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|
open Printer
open Util
open Term
open Termops
open Names
open Declarations
open Pp
open Entries
open Hiddentac
open Evd
open Tacmach
open Proof_type
open Tacticals
open Tactics
open Indfun_common
open Functional_principles_proofs
exception Toberemoved_with_rel of int*constr
exception Toberemoved
let pr_elim_scheme el =
let env = Global.env () in
let msg = str "params := " ++ Printer.pr_rel_context env el.params in
let env = Environ.push_rel_context el.params env in
let msg = msg ++ fnl () ++ str "predicates := "++ Printer.pr_rel_context env el.predicates in
let env = Environ.push_rel_context el.predicates env in
let msg = msg ++ fnl () ++ str "branches := " ++ Printer.pr_rel_context env el.branches in
let env = Environ.push_rel_context el.branches env in
let msg = msg ++ fnl () ++ str "args := " ++ Printer.pr_rel_context env el.args in
let env = Environ.push_rel_context el.args env in
msg ++ fnl () ++ str "concl := " ++ pr_lconstr_env env el.concl
let observe s =
if do_observe ()
then Pp.msgnl s
let pr_elim_scheme el =
let env = Global.env () in
let msg = str "params := " ++ Printer.pr_rel_context env el.params in
let env = Environ.push_rel_context el.params env in
let msg = msg ++ fnl () ++ str "predicates := "++ Printer.pr_rel_context env el.predicates in
let env = Environ.push_rel_context el.predicates env in
let msg = msg ++ fnl () ++ str "branches := " ++ Printer.pr_rel_context env el.branches in
let env = Environ.push_rel_context el.branches env in
let msg = msg ++ fnl () ++ str "args := " ++ Printer.pr_rel_context env el.args in
let env = Environ.push_rel_context el.args env in
msg ++ fnl () ++ str "concl := " ++ pr_lconstr_env env el.concl
let observe s =
if do_observe ()
then Pp.msgnl s
(*
Transform an inductive induction principle into
a functional one
*)
let compute_new_princ_type_from_rel rel_to_fun sorts princ_type =
let princ_type_info = compute_elim_sig princ_type in
let env = Global.env () in
let env_with_params = Environ.push_rel_context princ_type_info.params env in
let tbl = Hashtbl.create 792 in
let rec change_predicates_names (avoid:identifier list) (predicates:Sign.rel_context) : Sign.rel_context =
match predicates with
| [] -> []
|(Name x,v,t)::predicates ->
let id = Nameops.next_ident_away x avoid in
Hashtbl.add tbl id x;
(Name id,v,t)::(change_predicates_names (id::avoid) predicates)
| (Anonymous,_,_)::_ -> anomaly "Anonymous property binder "
in
let avoid = (Termops.ids_of_context env_with_params ) in
let princ_type_info =
{ princ_type_info with
predicates = change_predicates_names avoid princ_type_info.predicates
}
in
(* observe (str "starting princ_type := " ++ pr_lconstr_env env princ_type); *)
(* observe (str "princ_infos : " ++ pr_elim_scheme princ_type_info); *)
let change_predicate_sort i (x,_,t) =
let new_sort = sorts.(i) in
let args,_ = decompose_prod t in
let real_args =
if princ_type_info.indarg_in_concl
then List.tl args
else args
in
Nameops.out_name x,None,compose_prod real_args (mkSort new_sort)
in
let new_predicates =
list_map_i
change_predicate_sort
0
princ_type_info.predicates
in
let env_with_params_and_predicates = List.fold_right Environ.push_named new_predicates env_with_params in
let rel_as_kn =
fst (match princ_type_info.indref with
| Some (Libnames.IndRef ind) -> ind
| _ -> error "Not a valid predicate"
)
in
let ptes_vars = List.map (fun (id,_,_) -> id) new_predicates in
let is_pte =
let set = List.fold_right Idset.add ptes_vars Idset.empty in
fun t ->
match kind_of_term t with
| Var id -> Idset.mem id set
| _ -> false
in
let pre_princ =
it_mkProd_or_LetIn
~init:
(it_mkProd_or_LetIn
~init:(option_fold_right
mkProd_or_LetIn
princ_type_info.indarg
princ_type_info.concl
)
princ_type_info.args
)
princ_type_info.branches
in
let pre_princ = substl (List.map mkVar ptes_vars) pre_princ in
let is_dom c =
match kind_of_term c with
| Ind((u,_)) -> u = rel_as_kn
| Construct((u,_),_) -> u = rel_as_kn
| _ -> false
in
let get_fun_num c =
match kind_of_term c with
| Ind(_,num) -> num
| Construct((_,num),_) -> num
| _ -> assert false
in
let dummy_var = mkVar (id_of_string "________") in
let mk_replacement c i args =
let res = mkApp(rel_to_fun.(i),Array.map pop (array_get_start args)) in
(* observe (str "replacing " ++ pr_lconstr c ++ str " by " ++ pr_lconstr res); *)
res
in
let rec has_dummy_var t =
fold_constr
(fun b t -> b || (eq_constr t dummy_var) || (has_dummy_var t))
false
t
in
let rec compute_new_princ_type remove env pre_princ : types*(constr list) =
let (new_princ_type,_) as res =
match kind_of_term pre_princ with
| Rel n ->
begin
try match Environ.lookup_rel n env with
| _,_,t when is_dom t -> raise Toberemoved
| _ -> pre_princ,[] with Not_found -> assert false
end
| Prod(x,t,b) ->
compute_new_princ_type_for_binder remove mkProd env x t b
| Lambda(x,t,b) ->
compute_new_princ_type_for_binder remove mkLambda env x t b
| Ind _ | Construct _ when is_dom pre_princ -> raise Toberemoved
| App(f,args) when is_dom f ->
let var_to_be_removed = destRel (array_last args) in
let num = get_fun_num f in
raise (Toberemoved_with_rel (var_to_be_removed,mk_replacement pre_princ num args))
| App(f,args) ->
let args =
if is_pte f && remove
then array_get_start args
else args
in
let new_args,binders_to_remove =
Array.fold_right (compute_new_princ_type_with_acc remove env)
args
([],[])
in
let new_f,binders_to_remove_from_f = compute_new_princ_type remove env f in
applist(new_f, new_args),
list_union_eq eq_constr binders_to_remove_from_f binders_to_remove
| LetIn(x,v,t,b) ->
compute_new_princ_type_for_letin remove env x v t b
| _ -> pre_princ,[]
in
(* let _ = match kind_of_term pre_princ with *)
(* | Prod _ -> *)
(* observe(str "compute_new_princ_type for "++ *)
(* pr_lconstr_env env pre_princ ++ *)
(* str" is "++ *)
(* pr_lconstr_env env new_princ_type ++ fnl ()) *)
(* | _ -> () in *)
res
and compute_new_princ_type_for_binder remove bind_fun env x t b =
begin
try
let new_t,binders_to_remove_from_t = compute_new_princ_type remove env t in
let new_x : name = get_name (ids_of_context env) x in
let new_env = Environ.push_rel (x,None,t) env in
let new_b,binders_to_remove_from_b = compute_new_princ_type remove new_env b in
if List.exists (eq_constr (mkRel 1)) binders_to_remove_from_b
then (pop new_b),filter_map (eq_constr (mkRel 1)) pop binders_to_remove_from_b
else
(
bind_fun(new_x,new_t,new_b),
list_union_eq
eq_constr
binders_to_remove_from_t
(List.map pop binders_to_remove_from_b)
)
with
| Toberemoved ->
(* observe (str "Decl of "++Ppconstr.pr_name x ++ str " is removed "); *)
let new_b,binders_to_remove_from_b = compute_new_princ_type remove env (substnl [dummy_var] 1 b) in
new_b, List.map pop binders_to_remove_from_b
| Toberemoved_with_rel (n,c) ->
(* observe (str "Decl of "++Ppconstr.pr_name x ++ str " is removed "); *)
let new_b,binders_to_remove_from_b = compute_new_princ_type remove env (substnl [c] n b) in
new_b, list_add_set_eq eq_constr (mkRel n) (List.map pop binders_to_remove_from_b)
end
and compute_new_princ_type_for_letin remove env x v t b =
begin
try
let new_t,binders_to_remove_from_t = compute_new_princ_type remove env t in
let new_v,binders_to_remove_from_v = compute_new_princ_type remove env v in
let new_x : name = get_name (ids_of_context env) x in
let new_env = Environ.push_rel (x,Some v,t) env in
let new_b,binders_to_remove_from_b = compute_new_princ_type remove new_env b in
if List.exists (eq_constr (mkRel 1)) binders_to_remove_from_b
then (pop new_b),filter_map (eq_constr (mkRel 1)) pop binders_to_remove_from_b
else
(
mkLetIn(new_x,new_v,new_t,new_b),
list_union_eq
eq_constr
(list_union_eq eq_constr binders_to_remove_from_t binders_to_remove_from_v)
(List.map pop binders_to_remove_from_b)
)
with
| Toberemoved ->
(* observe (str "Decl of "++Ppconstr.pr_name x ++ str " is removed "); *)
let new_b,binders_to_remove_from_b = compute_new_princ_type remove env (substnl [dummy_var] 1 b) in
new_b, List.map pop binders_to_remove_from_b
| Toberemoved_with_rel (n,c) ->
(* observe (str "Decl of "++Ppconstr.pr_name x ++ str " is removed "); *)
let new_b,binders_to_remove_from_b = compute_new_princ_type remove env (substnl [c] n b) in
new_b, list_add_set_eq eq_constr (mkRel n) (List.map pop binders_to_remove_from_b)
end
and compute_new_princ_type_with_acc remove env e (c_acc,to_remove_acc) =
let new_e,to_remove_from_e = compute_new_princ_type remove env e
in
new_e::c_acc,list_union_eq eq_constr to_remove_from_e to_remove_acc
in
(* observe (str "Computing new principe from " ++ pr_lconstr_env env_with_params_and_predicates pre_princ); *)
let pre_res,_ =
compute_new_princ_type princ_type_info.indarg_in_concl env_with_params_and_predicates pre_princ
in
let pre_res =
replace_vars
(list_map_i (fun i id -> (id, mkRel i)) 1 ptes_vars)
(lift (List.length ptes_vars) pre_res)
in
it_mkProd_or_LetIn
~init:(it_mkProd_or_LetIn
~init:pre_res (List.map (fun (id,t,b) -> Name(Hashtbl.find tbl id), t,b)
new_predicates)
)
princ_type_info.params
let change_property_sort toSort princ princName =
let princ_info = compute_elim_sig princ in
let change_sort_in_predicate (x,v,t) =
(x,None,
let args,_ = decompose_prod t in
compose_prod args (mkSort toSort)
)
in
let princName_as_constr = Tacinterp.constr_of_id (Global.env ()) princName in
let init =
let nargs = (princ_info.nparams + (List.length princ_info.predicates)) in
mkApp(princName_as_constr,
Array.init nargs
(fun i -> mkRel (nargs - i )))
in
it_mkLambda_or_LetIn
~init:
(it_mkLambda_or_LetIn ~init
(List.map change_sort_in_predicate princ_info.predicates)
)
princ_info.params
let pp_dur time time' =
str (string_of_float (System.time_difference time time'))
(* let qed () = save_named true *)
let defined () =
try
Command.save_named false
with
| UserError("extract_proof",msg) ->
Util.errorlabstrm
"defined"
((try
str "On goal : " ++ fnl () ++ pr_open_subgoals () ++ fnl ()
with _ -> mt ()
) ++msg)
| e -> raise e
let build_functional_principle interactive_proof old_princ_type sorts funs i proof_tac hook =
(* First we get the type of the old graph principle *)
let mutr_nparams = (compute_elim_sig old_princ_type).nparams in
(* let time1 = System.get_time () in *)
let new_principle_type =
compute_new_princ_type_from_rel
(Array.map mkConst funs)
sorts
old_princ_type
in
(* let time2 = System.get_time () in *)
(* Pp.msgnl (str "computing principle type := " ++ System.fmt_time_difference time1 time2); *)
(* observe (str "new_principle_type : " ++ pr_lconstr new_principle_type); *)
let new_princ_name =
next_global_ident_away true (id_of_string "___________princ_________") []
in
begin
Command.start_proof
new_princ_name
(Decl_kinds.Global,(Decl_kinds.Proof Decl_kinds.Theorem))
new_principle_type
(hook new_principle_type)
;
(* let _tim1 = System.get_time () in *)
Pfedit.by (proof_tac (Array.map mkConst funs) mutr_nparams);
(* let _tim2 = System.get_time () in *)
(* begin *)
(* let dur1 = System.time_difference tim1 tim2 in *)
(* Pp.msgnl (str ("Time to compute proof: ") ++ str (string_of_float dur1)); *)
(* end; *)
get_proof_clean true
end
let generate_functional_principle
interactive_proof
old_princ_type sorts new_princ_name funs i proof_tac
=
try
let f = funs.(i) in
let type_sort = Termops.new_sort_in_family InType in
let new_sorts =
match sorts with
| None -> Array.make (Array.length funs) (type_sort)
| Some a -> a
in
let base_new_princ_name,new_princ_name =
match new_princ_name with
| Some (id) -> id,id
| None ->
let id_of_f = id_of_label (con_label f) in
id_of_f,Indrec.make_elimination_ident id_of_f (family_of_sort type_sort)
in
let names = ref [new_princ_name] in
let hook new_principle_type _ _ =
if sorts = None
then
(* let id_of_f = id_of_label (con_label f) in *)
let register_with_sort fam_sort =
let s = Termops.new_sort_in_family fam_sort in
let name = Indrec.make_elimination_ident base_new_princ_name fam_sort in
let value = change_property_sort s new_principle_type new_princ_name in
(* Pp.msgnl (str "new principle := " ++ pr_lconstr value); *)
let ce =
{ const_entry_body = value;
const_entry_type = None;
const_entry_opaque = false;
const_entry_boxed = Options.boxed_definitions()
}
in
ignore(
Declare.declare_constant
name
(Entries.DefinitionEntry ce,
Decl_kinds.IsDefinition (Decl_kinds.Scheme)
)
);
Options.if_verbose
(fun id -> Pp.msgnl (Ppconstr.pr_id id ++ str " is defined"))
name;
names := name :: !names
in
register_with_sort InProp;
register_with_sort InSet
in
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 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 () *)
exception Not_Rec
let get_funs_constant mp dp =
let rec get_funs_constant const e : (Names.constant*int) array =
match kind_of_term (snd (decompose_lam e)) with
| Fix((_,(na,_,_))) ->
Array.mapi
(fun i na ->
match na with
| Name id ->
let const = make_con mp dp (label_of_id id) in
const,i
| Anonymous ->
anomaly "Anonymous fix"
)
na
| _ -> [|const,0|]
in
function const ->
let find_constant_body const =
match (Global.lookup_constant const ).const_body with
| Some b ->
let body = force b in
let body = Tacred.cbv_norm_flags
(Closure.RedFlags.mkflags [Closure.RedFlags.fZETA])
(Global.env ())
(Evd.empty)
body
in
body
| None -> error ( "Cannot define a principle over an axiom ")
in
let f = find_constant_body const in
let l_const = get_funs_constant const f in
(*
We need to check that all the functions found are in the same block
to prevent Reset stange thing
*)
let l_bodies = List.map find_constant_body (Array.to_list (Array.map fst l_const)) in
let l_params,l_fixes = List.split (List.map decompose_lam l_bodies) in
(* all the paremeter must be equal*)
let _check_params =
let first_params = List.hd l_params in
List.iter
(fun params ->
if not ((=) first_params params)
then error "Not a mutal recursive block"
)
l_params
in
(* The bodies has to be very similar *)
let _check_bodies =
try
let extract_info is_first body =
match kind_of_term body with
| Fix((idxs,_),(na,ta,ca)) -> (idxs,na,ta,ca)
| _ ->
if is_first && (List.length l_bodies = 1)
then raise Not_Rec
else error "Not a mutal recursive block"
in
let first_infos = extract_info true (List.hd l_bodies) in
let check body = (* Hope this is correct *)
if not (first_infos = (extract_info false body))
then error "Not a mutal recursive block"
in
List.iter check l_bodies
with Not_Rec -> ()
in
l_const
exception No_graph_found
exception Found_type of int
let make_scheme (fas : (constant*Rawterm.rawsort) list) : Entries.definition_entry list =
let env = Global.env ()
and sigma = Evd.empty in
let funs = List.map fst fas in
let first_fun = List.hd funs in
let funs_mp,funs_dp,_ = Names.repr_con first_fun in
let first_fun_kn =
try
fst (find_Function_infos first_fun).graph_ind
with Not_found -> raise No_graph_found
in
let this_block_funs_indexes = get_funs_constant funs_mp funs_dp first_fun in
let this_block_funs = Array.map fst this_block_funs_indexes in
let prop_sort = InProp in
let funs_indexes =
let this_block_funs_indexes = Array.to_list this_block_funs_indexes in
List.map
(function const -> List.assoc const this_block_funs_indexes)
funs
in
let ind_list =
List.map
(fun (idx) ->
let ind = first_fun_kn,idx in
let (mib,mip) = Global.lookup_inductive ind in
ind,mib,mip,true,prop_sort
)
funs_indexes
in
let l_schemes =
List.map
(Typing.type_of env sigma)
(Indrec.build_mutual_indrec env sigma ind_list)
in
let i = ref (-1) in
let sorts =
List.rev_map (fun (_,x) ->
Termops.new_sort_in_family (Pretyping.interp_elimination_sort x)
)
fas
in
(* We create the first priciple by tactic *)
let first_type,other_princ_types =
match l_schemes with
s::l_schemes -> s,l_schemes
| _ -> anomaly ""
in
let (_,(const,_,_)) =
build_functional_principle false
first_type
(Array.of_list sorts)
this_block_funs
0
(prove_princ_for_struct false 0 (Array.of_list funs))
(fun _ _ _ -> ())
in
incr i;
let opacity =
let finfos = find_Function_infos this_block_funs.(0) in
try
let equation = out_some finfos.equation_lemma in
(Global.lookup_constant equation).Declarations.const_opaque
with Failure "out_some" -> (* non recursive definition *)
false
in
let const = {const with const_entry_opaque = opacity } in
(* The others are just deduced *)
if other_princ_types = []
then
[const]
else
let other_fun_princ_types =
let funs = Array.map mkConst this_block_funs in
let sorts = Array.of_list sorts in
List.map (compute_new_princ_type_from_rel funs sorts) other_princ_types
in
let first_princ_body,first_princ_type = const.Entries.const_entry_body, const.Entries.const_entry_type in
let ctxt,fix = Sign.decompose_lam_assum first_princ_body in (* the principle has for forall ...., fix .*)
let (idxs,_),(_,ta,_ as decl) = destFix fix in
let other_result =
List.map (* we can now compute the other principles *)
(fun scheme_type ->
incr i;
observe (Printer.pr_lconstr scheme_type);
let type_concl = snd (Sign.decompose_prod_assum scheme_type) in
let applied_f = List.hd (List.rev (snd (decompose_app type_concl))) in
let f = fst (decompose_app applied_f) in
try (* we search the number of the function in the fix block (name of the function) *)
Array.iteri
(fun j t ->
let t = snd (Sign.decompose_prod_assum t) in
let applied_g = List.hd (List.rev (snd (decompose_app t))) in
let g = fst (decompose_app applied_g) in
if eq_constr f g
then raise (Found_type j);
observe (Printer.pr_lconstr f ++ str " <> " ++
Printer.pr_lconstr g)
)
ta;
(* If we reach this point, the two principle are not mutually recursive
We fall back to the previous method
*)
let (_,(const,_,_)) =
build_functional_principle
false
(List.nth other_princ_types (!i - 1))
(Array.of_list sorts)
this_block_funs
!i
(prove_princ_for_struct false !i (Array.of_list funs))
(fun _ _ _ -> ())
in
const
with Found_type i ->
let princ_body =
Termops.it_mkLambda_or_LetIn ~init:(mkFix((idxs,i),decl)) ctxt
in
{const with
Entries.const_entry_body = princ_body;
Entries.const_entry_type = Some scheme_type
}
)
other_fun_princ_types
in
const::other_result
let build_scheme fas =
let bodies_types =
make_scheme
(List.map
(fun (_,f,sort) ->
let f_as_constant =
try
match Nametab.global f with
| Libnames.ConstRef c -> c
| _ -> Util.error "Functional Scheme can only be used with functions"
with Not_found ->
Util.error ("Cannot find "^ Libnames.string_of_reference f)
in
(f_as_constant,sort)
)
fas
)
in
List.iter2
(fun (princ_id,_,_) def_entry ->
ignore
(Declare.declare_constant
princ_id
(Entries.DefinitionEntry def_entry,Decl_kinds.IsProof Decl_kinds.Theorem));
Options.if_verbose
(fun id -> Pp.msgnl (Ppconstr.pr_id id ++ str " is defined")) princ_id
)
fas
bodies_types
let build_case_scheme fa =
let env = Global.env ()
and sigma = Evd.empty in
(* let id_to_constr id = *)
(* Tacinterp.constr_of_id env id *)
(* in *)
let funs = (fun (_,f,_) ->
try Libnames.constr_of_global (Nametab.global f)
with Not_found ->
Util.error ("Cannot find "^ Libnames.string_of_reference f)) fa in
let first_fun = destConst funs in
let funs_mp,funs_dp,_ = Names.repr_con first_fun in
let first_fun_kn = try fst (find_Function_infos first_fun).graph_ind with Not_found -> raise No_graph_found in
let this_block_funs_indexes = get_funs_constant funs_mp funs_dp first_fun in
let this_block_funs = Array.map fst this_block_funs_indexes in
let prop_sort = InProp in
let funs_indexes =
let this_block_funs_indexes = Array.to_list this_block_funs_indexes in
List.assoc (destConst funs) this_block_funs_indexes
in
let ind_fun =
let ind = first_fun_kn,funs_indexes in
ind,prop_sort
in
let scheme_type = (Typing.type_of env sigma ) ((fun (ind,sf) -> Indrec.make_case_gen env sigma ind sf) ind_fun) in
let sorts =
(fun (_,_,x) ->
Termops.new_sort_in_family (Pretyping.interp_elimination_sort x)
)
fa
in
let princ_name = (fun (x,_,_) -> x) fa in
let _ =
(* observe (str "Generating " ++ Ppconstr.pr_id princ_name ++str " with " ++ *)
(* pr_lconstr scheme_type ++ str " and " ++ (fun a -> prlist_with_sep spc (fun c -> pr_lconstr (mkConst c)) (Array.to_list a)) this_block_funs *)
(* ); *)
generate_functional_principle
false
scheme_type
(Some ([|sorts|]))
(Some princ_name)
this_block_funs
0
(prove_princ_for_struct false 0 [|destConst funs|])
in
()
|