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Diffstat (limited to 'plugins/funind/functional_principles_types.ml')
| -rw-r--r-- | plugins/funind/functional_principles_types.ml | 737 |
1 files changed, 737 insertions, 0 deletions
diff --git a/plugins/funind/functional_principles_types.ml b/plugins/funind/functional_principles_types.ml new file mode 100644 index 00000000..b756492b --- /dev/null +++ b/plugins/funind/functional_principles_types.ml @@ -0,0 +1,737 @@ +open Printer +open Util +open Term +open Termops +open Namegen +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:rel_context) : rel_context = + match predicates with + | [] -> [] + |(Name x,v,t)::predicates -> + let id = Namegen.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 + Lemmas.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_ident_away_in_goal (id_of_string "___________princ_________") [] + in + begin + Lemmas.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 = Flags.boxed_definitions() + } + in + ignore( + Declare.declare_constant + name + (Entries.DefinitionEntry ce, + Decl_kinds.IsDefinition (Decl_kinds.Scheme) + ) + ); + Flags.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 ((strip_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 + ind,true,prop_sort + ) + funs_indexes + in + let l_schemes = + List.map + (Typing.type_of env sigma) + (Indrec.build_mutual_induction_scheme 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,_,_)) = + try + 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 _ _ _ -> ()) + 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 + + in + incr i; + let opacity = + let finfos = find_Function_infos this_block_funs.(0) in + try + let equation = Option.get finfos.equation_lemma in + (Global.lookup_constant equation).Declarations.const_opaque + with Option.IsNone -> (* 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 = 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 = (strip_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 = (strip_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 = + Dumpglob.pause (); + 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)); + Flags.if_verbose + (fun id -> Pp.msgnl (Ppconstr.pr_id id ++ str " is defined")) princ_id + ) + fas + bodies_types; + Dumpglob.continue () + + + +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.build_case_analysis_scheme_default 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 _ = + (* Pp.msgnl (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 + () |