x =
- (try trace (str "disc_proj_exist: " ++ my_print_constr env x);
- with _ -> ());
match kind_of_term x with
| App (c, l) ->
(if Term.eq_constr c (Lazy.force sig_).proj1
@@ -108,27 +104,27 @@ module Coercion = struct
: (Term.constr -> Term.constr) option
=
let x = nf_evar (evars_of !isevars) x and y = nf_evar (evars_of !isevars) y in
- (try debug 1 (str "Coerce called for " ++ (my_print_constr env x) ++
- str " and "++ my_print_constr env y ++
- str " with evars: " ++ spc () ++
- my_print_evardefs !isevars);
- with _ -> ());
+(* (try debug 1 (str "Coerce called for " ++ (my_print_constr env x) ++ *)
+(* str " and "++ my_print_constr env y ++ *)
+(* str " with evars: " ++ spc () ++ *)
+(* my_print_evardefs !isevars); *)
+(* with _ -> ()); *)
let rec coerce_unify env x y =
- (try debug 1 (str "coerce_unify from " ++ (my_print_constr env x) ++
- str " to "++ my_print_constr env y)
- with _ -> ());
+(* (try debug 1 (str "coerce_unify from " ++ (my_print_constr env x) ++ *)
+(* str " to "++ my_print_constr env y) *)
+(* with _ -> ()); *)
try
isevars := the_conv_x_leq env x y !isevars;
- (try debug 1 (str "Unified " ++ (my_print_constr env x) ++
- str " and "++ my_print_constr env y);
- with _ -> ());
+(* (try debug 1 (str "Unified " ++ (my_print_constr env x) ++ *)
+(* str " and "++ my_print_constr env y); *)
+(* with _ -> ()); *)
None
with Reduction.NotConvertible -> coerce' env (hnf env isevars x) (hnf env isevars y)
and coerce' env x y : (Term.constr -> Term.constr) option =
let subco () = subset_coerce env isevars x y in
- (try debug 1 (str "coerce' from " ++ (my_print_constr env x) ++
- str " to "++ my_print_constr env y);
- with _ -> ());
+(* (try debug 1 (str "coerce' from " ++ (my_print_constr env x) ++ *)
+(* str " to "++ my_print_constr env y); *)
+(* with _ -> ()); *)
match (kind_of_term x, kind_of_term y) with
| Sort s, Sort s' ->
(match s, s' with
@@ -158,11 +154,11 @@ module Coercion = struct
let existS = Lazy.force existS in
let prod = Lazy.force prod in
if len = Array.length l' && len = 2 && i = i'
+ && (i = Term.destInd existS.typ || i = Term.destInd prod.typ)
then
if i = Term.destInd existS.typ
then
begin
- trace (str "In coerce sigma types");
let (a, pb), (a', pb') =
pair_of_array l, pair_of_array l'
in
@@ -185,7 +181,6 @@ module Coercion = struct
let c2 = coerce_unify env' b b' in
match c1, c2 with
None, None ->
- trace (str "No coercion needed");
None
| _, _ ->
Some
@@ -198,9 +193,8 @@ module Coercion = struct
in
mkApp (existS.intro, [| a'; pb'; x ; y |]))
end
- else if i = Term.destInd prod.typ then
+ else
begin
- debug 1 (str "In coerce prod types");
let (a, b), (a', b') =
pair_of_array l, pair_of_array l'
in
@@ -219,14 +213,48 @@ module Coercion = struct
in
mkApp (prod.intro, [| a'; b'; x ; y |]))
end
- else subco ()
- else subco ()
- | _ -> subco ())
+ else
+ (* if len = 1 && len = Array.length l' && i = i' then *)
+(* let argx, argy = l.(0), l'.(0) in *)
+(* let indtyp = Inductiveops.type_of_inductive env i in *)
+(* let argname, argtype, _ = destProd indtyp in *)
+(* let eq = *)
+(* mkApp (Lazy.force eqind, [| argtype; argx; argy |]) *)
+(* in *)
+(* let pred = mkLambda (argname, argtype, *)
+(* mkApp (mkInd i, [| mkRel 1 |])) *)
+(* in *)
+(* let evar = make_existential dummy_loc env isevars eq in *)
+(* Some (fun x -> *)
+(* mkApp (Lazy.force eqrec, *)
+(* [| argtype; argx; pred; x; argy; evar |])) *)
+(* else *)subco ()
+ | x, y when x = y ->
+ let lam_type = Typing.type_of env (evars_of !isevars) c in
+ let rec coerce typ i co =
+ if i < Array.length l then
+ let hdx = l.(i) and hdy = l'.(i) in
+ let (n, eqT, restT) = destProd typ in
+ let pred = mkLambda (n, eqT, mkApp (lift 1 c, [| mkRel 1 |])) in
+ let eq = mkApp (Lazy.force eq_ind, [| eqT; hdx; hdy |]) in
+ let evar = make_existential dummy_loc env isevars eq in
+ let eq_app x = mkApp (Lazy.force eq_rect,
+ [| eqT; hdx; pred; x; hdy; evar|])
+ in
+ coerce (subst1 hdy restT) (succ i) (fun x -> eq_app (co x))
+ else co
+ in
+ if Array.length l = Array.length l' then (
+ trace (str"Inserting coercion at application");
+ Some (coerce lam_type 0 (fun x -> x))
+ ) else subco ()
+ | _ -> subco ())
| _, _ -> subco ()
and subset_coerce env isevars x y =
match disc_subset x with
Some (u, p) ->
+ (* trace (str "Inserting projection "); *)
let c = coerce_unify env u y in
let f x =
app_opt c (mkApp ((Lazy.force sig_).proj1,
@@ -372,13 +400,13 @@ module Coercion = struct
with Reduction.NotConvertible -> raise NoCoercion
let rec inh_conv_coerce_to_fail loc env isevars v t c1 =
- (try
- debug 1 (str "inh_conv_coerce_to_fail called for " ++
- Termops.print_constr_env env t ++ str " and "++ spc () ++
- Termops.print_constr_env env c1 ++ str " with evars: " ++ spc () ++
- Evd.pr_evar_defs isevars ++ str " in env: " ++ spc () ++
- Termops.print_env env);
- with _ -> ());
+(* (try *)
+(* debug 1 (str "inh_conv_coerce_to_fail called for " ++ *)
+(* Termops.print_constr_env env t ++ str " and "++ spc () ++ *)
+(* Termops.print_constr_env env c1 ++ str " with evars: " ++ spc () ++ *)
+(* Subtac_utils.pr_evar_defs isevars ++ str " in env: " ++ spc () ++ *)
+(* Termops.print_env env); *)
+(* with _ -> ()); *)
try (the_conv_x_leq env t c1 isevars, v, t)
with Reduction.NotConvertible ->
(try
@@ -437,14 +465,14 @@ module Coercion = struct
(* Look for cj' obtained from cj by inserting coercions, s.t. cj'.typ = t *)
- let inh_conv_coerce_to loc env isevars cj ((n, t) as tycon) =
- (try
- debug 1 (str "Subtac_coercion.inh_conv_coerce_to called for " ++
- Termops.print_constr_env env cj.uj_type ++ str " and "++ spc () ++
- Evarutil.pr_tycon_type env tycon ++ str " with evars: " ++ spc () ++
- Evd.pr_evar_defs isevars ++ str " in env: " ++ spc () ++
- Termops.print_env env);
- with _ -> ());
+ let inh_conv_coerce_to loc env isevars cj ((n, t) as _tycon) =
+(* (try *)
+(* trace (str "Subtac_coercion.inh_conv_coerce_to called for " ++ *)
+(* Termops.print_constr_env env cj.uj_type ++ str " and "++ spc () ++ *)
+(* Evarutil.pr_tycon_type env tycon ++ str " with evars: " ++ spc () ++ *)
+(* Subtac_utils.pr_evar_defs isevars ++ str " in env: " ++ spc () ++ *)
+(* Termops.print_env env); *)
+(* with _ -> ()); *)
match n with
None ->
let (evd', val', type') =
@@ -462,40 +490,38 @@ module Coercion = struct
| Some (init, cur) ->
(isevars, cj)
- let inh_conv_coerces_to loc env isevars t ((abs, t') as tycon) =
- (try
- debug 1 (str "Subtac_coercion.inh_conv_coerces_to called for " ++
- Termops.print_constr_env env t ++ str " and "++ spc () ++
- Evarutil.pr_tycon_type env tycon ++ str " with evars: " ++ spc () ++
- Evd.pr_evar_defs isevars ++ str " in env: " ++ spc () ++
- Termops.print_env env);
- with _ -> ());
+ let inh_conv_coerces_to loc env isevars t ((abs, t') as _tycon) =
+(* (try *)
+(* trace (str "Subtac_coercion.inh_conv_coerces_to called for " ++ *)
+(* Termops.print_constr_env env t ++ str " and "++ spc () ++ *)
+(* Evarutil.pr_tycon_type env tycon ++ str " with evars: " ++ spc () ++ *)
+(* Evd.pr_evar_defs isevars ++ str " in env: " ++ spc () ++ *)
+(* Termops.print_env env); *)
+(* with _ -> ()); *)
let nabsinit, nabs =
match abs with
None -> 0, 0
| Some (init, cur) -> init, cur
in
- let (rels, rng) =
(* a little more effort to get products is needed *)
- try decompose_prod_n nabs t
- with _ ->
- trace (str "decompose_prod_n failed");
- raise (Invalid_argument "Subtac_coercion.inh_conv_coerces_to")
- in
- (* The final range free variables must have been replaced by evars, we accept only that evars
- in rng are applied to free vars. *)
- if noccur_with_meta 0 (succ nabsinit) rng then (
- trace (str "No occur between 0 and " ++ int (succ nabsinit));
- let env', t, t' =
- let env' = List.fold_right (fun (n, t) env -> push_rel (n, None, t) env) rels env in
- env', rng, lift nabs t'
- in
- try
- pi1 (try inh_conv_coerce_to_fail loc env' isevars None t t'
- with NoCoercion ->
- coerce_itf loc env' isevars None t t')
- with NoSubtacCoercion ->
- let sigma = evars_of isevars in
- error_cannot_coerce env' sigma (t, t'))
- else isevars
+ try let rels, rng = decompose_prod_n nabs t in
+ (* The final range free variables must have been replaced by evars, we accept only that evars
+ in rng are applied to free vars. *)
+ if noccur_with_meta 0 (succ nabsinit) rng then (
+(* trace (str "No occur between 0 and " ++ int (succ nabsinit)); *)
+ let env', t, t' =
+ let env' = List.fold_right (fun (n, t) env -> push_rel (n, None, t) env) rels env in
+ env', rng, lift nabs t'
+ in
+ try
+ pi1 (try inh_conv_coerce_to_fail loc env' isevars None t t'
+ with NoCoercion ->
+ coerce_itf loc env' isevars None t t')
+ with NoSubtacCoercion ->
+ let sigma = evars_of isevars in
+ error_cannot_coerce env' sigma (t, t'))
+ else isevars
+ with _ -> isevars
+ (* trace (str "decompose_prod_n failed"); *)
+ (* raise (Invalid_argument "Subtac_coercion.inh_conv_coerces_to") *)
end
diff --git a/contrib/subtac/subtac_command.ml b/contrib/subtac/subtac_command.ml
index b433af2c..68ab8c46 100644
--- a/contrib/subtac/subtac_command.ml
+++ b/contrib/subtac/subtac_command.ml
@@ -57,7 +57,7 @@ let interp_gen kind isevars env
c =
let c' = Constrintern.intern_gen (kind=IsType) ~impls ~allow_soapp ~ltacvars (Evd.evars_of !isevars) env c in
let c' = Subtac_utils.rewrite_cases env c' in
- (try trace (str "Pretyping " ++ my_print_constr_expr c) with _ -> ());
+(* (try trace (str "Pretyping " ++ my_print_constr_expr c) with _ -> ()); *)
let c' = SPretyping.pretype_gen isevars env ([],[]) kind c' in
evar_nf isevars c'
@@ -150,14 +150,6 @@ let collect_non_rec env =
in
searchrec []
-
-let filter_map f l =
- let rec aux acc = function
- hd :: tl -> (match f hd with Some t -> aux (t :: acc) tl
- | None -> aux acc tl)
- | [] -> List.rev acc
- in aux [] l
-
let list_of_local_binders l =
let rec aux acc = function
Topconstr.LocalRawDef (n, c) :: tl -> aux ((n, Some c, None) :: acc) tl
@@ -176,25 +168,29 @@ let rec gen_rels = function
0 -> []
| n -> mkRel n :: gen_rels (pred n)
+let split_args n rel = match list_chop ((List.length rel) - n) rel with
+ (l1, x :: l2) -> l1, x, l2
+ | _ -> assert(false)
+
let build_wellfounded (recname, n, bl,arityc,body) r measure notation boxed =
let sigma = Evd.empty in
let isevars = ref (Evd.create_evar_defs sigma) in
let env = Global.env() in
- let pr c = my_print_constr env c in
- let prr = Printer.pr_rel_context env in
- let prn = Printer.pr_named_context env in
- let pr_rel env = Printer.pr_rel_context env in
let nc = named_context env in
let nc_len = named_context_length nc in
- let _ =
- try debug 2 (str "In named context: " ++ prn (named_context env) ++ str "Rewriting fixpoint: " ++ Ppconstr.pr_id recname ++
- Ppconstr.pr_binders bl ++ str " : " ++
- Ppconstr.pr_constr_expr arityc ++ str " := " ++ spc () ++
- Ppconstr.pr_constr_expr body)
- with _ -> ()
- in
+(* let pr c = my_print_constr env c in *)
+(* let prr = Printer.pr_rel_context env in *)
+(* let prn = Printer.pr_named_context env in *)
+(* let pr_rel env = Printer.pr_rel_context env in *)
+(* let _ = *)
+(* try debug 2 (str "In named context: " ++ prn (named_context env) ++ str "Rewriting fixpoint: " ++ Ppconstr.pr_id recname ++ *)
+(* Ppconstr.pr_binders bl ++ str " : " ++ *)
+(* Ppconstr.pr_constr_expr arityc ++ str " := " ++ spc () ++ *)
+(* Ppconstr.pr_constr_expr body) *)
+(* with _ -> () *)
+ (* in *)
let env', binders_rel = interp_context isevars env bl in
- let after, ((argname, _, argtyp) as arg), before = list_chop_hd (succ n) binders_rel in
+ let after, ((argname, _, argtyp) as arg), before = split_args (succ n) binders_rel in
let before_length, after_length = List.length before, List.length after in
let argid = match argname with Name n -> n | _ -> assert(false) in
let _liftafter = lift_binders 1 after_length after in
@@ -226,15 +222,14 @@ let build_wellfounded (recname, n, bl,arityc,body) r measure notation boxed =
in
let argid' = id_of_string (string_of_id argid ^ "'") in
let wfarg len = (Name argid', None,
- mkSubset (Name argid') argtyp
+ mkSubset (Name argid') (lift len argtyp)
(wf_rel_fun (mkRel 1) (mkRel (len + 1))))
in
let top_bl = after @ (arg :: before) in
let intern_bl = after @ (wfarg 1 :: arg :: before) in
let top_env = push_rel_context top_bl env in
- let intern_env = push_rel_context intern_bl env in
+ let _intern_env = push_rel_context intern_bl env in
let top_arity = interp_type isevars top_env arityc in
- (try debug 2 (str "Intern bl: " ++ prr intern_bl) with _ -> ());
let proj = (Lazy.force sig_).Coqlib.proj1 in
let projection =
mkApp (proj, [| argtyp ;
@@ -243,32 +238,32 @@ let build_wellfounded (recname, n, bl,arityc,body) r measure notation boxed =
mkRel 1
|])
in
- (try debug 2 (str "Top arity: " ++ my_print_constr top_env top_arity) with _ -> ());
+ (* (try debug 2 (str "Top arity: " ++ my_print_constr top_env top_arity) with _ -> ()); *)
let intern_arity = substnl [projection] after_length top_arity in
- (try debug 2 (str "Top arity after subst: " ++ my_print_constr intern_env intern_arity) with _ -> ());
+(* (try debug 2 (str "Top arity after subst: " ++ my_print_constr intern_env intern_arity) with _ -> ()); *)
let intern_before_env = push_rel_context before env in
let intern_fun_bl = after @ [wfarg 1] in
- (try debug 2 (str "Intern fun bl: " ++ prr intern_fun_bl) with _ -> ());
+(* (try debug 2 (str "Intern fun bl: " ++ prr intern_fun_bl) with _ -> ()); *)
let intern_fun_arity = intern_arity in
- (try debug 2 (str "Intern fun arity: " ++
- my_print_constr intern_env intern_fun_arity) with _ -> ());
+(* (try debug 2 (str "Intern fun arity: " ++ *)
+(* my_print_constr intern_env intern_fun_arity) with _ -> ()); *)
let intern_fun_arity_prod = it_mkProd_or_LetIn intern_fun_arity intern_fun_bl in
let intern_fun_binder = (Name recname, None, intern_fun_arity_prod) in
let fun_bl = after @ (intern_fun_binder :: [arg]) in
- (try debug 2 (str "Fun bl: " ++ pr_rel intern_before_env fun_bl ++ spc ()) with _ -> ());
+(* (try debug 2 (str "Fun bl: " ++ pr_rel intern_before_env fun_bl ++ spc ()) with _ -> ()); *)
let fun_env = push_rel_context fun_bl intern_before_env in
let fun_arity = interp_type isevars fun_env arityc in
let intern_body = interp_casted_constr isevars fun_env body fun_arity in
let intern_body_lam = it_mkLambda_or_LetIn intern_body fun_bl in
- let _ =
- try debug 2 (str "Fun bl: " ++ prr fun_bl ++ spc () ++
- str "Intern bl" ++ prr intern_bl ++ spc () ++
- str "Top bl" ++ prr top_bl ++ spc () ++
- str "Intern arity: " ++ pr intern_arity ++
- str "Top arity: " ++ pr top_arity ++ spc () ++
- str "Intern body " ++ pr intern_body_lam)
- with _ -> ()
- in
+(* let _ = *)
+(* try debug 2 (str "Fun bl: " ++ prr fun_bl ++ spc () ++ *)
+(* str "Intern bl" ++ prr intern_bl ++ spc () ++ *)
+(* str "Top bl" ++ prr top_bl ++ spc () ++ *)
+(* str "Intern arity: " ++ pr intern_arity ++ *)
+(* str "Top arity: " ++ pr top_arity ++ spc () ++ *)
+(* str "Intern body " ++ pr intern_body_lam) *)
+(* with _ -> () *)
+(* in *)
let _impl =
if Impargs.is_implicit_args()
then Impargs.compute_implicits top_env top_arity
@@ -292,53 +287,48 @@ let build_wellfounded (recname, n, bl,arityc,body) r measure notation boxed =
let def_appl = applist (fix_def, gen_rels (after_length + 1)) in
let def = it_mkLambda_or_LetIn def_appl binders_rel in
let typ = it_mkProd_or_LetIn top_arity binders_rel in
- debug 2 (str "Constructed def");
- debug 2 (my_print_constr intern_before_env def);
- debug 2 (str "Type: " ++ my_print_constr env typ);
let fullcoqc = Evarutil.nf_isevar !isevars def in
let fullctyp = Evarutil.nf_isevar !isevars typ in
- let _ = try trace (str "After evar normalization: " ++ spc () ++
- str "Coq term: " ++ my_print_constr env fullcoqc ++ spc ()
- ++ str "Coq type: " ++ my_print_constr env fullctyp)
- with _ -> ()
- in
+(* let _ = try trace (str "After evar normalization: " ++ spc () ++ *)
+(* str "Coq term: " ++ my_print_constr env fullcoqc ++ spc () *)
+(* ++ str "Coq type: " ++ my_print_constr env fullctyp) *)
+(* with _ -> () *)
+(* in *)
let evm = non_instanciated_map env isevars in
- let _ = try trace (str "Non instanciated evars map: " ++ Evd.pr_evar_map evm) with _ -> () in
+ (* let _ = try trace (str "Non instanciated evars map: " ++ Evd.pr_evar_map evm) with _ -> () in *)
let evars, evars_def = Eterm.eterm_obligations recname nc_len evm fullcoqc (Some fullctyp) in
- (try trace (str "Generated obligations : ");
- Array.iter
- (fun (n, t, _) -> trace (str "Evar " ++ str (string_of_id n) ++ spc () ++ my_print_constr env t))
- evars;
- with _ -> ());
- trace (str "Adding to obligations list");
- Subtac_obligations.add_entry recname evars_def fullctyp evars;
- trace (str "Added to obligations list")
-(*
+ (* (try trace (str "Generated obligations : "); *)
+(* Array.iter *)
+ (* (fun (n, t, _) -> trace (str "Evar " ++ str (string_of_id n) ++ spc () ++ my_print_constr env t)) *)
+ (* evars; *)
+ (* with _ -> ()); *)
+ Subtac_obligations.add_definition recname evars_def fullctyp evars
+
let build_mutrec l boxed =
- let sigma = Evd.empty
- and env0 = Global.env()
- in
+ let sigma = Evd.empty and env = Global.env () in
+ let nc = named_context env in
+ let nc_len = named_context_length nc in
let lnameargsardef =
- (*List.map (fun (f, d) -> Subtac_interp_fixpoint.rewrite_fixpoint env0 protos (f, d))*)
+ (*List.map (fun (f, d) -> Subtac_interp_fixpoint.rewrite_fixpoint env protos (f, d))*)
l
in
let lrecnames = List.map (fun ((f,_,_,_,_),_) -> f) lnameargsardef
and nv = List.map (fun ((_,n,_,_,_),_) -> n) lnameargsardef
in
(* Build the recursive context and notations for the recursive types *)
- let (rec_sign,rec_impls,arityl) =
+ let (rec_sign,rec_env,rec_impls,arityl) =
List.fold_left
- (fun (env,impls,arl) ((recname, n, bl,arityc,body),_) ->
+ (fun (sign,env,impls,arl) ((recname, n, bl,arityc,body),_) ->
let isevars = ref (Evd.create_evar_defs sigma) in
let arityc = Command.generalize_constr_expr arityc bl in
- let arity = interp_type isevars env0 arityc in
+ let arity = interp_type isevars env arityc in
let impl =
if Impargs.is_implicit_args()
- then Impargs.compute_implicits env0 arity
+ then Impargs.compute_implicits env arity
else [] in
let impls' =(recname,([],impl,compute_arguments_scope arity))::impls in
- (Environ.push_named (recname,None,arity) env, impls', (isevars, None, arity)::arl))
- (env0,[],[]) lnameargsardef in
+ ((recname,None,arity) :: sign, Environ.push_named (recname,None,arity) env, impls', (isevars, None, arity)::arl))
+ ([],env,[],[]) lnameargsardef in
let arityl = List.rev arityl in
let notations =
List.fold_right (fun (_,ntnopt) l -> option_cons ntnopt l)
@@ -357,11 +347,11 @@ let build_mutrec l boxed =
match info with
None ->
let def = abstract_constr_expr def bl in
- isevars, info, interp_casted_constr isevars rec_sign ~impls:([],rec_impls)
+ isevars, info, interp_casted_constr isevars rec_env ~impls:([],rec_impls)
def arity
| Some (n, artyp, wfrel, fun_bl, intern_bl, intern_arity) ->
- let rec_sign = push_rel_context fun_bl rec_sign in
- let cstr = interp_casted_constr isevars rec_sign ~impls:([],rec_impls)
+ let rec_env = push_rel_context fun_bl rec_env in
+ let cstr = interp_casted_constr isevars rec_env ~impls:([],rec_impls)
def intern_arity
in isevars, info, it_mkLambda_or_LetIn cstr fun_bl)
lnameargsardef arityl
@@ -369,162 +359,33 @@ let build_mutrec l boxed =
States.unfreeze fs; raise e in
States.unfreeze fs; def
in
-
let (lnonrec,(namerec,defrec,arrec,nvrec)) =
- collect_non_rec env0 lrecnames recdef arityl nv in
- let declare arrec defrec =
- let recvec =
- Array.map (subst_vars (List.rev (Array.to_list namerec))) defrec in
- let recdecls = (Array.map (fun id -> Name id) namerec, arrec, recvec) in
- let rec declare i fi =
- (try trace (str "Declaring: " ++ pr_id fi ++ spc () ++
- my_print_constr env0 (recvec.(i)));
- with _ -> ());
- let ce =
- { const_entry_body = mkFix ((nvrec,i),recdecls);
- const_entry_type = Some arrec.(i);
- const_entry_opaque = false;
- const_entry_boxed = boxed} in
- let kn = Declare.declare_constant fi (DefinitionEntry ce,IsDefinition Fixpoint)
- in (ConstRef kn)
- in
- (* declare the recursive definitions *)
- let lrefrec = Array.mapi declare namerec in
- Options.if_verbose ppnl (recursive_message lrefrec);
-
-
- (*(* The others are declared as normal definitions *)
- let var_subst id = (id, Constrintern.global_reference id) in
- let _ =
- List.fold_left
- (fun subst (f,def,t) ->
- let ce = { const_entry_body = replace_vars subst def;
- const_entry_type = Some t;
- const_entry_opaque = false;
- const_entry_boxed = boxed } in
- let _ =
- Declare.declare_constant f (DefinitionEntry ce,IsDefinition Definition)
- in
- warning ((string_of_id f)^" is non-recursively defined");
- (var_subst f) :: subst)
- (List.map var_subst (Array.to_list namerec))
- lnonrec
- in*)
- List.iter (fun (df,c,scope) ->
- Metasyntax.add_notation_interpretation df [] c scope) notations
- in
- let declare l =
- let recvec = Array.of_list l
- and arrec = Array.map pi3 arrec
- in declare arrec recvec
- in
+ collect_non_rec env lrecnames recdef arityl nv in
let recdefs = Array.length defrec in
- trace (int recdefs ++ str " recursive definitions");
(* Solve remaining evars *)
let rec collect_evars i acc =
if i < recdefs then
let (isevars, info, def) = defrec.(i) in
- let _ = try trace (str "In solve evars, isevars is: " ++ Evd.pr_evar_defs !isevars) with _ -> () in
+ (* let _ = try trace (str "In solve evars, isevars is: " ++ Evd.pr_evar_defs !isevars) with _ -> () in *)
let def = evar_nf isevars def in
let isevars = Evd.undefined_evars !isevars in
- let _ = try trace (str "In solve evars, undefined is: " ++ Evd.pr_evar_defs isevars) with _ -> () in
+ (* let _ = try trace (str "In solve evars, undefined is: " ++ Evd.pr_evar_defs isevars) with _ -> () in *)
let evm = Evd.evars_of isevars in
let _, _, typ = arrec.(i) in
let id = namerec.(i) in
- (* Generalize by the recursive prototypes *)
+ (* Generalize by the recursive prototypes *)
let def =
- Termops.it_mkNamedLambda_or_LetIn def (Environ.named_context rec_sign)
+ Termops.it_mkNamedLambda_or_LetIn def rec_sign
and typ =
- Termops.it_mkNamedProd_or_LetIn typ (Environ.named_context rec_sign)
+ Termops.it_mkNamedProd_or_LetIn typ rec_sign
in
- let evars_def, evars_typ, evars = Eterm.eterm_term evm def (Some typ) in
- (*let evars_typ = match evars_typ with Some t -> t | None -> assert(false) in*)
- (*let fi = id_of_string (string_of_id id ^ "_evars") in*)
- (*let ce =
- { const_entry_body = evars_def;
- const_entry_type = Some evars_typ;
- const_entry_opaque = false;
- const_entry_boxed = boxed} in
- let kn = Declare.declare_constant fi (DefinitionEntry ce,IsDefinition Definition) in
- definition_message fi;
- trace (str (string_of_id fi) ++ str " is defined");*)
- let evar_sum =
- if evars = [] then None
- else (
- (try trace (str "Building evars sum for : ");
- List.iter
- (fun (n, t) -> trace (str "Evar " ++ str (string_of_id n) ++ spc () ++ my_print_constr env0 t))
- evars;
- with _ -> ());
- let sum = Subtac_utils.build_dependent_sum evars in
- (try trace (str "Evars sum: " ++ my_print_constr env0 (snd sum));
- with _ -> ());
- Some sum)
- in
- collect_evars (succ i) ((id, evars_def, evar_sum) :: acc)
+ let evars, def = Eterm.eterm_obligations id nc_len evm def (Some typ) in
+ collect_evars (succ i) ((id, def, typ, evars) :: acc)
else acc
in
let defs = collect_evars 0 [] in
-
- (* Solve evars then create the definitions *)
- let real_evars =
- filter_map (fun (id, kn, sum) ->
- match sum with Some (sumtac, sumg) -> Some (id, kn, sumg, sumtac) | None -> None)
- defs
- in
- match real_evars with
- [] -> declare (List.rev_map (fun (id, c, _) ->
- snd (decompose_lam_n recdefs c)) defs)
- | l ->
-
- Subtac_utils.and_tac real_evars
- (fun f _ gr ->
- let _ = trace (str "Got a proof of: " ++ pr_global gr ++
- str "type: " ++ my_print_constr (Global.env ()) (Global.type_of_global gr)) in
- let constant = match gr with Libnames.ConstRef c -> c
- | _ -> assert(false)
- in
- try
- (*let value = Environ.constant_value (Global.env ()) constant in*)
- let pis = f (mkConst constant) in
- (try (trace (str "Accessors: " ++
- List.fold_right (fun (_, _, _, c) acc -> my_print_constr env0 c ++ spc () ++ acc)
- pis (mt()));
- trace (str "Applied existentials: " ++
- (List.fold_right
- (fun (id, kn, sumg, pi) acc ->
- let args = Subtac_utils.destruct_ex pi sumg in
- my_print_constr env0 (mkApp (kn, Array.of_list args)))
- pis (mt ()))))
- with _ -> ());
- let rec aux pis acc = function
- (id, kn, sum) :: tl ->
- (match sum with
- None -> aux pis (kn :: acc) tl
- | Some (_, sumg) ->
- let (id, kn, sumg, pi), pis = List.hd pis, List.tl pis in
- let args = Subtac_utils.destruct_ex pi sumg in
- let args =
- List.map (fun c ->
- try Reductionops.whd_betadeltaiota (Global.env ()) Evd.empty c
- with Not_found ->
- trace (str "Not_found while reducing " ++
- my_print_constr (Global.env ()) c);
- c
- ) args
- in
- let _, newdef = decompose_lam_n (recdefs + List.length args) kn in
- let constr = Term.substl (mkRel 1 :: List.rev args) newdef in
- aux pis (constr :: acc) tl)
- | [] -> List.rev acc
- in
- declare (aux pis [] defs)
- with Environ.NotEvaluableConst cer ->
- match cer with
- Environ.NoBody -> trace (str "Constant has no body")
- | Environ.Opaque -> trace (str "Constant is opaque")
- )
-*)
+ Subtac_obligations.add_mutual_definitions (List.rev defs) nvrec
+
let out_n = function
Some n -> n
| None -> 0
@@ -544,8 +405,7 @@ let build_recursive (lnameargsardef:(fixpoint_expr * decl_notation) list) boxed
errorlabstrm "Subtac_command.build_recursive"
(str "Well-founded fixpoints not allowed in mutually recursive blocks"))
lnameargsardef
- in assert(false)
- (*build_mutrec lnameargsardef boxed*)
+ in build_mutrec lnameargsardef boxed
diff --git a/contrib/subtac/subtac_obligations.ml b/contrib/subtac/subtac_obligations.ml
index 7b13b402..d6c1772f 100644
--- a/contrib/subtac/subtac_obligations.ml
+++ b/contrib/subtac/subtac_obligations.ml
@@ -12,6 +12,8 @@ open Decl_kinds
open Util
open Evd
+type obligation_info = (Names.identifier * Term.types * Intset.t) array
+
type obligation =
{ obl_name : identifier;
obl_type : types;
@@ -24,15 +26,42 @@ type obligations = (obligation array * int)
type program_info = {
prg_name: identifier;
prg_body: constr;
- prg_type: types;
+ prg_type: constr;
prg_obligations: obligations;
+ prg_deps : identifier list;
+ prg_nvrec : int array;
}
-let evar_of_obligation o = { evar_hyps = Environ.empty_named_context_val ;
+let assumption_message id =
+ Options.if_verbose message ((string_of_id id) ^ " is assumed")
+
+let default_tactic : Proof_type.tactic ref = ref Refiner.tclIDTAC
+
+let set_default_tactic t = default_tactic := t
+
+let evar_of_obligation o = { evar_hyps = Global.named_context_val () ;
evar_concl = o.obl_type ;
evar_body = Evar_empty ;
evar_extra = None }
+let subst_deps obls deps t =
+ Intset.fold
+ (fun x acc ->
+ let xobl = obls.(x) in
+ debug 3 (str "Trying to get body of obligation " ++ int x);
+ let oblb =
+ try out_some xobl.obl_body
+ with _ ->
+ debug 3 (str "Couldn't get body of obligation " ++ int x);
+ assert(false)
+ in
+ Term.subst1 oblb (Term.subst_var xobl.obl_name acc))
+ deps t
+
+let subst_deps_obl obls obl =
+ let t' = subst_deps obls obl.obl_deps obl.obl_type in
+ { obl with obl_type = t' }
+
module ProgMap = Map.Make(struct type t = identifier let compare = compare end)
let map_replace k v m = ProgMap.add k v (ProgMap.remove k m)
@@ -62,21 +91,6 @@ let _ =
Summary.survive_module = false;
Summary.survive_section = false }
-let declare_definition prg =
-(* let obls_constrs =
- Array.fold_right (fun x acc -> (out_some x.obl_evar.evar_body) :: acc) (fst prg.prg_obligations) []
- in*)
- let ce =
- { const_entry_body = prg.prg_body;
- const_entry_type = Some prg.prg_type;
- const_entry_opaque = false;
- const_entry_boxed = false}
- in
- let _constant = Declare.declare_constant
- prg.prg_name (DefinitionEntry ce,IsDefinition Definition)
- in
- Subtac_utils.definition_message prg.prg_name
-
open Evd
let terms_of_evar ev =
@@ -88,14 +102,72 @@ let terms_of_evar ev =
body, typ
| _ -> assert(false)
+let rec intset_to = function
+ -1 -> Intset.empty
+ | n -> Intset.add n (intset_to (pred n))
+
+let subst_body prg =
+ let obls, _ = prg.prg_obligations in
+ subst_deps obls (intset_to (pred (Array.length obls))) prg.prg_body
+
+let declare_definition prg =
+ let body = subst_body prg in
+ (try trace (str "Declaring: " ++ Ppconstr.pr_id prg.prg_name ++ spc () ++
+ my_print_constr (Global.env()) body);
+ with _ -> ());
+ let ce =
+ { const_entry_body = body;
+ const_entry_type = Some prg.prg_type;
+ const_entry_opaque = false;
+ const_entry_boxed = false}
+ in
+ let _constant = Declare.declare_constant
+ prg.prg_name (DefinitionEntry ce,IsDefinition Definition)
+ in
+ Subtac_utils.definition_message prg.prg_name
+
+open Pp
+open Ppconstr
+
+let declare_mutual_definition l =
+ let len = List.length l in
+ let namerec = Array.of_list (List.map (fun x -> x.prg_name) l) in
+ let arrec =
+ Array.of_list (List.map (fun x -> snd (decompose_prod_n len x.prg_type)) l)
+ in
+ let recvec =
+ Array.of_list
+ (List.map (fun x ->
+ let subs = (subst_body x) in
+ snd (decompose_lam_n len subs)) l)
+ in
+ let nvrec = (List.hd l).prg_nvrec in
+ let recdecls = (Array.map (fun id -> Name id) namerec, arrec, recvec) in
+ let rec declare i fi =
+ (try trace (str "Declaring: " ++ pr_id fi ++ spc () ++
+ my_print_constr (Global.env()) (recvec.(i)));
+ with _ -> ());
+ let ce =
+ { const_entry_body = mkFix ((nvrec,i),recdecls);
+ const_entry_type = Some arrec.(i);
+ const_entry_opaque = false;
+ const_entry_boxed = true} in
+ let kn = Declare.declare_constant fi (DefinitionEntry ce,IsDefinition Fixpoint)
+ in
+ ConstRef kn
+ in
+ let lrefrec = Array.mapi declare namerec in
+ Options.if_verbose ppnl (recursive_message lrefrec)
+
let declare_obligation obl body =
let ce =
{ const_entry_body = body;
const_entry_type = Some obl.obl_type;
- const_entry_opaque = true;
+ const_entry_opaque = false;
const_entry_boxed = false}
in
- let constant = Declare.declare_constant obl.obl_name (DefinitionEntry ce,IsProof Property)
+ let constant = Declare.declare_constant obl.obl_name
+ (DefinitionEntry ce,IsProof Property)
in
Subtac_utils.definition_message obl.obl_name;
{ obl with obl_body = Some (mkConst constant) }
@@ -113,36 +185,30 @@ let try_tactics obls =
| _ -> obl)
obls
-let add_entry n b t obls =
- Options.if_verbose pp (str (string_of_id n) ++ str " has type-checked");
- let init_obls e =
- Array.map
- (fun (n, t, d) ->
- { obl_name = n ; obl_body = None; obl_type = t; obl_deps = d })
- e
+let red = Reductionops.nf_betaiota
+
+let init_prog_info n b t deps nvrec obls =
+ let obls' =
+ Array.mapi
+ (fun i (n, t, d) ->
+ debug 2 (str "Adding obligation " ++ int i ++ str " with deps : " ++ str (string_of_intset d));
+ { obl_name = n ; obl_body = None;
+ obl_type = red t;
+ obl_deps = d })
+ obls
in
- if Array.length obls = 0 then (
- Options.if_verbose ppnl (str ".");
- declare_definition { prg_name = n ; prg_body = b ; prg_type = t ; prg_obligations = ([||], 0) } )
- else (
- let len = Array.length obls in
- let _ = Options.if_verbose ppnl (str ", generating " ++ int len ++ str " obligation(s)") in
- let obls = init_obls obls in
- let rem = Array.fold_left (fun acc obl -> if obl.obl_body = None then succ acc else acc) 0 obls in
- let prg = { prg_name = n ; prg_body = b ; prg_type = t ; prg_obligations = (obls, rem) } in
- if rem < len then
- Options.if_verbose ppnl (int rem ++ str " obligation(s) remaining.");
- if rem = 0 then
- declare_definition prg
- else
- from_prg := ProgMap.add n prg !from_prg)
-
-let error s = Util.error s
+ { prg_name = n ; prg_body = b; prg_type = red t; prg_obligations = (obls', Array.length obls');
+ prg_deps = deps; prg_nvrec = nvrec; }
+
+let pperror cmd = Util.errorlabstrm "Subtac" cmd
+let error s = pperror (str s)
let get_prog name =
let prg_infos = !from_prg in
match name with
- Some n -> ProgMap.find n prg_infos
+ Some n ->
+ (try ProgMap.find n prg_infos
+ with Not_found -> error ("No obligations for program " ^ string_of_id n))
| None ->
(let n = map_cardinal prg_infos in
match n with
@@ -150,57 +216,67 @@ let get_prog name =
| 1 -> map_first prg_infos
| _ -> error "More than one program with unsolved obligations")
+let obligations_solved prg = (snd prg.prg_obligations) = 0
+
let update_obls prg obls rem =
let prg' = { prg with prg_obligations = (obls, rem) } in
- if rem > 1 then (
- debug 2 (int rem ++ str " obligations remaining");
- from_prg := map_replace prg.prg_name prg' !from_prg)
+ from_prg := map_replace prg.prg_name prg' !from_prg;
+ if rem > 0 then (
+ Options.if_verbose msgnl (int rem ++ str " obligation(s) remaining");
+ )
else (
- declare_definition prg';
- from_prg := ProgMap.remove prg.prg_name !from_prg
- )
+ Options.if_verbose msgnl (str "No more obligations remaining");
+ match prg'.prg_deps with
+ [] ->
+ declare_definition prg';
+ from_prg := ProgMap.remove prg.prg_name !from_prg
+ | l ->
+ let progs = List.map (fun x -> ProgMap.find x !from_prg) prg'.prg_deps in
+ if List.for_all (fun x -> obligations_solved x) progs then
+ (declare_mutual_definition progs;
+ from_prg := List.fold_left
+ (fun acc x -> ProgMap.remove x.prg_name acc) !from_prg progs))
let is_defined obls x = obls.(x).obl_body <> None
-let deps_remaining obls x =
- let deps = obls.(x).obl_deps in
+let deps_remaining obls deps =
Intset.fold
(fun x acc ->
if is_defined obls x then acc
else x :: acc)
deps []
-let subst_deps obls obl =
- let t' =
- Intset.fold
- (fun x acc ->
- let xobl = obls.(x) in
- let oblb = out_some xobl.obl_body in
- Term.subst1 oblb (Term.subst_var xobl.obl_name acc))
- obl.obl_deps obl.obl_type
- in { obl with obl_type = t' }
-
-let subtac_obligation (user_num, name) =
+let solve_obligation prg num =
+ let user_num = succ num in
+ let obls, rem = prg.prg_obligations in
+ let obl = obls.(num) in
+ if obl.obl_body <> None then
+ pperror (str "Obligation" ++ spc () ++ int user_num ++ str "already" ++ spc() ++ str "solved.")
+ else
+ match deps_remaining obls obl.obl_deps with
+ [] ->
+ let obl = subst_deps_obl obls obl in
+ Command.start_proof obl.obl_name Subtac_utils.goal_proof_kind obl.obl_type
+ (fun strength gr ->
+ debug 2 (str "Proof of obligation " ++ int user_num ++ str " finished");
+ let obl = { obl with obl_body = Some (Libnames.constr_of_global gr) } in
+ let obls = Array.copy obls in
+ let _ = obls.(num) <- obl in
+ update_obls prg obls (pred rem));
+ trace (str "Started obligation " ++ int user_num ++ str " proof: " ++
+ Subtac_utils.my_print_constr (Global.env ()) obl.obl_type);
+ Pfedit.by !default_tactic
+ | l -> pperror (str "Obligation " ++ int user_num ++ str " depends on obligation(s) "
+ ++ str (string_of_list ", " (fun x -> string_of_int (succ x)) l))
+
+let subtac_obligation (user_num, name, typ) =
let num = pred user_num in
let prg = get_prog name in
let obls, rem = prg.prg_obligations in
if num < Array.length obls then
let obl = obls.(num) in
match obl.obl_body with
- None ->
- (match deps_remaining obls num with
- [] ->
- let obl = subst_deps obls obl in
- Command.start_proof obl.obl_name Subtac_utils.goal_proof_kind obl.obl_type
- (fun strength gr ->
- debug 2 (str "Proof of obligation " ++ int user_num ++ str " finished");
- let obl = { obl with obl_body = Some (Libnames.constr_of_global gr) } in
- let obls = Array.copy obls in
- let _ = obls.(num) <- obl in
- update_obls prg obls (pred rem));
- trace (str "Started obligation " ++ int user_num ++ str " proof")
- | l -> msgnl (str "Obligation " ++ int user_num ++ str " depends on obligation(s) "
- ++ str (string_of_list ", " (fun x -> string_of_int (succ x)) l)))
+ None -> solve_obligation prg num
| Some r -> error "Obligation already solved"
else error (sprintf "Unknown obligation number %i" (succ num))
@@ -217,33 +293,102 @@ let obligations_of_evars evars =
}) evars)
in arr, Array.length arr
+let solve_obligation_by_tac prg obls i tac =
+ let obl = obls.(i) in
+ match obl.obl_body with
+ Some _ -> false
+ | None ->
+ (try
+ if deps_remaining obls obl.obl_deps = [] then
+ let obl = subst_deps_obl obls obl in
+ let t = Subtac_utils.solve_by_tac (evar_of_obligation obl) tac in
+ obls.(i) <- { obl with obl_body = Some t };
+ true
+ else false
+ with _ -> false)
+
let solve_obligations n tac =
let prg = get_prog n in
let obls, rem = prg.prg_obligations in
let rem = ref rem in
+ let obls' = Array.copy obls in
+ let _ =
+ Array.iteri (fun i x ->
+ if solve_obligation_by_tac prg obls' i tac then
+ decr rem)
+ obls'
+ in
+ update_obls prg obls' !rem
+
+let add_definition n b t obls =
+ Options.if_verbose pp (str (string_of_id n) ++ str " has type-checked");
+ let prg = init_prog_info n b t [] (Array.make 0 0) obls in
+ let obls,_ = prg.prg_obligations in
+ if Array.length obls = 0 then (
+ Options.if_verbose ppnl (str ".");
+ declare_definition prg;
+ from_prg := ProgMap.remove prg.prg_name !from_prg)
+ else (
+ let len = Array.length obls in
+ let _ = Options.if_verbose ppnl (str ", generating " ++ int len ++ str " obligation(s)") in
+ from_prg := ProgMap.add n prg !from_prg;
+ solve_obligations (Some n) !default_tactic)
+
+let add_mutual_definitions l nvrec =
+ let deps = List.map (fun (n, b, t, obls) -> n) l in
+ let upd = List.fold_left
+ (fun acc (n, b, t, obls) ->
+ let prg = init_prog_info n b t deps nvrec obls in
+ ProgMap.add n prg acc)
+ !from_prg l
+ in
+ from_prg := upd;
+ List.iter (fun x -> solve_obligations (Some x) !default_tactic) deps
+
+let admit_obligations n =
+ let prg = get_prog n in
+ let obls, rem = prg.prg_obligations in
let obls' =
- Array.map (fun x ->
+ Array.mapi (fun i x ->
match x.obl_body with
- Some _ -> x
- | None ->
- try
- let t = Subtac_utils.solve_by_tac (evar_of_obligation x) tac in
- decr rem;
- { x with obl_body = Some t }
- with _ -> x)
+ None ->
+ let kn = Declare.declare_constant x.obl_name (ParameterEntry x.obl_type, IsAssumption Conjectural) in
+ assumption_message x.obl_name;
+ { x with obl_body = Some (mkConst kn) }
+ | Some _ -> x)
obls
in
- update_obls prg obls' !rem
+ update_obls prg obls' 0
+exception Found of int
+
+let array_find f arr =
+ try Array.iteri (fun i x -> if f x then raise (Found i)) arr;
+ raise Not_found
+ with Found i -> i
+
+let rec next_obligation n =
+ let prg = get_prog n in
+ let obls, rem = prg.prg_obligations in
+ let i =
+ array_find (fun x -> x.obl_body = None && deps_remaining obls x.obl_deps = [])
+ obls
+ in
+ if solve_obligation_by_tac prg obls i !default_tactic then (
+ update_obls prg obls (pred rem);
+ next_obligation n
+ ) else solve_obligation prg i
+
open Pp
let show_obligations n =
let prg = get_prog n in
+ let n = prg.prg_name in
let obls, rem = prg.prg_obligations in
msgnl (int rem ++ str " obligation(s) remaining: ");
Array.iteri (fun i x ->
match x.obl_body with
- None -> msgnl (int (succ i) ++ str " : " ++ spc () ++
- my_print_constr (Global.env ()) x.obl_type)
+ None -> msgnl (str "Obligation" ++ spc() ++ int (succ i) ++ spc () ++ str "of" ++ spc() ++ str (string_of_id n) ++ str ":" ++ spc () ++
+ my_print_constr (Global.env ()) x.obl_type ++ str "." ++ fnl ())
| Some _ -> ())
obls
diff --git a/contrib/subtac/subtac_obligations.mli b/contrib/subtac/subtac_obligations.mli
index 7d93d57b..3981d4c6 100644
--- a/contrib/subtac/subtac_obligations.mli
+++ b/contrib/subtac/subtac_obligations.mli
@@ -1,10 +1,21 @@
open Util
-val add_entry : Names.identifier -> Term.constr -> Term.types ->
- (Names.identifier * Term.types * Intset.t) array -> unit
+type obligation_info = (Names.identifier * Term.types * Intset.t) array
-val subtac_obligation : int * Names.identifier option -> unit
+val set_default_tactic : Proof_type.tactic -> unit
+
+val add_definition : Names.identifier -> Term.constr -> Term.types ->
+ obligation_info -> unit
+
+val add_mutual_definitions :
+ (Names.identifier * Term.constr * Term.types * obligation_info) list -> int array -> unit
+
+val subtac_obligation : int * Names.identifier option * Topconstr.constr_expr option -> unit
+
+val next_obligation : Names.identifier option -> unit
val solve_obligations : Names.identifier option -> Proof_type.tactic -> unit
val show_obligations : Names.identifier option -> unit
+
+val admit_obligations : Names.identifier option -> unit
diff --git a/contrib/subtac/subtac_pretyping.ml b/contrib/subtac/subtac_pretyping.ml
index a243ba34..4d1ac731 100644
--- a/contrib/subtac/subtac_pretyping.ml
+++ b/contrib/subtac/subtac_pretyping.ml
@@ -6,7 +6,7 @@
(* * GNU Lesser General Public License Version 2.1 *)
(************************************************************************)
-(* $Id: subtac_pretyping.ml 9326 2006-10-31 12:57:26Z msozeau $ *)
+(* $Id: subtac_pretyping.ml 9563 2007-01-31 09:37:18Z msozeau $ *)
open Global
open Pp
@@ -113,29 +113,23 @@ let env_with_binders env isevars l =
in aux (env, []) l
let subtac_process env isevars id l c tycon =
- let evars () = evars_of !isevars in
- let _ = trace (str "Creating env with binders") in
let env_binders, binders_rel = env_with_binders env isevars l in
- let _ = try (trace (str "New env created:" ++ my_print_context env_binders)) with _ -> () in
let tycon =
match tycon with
None -> empty_tycon
| Some t ->
let t = coqintern !isevars env_binders t in
- let _ = try trace (str "Internalized specification: " ++ my_print_rawconstr env_binders t) with _ -> () in
let coqt, ttyp = interp env_binders isevars t empty_tycon in
- let _ = try trace (str "Interpreted type: " ++ my_print_constr env_binders coqt) with _ -> () in
mk_tycon coqt
in
let c = coqintern !isevars env_binders c in
let c = Subtac_utils.rewrite_cases env c in
- let _ = try trace (str "Internalized term: " ++ my_print_rawconstr env c) with _ -> () in
let coqc, ctyp = interp env_binders isevars c tycon in
- let _ = try trace (str "Interpreted term: " ++ my_print_constr env_binders coqc ++ spc () ++
- str "Coq type: " ++ my_print_constr env_binders ctyp)
- with _ -> ()
- in
- let _ = try trace (str "Original evar map: " ++ Evd.pr_evar_map (evars ())) with _ -> () in
+(* let _ = try trace (str "Interpreted term: " ++ my_print_constr env_binders coqc ++ spc () ++ *)
+(* str "Coq type: " ++ my_print_constr env_binders ctyp) *)
+(* with _ -> () *)
+(* in *)
+(* let _ = try trace (str "Original evar map: " ++ Evd.pr_evar_map (evars ())) with _ -> () in *)
let fullcoqc = it_mkLambda_or_LetIn coqc binders_rel
and fullctyp = it_mkProd_or_LetIn ctyp binders_rel
@@ -143,13 +137,13 @@ let subtac_process env isevars id l c tycon =
let fullcoqc = Evarutil.nf_evar (evars_of !isevars) fullcoqc in
let fullctyp = Evarutil.nf_evar (evars_of !isevars) fullctyp in
- let _ = try trace (str "After evar normalization: " ++ spc () ++
- str "Coq term: " ++ my_print_constr env fullcoqc ++ spc ()
- ++ str "Coq type: " ++ my_print_constr env fullctyp)
- with _ -> ()
- in
+(* let _ = try trace (str "After evar normalization: " ++ spc () ++ *)
+(* str "Coq term: " ++ my_print_constr env fullcoqc ++ spc () *)
+(* ++ str "Coq type: " ++ my_print_constr env fullctyp) *)
+(* with _ -> () *)
+(* in *)
let evm = non_instanciated_map env isevars in
- let _ = try trace (str "Non instanciated evars map: " ++ Evd.pr_evar_map evm) with _ -> () in
+(* let _ = try trace (str "Non instanciated evars map: " ++ Evd.pr_evar_map evm) with _ -> () in *)
evm, fullcoqc, fullctyp
open Subtac_obligations
@@ -159,5 +153,4 @@ let subtac_proof env isevars id l c tycon =
let nc_len = named_context_length nc in
let evm, coqc, coqt = subtac_process env isevars id l c tycon in
let evars, def = Eterm.eterm_obligations id nc_len evm coqc (Some coqt) in
- trace (str "Adding to obligations list");
- add_entry id def coqt evars
+ add_definition id def coqt evars
diff --git a/contrib/subtac/subtac_pretyping_F.ml b/contrib/subtac/subtac_pretyping_F.ml
index 46af5886..6244aef3 100644
--- a/contrib/subtac/subtac_pretyping_F.ml
+++ b/contrib/subtac/subtac_pretyping_F.ml
@@ -6,7 +6,7 @@
(* * GNU Lesser General Public License Version 2.1 *)
(************************************************************************)
-(* $Id: subtac_pretyping_F.ml 9316 2006-10-29 22:49:11Z herbelin $ *)
+(* $Id: subtac_pretyping_F.ml 9563 2007-01-31 09:37:18Z msozeau $ *)
open Pp
open Util
@@ -40,7 +40,7 @@ open Inductiveops
module SubtacPretyping_F (Coercion : Coercion.S) = struct
- module Cases = Cases.Cases_F(Coercion)
+ module Cases = Subtac_cases.Cases_F(Coercion)
(* Allow references to syntaxically inexistent variables (i.e., if applied on an inductive) *)
let allow_anonymous_refs = ref true
@@ -161,7 +161,12 @@ module SubtacPretyping_F (Coercion : Coercion.S) = struct
(* [pretype tycon env isevars lvar lmeta cstr] attempts to type [cstr] *)
(* in environment [env], with existential variables [(evars_of isevars)] and *)
(* the type constraint tycon *)
- let rec pretype (tycon : type_constraint) env isevars lvar = function
+ let rec pretype (tycon : type_constraint) env isevars lvar c =
+(* let _ = try Subtac_utils.trace (str "pretype " ++ Subtac_utils.my_print_rawconstr env c ++ *)
+(* str " with tycon " ++ Evarutil.pr_tycon env tycon) *)
+(* with _ -> () *)
+(* in *)
+ match c with
| RRef (loc,ref) ->
inh_conv_coerce_to_tycon loc env isevars
(pretype_ref isevars env ref)
@@ -321,7 +326,7 @@ module SubtacPretyping_F (Coercion : Coercion.S) = struct
let t = Retyping.get_type_of env sigma c in
make_judge c t
| _ -> resj in
- inh_conv_coerce_to_tycon loc env isevars resj tycon
+ inh_conv_coerce_to_tycon loc env isevars resj tycon
| RLambda(loc,name,c1,c2) ->
let (name',dom,rng) = evd_comb1 (split_tycon loc env) isevars tycon in
diff --git a/contrib/subtac/subtac_utils.ml b/contrib/subtac/subtac_utils.ml
index 7b96758a..01dee3e9 100644
--- a/contrib/subtac/subtac_utils.ml
+++ b/contrib/subtac/subtac_utils.ml
@@ -5,6 +5,8 @@ open Term
open Names
open Util
+let ($) f x = f x
+
(****************************************************************************)
(* Library linking *)
@@ -45,10 +47,23 @@ let build_sig () =
let sig_ = lazy (build_sig ())
-let eqind = lazy (init_constant ["Init"; "Logic"] "eq")
-let eqind_ref = lazy (init_reference ["Init"; "Logic"] "eq")
+let eq_ind = lazy (init_constant ["Init"; "Logic"] "eq")
+let eq_rec = lazy (init_constant ["Init"; "Logic"] "eq_rec")
+let eq_rect = lazy (init_constant ["Init"; "Logic"] "eq_rect")
+let eq_refl = lazy (init_constant ["Init"; "Logic"] "refl_equal")
+let eq_ind_ref = lazy (init_reference ["Init"; "Logic"] "eq")
let refl_equal_ref = lazy (init_reference ["Init"; "Logic"] "refl_equal")
+let eqdep_ind = lazy (init_constant [ "Logic";"Eqdep"] "eq_dep")
+let eqdep_rec = lazy (init_constant ["Logic";"Eqdep"] "eq_dep_rec")
+let eqdep_ind_ref = lazy (init_reference [ "Logic";"Eqdep"] "eq_dep")
+let eqdep_intro_ref = lazy (init_reference [ "Logic";"Eqdep"] "eq_dep_intro")
+
+let jmeq_ind = lazy (init_constant ["Logic";"JMeq"] "JMeq")
+let jmeq_rec = lazy (init_constant ["Logic";"JMeq"] "JMeq_rec")
+let jmeq_ind_ref = lazy (init_reference ["Logic";"JMeq"] "JMeq")
+let jmeq_refl_ref = lazy (init_reference ["Logic";"JMeq"] "JMeq_refl")
+
let ex_ind = lazy (init_constant ["Init"; "Logic"] "ex")
let ex_intro = lazy (init_reference ["Init"; "Logic"] "ex_intro")
@@ -79,6 +94,7 @@ open Pp
let my_print_constr = Termops.print_constr_env
let my_print_constr_expr = Ppconstr.pr_constr_expr
+let my_print_rel_context env ctx = Printer.pr_rel_context env ctx
let my_print_context = Termops.print_rel_context
let my_print_named_context = Termops.print_named_context
let my_print_env = Termops.print_env
@@ -87,7 +103,7 @@ let my_print_evardefs = Evd.pr_evar_defs
let my_print_tycon_type = Evarutil.pr_tycon_type
-let debug_level = 1
+let debug_level = 2
let debug_on = true
@@ -132,8 +148,9 @@ let print_args env args =
let make_existential loc env isevars c =
let evar = Evarutil.e_new_evar isevars env ~src:(loc, QuestionMark) c in
let (key, args) = destEvar evar in
- (try debug 2 (str "Constructed evar " ++ int key ++ str " applied to args: " ++
- print_args env args) with _ -> ());
+ (try trace (str "Constructed evar " ++ int key ++ str " applied to args: " ++
+ print_args env args ++ str " for type: "++
+ my_print_constr env c) with _ -> ());
evar
let make_existential_expr loc env c =
@@ -177,6 +194,12 @@ open Tactics
open Tacticals
let id x = x
+let filter_map f l =
+ let rec aux acc = function
+ hd :: tl -> (match f hd with Some t -> aux (t :: acc) tl
+ | None -> aux acc tl)
+ | [] -> List.rev acc
+ in aux [] l
let build_dependent_sum l =
let rec aux names conttac conttype = function
@@ -279,45 +302,137 @@ let destruct_ex ext ex =
open Rawterm
-
+let rec concatMap f l =
+ match l with
+ hd :: tl -> f hd @ concatMap f tl
+ | [] -> []
+
let list_mapi f =
let rec aux i = function
hd :: tl -> f i hd :: aux (succ i) tl
| [] -> []
in aux 0
-let rewrite_cases_aux (loc, po, tml, eqns) =
- let tml = list_mapi (fun i (c, (n, opt)) -> c,
- ((match n with
- Name id -> (match c with
- | RVar (_, id') when id = id' ->
- Name (id_of_string (string_of_id id ^ "'"))
- | _ -> n)
- | Anonymous -> Name (id_of_string ("x" ^ string_of_int i))),
- opt)) tml
- in
+(*
+let make_discr (loc, po, tml, eqns) =
let mkHole = RHole (dummy_loc, InternalHole) in
- let mkeq c n = RApp (dummy_loc, RRef (dummy_loc, (Lazy.force eqind_ref)),
- [mkHole; c; n])
+
+ let rec vars_of_pat = function
+ RPatVar (loc, n) -> (match n with Anonymous -> [] | Name n -> [n])
+ | RPatCstr (loc, csrt, pats, _) ->
+ concatMap vars_of_pat pats
in
- let eqs_types =
- List.map
- (fun (c, (n, _)) ->
- let id = match n with Name id -> id | _ -> assert false in
- let heqid = id_of_string ("Heq" ^ string_of_id id) in
- Name heqid, mkeq c (RVar (dummy_loc, id)))
- tml
+ let rec constr_of_pat l = function
+ RPatVar (loc, n) ->
+ (match n with
+ Anonymous ->
+ let n = next_name_away_from "x" l in
+ RVar n, (n :: l)
+ | Name n -> RVar n, l)
+ | RPatCstr (loc, csrt, pats, _) ->
+ let (args, vars) =
+ List.fold_left
+ (fun (args, vars) x ->
+ let c, vars = constr_of_pat vars x in
+ c :: args, vars)
+ ([], l) pats
+ in
+ RApp ((RRef (dummy_loc, ConstructRef cstr)), args), vars
in
- let po =
- List.fold_right
- (fun (n,t) acc ->
- RProd (dummy_loc, Anonymous, t, acc))
- eqs_types (match po with
- Some e -> e
- | None -> mkHole)
+ let rec constr_of_pat l = function
+ RPatVar (loc, n) ->
+ (match n with
+ Anonymous ->
+ let n = next_name_away_from "x" l in
+ RVar n, (n :: l)
+ | Name n -> RVar n, l)
+ | RPatCstr (loc, csrt, pats, _) ->
+ let (args, vars) =
+ List.fold_left
+ (fun (args, vars) x ->
+ let c, vars = constr_of_pat vars x in
+ c :: args, vars)
+ ([], l) pats
+ in
+ RApp ((RRef (dummy_loc, ConstructRef cstr)), args), vars
in
- let eqns =
- List.map (fun (loc, idl, cpl, c) ->
+ let constrs_of_pats v l =
+ List.fold_left
+ (fun (v, acc) x ->
+ let x', v' = constr_of_pat v x in
+ (l', v' :: acc))
+ (v, []) l
+ in
+ let rec pat_of_pat l = function
+ RPatVar (loc, n) ->
+ let n', l = match n with
+ Anonymous ->
+ let n = next_name_away_from "x" l in
+ n, n :: l
+ | Name n -> n, n :: l
+ in
+ RPatVar (loc, Name n'), l
+ | RPatCstr (loc, cstr, pats, (loc, alias)) ->
+ let args, vars, s =
+ List.fold_left (fun (args, vars) x ->
+ let pat', vars = pat_of_pat vars pat in
+ pat' :: args, vars)
+ ([], alias :: l) pats
+ in RPatCstr (loc, cstr, args, (loc, alias)), vars
+ in
+ let pats_of_pats l =
+ List.fold_left
+ (fun (v, acc) x ->
+ let x', v' = pat_of_pat v x in
+ (v', x' :: acc))
+ ([], []) l
+ in
+ let eq_of_pat p used c =
+ let constr, vars' = constr_of_pat used p in
+ let eq = RApp (dummy_loc, RRef (dummy_loc, Lazy.force eqind_ref), [mkHole; constr; c]) in
+ vars', eq
+ in
+ let eqs_of_pats ps used cstrs =
+ List.fold_left2
+ (fun (vars, eqs) pat c ->
+ let (vars', eq) = eq_of_pat pat c in
+ match eqs with
+ None -> Some eq
+ | Some eqs ->
+ Some (RApp (dummy_loc, RRef (dummy_loc, Lazy.force and_ref), [eq, eqs])))
+ (used, None) ps cstrs
+ in
+ let quantify c l =
+ List.fold_left
+ (fun acc name -> RProd (dummy_loc, name, mkHole, acc))
+ c l
+ in
+ let quantpats =
+ List.fold_left
+ (fun (acc, pats) ((loc, idl, cpl, c) as x) ->
+ let vars, cpl = pats_of_pats cpl in
+ let l', constrs = constrs_of_pats vars cpl in
+ let discrs =
+ List.map (fun (_, _, cpl', _) ->
+ let qvars, eqs = eqs_of_pats cpl' l' constrs in
+ let neg = RApp (dummy_loc, RRef (dummy_loc, Lazy.force not_ref), [out_some eqs]) in
+ let pat_ineq = quantify qvars neg in
+
+ )
+ pats in
+
+
+
+
+
+
+
+ (x, pat_ineq))
+ in
+ List.fold_left
+ (fun acc ((loc, idl, cpl, c0) pat) ->
+
+
let c' =
List.fold_left
(fun acc (n, t) ->
@@ -325,27 +440,74 @@ let rewrite_cases_aux (loc, po, tml, eqns) =
c eqs_types
in (loc, idl, cpl, c'))
eqns
- in
- let mk_refl_equal c = RApp (dummy_loc, RRef (dummy_loc, Lazy.force refl_equal_ref),
- [mkHole; c])
- in
- let refls = List.map (fun (c, _) -> mk_refl_equal c) tml in
- let case = RCases (loc,Some po,tml,eqns) in
- let app = RApp (dummy_loc, case, refls) in
- app
-
-let rec rewrite_cases c =
- match c with
- RCases _ -> let c' = map_rawconstr rewrite_cases c in
- (match c' with
- | RCases (x, y, z, w) -> rewrite_cases_aux (x,y,z,w)
- | _ -> assert(false))
- | _ -> map_rawconstr rewrite_cases c
+ i
+*)
+(* let rewrite_cases_aux (loc, po, tml, eqns) = *)
+(* let tml = list_mapi (fun i (c, (n, opt)) -> c, *)
+(* ((match n with *)
+(* Name id -> (match c with *)
+(* | RVar (_, id') when id = id' -> *)
+(* Name (id_of_string (string_of_id id ^ "'")) *)
+(* | _ -> n) *)
+(* | Anonymous -> Name (id_of_string ("x" ^ string_of_int i))), *)
+(* opt)) tml *)
+(* in *)
+(* let mkHole = RHole (dummy_loc, InternalHole) in *)
+(* (\* let mkeq c n = RApp (dummy_loc, RRef (dummy_loc, (Lazy.force eqind_ref)), *\) *)
+(* (\* [mkHole; c; n]) *\) *)
+(* (\* in *\) *)
+(* let mkeq c n = RApp (dummy_loc, RRef (dummy_loc, (Lazy.force eqdep_ind_ref)), *)
+(* [mkHole; c; mkHole; n]) *)
+(* in *)
+(* let eqs_types = *)
+(* List.map *)
+(* (fun (c, (n, _)) -> *)
+(* let id = match n with Name id -> id | _ -> assert false in *)
+(* let heqid = id_of_string ("Heq" ^ string_of_id id) in *)
+(* Name heqid, mkeq c (RVar (dummy_loc, id))) *)
+(* tml *)
+(* in *)
+(* let po = *)
+(* List.fold_right *)
+(* (fun (n,t) acc -> *)
+(* RProd (dummy_loc, Anonymous, t, acc)) *)
+(* eqs_types (match po with *)
+(* Some e -> e *)
+(* | None -> mkHole) *)
+(* in *)
+(* let eqns = *)
+(* List.map (fun (loc, idl, cpl, c) -> *)
+(* let c' = *)
+(* List.fold_left *)
+(* (fun acc (n, t) -> *)
+(* RLambda (dummy_loc, n, mkHole, acc)) *)
+(* c eqs_types *)
+(* in (loc, idl, cpl, c')) *)
+(* eqns *)
+(* in *)
+(* let mk_refl_equal c = RApp (dummy_loc, RRef (dummy_loc, Lazy.force refl_equal_ref), *)
+(* [mkHole; c]) *)
+(* in *)
+(* (\*let mk_refl_equal c = RApp (dummy_loc, RRef (dummy_loc, Lazy.force refl_equal_ref), *)
+(* [mkHole; c]) *)
+(* in*\) *)
+(* let refls = List.map (fun (c, _) -> mk_refl_equal c) tml in *)
+(* let case = RCases (loc,Some po,tml,eqns) in *)
+(* let app = RApp (dummy_loc, case, refls) in *)
+(* app *)
+
+(* let rec rewrite_cases c = *)
+(* match c with *)
+(* RCases _ -> let c' = map_rawconstr rewrite_cases c in *)
+(* (match c' with *)
+(* | RCases (x, y, z, w) -> rewrite_cases_aux (x,y,z,w) *)
+(* | _ -> assert(false)) *)
+(* | _ -> map_rawconstr rewrite_cases c *)
-let rewrite_cases env c =
- let c' = rewrite_cases c in
- let _ = trace (str "Rewrote cases: " ++ spc () ++ my_print_rawconstr env c') in
- c'
+(* let rewrite_cases env c = *)
+(* let c' = rewrite_cases c in *)
+(* let _ = trace (str "Rewrote cases: " ++ spc () ++ my_print_rawconstr env c') in *)
+(* c' *)
let list_mapi f =
let rec aux i = function
@@ -371,7 +533,7 @@ let rewrite_cases_aux (loc, po, tml, eqns) =
in
let mkHole = RHole (dummy_loc, InternalHole) in
let mkCoerceCast c = RCast (dummy_loc, c, CastCoerce, mkHole) in
- let mkeq c n = RApp (dummy_loc, RRef (dummy_loc, (Lazy.force eqind_ref)),
+ let mkeq c n = RApp (dummy_loc, RRef (dummy_loc, (Lazy.force eq_ind_ref)),
[mkHole; c; n])
in
let eqs_types =
@@ -419,10 +581,10 @@ let rec rewrite_cases c =
| _ -> assert(false))
| _ -> map_rawconstr rewrite_cases c
-let rewrite_cases env c =
- let c' = rewrite_cases c in
- let _ = trace (str "Rewrote cases: " ++ spc () ++ my_print_rawconstr env c') in
- c'
+let rewrite_cases env c = c
+(* let c' = rewrite_cases c in *)
+(* let _ = trace (str "Rewrote cases: " ++ spc () ++ my_print_rawconstr env c') in *)
+(* c' *)
let id_of_name = function
Name n -> n
@@ -439,16 +601,107 @@ let recursive_message v =
spc () ++ str "are recursively defined")
(* Solve an obligation using tactics, return the corresponding proof term *)
+(*
let solve_by_tac ev t =
debug 1 (str "Solving goal using tactics: " ++ Evd.pr_evar_info ev);
let goal = Proof_trees.mk_goal ev.evar_hyps ev.evar_concl None in
+ debug 1 (str "Goal created");
let ts = Tacmach.mk_pftreestate goal in
+ debug 1 (str "Got pftreestate");
let solved_state = Tacmach.solve_pftreestate t ts in
- let c = Tacmach.extract_pftreestate solved_state in
+ debug 1 (str "Solved goal");
+ let _, l = Tacmach.extract_open_pftreestate solved_state in
+ List.iter (fun (_, x) -> debug 1 (str "left hole of type " ++ my_print_constr (Global.env()) x)) l;
+ let c = Tacmach.extract_pftreestate solved_state in
+ debug 1 (str "Extracted term");
debug 1 (str "Term constructed in solve by tac: " ++ my_print_constr (Global.env ()) c);
c
+ *)
+
+let solve_by_tac evi t =
+ debug 2 (str "Solving goal using tactics: " ++ Evd.pr_evar_info evi);
+ let id = id_of_string "H" in
+ try
+ Pfedit.start_proof id goal_kind evi.evar_hyps evi.evar_concl
+ (fun _ _ -> ());
+ debug 2 (str "Started proof");
+ Pfedit.by (tclCOMPLETE t);
+ let _,(const,_,_) = Pfedit.cook_proof () in
+ Pfedit.delete_current_proof (); const.Entries.const_entry_body
+ with e ->
+ Pfedit.delete_current_proof();
+ raise Exit
let rec string_of_list sep f = function
[] -> ""
| x :: [] -> f x
| x :: ((y :: _) as tl) -> f x ^ sep ^ string_of_list sep f tl
+
+let string_of_intset d =
+ string_of_list "," string_of_int (Intset.elements d)
+
+(**********************************************************)
+(* Pretty-printing *)
+open Printer
+open Ppconstr
+open Nameops
+open Termops
+open Evd
+
+let pr_meta_map evd =
+ let ml = meta_list evd in
+ let pr_name = function
+ Name id -> str"[" ++ pr_id id ++ str"]"
+ | _ -> mt() in
+ let pr_meta_binding = function
+ | (mv,Cltyp (na,b)) ->
+ hov 0
+ (pr_meta mv ++ pr_name na ++ str " : " ++
+ print_constr b.rebus ++ fnl ())
+ | (mv,Clval(na,b,_)) ->
+ hov 0
+ (pr_meta mv ++ pr_name na ++ str " := " ++
+ print_constr b.rebus ++ fnl ())
+ in
+ prlist pr_meta_binding ml
+
+let pr_idl idl = prlist_with_sep pr_spc pr_id idl
+
+let pr_evar_info evi =
+ let phyps =
+ (*pr_idl (List.rev (ids_of_named_context (evar_context evi))) *)
+ Printer.pr_named_context (Global.env()) (evar_context evi)
+ in
+ let pty = print_constr evi.evar_concl in
+ let pb =
+ match evi.evar_body with
+ | Evar_empty -> mt ()
+ | Evar_defined c -> spc() ++ str"=> " ++ print_constr c
+ in
+ hov 2 (str"[" ++ phyps ++ spc () ++ str"|- " ++ pty ++ pb ++ str"]")
+
+let pr_evar_map sigma =
+ h 0
+ (prlist_with_sep pr_fnl
+ (fun (ev,evi) ->
+ h 0 (str(string_of_existential ev)++str"=="++ pr_evar_info evi))
+ (to_list sigma))
+
+let pr_constraints pbs =
+ h 0
+ (prlist_with_sep pr_fnl (fun (pbty,t1,t2) ->
+ print_constr t1 ++ spc() ++
+ str (match pbty with
+ | Reduction.CONV -> "=="
+ | Reduction.CUMUL -> "<=") ++
+ spc() ++ print_constr t2) pbs)
+
+let pr_evar_defs evd =
+ let pp_evm =
+ let evars = evars_of evd in
+ if evars = empty then mt() else
+ str"EVARS:"++brk(0,1)++pr_evar_map evars++fnl() in
+ let pp_met =
+ if meta_list evd = [] then mt() else
+ str"METAS:"++brk(0,1)++pr_meta_map evd in
+ v 0 (pp_evm ++ pp_met)
diff --git a/contrib/subtac/subtac_utils.mli b/contrib/subtac/subtac_utils.mli
index ebfc5123..482640f9 100644
--- a/contrib/subtac/subtac_utils.mli
+++ b/contrib/subtac/subtac_utils.mli
@@ -12,6 +12,7 @@ open Evarutil
open Names
open Sign
+val ($) : ('a -> 'b) -> 'a -> 'b
val contrib_name : string
val subtac_dir : string list
val fix_sub_module : string
@@ -31,9 +32,19 @@ val proj1_sig_ref : reference
val proj2_sig_ref : reference
val build_sig : unit -> coq_sigma_data
val sig_ : coq_sigma_data lazy_t
-val eqind : constr lazy_t
-val eqind_ref : global_reference lazy_t
+
+val eq_ind : constr lazy_t
+val eq_rec : constr lazy_t
+val eq_rect : constr lazy_t
+val eq_refl : constr lazy_t
+val eq_ind_ref : global_reference lazy_t
val refl_equal_ref : global_reference lazy_t
+
+val eqdep_ind : constr lazy_t
+val eqdep_rec : constr lazy_t
+val eqdep_ind_ref : global_reference lazy_t
+val eqdep_intro_ref : global_reference lazy_t
+
val boolind : constr lazy_t
val sumboolind : constr lazy_t
val natind : constr lazy_t
@@ -48,10 +59,12 @@ val acc : constr lazy_t
val acc_inv : constr lazy_t
val extconstr : constr -> constr_expr
val extsort : sorts -> constr_expr
+
val my_print_constr : env -> constr -> std_ppcmds
val my_print_constr_expr : constr_expr -> std_ppcmds
val my_print_evardefs : evar_defs -> std_ppcmds
val my_print_context : env -> std_ppcmds
+val my_print_rel_context : env -> rel_context -> std_ppcmds
val my_print_named_context : env -> std_ppcmds
val my_print_env : env -> std_ppcmds
val my_print_rawconstr : env -> rawconstr -> std_ppcmds
@@ -98,3 +111,6 @@ val recursive_message : global_reference array -> std_ppcmds
val solve_by_tac : evar_info -> Tacmach.tactic -> constr
val string_of_list : string -> ('a -> string) -> 'a list -> string
+val string_of_intset : Intset.t -> string
+
+val pr_evar_defs : evar_defs -> Pp.std_ppcmds
diff --git a/contrib/subtac/test/ListsTest.v b/contrib/subtac/test/ListsTest.v
index 8429c267..b8d13fe6 100644
--- a/contrib/subtac/test/ListsTest.v
+++ b/contrib/subtac/test/ListsTest.v
@@ -1,95 +1,76 @@
+(* -*- coq-prog-args: ("-emacs-U" "-debug") -*- *)
Require Import Coq.subtac.Utils.
Require Import List.
-Variable A : Set.
-
-Program Definition myhd : forall { l : list A | length l <> 0 }, A :=
- fun l =>
- match `l with
- | nil => _
- | hd :: tl => hd
- end.
-Proof.
- destruct l ; simpl ; intro H.
- rewrite H in n ; intuition.
-Defined.
+Set Implicit Arguments.
+Section Accessors.
+ Variable A : Set.
-Extraction myhd.
-Extraction Inline proj1_sig.
+ Program Definition myhd : forall { l : list A | length l <> 0 }, A :=
+ fun l =>
+ match l with
+ | nil => !
+ | hd :: tl => hd
+ end.
-Program Definition mytail : forall { l : list A | length l <> 0 }, list A :=
- fun l =>
+ Program Definition mytail (l : list A | length l <> 0) : list A :=
match l with
- | nil => _
- | hd :: tl => tl
+ | nil => !
+ | hd :: tl => tl
end.
-Proof.
-destruct l ; simpl ; intro H ; rewrite H in n ; intuition.
-Defined.
-
-Extraction mytail.
-
-Variable a : A.
+End Accessors.
-Program Definition test_hd : A := myhd (cons a nil).
-Proof.
-simpl ; auto.
-Defined.
-
-Extraction test_hd.
+Program Definition test_hd : nat := myhd (cons 1 nil).
+(*Eval compute in test_hd*)
(*Program Definition test_tail : list A := mytail nil.*)
+Section app.
+ Variable A : Set.
+ Program Fixpoint app (l : list A) (l' : list A) { struct l } :
+ { r : list A | length r = length l + length l' } :=
+ match l with
+ | nil => l'
+ | hd :: tl => hd :: (tl ++ l')
+ end
+ where "x ++ y" := (app x y).
+
+ Next Obligation.
+ intros.
+ destruct_call app ; subtac_simpl.
+ Defined.
+
+ Program Lemma app_id_l : forall l : list A, l = nil ++ l.
+ Proof.
+ simpl ; auto.
+ Qed.
+
+ Program Lemma app_id_r : forall l : list A, l = l ++ nil.
+ Proof.
+ induction l ; simpl ; auto.
+ rewrite <- IHl ; auto.
+ Qed.
+
+End app.
+
+Extraction app.
+
+Section Nth.
+
+ Variable A : Set.
+
+ Program Fixpoint nth (l : list A) (n : nat | n < length l) { struct l } : A :=
+ match n, l with
+ | 0, hd :: _ => hd
+ | S n', _ :: tl => nth tl n'
+ | _, nil => !
+ end.
-
-
-Program Fixpoint append (l : list A) (l' : list A) { struct l } :
- { r : list A | length r = length l + length l' } :=
- match l with
- | nil => l'
- | hd :: tl => hd :: (append tl l')
- end.
-subst ; auto.
-simpl ; rewrite (subset_simpl (append tl0 l')).
-simpl ; subst.
-simpl ; auto.
-Defined.
-
-Extraction append.
-
-
-Program Lemma append_app' : forall l : list A, l = append nil l.
-Proof.
-simpl ; auto.
-Qed.
-
-Program Lemma append_app : forall l : list A, l = append l nil.
-Proof.
-intros.
-induction l ; simpl ; auto.
-simpl in IHl.
-rewrite <- IHl.
-reflexivity.
-Qed.
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
+ Next Obligation.
+ Proof.
+ inversion l0.
+ Defined.
+End Nth.
diff --git a/contrib/subtac/test/euclid.v b/contrib/subtac/test/euclid.v
index ba5bdf23..a5a8b85f 100644
--- a/contrib/subtac/test/euclid.v
+++ b/contrib/subtac/test/euclid.v
@@ -1,66 +1,27 @@
-
-Notation "( x & y )" := (@existS _ _ x y) : core_scope.
-Unset Printing All.
-
-Definition t := fun (Evar46 : forall a : nat, (fun y : nat => @eq nat a y) a) (a : nat) =>
-@existS nat (fun x : nat => @sig nat (fun y : nat => @eq nat x y)) a
- (@exist nat (fun y : nat => @eq nat a y) a (Evar46 a)).
-
-Program Definition testsig (a : nat) : { x : nat & { y : nat | x = y } } :=
- (a & a).
-reflexivity.
-Defined.
-
-Extraction testsig.
-Extraction sig.
-Extract Inductive sig => "" [ "" ].
-Extraction testsig.
-
+Require Import Coq.subtac.Utils.
Require Import Coq.Arith.Compare_dec.
-
-Require Import Omega.
-
-Lemma minus_eq_add : forall x y z w, y <= x -> x - y = y * z + w -> x = y * S z + w.
-intros.
-assert(y * S z = y * z + y).
-auto.
-rewrite H1.
-omega.
-Qed.
-
-Program Fixpoint euclid (a : nat) (b : { b : nat | b <> O }) {wf a lt} :
+Notation "( x & y )" := (existS _ x y) : core_scope.
+
+Program Fixpoint euclid (a : nat) (b : { b : nat | b <> O }) {wf lt a} :
{ q : nat & { r : nat | a = b * q + r /\ r < b } } :=
if le_lt_dec b a then let (q', r) := euclid (a - b) b in
(S q' & r)
else (O & a).
-intro euclid.
-simpl ; intros.
-Print euclid_evars.
-eapply euclid_evars with euclid.
-refine (euclid_evars _ _ _ euclid a Acc_a b).
-; simpl ; intros.
-Show Existentials.
-induction b0 ; induction r.
-simpl in H.
-simpl.
-simpl in p0.
-destruct p0.
-split.
+Require Import Omega.
+
+Obligations.
+Solve Obligations using subtac_simpl ; omega.
+
+Next Obligation.
+ assert(x0 * S q' = x0 * q' + x0) by auto with arith ; omega.
+Defined.
-apply minus_eq_add.
-omega.
-auto with arith.
-auto.
-simpl.
-induction b0 ; simpl.
-split ; auto.
-omega.
-exact (euclid a0 Acc_a0 b0).
+Program Definition test_euclid : (prod nat nat) := let (q, r) := euclid 4 2 in (q, q).
-exact (Acc_a).
-auto.
-auto.
-Focus 1.
+Eval lazy beta zeta delta iota in test_euclid.
+Program Definition testsig (a : nat) : { x : nat & { y : nat | x < y } } :=
+ (a & S a).
+Check testsig.
diff --git a/contrib/xml/proof2aproof.ml b/contrib/xml/proof2aproof.ml
index 92cbf6df..30dc7b71 100644
--- a/contrib/xml/proof2aproof.ml
+++ b/contrib/xml/proof2aproof.ml
@@ -112,8 +112,6 @@ let extract_open_proof sigma pf =
ProofTreeHash.add proof_tree_to_flattened_proof_tree node flat_proof ;
proof_extractor vl flat_proof
- | {PT.ref=Some(PT.Change_evars,[pf])} -> (proof_extractor vl) pf
-
| {PT.ref=None;PT.goal=goal} ->
let visible_rels =
Util.map_succeed
diff --git a/contrib/xml/proofTree2Xml.ml4 b/contrib/xml/proofTree2Xml.ml4
index dbdc79a8..9afd07a6 100644
--- a/contrib/xml/proofTree2Xml.ml4
+++ b/contrib/xml/proofTree2Xml.ml4
@@ -93,7 +93,7 @@ let string_of_prim_rule x = match x with
| Proof_type.ThinBody _-> "ThinBody"
| Proof_type.Move (_,_,_) -> "Move"
| Proof_type.Rename (_,_) -> "Rename"
-
+ | Proof_type.Change_evars -> "Change_evars"
let
print_proof_tree curi sigma pf proof_tree_to_constr
@@ -189,11 +189,6 @@ Pp.ppnl (Pp.(++) (Pp.str
[<(build_hyps new_hyps) ; (aux flat_proof nhyps)>]
end
- | {PT.ref=Some(PT.Change_evars,nodes)} ->
- X.xml_nempty "Change_evars" of_attribute
- (List.fold_left
- (fun i n -> [< i ; (aux n old_hyps) >]) [<>] nodes)
-
| {PT.ref=Some((PT.Nested(PT.Proof_instr (_,_),_)|PT.Decl_proof _),nodes)} ->
Util.anomaly "Not Implemented"