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|
(* -*- compile-command: "make -C .. bin/coqtop.byte" -*- *)
(************************************************************************)
(* 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 camlp4deps: "parsing/grammar.cma" i*)
(* $Id: class_tactics.ml4 11150 2008-06-19 11:38:27Z msozeau $ *)
open Pp
open Util
open Names
open Nameops
open Term
open Termops
open Sign
open Reduction
open Proof_type
open Proof_trees
open Declarations
open Tacticals
open Tacmach
open Evar_refiner
open Tactics
open Pattern
open Clenv
open Auto
open Rawterm
open Hiddentac
open Typeclasses
open Typeclasses_errors
open Classes
open Topconstr
open Pfedit
open Command
open Libnames
open Evd
let default_eauto_depth = 100
let typeclasses_db = "typeclass_instances"
let check_imported_library d =
let d' = List.map id_of_string d in
let dir = make_dirpath (List.rev d') in
if not (Library.library_is_loaded dir) then
error ("Library "^(list_last d)^" has to be imported first")
let classes_dirpath =
make_dirpath (List.map id_of_string ["Classes";"Coq"])
let init_setoid () =
if is_dirpath_prefix_of classes_dirpath (Lib.cwd ()) then ()
else check_imported_library ["Coq";"Setoids";"Setoid"]
(** Typeclasses instance search tactic / eauto *)
open Auto
let e_give_exact c gl =
let t1 = (pf_type_of gl c) and t2 = pf_concl gl in
if occur_existential t1 or occur_existential t2 then
tclTHEN (Clenvtac.unify t1) (exact_check c) gl
else exact_check c gl
let assumption id = e_give_exact (mkVar id)
open Unification
let auto_unif_flags = {
modulo_conv_on_closed_terms = Some full_transparent_state;
use_metas_eagerly = true;
modulo_delta = var_full_transparent_state;
}
let unify_e_resolve st (c,clenv) gls =
let clenv' = connect_clenv gls clenv in
let clenv' = clenv_unique_resolver false
~flags:{auto_unif_flags with modulo_delta = st} clenv' gls
in
Clenvtac.clenv_refine true clenv' gls
let unify_resolve st (c,clenv) gls =
let clenv' = connect_clenv gls clenv in
let clenv' = clenv_unique_resolver false
~flags:{auto_unif_flags with modulo_delta = st} clenv' gls
in
Clenvtac.clenv_refine false clenv' gls
let rec e_trivial_fail_db db_list local_db goal =
let tacl =
Eauto.registered_e_assumption ::
(tclTHEN Tactics.intro
(function g'->
let d = pf_last_hyp g' in
let hintl = make_resolve_hyp (pf_env g') (project g') d in
(e_trivial_fail_db db_list
(add_hint_list hintl local_db) g'))) ::
(List.map pi1 (e_trivial_resolve db_list local_db (pf_concl goal)) )
in
tclFIRST (List.map tclCOMPLETE tacl) goal
and e_my_find_search db_list local_db hdc concl =
let hdc = head_of_constr_reference hdc in
let hintl =
if occur_existential concl then
list_map_append
(fun (st, db) -> List.map (fun x -> (st, x)) (Hint_db.map_all hdc db))
(local_db::db_list)
else
list_map_append
(fun (st, db) -> List.map (fun x -> (st, x)) (Hint_db.map_auto (hdc,concl) db))
(local_db::db_list)
in
let tac_of_hint =
fun (st, {pri=b; pat = p; code=t}) ->
let tac =
match t with
| Res_pf (term,cl) -> unify_resolve st (term,cl)
| ERes_pf (term,cl) -> unify_e_resolve st (term,cl)
| Give_exact (c) -> e_give_exact c
| Res_pf_THEN_trivial_fail (term,cl) ->
tclTHEN (unify_e_resolve st (term,cl))
(e_trivial_fail_db db_list local_db)
| Unfold_nth c -> unfold_in_concl [all_occurrences,c]
| Extern tacast -> conclPattern concl
(Option.get p) tacast
in
(tac,b,fmt_autotactic t)
in
List.map tac_of_hint hintl
and e_trivial_resolve db_list local_db gl =
try
e_my_find_search db_list local_db
(List.hd (head_constr_bound gl [])) gl
with Bound | Not_found -> []
let e_possible_resolve db_list local_db gl =
try
e_my_find_search db_list local_db
(List.hd (head_constr_bound gl [])) gl
with Bound | Not_found -> []
let find_first_goal gls =
try first_goal gls with UserError _ -> assert false
type search_state = {
depth : int; (*r depth of search before failing *)
tacres : goal list sigma * validation;
pri : int;
last_tactic : std_ppcmds;
dblist : Auto.hint_db list;
localdb : Auto.hint_db list }
let filter_hyp t =
match kind_of_term t with
| Evar _ | Meta _ | Sort _ -> false
| _ -> true
let rec catchable = function
| Refiner.FailError _ -> true
| Stdpp.Exc_located (_, e) -> catchable e
| e -> Logic.catchable_exception e
module SearchProblem = struct
type state = search_state
let debug = ref false
let success s = (sig_it (fst s.tacres)) = []
let pr_ev evs ev = Printer.pr_constr_env (Evd.evar_env ev) (Evarutil.nf_evar evs ev.Evd.evar_concl)
let pr_goals gls =
let evars = Evarutil.nf_evars (Refiner.project gls) in
prlist (pr_ev evars) (sig_it gls)
let filter_tactics (glls,v) l =
(* if !debug then *)
(* (let _ = Proof_trees.db_pr_goal (List.hd (sig_it glls)) in *)
(* let evars = Evarutil.nf_evars (Refiner.project glls) in *)
(* msg (str"Goal: " ++ pr_ev evars (List.hd (sig_it glls)) ++ str"\n")); *)
let rec aux = function
| [] -> []
| (tac,pri,pptac) :: tacl ->
try
(* if !debug then msg (str"\nTrying tactic: " ++ pptac ++ str"\n"); *)
let (lgls,ptl) = apply_tac_list tac glls in
let v' p = v (ptl p) in
(* if !debug then *)
(* begin *)
(* let evars = Evarutil.nf_evars (Refiner.project glls) in *)
(* msg (str"\nOn goal: " ++ pr_ev evars (List.hd (sig_it glls)) ++ str"\n"); *)
(* msg (hov 1 (pptac ++ str" gives: \n" ++ pr_goals lgls ++ str"\n")) *)
(* end; *)
((lgls,v'),pri,pptac) :: aux tacl
with e when catchable e -> aux tacl
in aux l
let nb_empty_evars s =
Evd.fold (fun ev evi acc -> if evi.evar_body = Evar_empty then succ acc else acc) s 0
(* Ordering of states is lexicographic on depth (greatest first) then
priority (lowest pri means higher priority), then number of remaining goals. *)
let compare s s' =
let d = s'.depth - s.depth in
let nbgoals s =
List.length (sig_it (fst s.tacres)) +
nb_empty_evars (sig_sig (fst s.tacres))
in
if d <> 0 && d <> 1 then d else
let pri = s.pri - s'.pri in
if pri <> 0 then pri
else nbgoals s - nbgoals s'
let branching s =
if s.depth = 0 then
[]
else
let lg = fst s.tacres in
let nbgl = List.length (sig_it lg) in
assert (nbgl > 0);
let g = find_first_goal lg in
let assumption_tacs =
let l =
filter_tactics s.tacres
(List.map
(fun id -> (Eauto.e_give_exact_constr (mkVar id), 0,
(str "exact" ++ spc () ++ pr_id id)))
(List.filter (fun id -> filter_hyp (pf_get_hyp_typ g id))
(pf_ids_of_hyps g)))
in
List.map (fun (res,pri,pp) -> { s with tacres = res; pri = 0;
last_tactic = pp; localdb = List.tl s.localdb }) l
in
(* let intro_tac = *)
(* List.map *)
(* (fun ((lgls,_) as res,pri,pp) -> *)
(* let g' = first_goal lgls in *)
(* let hintl = *)
(* make_resolve_hyp (pf_env g') (project g') (pf_last_hyp g') *)
(* in *)
(* let ldb = Hint_db.add_list hintl (match s.localdb with [] -> assert false | hd :: _ -> hd) in *)
(* { s with tacres = res; *)
(* last_tactic = pp; *)
(* pri = pri; *)
(* localdb = ldb :: List.tl s.localdb }) *)
(* (filter_tactics s.tacres [Tactics.intro,1,(str "intro")]) *)
(* in *)
let possible_resolve ((lgls,_) as res, pri, pp) =
let nbgl' = List.length (sig_it lgls) in
if nbgl' < nbgl then
{ s with tacres = res; last_tactic = pp; pri = pri;
localdb = List.tl s.localdb }
else
{ s with
depth = pred s.depth; tacres = res;
last_tactic = pp; pri = pri;
localdb =
list_addn (nbgl'-nbgl) (List.hd s.localdb) s.localdb }
in
let rec_tacs =
let l =
filter_tactics s.tacres (e_possible_resolve s.dblist (List.hd s.localdb) (pf_concl g))
in
List.map possible_resolve l
in
List.sort compare (assumption_tacs (* @intro_tac @ custom_tac *) @ rec_tacs)
let pp s =
msg (hov 0 (str " depth=" ++ int s.depth ++ spc () ++
s.last_tactic ++ str "\n"))
end
module Search = Explore.Make(SearchProblem)
let filter_pat c =
try
let morg = Nametab.global (Qualid (dummy_loc, qualid_of_string "Coq.Classes.Morphisms.Morphism")) in
let morc = constr_of_global morg in
match kind_of_term c with
| App(morph, [| t; r; m |]) when eq_constr morph morc ->
(fun y ->
(match y.pat with
Some (PApp (PRef mor, [| t'; r'; m' |])) when mor = morg ->
(match m' with
| PRef c -> if isConst m then eq_constr (constr_of_global c) m else false
| _ -> true)
| _ -> true))
| _ -> fun _ -> true
with _ -> fun _ -> true
let morphism_class =
lazy (class_info (Nametab.global (Qualid (dummy_loc, qualid_of_string "Coq.Classes.Morphisms.Morphism"))))
let morphism_proxy_class =
lazy (class_info (Nametab.global (Qualid (dummy_loc, qualid_of_string "Coq.Classes.Morphisms.MorphismProxy"))))
let filter c =
try let morc = constr_of_global (Nametab.global (Qualid (dummy_loc, qualid_of_string "Coq.Classes.Morphisms.Morphism"))) in
match kind_of_term c with
| App(morph, [| t; r; m |]) when eq_constr morph morc ->
(fun y ->
let (_, r) = decompose_prod y in
(match kind_of_term r with
App (morph', [| t'; r'; m' |]) when eq_constr morph' morc ->
(match kind_of_term m' with
| Rel n -> true
| Const c -> eq_constr m m'
| App _ -> true
| _ -> false)
| _ -> false))
| _ -> fun _ -> true
with _ -> fun _ -> true
let make_initial_state n gls dblist localdbs =
{ depth = n;
tacres = gls;
pri = 0;
last_tactic = (mt ());
dblist = dblist;
localdb = localdbs }
let e_depth_search debug s =
let tac = if debug then
(SearchProblem.debug := true; Search.debug_depth_first) else Search.depth_first in
let s = tac s in
s.tacres
let e_breadth_search debug s =
try
let tac =
if debug then Search.debug_breadth_first else Search.breadth_first
in let s = tac s in s.tacres
with Not_found -> error "EAuto: breadth first search failed"
let e_search_auto debug (in_depth,p) lems db_list gls =
let sigma = Evd.sig_sig (fst gls) and gls' = Evd.sig_it (fst gls) in
let local_dbs = List.map (fun gl -> make_local_hint_db true lems ({it = gl; sigma = sigma})) gls' in
let state = make_initial_state p gls db_list local_dbs in
if in_depth then
e_depth_search debug state
else
e_breadth_search debug state
let full_eauto debug n lems gls =
let dbnames = current_db_names () in
let dbnames = list_subtract dbnames ["v62"] in
let db_list = List.map searchtable_map dbnames in
e_search_auto debug n lems db_list gls
let nf_goal (gl, valid) =
{ gl with sigma = Evarutil.nf_evars gl.sigma }, valid
let typeclasses_eauto debug n lems gls =
let dbnames = [typeclasses_db] in
let db_list = List.map
(fun x ->
try searchtable_map x
with Not_found -> (empty_transparent_state, Hint_db.empty))
dbnames
in
e_search_auto debug n lems db_list gls
exception Found of evar_map
let valid goals p res_sigma l =
let evm =
List.fold_left2
(fun sigma (ev, evi) prf ->
let cstr, obls = Refiner.extract_open_proof !res_sigma prf in
if not (Evd.is_defined sigma ev) then
Evd.define sigma ev cstr
else sigma)
!res_sigma goals l
in raise (Found evm)
let resolve_all_evars_once debug (mode, depth) env p evd =
let evm = Evd.evars_of evd in
let goals, evm' =
Evd.fold
(fun ev evi (gls, evm) ->
if evi.evar_body = Evar_empty
&& Typeclasses.is_resolvable evi
&& p ev evi then ((ev,evi) :: gls, Evd.add evm ev (Typeclasses.mark_unresolvable evi)) else
(gls, Evd.add evm ev evi))
evm ([], Evd.empty)
in
let goals = List.rev goals in
let gls = { it = List.map snd goals; sigma = evm' } in
let res_sigma = ref evm' in
let gls', valid' = typeclasses_eauto debug (mode, depth) [] (gls, valid goals p res_sigma) in
res_sigma := Evarutil.nf_evars (sig_sig gls');
try ignore(valid' []); assert(false)
with Found evm' -> Evarutil.nf_evar_defs (Evd.evars_reset_evd evm' evd)
exception FoundTerm of constr
let resolve_one_typeclass env gl =
let gls = { it = [ Evd.make_evar (Environ.named_context_val env) gl ] ; sigma = Evd.empty } in
let valid x = raise (FoundTerm (fst (Refiner.extract_open_proof Evd.empty (List.hd x)))) in
let gls', valid' = typeclasses_eauto false (true, default_eauto_depth) [] (gls, valid) in
try ignore(valid' []); assert false with FoundTerm t ->
let term = Evarutil.nf_evar (sig_sig gls') t in
if occur_existential term then raise Not_found else term
let has_undefined p oevd evd =
Evd.fold (fun ev evi has -> has ||
(evi.evar_body = Evar_empty && p ev evi &&
(try Typeclasses.is_resolvable (Evd.find oevd ev) with _ -> true)))
(Evd.evars_of evd) false
let evars_of_term init c =
let rec evrec acc c =
match kind_of_term c with
| Evar (n, _) -> Intset.add n acc
| _ -> fold_constr evrec acc c
in
evrec init c
let intersects s t =
Intset.exists (fun el -> Intset.mem el t) s
let rec merge_deps deps = function
| [] -> [deps]
| hd :: tl ->
if intersects deps hd then
merge_deps (Intset.union deps hd) tl
else hd :: merge_deps deps tl
let split_evars evm =
Evd.fold (fun ev evi acc ->
let deps = evars_of_term (Intset.singleton ev) evi.evar_concl in
merge_deps deps acc)
evm []
let select_evars evs evm =
Evd.fold (fun ev evi acc ->
if Intset.mem ev evs then Evd.add acc ev evi else acc)
evm Evd.empty
let resolve_all_evars debug m env p oevd do_split fail =
let oevm = Evd.evars_of oevd in
let split = if do_split then split_evars (Evd.evars_of (Evd.undefined_evars oevd)) else [Intset.empty] in
let p = if do_split then
fun comp ev evi -> (Intset.mem ev comp || not (Evd.mem oevm ev)) && p ev evi
else fun _ -> p
in
let rec aux n p evd =
if has_undefined p oevm evd then
if n > 0 then
let evd' = resolve_all_evars_once debug m env p evd in
aux (pred n) p evd'
else None
else Some evd
in
let rec docomp evd = function
| [] -> evd
| comp :: comps ->
let res = try aux 3 (p comp) evd with Not_found -> None in
match res with
| None ->
if fail then
(* Unable to satisfy the constraints. *)
let evm = Evd.evars_of evd in
let evm = if do_split then select_evars comp evm else evm in
let _, ev = Evd.fold
(fun ev evi (b,acc) ->
(* focus on one instance if only one was searched for *)
if class_of_constr evi.evar_concl <> None then
if not b then
true, Some ev
else b, None
else b, acc) evm (false, None)
in
Typeclasses_errors.unsatisfiable_constraints env (Evd.evars_reset_evd evm evd) ev
else (* Best effort: do nothing *) oevd
| Some evd' -> docomp evd' comps
in docomp oevd split
(* let resolve_all_evars debug m env p oevd = *)
(* let oevm = Evd.evars_of oevd in *)
(* try *)
(* let rec aux n evd = *)
(* if has_undefined p oevm evd then *)
(* if n > 0 then *)
(* let evd' = resolve_all_evars_once debug m env p evd in *)
(* aux (pred n) evd' *)
(* else None *)
(* else Some evd *)
(* in aux 3 oevd *)
(* with Not_found -> None *)
VERNAC COMMAND EXTEND Typeclasses_Unfold_Settings
| [ "Typeclasses" "unfold" reference_list(cl) ] -> [
add_hints false [typeclasses_db] (Vernacexpr.HintsUnfold cl)
]
END
(** Typeclass-based rewriting. *)
let respect_proj = lazy (mkConst (snd (List.hd (Lazy.force morphism_class).cl_projs)))
let make_dir l = make_dirpath (List.map id_of_string (List.rev l))
let try_find_reference dir s =
let sp = Libnames.make_path (make_dir ("Coq"::dir)) (id_of_string s) in
constr_of_global (Nametab.absolute_reference sp)
let gen_constant dir s = Coqlib.gen_constant "Class_setoid" dir s
let coq_proj1 = lazy(gen_constant ["Init"; "Logic"] "proj1")
let coq_proj2 = lazy(gen_constant ["Init"; "Logic"] "proj2")
let iff = lazy (gen_constant ["Init"; "Logic"] "iff")
let coq_all = lazy (gen_constant ["Init"; "Logic"] "all")
let impl = lazy (gen_constant ["Program"; "Basics"] "impl")
let arrow = lazy (gen_constant ["Program"; "Basics"] "arrow")
let coq_id = lazy (gen_constant ["Program"; "Basics"] "id")
let reflexive_type = lazy (try_find_reference ["Classes"; "RelationClasses"] "Reflexive")
let reflexive_proof = lazy (try_find_reference ["Classes"; "RelationClasses"] "reflexivity")
let symmetric_type = lazy (try_find_reference ["Classes"; "RelationClasses"] "Symmetric")
let symmetric_proof = lazy (try_find_reference ["Classes"; "RelationClasses"] "symmetry")
let transitive_type = lazy (try_find_reference ["Classes"; "RelationClasses"] "Transitive")
let transitive_proof = lazy (try_find_reference ["Classes"; "RelationClasses"] "transitivity")
let coq_inverse = lazy (gen_constant (* ["Classes"; "RelationClasses"] "inverse" *)
["Program"; "Basics"] "flip")
let inverse car rel = mkApp (Lazy.force coq_inverse, [| car ; car; mkProp; rel |])
let complement = lazy (gen_constant ["Classes"; "RelationClasses"] "complement")
let pointwise_relation = lazy (gen_constant ["Classes"; "RelationClasses"] "pointwise_relation")
let respectful_dep = lazy (gen_constant ["Classes"; "Morphisms"] "respectful_dep")
let respectful = lazy (gen_constant ["Classes"; "Morphisms"] "respectful")
let equivalence = lazy (gen_constant ["Classes"; "RelationClasses"] "Equivalence")
let default_relation = lazy (gen_constant ["Classes"; "SetoidTactics"] "DefaultRelation")
let coq_relation = lazy (gen_constant ["Relations";"Relation_Definitions"] "relation")
let mk_relation a = mkApp (Lazy.force coq_relation, [| a |])
let coq_relationT = lazy (gen_constant ["Classes";"Relations"] "relationT")
let setoid_refl_proj = lazy (gen_constant ["Classes"; "SetoidClass"] "Equivalence_Reflexive")
let setoid_equiv = lazy (gen_constant ["Classes"; "SetoidClass"] "equiv")
let setoid_morphism = lazy (gen_constant ["Classes"; "SetoidClass"] "setoid_morphism")
let setoid_refl_proj = lazy (gen_constant ["Classes"; "SetoidClass"] "Equivalence_Reflexive")
let arrow_morphism a b =
if isprop a && isprop b then
Lazy.force impl
else
mkApp(Lazy.force arrow, [|a;b|])
let setoid_refl pars x =
applistc (Lazy.force setoid_refl_proj) (pars @ [x])
let morphism_type = lazy (constr_of_global (Lazy.force morphism_class).cl_impl)
let morphism_proxy_type = lazy (constr_of_global (Lazy.force morphism_proxy_class).cl_impl)
exception Found of (constr * constr * (types * types) list * constr * constr array *
(constr * (constr * constr * constr * constr)) option array)
let is_equiv env sigma t =
isConst t && Reductionops.is_conv env sigma (Lazy.force setoid_equiv) t
let split_head = function
hd :: tl -> hd, tl
| [] -> assert(false)
exception DependentMorphism
let build_signature isevars env m (cstrs : 'a option list) (finalcstr : 'a Lazy.t option) (f : 'a -> constr) =
let new_evar isevars env t =
Evarutil.e_new_evar isevars env
(* ~src:(dummy_loc, ImplicitArg (ConstRef (Lazy.force respectful), (n, Some na))) *) t
in
let mk_relty ty obj =
match obj with
| None ->
let relty = mk_relation ty in
new_evar isevars env relty
| Some x -> f x
in
let rec aux env ty l =
let t = Reductionops.whd_betadeltaiota env (Evd.evars_of !isevars) ty in
match kind_of_term t, l with
| Prod (na, ty, b), obj :: cstrs ->
if dependent (mkRel 1) ty then raise DependentMorphism;
let (b, arg, evars) = aux (Environ.push_rel (na, None, ty) env) b cstrs in
let ty = Reductionops.nf_betaiota ty in
let relty = mk_relty ty obj in
let arg' = mkApp (Lazy.force respectful, [| ty ; b ; relty ; arg |]) in
mkProd(na, ty, b), arg', (ty, relty) :: evars
| _, obj :: _ -> anomaly "build_signature: not enough products"
| _, [] ->
(match finalcstr with
None ->
let t = Reductionops.nf_betaiota ty in
let rel = mk_relty t None in
t, rel, [t, rel]
| Some codom -> let (t, rel) = Lazy.force codom in
t, rel, [t, rel])
in aux env m cstrs
let morphism_proof env evars carrier relation x =
let goal =
mkApp (Lazy.force morphism_proxy_type, [| carrier ; relation; x |])
in Evarutil.e_new_evar evars env goal
let find_class_proof proof_type proof_method env carrier relation =
try
let goal =
mkApp (Lazy.force proof_type, [| carrier ; relation |])
in
let inst = resolve_one_typeclass env goal in
mkApp (Lazy.force proof_method, [| carrier ; relation ; inst |])
with e when Logic.catchable_exception e -> raise Not_found
let reflexive_proof env = find_class_proof reflexive_type reflexive_proof env
let symmetric_proof env = find_class_proof symmetric_type symmetric_proof env
let transitive_proof env = find_class_proof transitive_type transitive_proof env
exception FoundInt of int
let array_find (arr: 'a array) (pred: int -> 'a -> bool): int =
try
for i=0 to Array.length arr - 1 do if pred i (arr.(i)) then raise (FoundInt i) done;
raise Not_found
with FoundInt i -> i
let resolve_morphism env sigma oldt m ?(fnewt=fun x -> x) args args' cstr evars =
let morph_instance, proj, sigargs, m', args, args' =
let first = try (array_find args' (fun i b -> b <> None)) with Not_found -> raise (Invalid_argument "resolve_morphism") in
let morphargs, morphobjs = array_chop first args in
let morphargs', morphobjs' = array_chop first args' in
let appm = mkApp(m, morphargs) in
let appmtype = Typing.type_of env sigma appm in
let cstrs = List.map (function None -> None | Some (_, (a, r, _, _)) -> Some (a, r)) (Array.to_list morphobjs') in
let appmtype', signature, sigargs = build_signature evars env appmtype cstrs cstr (fun (a, r) -> r) in
let cl_args = [| appmtype' ; signature ; appm |] in
let app = mkApp (Lazy.force morphism_type, cl_args) in
let morph = Evarutil.e_new_evar evars env app in
let proj =
mkApp (Lazy.force respect_proj,
Array.append cl_args [|morph|])
in
morph, proj, sigargs, appm, morphobjs, morphobjs'
in
let projargs, respars, typeargs =
array_fold_left2
(fun (acc, sigargs, typeargs') x y ->
let (carrier, relation), sigargs = split_head sigargs in
match y with
None ->
let proof = morphism_proof env evars carrier relation x in
[ proof ; x ; x ] @ acc, sigargs, x :: typeargs'
| Some (p, (_, _, _, t')) ->
[ p ; t'; x ] @ acc, sigargs, t' :: typeargs')
([], sigargs, []) args args'
in
let proof = applistc proj (List.rev projargs) in
let newt = applistc m' (List.rev typeargs) in
match respars with
[ a, r ] -> (proof, (a, r, oldt, fnewt newt))
| _ -> assert(false)
(* Adapted from setoid_replace. *)
type hypinfo = {
cl : clausenv;
prf : constr;
car : constr;
rel : constr;
l2r : bool;
c1 : constr;
c2 : constr;
c : constr option;
abs : (constr * types) option;
}
let evd_convertible env evd x y =
try ignore(Evarconv.the_conv_x env x y evd); true
with _ -> false
let decompose_setoid_eqhyp env sigma c left2right =
let ctype = Typing.type_of env sigma c in
let eqclause = Clenv.mk_clenv_from_env env sigma None (c,ctype) in
let (equiv, args) = decompose_app (Clenv.clenv_type eqclause) in
let rec split_last_two = function
| [c1;c2] -> [],(c1, c2)
| x::y::z ->
let l,res = split_last_two (y::z) in x::l, res
| _ -> error "The term provided is not an applied relation" in
let others,(c1,c2) = split_last_two args in
let ty1, ty2 =
Typing.mtype_of env eqclause.evd c1, Typing.mtype_of env eqclause.evd c2
in
if not (evd_convertible env eqclause.evd ty1 ty2) then
error "The term does not end with an applied homogeneous relation"
else
{ cl=eqclause; prf=(Clenv.clenv_value eqclause);
car=ty1; rel=mkApp (equiv, Array.of_list others);
l2r=left2right; c1=c1; c2=c2; c=Some c; abs=None }
let rewrite_unif_flags = {
Unification.modulo_conv_on_closed_terms = None;
Unification.use_metas_eagerly = true;
Unification.modulo_delta = empty_transparent_state;
}
let conv_transparent_state = (Idpred.empty, Cpred.full)
let rewrite2_unif_flags = {
Unification.modulo_conv_on_closed_terms = Some conv_transparent_state;
Unification.use_metas_eagerly = true;
Unification.modulo_delta = empty_transparent_state;
}
let convertible env evd x y =
Reductionops.is_conv env (Evd.evars_of evd) x y
let allowK = true
let refresh_hypinfo env sigma hypinfo =
if !hypinfo.abs = None then
let {l2r=l2r; c = c} = !hypinfo in
match c with
| Some c ->
(* Refresh the clausenv to not get the same meta twice in the goal. *)
hypinfo := decompose_setoid_eqhyp env sigma c l2r;
| _ -> ()
else ()
let unify_eqn env sigma hypinfo t =
try
let {cl=cl; prf=prf; car=car; rel=rel; l2r=l2r; c1=c1; c2=c2; c=c; abs=abs} = !hypinfo in
let env', prf, c1, c2, car, rel =
let left = if l2r then c1 else c2 in
match abs with
Some (absprf, absprfty) ->
(*if convertible env cl.evd left t then
cl, prf, c1, c2, car, rel
else raise Not_found*)
let env' = clenv_unify allowK ~flags:rewrite2_unif_flags CONV left t cl in
let env' =
let mvs = clenv_dependent false env' in
clenv_pose_metas_as_evars env' mvs
in
let c1 = Clenv.clenv_nf_meta env' c1
and c2 = Clenv.clenv_nf_meta env' c2
and car = Clenv.clenv_nf_meta env' car
and rel = Clenv.clenv_nf_meta env' rel in
hypinfo := { !hypinfo with
cl = env';
abs = Some (Clenv.clenv_value env', Clenv.clenv_type env') };
env', prf, c1, c2, car, rel
| None ->
let env' =
try clenv_unify allowK ~flags:rewrite_unif_flags
CONV left t cl
with Pretype_errors.PretypeError _ ->
(* For Ring essentially, only when doing setoid_rewrite *)
clenv_unify allowK ~flags:rewrite2_unif_flags
CONV left t cl
in
let env' =
let mvs = clenv_dependent false env' in
clenv_pose_metas_as_evars env' mvs
in
let c1 = Clenv.clenv_nf_meta env' c1
and c2 = Clenv.clenv_nf_meta env' c2
and car = Clenv.clenv_nf_meta env' car
and rel = Clenv.clenv_nf_meta env' rel in
let prf = Clenv.clenv_value env' in
let ty1 = Typing.mtype_of env'.env env'.evd c1
and ty2 = Typing.mtype_of env'.env env'.evd c2
in
if convertible env env'.evd ty1 ty2 then (
if occur_meta prf then refresh_hypinfo env sigma hypinfo;
env', prf, c1, c2, car, rel)
else raise Reduction.NotConvertible
in
let res =
if l2r then (prf, (car, rel, c1, c2))
else
try (mkApp (symmetric_proof env car rel, [| c1 ; c2 ; prf |]), (car, rel, c2, c1))
with Not_found ->
(prf, (car, inverse car rel, c2, c1))
in Some (env', res)
with _ -> None
let unfold_impl t =
match kind_of_term t with
| App (arrow, [| a; b |])(* when eq_constr arrow (Lazy.force impl) *) ->
mkProd (Anonymous, a, lift 1 b)
| _ -> assert false
let unfold_id t =
match kind_of_term t with
| App (id, [| a; b |]) (* when eq_constr id (Lazy.force coq_id) *) -> b
| _ -> assert false
let unfold_all t =
match kind_of_term t with
| App (id, [| a; b |]) (* when eq_constr id (Lazy.force coq_all) *) ->
(match kind_of_term b with
| Lambda (n, ty, b) -> mkProd (n, ty, b)
| _ -> assert false)
| _ -> assert false
let decomp_prod env evm n c =
snd (Reductionops.decomp_n_prod env evm n c)
let rec decomp_pointwise n c =
if n = 0 then c
else
match kind_of_term c with
| App (pointwise, [| a; b; relb |]) -> decomp_pointwise (pred n) relb
| _ -> raise Not_found
let lift_cstr env sigma evars args cstr =
let cstr () =
let start =
match cstr with
| Some codom -> Lazy.force codom
| None -> let car = Evarutil.e_new_evar evars env (new_Type ()) in
let rel = Evarutil.e_new_evar evars env (mk_relation car) in
(car, rel)
in
Array.fold_right
(fun arg (car, rel) ->
let ty = Typing.type_of env sigma arg in
let car' = mkProd (Anonymous, ty, car) in
let rel' = mkApp (Lazy.force pointwise_relation, [| ty; car; rel |]) in
(car', rel'))
args start
in Some (Lazy.lazy_from_fun cstr)
let unlift_cstr env sigma = function
| None -> None
| Some codom ->
let cstr () =
let car, rel = Lazy.force codom in
decomp_prod env sigma 1 car, decomp_pointwise 1 rel
in Some (Lazy.lazy_from_fun cstr)
type rewrite_flags = { under_lambdas : bool; on_morphisms : bool }
let default_flags = { under_lambdas = true; on_morphisms = true; }
let build_new gl env sigma flags loccs hypinfo concl cstr evars =
let (nowhere_except_in,occs) = loccs in
let is_occ occ =
if nowhere_except_in then List.mem occ occs else not (List.mem occ occs) in
let rec aux env t occ cstr =
let unif = unify_eqn env sigma hypinfo t in
let occ = if unif = None then occ else succ occ in
match unif with
| Some (env', (prf, hypinfo as x)) when is_occ occ ->
begin
evars := Evd.evar_merge !evars
(Evd.evars_of (Evd.undefined_evars (Evarutil.nf_evar_defs env'.evd)));
match cstr with
| None -> Some x, occ
| Some _ ->
let (car, r, orig, dest) = hypinfo in
let res =
resolve_morphism env sigma t ~fnewt:unfold_id
(mkApp (Lazy.force coq_id, [| car |]))
[| orig |] [| Some x |] cstr evars
in Some res, occ
end
| _ ->
match kind_of_term t with
| App (m, args) ->
let rewrite_args occ =
let args', occ =
Array.fold_left
(fun (acc, occ) arg -> let res, occ = aux env arg occ None in (res :: acc, occ))
([], occ) args
in
let res =
if List.for_all (fun x -> x = None) args' then None
else
let args' = Array.of_list (List.rev args') in
(Some (resolve_morphism env sigma t m args args' cstr evars))
in res, occ
in
if flags.on_morphisms then
let m', occ = aux env m occ (lift_cstr env sigma evars args cstr) in
match m' with
| None -> rewrite_args occ (* Standard path, try rewrite on arguments *)
| Some (prf, (car, rel, c1, c2)) ->
(* We rewrote the function and get a proof of pointwise rel for the arguments.
We just apply it. *)
let nargs = Array.length args in
let res =
mkApp (prf, args),
(decomp_prod env (Evd.evars_of !evars) nargs car,
decomp_pointwise nargs rel, mkApp(c1, args), mkApp(c2, args))
in Some res, occ
else rewrite_args occ
| Prod (n, x, b) when not (dependent (mkRel 1) b) ->
let x', occ = aux env x occ None in
(* if x' = None && flags.under_lambdas then *)
(* let lam = mkLambda (n, x, b) in *)
(* let lam', occ = aux env lam occ None in *)
(* let res = *)
(* match lam' with *)
(* | None -> None *)
(* | Some (prf, (car, rel, c1, c2)) -> *)
(* Some (resolve_morphism env sigma t *)
(* ~fnewt:unfold_all *)
(* (Lazy.force coq_all) [| x ; lam |] [| None; lam' |] *)
(* cstr evars) *)
(* in res, occ *)
(* else *)
let b = subst1 mkProp b in
let b', occ = aux env b occ None in
let res =
if x' = None && b' = None then None
else
Some (resolve_morphism env sigma t
~fnewt:unfold_impl
(arrow_morphism (Typing.type_of env sigma x) (Typing.type_of env sigma b))
[| x ; b |] [| x' ; b' |]
cstr evars)
in res, occ
| Prod (n, ty, b) ->
let lam = mkLambda (n, ty, b) in
let lam', occ = aux env lam occ None in
let res =
match lam' with
| None -> None
| Some (prf, (car, rel, c1, c2)) ->
Some (resolve_morphism env sigma t
~fnewt:unfold_all
(Lazy.force coq_all) [| ty ; lam |] [| None; lam' |]
cstr evars)
in res, occ
| Lambda (n, t, b) when flags.under_lambdas ->
let env' = Environ.push_rel (n, None, t) env in
refresh_hypinfo env' sigma hypinfo;
let b', occ = aux env' b occ (unlift_cstr env sigma cstr) in
let res =
match b' with
| None -> None
| Some (prf, (car, rel, c1, c2)) ->
let prf' = mkLambda (n, t, prf) in
let car' = mkProd (n, t, car) in
let rel' = mkApp (Lazy.force pointwise_relation, [| t; car; rel |]) in
let c1' = mkLambda(n, t, c1) and c2' = mkLambda (n, t, c2) in
Some (prf', (car', rel', c1', c2'))
in res, occ
| _ -> None, occ
in
let eq,nbocc_min_1 = aux env concl 0 cstr in
let rest = List.filter (fun o -> o > nbocc_min_1) occs in
if rest <> [] then error_invalid_occurrence rest;
eq
let resolve_typeclass_evars d p env evd onlyargs split fail =
let pred =
if onlyargs then
(fun ev evi -> Typeclasses.is_implicit_arg (snd (Evd.evar_source ev evd)) &&
class_of_constr evi.Evd.evar_concl <> None)
else
(fun ev evi -> class_of_constr evi.Evd.evar_concl <> None)
in resolve_all_evars d p env pred evd split fail
let cl_rewrite_clause_aux ?(flags=default_flags) hypinfo goal_meta occs clause gl =
let concl, is_hyp =
match clause with
Some ((_, id), _) -> pf_get_hyp_typ gl id, Some id
| None -> pf_concl gl, None
in
let cstr =
match is_hyp with
None -> (mkProp, inverse mkProp (Lazy.force impl))
| Some _ -> (mkProp, Lazy.force impl)
in
let evars = ref (Evd.create_evar_defs Evd.empty) in
let env = pf_env gl in
let sigma = project gl in
let eq = build_new gl env sigma flags occs hypinfo concl (Some (Lazy.lazy_from_val cstr)) evars
in
match eq with
| Some (p, (_, _, oldt, newt)) ->
(try
evars := Typeclasses.resolve_typeclasses env ~split:false ~fail:true !evars;
let p = Evarutil.nf_isevar !evars p in
let newt = Evarutil.nf_isevar !evars newt in
let undef = Evd.undefined_evars !evars in
let abs = Option.map (fun (x, y) -> Evarutil.nf_isevar !evars x,
Evarutil.nf_isevar !evars y) !hypinfo.abs in
let rewtac =
match is_hyp with
| Some id ->
let term =
match abs with
| None -> p
| Some (t, ty) ->
mkApp (mkLambda (Name (id_of_string "lemma"), ty, p), [| t |])
in
cut_replacing id newt
(fun x -> Tactics.refine (mkApp (term, [| mkVar id |])))
| None ->
(match abs with
| None ->
let name = next_name_away_with_default "H" Anonymous (pf_ids_of_hyps gl) in
tclTHENLAST
(Tacmach.internal_cut_no_check name newt)
(tclTHEN (Tactics.revert [name]) (Tactics.refine p))
| Some (t, ty) ->
Tactics.refine
(mkApp (mkLambda (Name (id_of_string "newt"), newt,
mkLambda (Name (id_of_string "lemma"), ty,
mkApp (p, [| mkRel 2 |]))),
[| mkMeta goal_meta; t |])))
in
let evartac =
let evd = Evd.evars_of undef in
if not (evd = Evd.empty) then Refiner.tclEVARS (Evd.merge sigma evd)
else tclIDTAC
in tclTHENLIST [evartac; rewtac] gl
with
| Stdpp.Exc_located (_, TypeClassError (env, (UnsatisfiableConstraints _ as e)))
| TypeClassError (env, (UnsatisfiableConstraints _ as e)) ->
tclFAIL 0 (str" setoid rewrite failed: unable to satisfy the rewriting constraints."
++ fnl () ++ Himsg.explain_typeclass_error env e) gl)
(* | Not_found -> *)
(* tclFAIL 0 (str" setoid rewrite failed: unable to satisfy the rewriting constraints.") gl) *)
| None ->
let {l2r=l2r; c1=x; c2=y} = !hypinfo in
raise (Pretype_errors.PretypeError
(pf_env gl,
Pretype_errors.NoOccurrenceFound ((if l2r then x else y), is_hyp)))
(* tclFAIL 1 (str"setoid rewrite failed") gl *)
let cl_rewrite_clause_aux ?(flags=default_flags) hypinfo goal_meta occs clause gl =
try cl_rewrite_clause_aux ~flags hypinfo goal_meta occs clause gl
with DependentMorphism -> tclFAIL 0 (str " setoid rewrite failed: cannot handle dependent morphisms") gl
let cl_rewrite_clause c left2right occs clause gl =
init_setoid ();
let meta = Evarutil.new_meta() in
let gl = { gl with sigma = Typeclasses.mark_unresolvables gl.sigma } in
let hypinfo = ref (decompose_setoid_eqhyp (pf_env gl) (project gl) c left2right) in
cl_rewrite_clause_aux hypinfo meta occs clause gl
open Genarg
open Extraargs
let occurrences_of = function
| n::_ as nl when n < 0 -> (false,List.map abs nl)
| nl ->
if List.exists (fun n -> n < 0) nl then
error "Illegal negative occurrence number";
(true,nl)
TACTIC EXTEND class_rewrite
| [ "clrewrite" orient(o) constr(c) "in" hyp(id) "at" occurrences(occ) ] -> [ cl_rewrite_clause c o (occurrences_of occ) (Some (([],id), [])) ]
| [ "clrewrite" orient(o) constr(c) "at" occurrences(occ) "in" hyp(id) ] -> [ cl_rewrite_clause c o (occurrences_of occ) (Some (([],id), [])) ]
| [ "clrewrite" orient(o) constr(c) "in" hyp(id) ] -> [ cl_rewrite_clause c o all_occurrences (Some (([],id), [])) ]
| [ "clrewrite" orient(o) constr(c) "at" occurrences(occ) ] -> [ cl_rewrite_clause c o (occurrences_of occ) None ]
| [ "clrewrite" orient(o) constr(c) ] -> [ cl_rewrite_clause c o all_occurrences None ]
END
let clsubstitute o c =
let is_tac id = match kind_of_term c with Var id' when id' = id -> true | _ -> false in
Tacticals.onAllClauses
(fun cl ->
match cl with
| Some ((_,id),_) when is_tac id -> tclIDTAC
| _ -> tclTRY (cl_rewrite_clause c o all_occurrences cl))
TACTIC EXTEND substitute
| [ "substitute" orient(o) constr(c) ] -> [ clsubstitute o c ]
END
let pr_debug _prc _prlc _prt b =
if b then Pp.str "debug" else Pp.mt()
ARGUMENT EXTEND debug TYPED AS bool PRINTED BY pr_debug
| [ "debug" ] -> [ true ]
| [ ] -> [ false ]
END
let pr_mode _prc _prlc _prt m =
match m with
Some b ->
if b then Pp.str "depth-first" else Pp.str "breadth-fist"
| None -> Pp.mt()
ARGUMENT EXTEND search_mode TYPED AS bool option PRINTED BY pr_mode
| [ "dfs" ] -> [ Some true ]
| [ "bfs" ] -> [ Some false ]
| [] -> [ None ]
END
let pr_depth _prc _prlc _prt = function
Some i -> Util.pr_int i
| None -> Pp.mt()
ARGUMENT EXTEND depth TYPED AS int option PRINTED BY pr_depth
| [ int_or_var_opt(v) ] -> [ match v with Some (ArgArg i) -> Some i | _ -> None ]
END
let solve_inst debug mode depth env evd onlyargs split fail =
resolve_typeclass_evars debug (mode, depth) env evd onlyargs split fail
let _ =
Typeclasses.solve_instanciations_problem :=
solve_inst false true default_eauto_depth
VERNAC COMMAND EXTEND Typeclasses_Settings
| [ "Typeclasses" "eauto" ":=" debug(d) search_mode(s) depth(depth) ] -> [
let mode = match s with Some t -> t | None -> true in
let depth = match depth with Some i -> i | None -> default_eauto_depth in
Typeclasses.solve_instanciations_problem :=
solve_inst d mode depth
]
END
TACTIC EXTEND typeclasses_eauto
| [ "typeclasses" "eauto" debug(d) search_mode(s) depth(depth) ] -> [
let mode = match s with Some t -> t | None -> true in
let depth = match depth with Some i -> i | None -> default_eauto_depth in
fun gl ->
let gls = {it = [sig_it gl]; sigma = project gl} in
let vals v = List.hd v in
typeclasses_eauto d (mode, depth) [] (gls, vals) ]
END
(* fun gl -> *)
(* let env = pf_env gl in *)
(* let sigma = project gl in *)
(* let proj = sig_it gl in *)
(* let evd = Evd.create_evar_defs (Evd.add Evd.empty 1 proj) in *)
(* let mode = match s with Some t -> t | None -> true in *)
(* let depth = match depth with Some i -> i | None -> default_eauto_depth in *)
(* match resolve_typeclass_evars d (mode, depth) env evd false with *)
(* | Some evd' -> *)
(* let goal = Evd.find (Evd.evars_of evd') 1 in *)
(* (match goal.evar_body with *)
(* | Evar_empty -> tclIDTAC gl *)
(* | Evar_defined b -> refine b gl) *)
(* | None -> tclIDTAC gl *)
(* ] *)
let _ =
Classes.refine_ref := Refine.refine
(* Compatibility with old Setoids *)
TACTIC EXTEND setoid_rewrite
[ "setoid_rewrite" orient(o) constr(c) ]
-> [ cl_rewrite_clause c o all_occurrences None ]
| [ "setoid_rewrite" orient(o) constr(c) "in" hyp(id) ] ->
[ cl_rewrite_clause c o all_occurrences (Some (([],id), []))]
| [ "setoid_rewrite" orient(o) constr(c) "at" occurrences(occ) ] ->
[ cl_rewrite_clause c o (occurrences_of occ) None]
| [ "setoid_rewrite" orient(o) constr(c) "at" occurrences(occ) "in" hyp(id)] ->
[ cl_rewrite_clause c o (occurrences_of occ) (Some (([],id), []))]
| [ "setoid_rewrite" orient(o) constr(c) "in" hyp(id) "at" occurrences(occ)] ->
[ cl_rewrite_clause c o (occurrences_of occ) (Some (([],id), []))]
END
(* let solve_obligation lemma = *)
(* tclTHEN (Tacinterp.interp (Tacexpr.TacAtom (dummy_loc, Tacexpr.TacAnyConstructor None))) *)
(* (eapply_with_bindings (Constrintern.interp_constr Evd.empty (Global.env()) lemma, NoBindings)) *)
let mkappc s l = CAppExpl (dummy_loc,(None,(Libnames.Ident (dummy_loc,id_of_string s))),l)
let declare_an_instance n s args =
((dummy_loc,Name n), Explicit,
CAppExpl (dummy_loc, (None, Qualid (dummy_loc, qualid_of_string s)),
args))
let declare_instance a aeq n s = declare_an_instance n s [a;aeq]
let anew_instance binders instance fields =
new_instance binders instance fields
~on_free_vars:Classes.fail_on_free_vars
None
let require_library dirpath =
let qualid = (dummy_loc, Libnames.qualid_of_dirpath (Libnames.dirpath_of_string dirpath)) in
Library.require_library [qualid] (Some false)
let declare_instance_refl binders a aeq n lemma =
let instance = declare_instance a aeq (add_suffix n "_Reflexive") "Coq.Classes.RelationClasses.Reflexive"
in anew_instance binders instance
[((dummy_loc,id_of_string "reflexivity"),[],lemma)]
let declare_instance_sym binders a aeq n lemma =
let instance = declare_instance a aeq (add_suffix n "_Symmetric") "Coq.Classes.RelationClasses.Symmetric"
in anew_instance binders instance
[((dummy_loc,id_of_string "symmetry"),[],lemma)]
let declare_instance_trans binders a aeq n lemma =
let instance = declare_instance a aeq (add_suffix n "_Transitive") "Coq.Classes.RelationClasses.Transitive"
in anew_instance binders instance
[((dummy_loc,id_of_string "transitivity"),[],lemma)]
let constr_tac = Tacinterp.interp (Tacexpr.TacAtom (dummy_loc, Tacexpr.TacAnyConstructor (false,None)))
let declare_relation ?(binders=[]) a aeq n refl symm trans =
init_setoid ();
match (refl,symm,trans) with
(None, None, None) ->
let instance = declare_instance a aeq n "Coq.Classes.SetoidTactics.DefaultRelation"
in ignore(anew_instance binders instance [])
| (Some lemma1, None, None) ->
ignore (declare_instance_refl binders a aeq n lemma1)
| (None, Some lemma2, None) ->
ignore (declare_instance_sym binders a aeq n lemma2)
| (None, None, Some lemma3) ->
ignore (declare_instance_trans binders a aeq n lemma3)
| (Some lemma1, Some lemma2, None) ->
ignore (declare_instance_refl binders a aeq n lemma1);
ignore (declare_instance_sym binders a aeq n lemma2)
| (Some lemma1, None, Some lemma3) ->
let _lemma_refl = declare_instance_refl binders a aeq n lemma1 in
let _lemma_trans = declare_instance_trans binders a aeq n lemma3 in
let instance = declare_instance a aeq n "Coq.Classes.RelationClasses.PreOrder"
in ignore(
anew_instance binders instance
[((dummy_loc,id_of_string "PreOrder_Reflexive"), [], lemma1);
((dummy_loc,id_of_string "PreOrder_Transitive"),[], lemma3)])
| (None, Some lemma2, Some lemma3) ->
let _lemma_sym = declare_instance_sym binders a aeq n lemma2 in
let _lemma_trans = declare_instance_trans binders a aeq n lemma3 in
let instance = declare_instance a aeq n "Coq.Classes.RelationClasses.PER"
in ignore(
anew_instance binders instance
[((dummy_loc,id_of_string "PER_Symmetric"), [], lemma2);
((dummy_loc,id_of_string "PER_Transitive"),[], lemma3)])
| (Some lemma1, Some lemma2, Some lemma3) ->
let _lemma_refl = declare_instance_refl binders a aeq n lemma1 in
let _lemma_sym = declare_instance_sym binders a aeq n lemma2 in
let _lemma_trans = declare_instance_trans binders a aeq n lemma3 in
let instance = declare_instance a aeq n "Coq.Classes.RelationClasses.Equivalence"
in ignore(
anew_instance binders instance
[((dummy_loc,id_of_string "Equivalence_Reflexive"), [], lemma1);
((dummy_loc,id_of_string "Equivalence_Symmetric"), [], lemma2);
((dummy_loc,id_of_string "Equivalence_Transitive"),[], lemma3)])
type 'a binders_let_argtype = (local_binder list, 'a) Genarg.abstract_argument_type
let (wit_binders_let : Genarg.tlevel binders_let_argtype),
(globwit_binders_let : Genarg.glevel binders_let_argtype),
(rawwit_binders_let : Genarg.rlevel binders_let_argtype) =
Genarg.create_arg "binders_let"
open Pcoq.Constr
VERNAC COMMAND EXTEND AddRelation
| [ "Add" "Relation" constr(a) constr(aeq) "reflexivity" "proved" "by" constr(lemma1)
"symmetry" "proved" "by" constr(lemma2) "as" ident(n) ] ->
[ declare_relation a aeq n (Some lemma1) (Some lemma2) None ]
| [ "Add" "Relation" constr(a) constr(aeq) "reflexivity" "proved" "by" constr(lemma1)
"as" ident(n) ] ->
[ declare_relation a aeq n (Some lemma1) None None ]
| [ "Add" "Relation" constr(a) constr(aeq) "as" ident(n) ] ->
[ declare_relation a aeq n None None None ]
END
VERNAC COMMAND EXTEND AddRelation2
[ "Add" "Relation" constr(a) constr(aeq) "symmetry" "proved" "by" constr(lemma2)
"as" ident(n) ] ->
[ declare_relation a aeq n None (Some lemma2) None ]
| [ "Add" "Relation" constr(a) constr(aeq) "symmetry" "proved" "by" constr(lemma2) "transitivity" "proved" "by" constr(lemma3) "as" ident(n) ] ->
[ declare_relation a aeq n None (Some lemma2) (Some lemma3) ]
END
VERNAC COMMAND EXTEND AddRelation3
[ "Add" "Relation" constr(a) constr(aeq) "reflexivity" "proved" "by" constr(lemma1)
"transitivity" "proved" "by" constr(lemma3) "as" ident(n) ] ->
[ declare_relation a aeq n (Some lemma1) None (Some lemma3) ]
| [ "Add" "Relation" constr(a) constr(aeq) "reflexivity" "proved" "by" constr(lemma1)
"symmetry" "proved" "by" constr(lemma2) "transitivity" "proved" "by" constr(lemma3)
"as" ident(n) ] ->
[ declare_relation a aeq n (Some lemma1) (Some lemma2) (Some lemma3) ]
| [ "Add" "Relation" constr(a) constr(aeq) "transitivity" "proved" "by" constr(lemma3)
"as" ident(n) ] ->
[ declare_relation a aeq n None None (Some lemma3) ]
END
VERNAC COMMAND EXTEND AddParametricRelation
| [ "Add" "Parametric" "Relation" binders_let(b) ":" constr(a) constr(aeq)
"reflexivity" "proved" "by" constr(lemma1)
"symmetry" "proved" "by" constr(lemma2) "as" ident(n) ] ->
[ declare_relation ~binders:b a aeq n (Some lemma1) (Some lemma2) None ]
| [ "Add" "Parametric" "Relation" binders_let(b) ":" constr(a) constr(aeq)
"reflexivity" "proved" "by" constr(lemma1)
"as" ident(n) ] ->
[ declare_relation ~binders:b a aeq n (Some lemma1) None None ]
| [ "Add" "Parametric" "Relation" binders_let(b) ":" constr(a) constr(aeq) "as" ident(n) ] ->
[ declare_relation ~binders:b a aeq n None None None ]
END
VERNAC COMMAND EXTEND AddParametricRelation2
[ "Add" "Parametric" "Relation" binders_let(b) ":" constr(a) constr(aeq) "symmetry" "proved" "by" constr(lemma2)
"as" ident(n) ] ->
[ declare_relation ~binders:b a aeq n None (Some lemma2) None ]
| [ "Add" "Parametric" "Relation" binders_let(b) ":" constr(a) constr(aeq) "symmetry" "proved" "by" constr(lemma2) "transitivity" "proved" "by" constr(lemma3) "as" ident(n) ] ->
[ declare_relation ~binders:b a aeq n None (Some lemma2) (Some lemma3) ]
END
VERNAC COMMAND EXTEND AddParametricRelation3
[ "Add" "Parametric" "Relation" binders_let(b) ":" constr(a) constr(aeq) "reflexivity" "proved" "by" constr(lemma1)
"transitivity" "proved" "by" constr(lemma3) "as" ident(n) ] ->
[ declare_relation ~binders:b a aeq n (Some lemma1) None (Some lemma3) ]
| [ "Add" "Parametric" "Relation" binders_let(b) ":" constr(a) constr(aeq) "reflexivity" "proved" "by" constr(lemma1)
"symmetry" "proved" "by" constr(lemma2) "transitivity" "proved" "by" constr(lemma3)
"as" ident(n) ] ->
[ declare_relation ~binders:b a aeq n (Some lemma1) (Some lemma2) (Some lemma3) ]
| [ "Add" "Parametric" "Relation" binders_let(b) ":" constr(a) constr(aeq) "transitivity" "proved" "by" constr(lemma3)
"as" ident(n) ] ->
[ declare_relation ~binders:b a aeq n None None (Some lemma3) ]
END
let mk_qualid s =
Libnames.Qualid (dummy_loc, Libnames.qualid_of_string s)
let cHole = CHole (dummy_loc, None)
open Entries
open Libnames
let respect_projection r ty =
let ctx, inst = Sign.decompose_prod_assum ty in
let mor, args = destApp inst in
let instarg = mkApp (r, rel_vect 0 (List.length ctx)) in
let app = mkApp (Lazy.force respect_proj,
Array.append args [| instarg |]) in
it_mkLambda_or_LetIn app ctx
let declare_projection n instance_id r =
let ty = Global.type_of_global r in
let c = constr_of_global r in
let term = respect_projection c ty in
let typ = Typing.type_of (Global.env ()) Evd.empty term in
let ctx, typ = Sign.decompose_prod_assum typ in
let typ =
let n =
let rec aux t =
match kind_of_term t with
App (f, [| a ; a' ; rel; rel' |]) when eq_constr f (Lazy.force respectful) ->
succ (aux rel')
| _ -> 0
in
let init =
match kind_of_term typ with
App (f, args) when eq_constr f (Lazy.force respectful) ->
mkApp (f, fst (array_chop (Array.length args - 2) args))
| _ -> typ
in aux init
in
let ctx,ccl = Reductionops.decomp_n_prod (Global.env()) Evd.empty (3 * n) typ
in it_mkProd_or_LetIn ccl ctx
in
let typ = it_mkProd_or_LetIn typ ctx in
let cst =
{ const_entry_body = term;
const_entry_type = Some typ;
const_entry_opaque = false;
const_entry_boxed = false }
in
ignore(Declare.declare_constant n (Entries.DefinitionEntry cst, Decl_kinds.IsDefinition Decl_kinds.Definition))
let build_morphism_signature m =
let env = Global.env () in
let m = Constrintern.interp_constr Evd.empty env m in
let t = Typing.type_of env Evd.empty m in
let isevars = ref (Evd.create_evar_defs Evd.empty) in
let cstrs =
let rec aux t =
match kind_of_term t with
| Prod (na, a, b) ->
None :: aux b
| _ -> []
in aux t
in
let t', sig_, evars = build_signature isevars env t cstrs None snd in
let _ = List.iter
(fun (ty, rel) ->
let default = mkApp (Lazy.force default_relation, [| ty; rel |]) in
ignore (Evarutil.e_new_evar isevars env default))
evars
in
let morph =
mkApp (Lazy.force morphism_type, [| t; sig_; m |])
in
let evd =
Typeclasses.resolve_typeclasses ~fail:true ~onlyargs:false env !isevars in
let m = Evarutil.nf_isevar evd morph in
Evarutil.check_evars env Evd.empty evd m; m
let default_morphism sign m =
let env = Global.env () in
let isevars = ref (Evd.create_evar_defs Evd.empty) in
let t = Typing.type_of env Evd.empty m in
let _, sign, evars =
try build_signature isevars env t (fst sign) (snd sign) (fun (ty, rel) -> rel)
with DependentMorphism -> error "Cannot infer the signature of dependent morphisms"
in
let morph =
mkApp (Lazy.force morphism_type, [| t; sign; m |])
in
let mor = resolve_one_typeclass env morph in
mor, respect_projection mor morph
let add_setoid binders a aeq t n =
init_setoid ();
let _lemma_refl = declare_instance_refl binders a aeq n (mkappc "Seq_refl" [a;aeq;t]) in
let _lemma_sym = declare_instance_sym binders a aeq n (mkappc "Seq_sym" [a;aeq;t]) in
let _lemma_trans = declare_instance_trans binders a aeq n (mkappc "Seq_trans" [a;aeq;t]) in
let instance = declare_instance a aeq n "Coq.Classes.RelationClasses.Equivalence"
in ignore(
anew_instance binders instance
[((dummy_loc,id_of_string "Equivalence_Reflexive"), [], mkappc "Seq_refl" [a;aeq;t]);
((dummy_loc,id_of_string "Equivalence_Symmetric"), [], mkappc "Seq_sym" [a;aeq;t]);
((dummy_loc,id_of_string "Equivalence_Transitive"),[], mkappc "Seq_trans" [a;aeq;t])])
let add_morphism_infer m n =
init_setoid ();
let instance_id = add_suffix n "_Morphism" in
let instance = try build_morphism_signature m
with DependentMorphism -> error "Cannot infer the signature of dependent morphisms"
in
if Lib.is_modtype () then
let cst = Declare.declare_internal_constant instance_id
(Entries.ParameterEntry (instance,false), Decl_kinds.IsAssumption Decl_kinds.Logical)
in
add_instance (Typeclasses.new_instance (Lazy.force morphism_class) None false cst);
declare_projection n instance_id (ConstRef cst)
else
let kind = Decl_kinds.Global, Decl_kinds.DefinitionBody Decl_kinds.Instance in
Flags.silently
(fun () ->
Command.start_proof instance_id kind instance
(fun _ -> function
Libnames.ConstRef cst ->
add_instance (Typeclasses.new_instance (Lazy.force morphism_class) None false cst);
declare_projection n instance_id (ConstRef cst)
| _ -> assert false);
Pfedit.by (Tacinterp.interp <:tactic< Coq.Classes.SetoidTactics.add_morphism_tactic>>)) ();
Flags.if_verbose (fun x -> msg (Printer.pr_open_subgoals x)) ()
let add_morphism binders m s n =
init_setoid ();
let instance_id = add_suffix n "_Morphism" in
let instance =
((dummy_loc,Name instance_id), Explicit,
CAppExpl (dummy_loc,
(None, Qualid (dummy_loc, Libnames.qualid_of_string "Coq.Classes.Morphisms.Morphism")),
[cHole; s; m]))
in
let tac = Tacinterp.interp <:tactic<add_morphism_tactic>> in
ignore(new_instance binders instance []
~on_free_vars:Classes.fail_on_free_vars
~tac ~hook:(fun cst -> declare_projection n instance_id (ConstRef cst))
None)
VERNAC COMMAND EXTEND AddSetoid1
[ "Add" "Setoid" constr(a) constr(aeq) constr(t) "as" ident(n) ] ->
[ add_setoid [] a aeq t n ]
| [ "Add" "Parametric" "Setoid" binders_let(binders) ":" constr(a) constr(aeq) constr(t) "as" ident(n) ] ->
[ add_setoid binders a aeq t n ]
| [ "Add" "Morphism" constr(m) ":" ident(n) ] ->
[ add_morphism_infer m n ]
| [ "Add" "Morphism" constr(m) "with" "signature" lconstr(s) "as" ident(n) ] ->
[ add_morphism [] m s n ]
| [ "Add" "Parametric" "Morphism" binders_let(binders) ":" constr(m) "with" "signature" lconstr(s) "as" ident(n) ] ->
[ add_morphism binders m s n ]
END
(** Bind to "rewrite" too *)
(** Taken from original setoid_replace, to emulate the old rewrite semantics where
lemmas are first instantiated and then rewrite proceeds. *)
let check_evar_map_of_evars_defs evd =
let metas = Evd.meta_list evd in
let check_freemetas_is_empty rebus =
Evd.Metaset.iter
(fun m ->
if Evd.meta_defined evd m then () else
raise
(Logic.RefinerError (Logic.UnresolvedBindings [Evd.meta_name evd m])))
in
List.iter
(fun (_,binding) ->
match binding with
Evd.Cltyp (_,{Evd.rebus=rebus; Evd.freemetas=freemetas}) ->
check_freemetas_is_empty rebus freemetas
| Evd.Clval (_,({Evd.rebus=rebus1; Evd.freemetas=freemetas1},_),
{Evd.rebus=rebus2; Evd.freemetas=freemetas2}) ->
check_freemetas_is_empty rebus1 freemetas1 ;
check_freemetas_is_empty rebus2 freemetas2
) metas
let unification_rewrite l2r c1 c2 cl car rel but gl =
let (env',c') =
try
(* ~flags:(false,true) to allow to mark occurrences that must not be
rewritten simply by replacing them with let-defined definitions
in the context *)
Unification.w_unify_to_subterm ~flags:rewrite_unif_flags (pf_env gl) ((if l2r then c1 else c2),but) cl.evd
with
Pretype_errors.PretypeError _ ->
(* ~flags:(true,true) to make Ring work (since it really
exploits conversion) *)
Unification.w_unify_to_subterm ~flags:rewrite2_unif_flags
(pf_env gl) ((if l2r then c1 else c2),but) cl.evd
in
let cl' = {cl with evd = env'} in
let c1 = Clenv.clenv_nf_meta cl' c1
and c2 = Clenv.clenv_nf_meta cl' c2 in
check_evar_map_of_evars_defs env';
let prf = Clenv.clenv_value cl' in
let prfty = Clenv.clenv_type cl' in
let cl' = { cl' with templval = mk_freelisted prf ; templtyp = mk_freelisted prfty } in
{cl=cl'; prf=(mkRel 1); car=car; rel=rel; l2r=l2r; c1=c1; c2=c2; c=None; abs=Some (prf, prfty)}
let get_hyp gl c clause l2r =
let hi = decompose_setoid_eqhyp (pf_env gl) (project gl) c l2r in
let but = match clause with Some id -> pf_get_hyp_typ gl id | None -> pf_concl gl in
unification_rewrite hi.l2r hi.c1 hi.c2 hi.cl hi.car hi.rel but gl
let general_rewrite_flags = { under_lambdas = false; on_morphisms = false }
let general_s_rewrite l2r occs c ~new_goals gl =
let meta = Evarutil.new_meta() in
let hypinfo = ref (get_hyp gl c None l2r) in
cl_rewrite_clause_aux ~flags:general_rewrite_flags hypinfo meta occs None gl
let general_s_rewrite_in id l2r occs c ~new_goals gl =
let meta = Evarutil.new_meta() in
let hypinfo = ref (get_hyp gl c (Some id) l2r) in
cl_rewrite_clause_aux ~flags:general_rewrite_flags hypinfo meta occs (Some (([],id), [])) gl
let general_s_rewrite_clause x =
init_setoid ();
match x with
| None -> general_s_rewrite
| Some id -> general_s_rewrite_in id
let _ = Equality.register_general_setoid_rewrite_clause general_s_rewrite_clause
(* [setoid_]{reflexivity,symmetry,transitivity} tactics *)
let relation_of_constr c =
match kind_of_term c with
| App (f, args) when Array.length args >= 2 ->
let relargs, args = array_chop (Array.length args - 2) args in
mkApp (f, relargs), args
| _ -> error "Not an applied relation"
let is_loaded d =
let d' = List.map id_of_string d in
let dir = make_dirpath (List.rev d') in
Library.library_is_loaded dir
let try_loaded f gl =
if is_loaded ["Coq";"Classes";"RelationClasses"] then f gl
else tclFAIL 0 (str"You need to require Coq.Classes.RelationClasses first") gl
let setoid_reflexivity gl =
let env = pf_env gl in
let rel, args = relation_of_constr (pf_concl gl) in
try
apply (reflexive_proof env (pf_type_of gl args.(0)) rel) gl
with Not_found ->
tclFAIL 0 (str" The relation " ++ Printer.pr_constr_env env rel ++ str" is not a declared reflexive relation")
gl
let setoid_symmetry gl =
let env = pf_env gl in
let rel, args = relation_of_constr (pf_concl gl) in
try
apply (symmetric_proof env (pf_type_of gl args.(0)) rel) gl
with Not_found ->
tclFAIL 0 (str" The relation " ++ Printer.pr_constr_env env rel ++ str" is not a declared symmetric relation")
gl
let setoid_transitivity c gl =
let env = pf_env gl in
let rel, args = relation_of_constr (pf_concl gl) in
try
apply_with_bindings
((transitive_proof env (pf_type_of gl args.(0)) rel),
Rawterm.ExplicitBindings [ dummy_loc, Rawterm.NamedHyp (id_of_string "y"), c ]) gl
with Not_found ->
tclFAIL 0
(str" The relation " ++ Printer.pr_constr_env env rel ++ str" is not a declared transitive relation") gl
let setoid_symmetry_in id gl =
let ctype = pf_type_of gl (mkVar id) in
let binders,concl = Sign.decompose_prod_assum ctype in
let (equiv, args) = decompose_app concl in
let rec split_last_two = function
| [c1;c2] -> [],(c1, c2)
| x::y::z -> let l,res = split_last_two (y::z) in x::l, res
| _ -> error "The term provided is not an equivalence"
in
let others,(c1,c2) = split_last_two args in
let he,c1,c2 = mkApp (equiv, Array.of_list others),c1,c2 in
let new_hyp' = mkApp (he, [| c2 ; c1 |]) in
let new_hyp = it_mkProd_or_LetIn new_hyp' binders in
tclTHENS (cut new_hyp)
[ intro_replacing id;
tclTHENLIST [ intros; setoid_symmetry; apply (mkVar id); Tactics.assumption ] ]
gl
let _ = Tactics.register_setoid_reflexivity setoid_reflexivity
let _ = Tactics.register_setoid_symmetry setoid_symmetry
let _ = Tactics.register_setoid_symmetry_in setoid_symmetry_in
let _ = Tactics.register_setoid_transitivity setoid_transitivity
TACTIC EXTEND setoid_symmetry
[ "setoid_symmetry" ] -> [ setoid_symmetry ]
| [ "setoid_symmetry" "in" hyp(n) ] -> [ setoid_symmetry_in n ]
END
TACTIC EXTEND setoid_reflexivity
[ "setoid_reflexivity" ] -> [ setoid_reflexivity ]
END
TACTIC EXTEND setoid_transitivity
[ "setoid_transitivity" constr(t) ] -> [ setoid_transitivity t ]
END
let try_classes t gls =
try t gls
with (Pretype_errors.PretypeError _) as e -> raise e
TACTIC EXTEND try_classes
[ "try_classes" tactic(t) ] -> [ try_classes (snd t) ]
END
open Rawterm
let constrexpr = Pcoq.Tactic.open_constr
type 'a constr_expr_argtype = (open_constr_expr, 'a) Genarg.abstract_argument_type
let (wit_constrexpr : Genarg.tlevel constr_expr_argtype),
(globwit_constrexpr : Genarg.glevel constr_expr_argtype),
(rawwit_const_expr : Genarg.rlevel constr_expr_argtype) =
Genarg.create_arg "constrexpr"
open Environ
open Refiner
TACTIC EXTEND apply_typeclasses
[ "typeclass_app" raw(t) ] -> [ fun gl ->
let nprod = nb_prod (pf_concl gl) in
let env = pf_env gl in
let evars = ref (create_evar_defs (project gl)) in
let j = Pretyping.Default.understand_judgment_tcc evars env t in
let n = nb_prod j.uj_type - nprod in
if n<0 then error "Apply_tc: theorem has not enough premisses.";
Refiner.tclTHEN (Refiner.tclEVARS (Evd.evars_of !evars))
(fun gl ->
let clause = make_clenv_binding_apply gl (Some n) (j.uj_val,j.uj_type) NoBindings in
let cl' = evar_clenv_unique_resolver true ~flags:default_unify_flags clause gl in
let evd' = Typeclasses.resolve_typeclasses cl'.env ~fail:true cl'.evd in
Clenvtac.clenv_refine true {cl' with evd = evd'} gl) gl
]
END
|