diff options
Diffstat (limited to 'plugins')
| -rw-r--r-- | plugins/cc/cctac.ml | 9 | ||||
| -rw-r--r-- | plugins/funind/functional_principles_proofs.ml | 38 | ||||
| -rw-r--r-- | plugins/funind/functional_principles_types.ml | 10 | ||||
| -rw-r--r-- | plugins/funind/indfun.ml | 8 | ||||
| -rw-r--r-- | plugins/funind/invfun.ml | 4 | ||||
| -rw-r--r-- | plugins/funind/merge.ml | 14 | ||||
| -rw-r--r-- | plugins/funind/recdef.ml | 4 | ||||
| -rw-r--r-- | plugins/ltac/extratactics.ml4 | 9 | ||||
| -rw-r--r-- | plugins/ltac/pptactic.ml | 2 | ||||
| -rw-r--r-- | plugins/ltac/rewrite.ml | 37 | ||||
| -rw-r--r-- | plugins/ltac/tacentries.ml | 2 | ||||
| -rw-r--r-- | plugins/ltac/tacintern.ml | 2 | ||||
| -rw-r--r-- | plugins/ltac/tacinterp.ml | 6 | ||||
| -rw-r--r-- | plugins/ltac/tacsubst.ml | 3 | ||||
| -rw-r--r-- | plugins/ltac/tauto.ml | 4 | ||||
| -rw-r--r-- | plugins/micromega/MExtraction.v | 10 | ||||
| -rw-r--r-- | plugins/micromega/micromega.ml | 1809 | ||||
| -rw-r--r-- | plugins/micromega/micromega.mli | 522 | ||||
| -rw-r--r-- | plugins/micromega/vo.itarget | 1 | ||||
| -rw-r--r-- | plugins/omega/coq_omega.ml | 4 | ||||
| -rw-r--r-- | plugins/quote/quote.ml | 71 |
21 files changed, 123 insertions, 2446 deletions
diff --git a/plugins/cc/cctac.ml b/plugins/cc/cctac.ml index b3017f359b..43c06a54d4 100644 --- a/plugins/cc/cctac.ml +++ b/plugins/cc/cctac.ml @@ -231,9 +231,9 @@ let make_prb gls depth additionnal_terms = let build_projection intype (cstr:pconstructor) special default gls= let open Tacmach.New in let ci= (snd(fst cstr)) in - let body=Equality.build_selector (pf_env gls) (project gls) ci (mkRel 1) intype special default in + let sigma, body=Equality.build_selector (pf_env gls) (project gls) ci (mkRel 1) intype special default in let id=pf_get_new_id (Id.of_string "t") gls in - mkLambda(Name id,intype,body) + sigma, mkLambda(Name id,intype,body) (* generate an adhoc tactic following the proof tree *) @@ -346,12 +346,13 @@ let rec proof_tac p : unit Proofview.tactic = let special=mkRel (1+nargs-argind) in refresh_universes (type_of ti) (fun intype -> refresh_universes (type_of default) (fun outtype -> - let proj = + let sigma, proj = build_projection intype cstr special default gl in let injt= app_global_with_holes _f_equal [|intype;outtype;proj;ti;tj|] 1 in - Tacticals.New.tclTHEN injt (proof_tac prf))) + Tacticals.New.tclTHEN (Proofview.Unsafe.tclEVARS sigma) + (Tacticals.New.tclTHEN injt (proof_tac prf)))) with e when Proofview.V82.catchable_exception e -> Proofview.tclZERO e end } diff --git a/plugins/funind/functional_principles_proofs.ml b/plugins/funind/functional_principles_proofs.ml index 434fb14a6e..0041797de7 100644 --- a/plugins/funind/functional_principles_proofs.ml +++ b/plugins/funind/functional_principles_proofs.ml @@ -944,7 +944,7 @@ let generalize_non_dep hyp g = ((* observe_tac "thin" *) (thin to_revert)) g -let id_of_decl = RelDecl.get_name %> Nameops.out_name +let id_of_decl = RelDecl.get_name %> Nameops.Name.get_id let var_of_decl = id_of_decl %> mkVar let revert idl = tclTHEN @@ -1127,11 +1127,11 @@ let prove_princ_for_struct (evd:Evd.evar_map ref) interactive_proof fun_num fnam ) in observe (str "full_params := " ++ - prlist_with_sep spc (RelDecl.get_name %> Nameops.out_name %> Ppconstr.pr_id) + prlist_with_sep spc (RelDecl.get_name %> Nameops.Name.get_id %> Ppconstr.pr_id) full_params ); observe (str "princ_params := " ++ - prlist_with_sep spc (RelDecl.get_name %> Nameops.out_name %> Ppconstr.pr_id) + prlist_with_sep spc (RelDecl.get_name %> Nameops.Name.get_id %> Ppconstr.pr_id) princ_params ); observe (str "fbody_with_full_params := " ++ @@ -1158,7 +1158,7 @@ let prove_princ_for_struct (evd:Evd.evar_map ref) interactive_proof fun_num fnam (fun i types -> let types = prod_applist (project g) types (List.rev_map var_of_decl princ_params) in { idx = idxs.(i) - fix_offset; - name = Nameops.out_name (fresh_id names.(i)); + name = Nameops.Name.get_id (fresh_id names.(i)); types = types; offset = fix_offset; nb_realargs = @@ -1181,7 +1181,7 @@ let prove_princ_for_struct (evd:Evd.evar_map ref) interactive_proof fun_num fnam let first_args = Array.init nargs (fun i -> mkRel (nargs -i)) in let app_f = mkApp(f,first_args) in let pte_args = (Array.to_list first_args)@[app_f] in - let app_pte = applist(mkVar (Nameops.out_name pte),pte_args) in + let app_pte = applist(mkVar (Nameops.Name.get_id pte),pte_args) in let body_with_param,num = let body = get_body fnames.(i) in let body_with_full_params = @@ -1208,9 +1208,9 @@ let prove_princ_for_struct (evd:Evd.evar_map ref) interactive_proof fun_num fnam num_in_block = num } in -(* observe (str "binding " ++ Ppconstr.pr_id (Nameops.out_name pte) ++ *) +(* observe (str "binding " ++ Ppconstr.pr_id (Nameops.Name.get_id pte) ++ *) (* str " to " ++ Ppconstr.pr_id info.name); *) - (Id.Map.add (Nameops.out_name pte) info acc_map,info::acc_info) + (Id.Map.add (Nameops.Name.get_id pte) info acc_map,info::acc_info) ) 0 (Id.Map.empty,[]) @@ -1284,7 +1284,7 @@ let prove_princ_for_struct (evd:Evd.evar_map ref) interactive_proof fun_num fnam (do_replace evd full_params (fix_info.idx + List.length princ_params) - (args_id@(List.map (RelDecl.get_name %> Nameops.out_name) princ_params)) + (args_id@(List.map (RelDecl.get_name %> Nameops.Name.get_id) princ_params)) (all_funs.(fix_info.num_in_block)) fix_info.num_in_block all_funs @@ -1563,17 +1563,17 @@ let prove_principle_for_gen | _ -> assert false in (* observe (str "rec_arg_id := " ++ pr_lconstr (mkVar rec_arg_id)); *) - let subst_constrs = List.map (get_name %> Nameops.out_name %> mkVar) (pre_rec_arg@princ_info.params) in + let subst_constrs = List.map (get_name %> Nameops.Name.get_id %> mkVar) (pre_rec_arg@princ_info.params) in let relation = substl subst_constrs relation in let input_type = substl subst_constrs rec_arg_type in - let wf_thm_id = Nameops.out_name (fresh_id (Name (Id.of_string "wf_R"))) in + let wf_thm_id = Nameops.Name.get_id (fresh_id (Name (Id.of_string "wf_R"))) in let acc_rec_arg_id = - Nameops.out_name (fresh_id (Name (Id.of_string ("Acc_"^(Id.to_string rec_arg_id))))) + Nameops.Name.get_id (fresh_id (Name (Id.of_string ("Acc_"^(Id.to_string rec_arg_id))))) in let revert l = tclTHEN (Proofview.V82.of_tactic (Tactics.generalize (List.map mkVar l))) (Proofview.V82.of_tactic (clear l)) in - let fix_id = Nameops.out_name (fresh_id (Name hrec_id)) in + let fix_id = Nameops.Name.get_id (fresh_id (Name hrec_id)) in let prove_rec_arg_acc g = ((* observe_tac "prove_rec_arg_acc" *) (tclCOMPLETE @@ -1591,7 +1591,7 @@ let prove_principle_for_gen ) g in - let args_ids = List.map (get_name %> Nameops.out_name) princ_info.args in + let args_ids = List.map (get_name %> Nameops.Name.get_id) princ_info.args in let lemma = match !tcc_lemma_ref with | Undefined -> user_err Pp.(str "No tcc proof !!") @@ -1639,7 +1639,7 @@ let prove_principle_for_gen [ observe_tac "start_tac" start_tac; h_intros - (List.rev_map (get_name %> Nameops.out_name) + (List.rev_map (get_name %> Nameops.Name.get_id) (princ_info.args@princ_info.branches@princ_info.predicates@princ_info.params) ); (* observe_tac "" *) Proofview.V82.of_tactic (assert_by @@ -1677,14 +1677,14 @@ let prove_principle_for_gen in let acc_inv = lazy (mkApp(Lazy.force acc_inv, [|mkVar acc_rec_arg_id|])) in let predicates_names = - List.map (get_name %> Nameops.out_name) princ_info.predicates + List.map (get_name %> Nameops.Name.get_id) princ_info.predicates in let pte_info = { proving_tac = (fun eqs -> (* msgnl (str "tcc_list := "++ prlist_with_sep spc Ppconstr.pr_id !tcc_list); *) -(* msgnl (str "princ_info.args := "++ prlist_with_sep spc Ppconstr.pr_id (List.map (fun (na,_,_) -> (Nameops.out_name na)) princ_info.args)); *) -(* msgnl (str "princ_info.params := "++ prlist_with_sep spc Ppconstr.pr_id (List.map (fun (na,_,_) -> (Nameops.out_name na)) princ_info.params)); *) +(* msgnl (str "princ_info.args := "++ prlist_with_sep spc Ppconstr.pr_id (List.map (fun (na,_,_) -> (Nameops.Name.get_id na)) princ_info.args)); *) +(* msgnl (str "princ_info.params := "++ prlist_with_sep spc Ppconstr.pr_id (List.map (fun (na,_,_) -> (Nameops.Name.get_id na)) princ_info.params)); *) (* msgnl (str "acc_rec_arg_id := "++ Ppconstr.pr_id acc_rec_arg_id); *) (* msgnl (str "eqs := "++ prlist_with_sep spc Ppconstr.pr_id eqs); *) @@ -1693,7 +1693,7 @@ let prove_principle_for_gen is_mes acc_inv fix_id (!tcc_list@(List.map - (get_name %> Nameops.out_name) + (get_name %> Nameops.Name.get_id) (princ_info.args@princ_info.params) )@ ([acc_rec_arg_id])) eqs ) @@ -1722,7 +1722,7 @@ let prove_principle_for_gen (* observe_tac "instanciate_hyps_with_args" *) (instanciate_hyps_with_args make_proof - (List.map (get_name %> Nameops.out_name) princ_info.branches) + (List.map (get_name %> Nameops.Name.get_id) princ_info.branches) (List.rev args_ids) ) gl' diff --git a/plugins/funind/functional_principles_types.ml b/plugins/funind/functional_principles_types.ml index 18d63dd94b..9425271671 100644 --- a/plugins/funind/functional_principles_types.ml +++ b/plugins/funind/functional_principles_types.ml @@ -62,7 +62,7 @@ let compute_new_princ_type_from_rel rel_to_fun sorts princ_type = then List.tl args else args in - Context.Named.Declaration.LocalAssum (Nameops.out_name (Context.Rel.Declaration.get_name decl), + Context.Named.Declaration.LocalAssum (Nameops.Name.get_id (Context.Rel.Declaration.get_name decl), Term.compose_prod real_args (mkSort new_sort)) in let new_predicates = @@ -185,11 +185,11 @@ let compute_new_princ_type_from_rel rel_to_fun sorts princ_type = with | Toberemoved -> -(* observe (str "Decl of "++Ppconstr.pr_name x ++ str " is removed "); *) +(* observe (str "Decl of "++Ppconstr.Name.print 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 "); *) +(* observe (str "Decl of "++Ppconstr.Name.print 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 @@ -214,11 +214,11 @@ let compute_new_princ_type_from_rel rel_to_fun sorts princ_type = with | Toberemoved -> -(* observe (str "Decl of "++Ppconstr.pr_name x ++ str " is removed "); *) +(* observe (str "Decl of "++Ppconstr.Name.print 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 "); *) +(* observe (str "Decl of "++Ppconstr.Name.print 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 diff --git a/plugins/funind/indfun.ml b/plugins/funind/indfun.ml index 74c0eb4cc7..4946285e16 100644 --- a/plugins/funind/indfun.ml +++ b/plugins/funind/indfun.ml @@ -200,13 +200,13 @@ let is_rec names = | GIf(b,_,lhs,rhs) -> (lookup names b) || (lookup names lhs) || (lookup names rhs) | GProd(na,_,t,b) | GLambda(na,_,t,b) -> - lookup names t || lookup (Nameops.name_fold Id.Set.remove na names) b + lookup names t || lookup (Nameops.Name.fold_right Id.Set.remove na names) b | GLetIn(na,b,t,c) -> - lookup names b || Option.cata (lookup names) true t || lookup (Nameops.name_fold Id.Set.remove na names) c + lookup names b || Option.cata (lookup names) true t || lookup (Nameops.Name.fold_right Id.Set.remove na names) c | GLetTuple(nal,_,t,b) -> lookup names t || lookup (List.fold_left - (fun acc na -> Nameops.name_fold Id.Set.remove na acc) + (fun acc na -> Nameops.Name.fold_right Id.Set.remove na acc) names nal ) @@ -885,7 +885,7 @@ let make_graph (f_ref:global_reference) = | Constrexpr.CLocalAssum (nal,_,_) -> List.map (fun (loc,n) -> CAst.make ?loc @@ - CRef(Libnames.Ident(loc, Nameops.out_name n),None)) + CRef(Libnames.Ident(loc, Nameops.Name.get_id n),None)) nal | Constrexpr.CLocalPattern _ -> assert false ) diff --git a/plugins/funind/invfun.ml b/plugins/funind/invfun.ml index d68bdc2153..12232dd83d 100644 --- a/plugins/funind/invfun.ml +++ b/plugins/funind/invfun.ml @@ -421,7 +421,7 @@ let prove_fun_correct evd functional_induction funs_constr graphs_constr schemes let params_bindings,avoid = List.fold_left2 (fun (bindings,avoid) decl p -> - let id = Namegen.next_ident_away (Nameops.out_name (RelDecl.get_name decl)) avoid in + let id = Namegen.next_ident_away (Nameops.Name.get_id (RelDecl.get_name decl)) avoid in p::bindings,id::avoid ) ([],pf_ids_of_hyps g) @@ -431,7 +431,7 @@ let prove_fun_correct evd functional_induction funs_constr graphs_constr schemes let lemmas_bindings = List.rev (fst (List.fold_left2 (fun (bindings,avoid) decl p -> - let id = Namegen.next_ident_away (Nameops.out_name (RelDecl.get_name decl)) avoid in + let id = Namegen.next_ident_away (Nameops.Name.get_id (RelDecl.get_name decl)) avoid in (nf_zeta p)::bindings,id::avoid) ([],avoid) princ_infos.predicates diff --git a/plugins/funind/merge.ml b/plugins/funind/merge.ml index b2c8489ce1..7634437171 100644 --- a/plugins/funind/merge.ml +++ b/plugins/funind/merge.ml @@ -133,20 +133,6 @@ let prNamedRLDecl s lc = prstr "\n"; end -let showind (id:Id.t) = - let cstrid = Constrintern.global_reference id in - let (ind1, u),cstrlist = Inductiveops.find_inductive (Global.env()) Evd.empty (EConstr.of_constr cstrid) in - let mib1,ib1 = Inductive.lookup_mind_specif (Global.env()) ind1 in - let u = EConstr.Unsafe.to_instance u in - List.iter (fun decl -> - print_string (string_of_name (Context.Rel.Declaration.get_name decl) ^ ":"); - prconstr (RelDecl.get_type decl); print_string "\n") - ib1.mind_arity_ctxt; - Printf.printf "arity :"; prconstr (Inductiveops.type_of_inductive (Global.env ()) (ind1, u)); - Array.iteri - (fun i x -> Printf.printf"type constr %d :" i ; prconstr x) - ib1.mind_user_lc - (** {2 Misc} *) exception Found of int diff --git a/plugins/funind/recdef.ml b/plugins/funind/recdef.ml index 2f9f708768..62eba9513d 100644 --- a/plugins/funind/recdef.ml +++ b/plugins/funind/recdef.ml @@ -879,7 +879,7 @@ let rec make_rewrite_list expr_info max = function let k_na,_,t = destProd sigma t_eq in let _,_,t = destProd sigma t in let def_na,_,_ = destProd sigma t in - Nameops.out_name k_na,Nameops.out_name def_na + Nameops.Name.get_id k_na,Nameops.Name.get_id def_na in Proofview.V82.of_tactic (general_rewrite_bindings false Locus.AllOccurrences true (* dep proofs also: *) true @@ -905,7 +905,7 @@ let make_rewrite expr_info l hp max = let k_na,_,t = destProd sigma t_eq in let _,_,t = destProd sigma t in let def_na,_,_ = destProd sigma t in - Nameops.out_name k_na,Nameops.out_name def_na + Nameops.Name.get_id k_na,Nameops.Name.get_id def_na in observe_tac (str "general_rewrite_bindings") (Proofview.V82.of_tactic (general_rewrite_bindings false Locus.AllOccurrences diff --git a/plugins/ltac/extratactics.ml4 b/plugins/ltac/extratactics.ml4 index cba9c13648..9726a5b401 100644 --- a/plugins/ltac/extratactics.ml4 +++ b/plugins/ltac/extratactics.ml4 @@ -306,7 +306,8 @@ let project_hint pri l2r r = | _ -> assert false in let p = if l2r then build_coq_iff_left_proj () else build_coq_iff_right_proj () in - let p = EConstr.of_constr @@ Universes.constr_of_global p in + let sigma, p = Evd.fresh_global env sigma p in + let p = EConstr.of_constr p in let c = Reductionops.whd_beta sigma (mkApp (c, Context.Rel.to_extended_vect mkRel 0 sign)) in let c = it_mkLambda_or_LetIn (mkApp (p,[|mkArrow a (lift 1 b);mkArrow b (lift 1 a);c|])) sign in @@ -735,7 +736,6 @@ let rewrite_except h = let refl_equal = let coq_base_constant s = - Universes.constr_of_global @@ Coqlib.gen_reference_in_modules "RecursiveDefinition" (Coqlib.init_modules @ [["Coq";"Arith";"Le"];["Coq";"Arith";"Lt"]]) s in function () -> (coq_base_constant "eq_refl") @@ -747,8 +747,9 @@ let refl_equal = let mkCaseEq a : unit Proofview.tactic = Proofview.Goal.enter { enter = begin fun gl -> let type_of_a = Tacmach.New.pf_unsafe_type_of gl a in - Tacticals.New.tclTHENLIST - [Tactics.generalize [(mkApp(EConstr.of_constr (delayed_force refl_equal), [| type_of_a; a|]))]; + Tacticals.New.pf_constr_of_global (delayed_force refl_equal) >>= fun req -> + Tacticals.New.tclTHENLIST + [Tactics.generalize [(mkApp(req, [| type_of_a; a|]))]; Proofview.Goal.enter { enter = begin fun gl -> let concl = Proofview.Goal.concl gl in let env = Proofview.Goal.env gl in diff --git a/plugins/ltac/pptactic.ml b/plugins/ltac/pptactic.ml index 4e254ea766..580c21d40e 100644 --- a/plugins/ltac/pptactic.ml +++ b/plugins/ltac/pptactic.ml @@ -571,7 +571,7 @@ type 'a extra_genarg_printer = str "=>" ++ brk (1,4) ++ pr t)) | All t -> str "_" ++ spc () ++ str "=>" ++ brk (1,4) ++ pr t - let pr_funvar n = spc () ++ pr_name n + let pr_funvar n = spc () ++ Name.print n let pr_let_clause k pr (id,(bl,t)) = hov 0 (keyword k ++ spc () ++ pr_lident id ++ prlist pr_funvar bl ++ diff --git a/plugins/ltac/rewrite.ml b/plugins/ltac/rewrite.ml index 966b11d0e7..dadcfb9f26 100644 --- a/plugins/ltac/rewrite.ml +++ b/plugins/ltac/rewrite.ml @@ -751,17 +751,23 @@ let default_flags = { under_lambdas = true; on_morphisms = true; } let get_opt_rew_rel = function RewPrf (rel, prf) -> Some rel | _ -> None -let make_eq () = -(*FIXME*) EConstr.of_constr (Universes.constr_of_global (Coqlib.build_coq_eq ())) -let make_eq_refl () = -(*FIXME*) EConstr.of_constr (Universes.constr_of_global (Coqlib.build_coq_eq_refl ())) +let new_global (evars, cstrs) gr = + let Sigma (c, sigma, _) = Evarutil.new_global (Sigma.Unsafe.of_evar_map evars) gr + in (Sigma.to_evar_map sigma, cstrs), c -let get_rew_prf r = match r.rew_prf with - | RewPrf (rel, prf) -> rel, prf +let make_eq sigma = + new_global sigma (Coqlib.build_coq_eq ()) +let make_eq_refl sigma = + new_global sigma (Coqlib.build_coq_eq_refl ()) + +let get_rew_prf evars r = match r.rew_prf with + | RewPrf (rel, prf) -> evars, (rel, prf) | RewCast c -> - let rel = mkApp (make_eq (), [| r.rew_car |]) in - rel, mkCast (mkApp (make_eq_refl (), [| r.rew_car; r.rew_from |]), - c, mkApp (rel, [| r.rew_from; r.rew_to |])) + let evars, eq = make_eq evars in + let evars, eq_refl = make_eq_refl evars in + let rel = mkApp (eq, [| r.rew_car |]) in + evars, (rel, mkCast (mkApp (eq_refl, [| r.rew_car; r.rew_from |]), + c, mkApp (rel, [| r.rew_from; r.rew_to |]))) let poly_subrelation sort = if sort then PropGlobal.subrelation else TypeGlobal.subrelation @@ -827,7 +833,8 @@ let resolve_morphism env avoid oldt m ?(fnewt=fun x -> x) args args' (b,cstr) ev env evars carrier relation x in [ proof ; x ; x ] @ acc, subst, evars, sigargs, x :: typeargs' | Some r -> - [ snd (get_rew_prf r); r.rew_to; x ] @ acc, subst, evars, + let evars, proof = get_rew_prf evars r in + [ snd proof; r.rew_to; x ] @ acc, subst, evars, sigargs, r.rew_to :: typeargs') | None -> if not (Option.is_empty y) then @@ -847,7 +854,8 @@ let apply_constraint env avoid car rel prf cstr res = | Some r -> resolve_subrelation env avoid car rel (fst cstr) prf r res let coerce env avoid cstr res = - let rel, prf = get_rew_prf res in + let evars, (rel, prf) = get_rew_prf res.rew_evars res in + let res = { res with rew_evars = evars } in apply_constraint env avoid res.rew_car rel prf cstr res let apply_rule unify loccs : int pure_strategy = @@ -868,8 +876,7 @@ let apply_rule unify loccs : int pure_strategy = else if Termops.eq_constr (fst rew.rew_evars) t rew.rew_to then (occ, Identity) else let res = { rew with rew_car = ty } in - let rel, prf = get_rew_prf res in - let res = Success (apply_constraint env unfresh rew.rew_car rel prf cstr res) in + let res = Success (coerce env unfresh cstr res) in (occ, res) } @@ -1231,9 +1238,7 @@ let subterm all flags (s : 'a pure_strategy) : 'a pure_strategy = in let res = match res with - | Success r -> - let rel, prf = get_rew_prf r in - Success (apply_constraint env unfresh r.rew_car rel prf (prop,cstr) r) + | Success r -> Success (coerce env unfresh (prop,cstr) r) | Fail | Identity -> res in state, res | _ -> state, Fail diff --git a/plugins/ltac/tacentries.ml b/plugins/ltac/tacentries.ml index 75f89a81e1..f44ccbd3b5 100644 --- a/plugins/ltac/tacentries.ml +++ b/plugins/ltac/tacentries.ml @@ -502,7 +502,7 @@ let print_ltacs () = | Tacexpr.TacFun (l, t) -> (l, t) | _ -> ([], body) in - let pr_ltac_fun_arg n = spc () ++ pr_name n in + let pr_ltac_fun_arg n = spc () ++ Name.print n in hov 2 (pr_qualid qid ++ prlist pr_ltac_fun_arg l) in Feedback.msg_notice (prlist_with_sep fnl pr_entry entries) diff --git a/plugins/ltac/tacintern.ml b/plugins/ltac/tacintern.ml index 2dc3bb3786..0096abfa69 100644 --- a/plugins/ltac/tacintern.ml +++ b/plugins/ltac/tacintern.ml @@ -718,7 +718,7 @@ let split_ltac_fun = function | TacFun (l,t) -> (l,t) | t -> ([],t) -let pr_ltac_fun_arg n = spc () ++ pr_name n +let pr_ltac_fun_arg n = spc () ++ Name.print n let print_ltac id = try diff --git a/plugins/ltac/tacinterp.ml b/plugins/ltac/tacinterp.ml index 6b0914ff95..594c4fa15f 100644 --- a/plugins/ltac/tacinterp.ml +++ b/plugins/ltac/tacinterp.ml @@ -1113,11 +1113,11 @@ let cons_and_check_name id l = let rec read_match_goal_hyps lfun ist env sigma lidh = function | (Hyp ((loc,na) as locna,mp))::tl -> - let lidh' = name_fold cons_and_check_name na lidh in + let lidh' = Name.fold_right cons_and_check_name na lidh in Hyp (locna,read_pattern lfun ist env sigma mp):: (read_match_goal_hyps lfun ist env sigma lidh' tl) | (Def ((loc,na) as locna,mv,mp))::tl -> - let lidh' = name_fold cons_and_check_name na lidh in + let lidh' = Name.fold_right cons_and_check_name na lidh in Def (locna,read_pattern lfun ist env sigma mv, read_pattern lfun ist env sigma mp):: (read_match_goal_hyps lfun ist env sigma lidh' tl) | [] -> [] @@ -1420,7 +1420,7 @@ and tactic_of_value ist vle = (str "A fully applied tactic is expected:" ++ spc() ++ Pp.str "missing " ++ Pp.str (String.plural numargs "argument") ++ Pp.str " for " ++ Pp.str (String.plural numargs "variable") ++ Pp.str " " ++ - pr_enum pr_name vars ++ Pp.str ".") + pr_enum Name.print vars ++ Pp.str ".") | VRec _ -> Tacticals.New.tclZEROMSG (str "A fully applied tactic is expected.") else if has_type vle (topwit wit_tactic) then let tac = out_gen (topwit wit_tactic) vle in diff --git a/plugins/ltac/tacsubst.ml b/plugins/ltac/tacsubst.ml index f5e6f05cee..2858df3130 100644 --- a/plugins/ltac/tacsubst.ml +++ b/plugins/ltac/tacsubst.ml @@ -14,7 +14,6 @@ open Stdarg open Tacarg open Misctypes open Globnames -open Term open Genredexpr open Patternops @@ -91,7 +90,7 @@ open Printer let subst_global_reference subst = let subst_global ref = let ref',t' = subst_global subst ref in - if not (eq_constr (Universes.constr_of_global ref') t') then + if not (is_global ref' t') then Feedback.msg_warning (strbrk "The reference " ++ pr_global ref ++ str " is not " ++ str " expanded to \"" ++ pr_lconstr t' ++ str "\", but to " ++ pr_global ref') ; diff --git a/plugins/ltac/tauto.ml b/plugins/ltac/tauto.ml index 4ec111e014..d8e21d81d1 100644 --- a/plugins/ltac/tauto.ml +++ b/plugins/ltac/tauto.ml @@ -220,9 +220,7 @@ let apply_nnpp _ ist = Proofview.tclBIND (Proofview.tclUNIT ()) begin fun () -> try - let nnpp = Universes.constr_of_global (Nametab.global_of_path coq_nnpp_path) in - let nnpp = EConstr.of_constr nnpp in - apply nnpp + Tacticals.New.pf_constr_of_global (Nametab.global_of_path coq_nnpp_path) >>= apply with Not_found -> tclFAIL 0 (Pp.mt ()) end diff --git a/plugins/micromega/MExtraction.v b/plugins/micromega/MExtraction.v index d28bb82863..4d5c3b1d5b 100644 --- a/plugins/micromega/MExtraction.v +++ b/plugins/micromega/MExtraction.v @@ -38,17 +38,17 @@ Extract Inductive sumor => option [ Some None ]. Let's rather use the ocaml && *) Extract Inlined Constant andb => "(&&)". -Require Import Reals. +Import Reals.Rdefinitions. -Extract Constant R => "int". -Extract Constant R0 => "0". -Extract Constant R1 => "1". +Extract Constant R => "int". +Extract Constant R0 => "0". +Extract Constant R1 => "1". Extract Constant Rplus => "( + )". Extract Constant Rmult => "( * )". Extract Constant Ropp => "fun x -> - x". Extract Constant Rinv => "fun x -> 1 / x". -Extraction "micromega.ml" +Extraction "plugins/micromega/micromega.ml" List.map simpl_cone (*map_cone indexes*) denorm Qpower vm_add n_of_Z N.of_nat ZTautoChecker ZWeakChecker QTautoChecker RTautoChecker find. diff --git a/plugins/micromega/micromega.ml b/plugins/micromega/micromega.ml deleted file mode 100644 index 5cf1da8ea8..0000000000 --- a/plugins/micromega/micromega.ml +++ /dev/null @@ -1,1809 +0,0 @@ -(** val negb : bool -> bool **) - -let negb = function -| true -> false -| false -> true - -type nat = -| O -| S of nat - -(** val app : 'a1 list -> 'a1 list -> 'a1 list **) - -let rec app l m = - match l with - | [] -> m - | a::l1 -> a::(app l1 m) - -type comparison = -| Eq -| Lt -| Gt - -(** val compOpp : comparison -> comparison **) - -let compOpp = function -| Eq -> Eq -| Lt -> Gt -| Gt -> Lt - -module Coq__1 = struct - (** val add : nat -> nat -> nat **) - let rec add n0 m = - match n0 with - | O -> m - | S p -> S (add p m) -end -let add = Coq__1.add - - -type positive = -| XI of positive -| XO of positive -| XH - -type n = -| N0 -| Npos of positive - -type z = -| Z0 -| Zpos of positive -| Zneg of positive - -module Pos = - struct - type mask = - | IsNul - | IsPos of positive - | IsNeg - end - -module Coq_Pos = - struct - (** val succ : positive -> positive **) - - let rec succ = function - | XI p -> XO (succ p) - | XO p -> XI p - | XH -> XO XH - - (** val add : positive -> positive -> positive **) - - let rec add x y = - match x with - | XI p -> - (match y with - | XI q0 -> XO (add_carry p q0) - | XO q0 -> XI (add p q0) - | XH -> XO (succ p)) - | XO p -> - (match y with - | XI q0 -> XI (add p q0) - | XO q0 -> XO (add p q0) - | XH -> XI p) - | XH -> - (match y with - | XI q0 -> XO (succ q0) - | XO q0 -> XI q0 - | XH -> XO XH) - - (** val add_carry : positive -> positive -> positive **) - - and add_carry x y = - match x with - | XI p -> - (match y with - | XI q0 -> XI (add_carry p q0) - | XO q0 -> XO (add_carry p q0) - | XH -> XI (succ p)) - | XO p -> - (match y with - | XI q0 -> XO (add_carry p q0) - | XO q0 -> XI (add p q0) - | XH -> XO (succ p)) - | XH -> - (match y with - | XI q0 -> XI (succ q0) - | XO q0 -> XO (succ q0) - | XH -> XI XH) - - (** val pred_double : positive -> positive **) - - let rec pred_double = function - | XI p -> XI (XO p) - | XO p -> XI (pred_double p) - | XH -> XH - - type mask = Pos.mask = - | IsNul - | IsPos of positive - | IsNeg - - (** val succ_double_mask : mask -> mask **) - - let succ_double_mask = function - | IsNul -> IsPos XH - | IsPos p -> IsPos (XI p) - | IsNeg -> IsNeg - - (** val double_mask : mask -> mask **) - - let double_mask = function - | IsPos p -> IsPos (XO p) - | x0 -> x0 - - (** val double_pred_mask : positive -> mask **) - - let double_pred_mask = function - | XI p -> IsPos (XO (XO p)) - | XO p -> IsPos (XO (pred_double p)) - | XH -> IsNul - - (** val sub_mask : positive -> positive -> mask **) - - let rec sub_mask x y = - match x with - | XI p -> - (match y with - | XI q0 -> double_mask (sub_mask p q0) - | XO q0 -> succ_double_mask (sub_mask p q0) - | XH -> IsPos (XO p)) - | XO p -> - (match y with - | XI q0 -> succ_double_mask (sub_mask_carry p q0) - | XO q0 -> double_mask (sub_mask p q0) - | XH -> IsPos (pred_double p)) - | XH -> - (match y with - | XH -> IsNul - | _ -> IsNeg) - - (** val sub_mask_carry : positive -> positive -> mask **) - - and sub_mask_carry x y = - match x with - | XI p -> - (match y with - | XI q0 -> succ_double_mask (sub_mask_carry p q0) - | XO q0 -> double_mask (sub_mask p q0) - | XH -> IsPos (pred_double p)) - | XO p -> - (match y with - | XI q0 -> double_mask (sub_mask_carry p q0) - | XO q0 -> succ_double_mask (sub_mask_carry p q0) - | XH -> double_pred_mask p) - | XH -> IsNeg - - (** val sub : positive -> positive -> positive **) - - let sub x y = - match sub_mask x y with - | IsPos z0 -> z0 - | _ -> XH - - (** val mul : positive -> positive -> positive **) - - let rec mul x y = - match x with - | XI p -> add y (XO (mul p y)) - | XO p -> XO (mul p y) - | XH -> y - - (** val size_nat : positive -> nat **) - - let rec size_nat = function - | XI p2 -> S (size_nat p2) - | XO p2 -> S (size_nat p2) - | XH -> S O - - (** val compare_cont : - comparison -> positive -> positive -> comparison **) - - let rec compare_cont r x y = - match x with - | XI p -> - (match y with - | XI q0 -> compare_cont r p q0 - | XO q0 -> compare_cont Gt p q0 - | XH -> Gt) - | XO p -> - (match y with - | XI q0 -> compare_cont Lt p q0 - | XO q0 -> compare_cont r p q0 - | XH -> Gt) - | XH -> - (match y with - | XH -> r - | _ -> Lt) - - (** val compare : positive -> positive -> comparison **) - - let compare = - compare_cont Eq - - (** val gcdn : nat -> positive -> positive -> positive **) - - let rec gcdn n0 a b = - match n0 with - | O -> XH - | S n1 -> - (match a with - | XI a' -> - (match b with - | XI b' -> - (match compare a' b' with - | Eq -> a - | Lt -> gcdn n1 (sub b' a') a - | Gt -> gcdn n1 (sub a' b') b) - | XO b0 -> gcdn n1 a b0 - | XH -> XH) - | XO a0 -> - (match b with - | XI _ -> gcdn n1 a0 b - | XO b0 -> XO (gcdn n1 a0 b0) - | XH -> XH) - | XH -> XH) - - (** val gcd : positive -> positive -> positive **) - - let gcd a b = - gcdn (Coq__1.add (size_nat a) (size_nat b)) a b - - (** val of_succ_nat : nat -> positive **) - - let rec of_succ_nat = function - | O -> XH - | S x -> succ (of_succ_nat x) - end - -module N = - struct - (** val of_nat : nat -> n **) - - let of_nat = function - | O -> N0 - | S n' -> Npos (Coq_Pos.of_succ_nat n') - end - -(** val pow_pos : ('a1 -> 'a1 -> 'a1) -> 'a1 -> positive -> 'a1 **) - -let rec pow_pos rmul x = function -| XI i0 -> let p = pow_pos rmul x i0 in rmul x (rmul p p) -| XO i0 -> let p = pow_pos rmul x i0 in rmul p p -| XH -> x - -(** val nth : nat -> 'a1 list -> 'a1 -> 'a1 **) - -let rec nth n0 l default = - match n0 with - | O -> - (match l with - | [] -> default - | x::_ -> x) - | S m -> - (match l with - | [] -> default - | _::t0 -> nth m t0 default) - -(** val map : ('a1 -> 'a2) -> 'a1 list -> 'a2 list **) - -let rec map f = function -| [] -> [] -| a::t0 -> (f a)::(map f t0) - -(** val fold_right : ('a2 -> 'a1 -> 'a1) -> 'a1 -> 'a2 list -> 'a1 **) - -let rec fold_right f a0 = function -| [] -> a0 -| b::t0 -> f b (fold_right f a0 t0) - -module Z = - struct - (** val double : z -> z **) - - let double = function - | Z0 -> Z0 - | Zpos p -> Zpos (XO p) - | Zneg p -> Zneg (XO p) - - (** val succ_double : z -> z **) - - let succ_double = function - | Z0 -> Zpos XH - | Zpos p -> Zpos (XI p) - | Zneg p -> Zneg (Coq_Pos.pred_double p) - - (** val pred_double : z -> z **) - - let pred_double = function - | Z0 -> Zneg XH - | Zpos p -> Zpos (Coq_Pos.pred_double p) - | Zneg p -> Zneg (XI p) - - (** val pos_sub : positive -> positive -> z **) - - let rec pos_sub x y = - match x with - | XI p -> - (match y with - | XI q0 -> double (pos_sub p q0) - | XO q0 -> succ_double (pos_sub p q0) - | XH -> Zpos (XO p)) - | XO p -> - (match y with - | XI q0 -> pred_double (pos_sub p q0) - | XO q0 -> double (pos_sub p q0) - | XH -> Zpos (Coq_Pos.pred_double p)) - | XH -> - (match y with - | XI q0 -> Zneg (XO q0) - | XO q0 -> Zneg (Coq_Pos.pred_double q0) - | XH -> Z0) - - (** val add : z -> z -> z **) - - let add x y = - match x with - | Z0 -> y - | Zpos x' -> - (match y with - | Z0 -> x - | Zpos y' -> Zpos (Coq_Pos.add x' y') - | Zneg y' -> pos_sub x' y') - | Zneg x' -> - (match y with - | Z0 -> x - | Zpos y' -> pos_sub y' x' - | Zneg y' -> Zneg (Coq_Pos.add x' y')) - - (** val opp : z -> z **) - - let opp = function - | Z0 -> Z0 - | Zpos x0 -> Zneg x0 - | Zneg x0 -> Zpos x0 - - (** val sub : z -> z -> z **) - - let sub m n0 = - add m (opp n0) - - (** val mul : z -> z -> z **) - - let mul x y = - match x with - | Z0 -> Z0 - | Zpos x' -> - (match y with - | Z0 -> Z0 - | Zpos y' -> Zpos (Coq_Pos.mul x' y') - | Zneg y' -> Zneg (Coq_Pos.mul x' y')) - | Zneg x' -> - (match y with - | Z0 -> Z0 - | Zpos y' -> Zneg (Coq_Pos.mul x' y') - | Zneg y' -> Zpos (Coq_Pos.mul x' y')) - - (** val compare : z -> z -> comparison **) - - let compare x y = - match x with - | Z0 -> - (match y with - | Z0 -> Eq - | Zpos _ -> Lt - | Zneg _ -> Gt) - | Zpos x' -> - (match y with - | Zpos y' -> Coq_Pos.compare x' y' - | _ -> Gt) - | Zneg x' -> - (match y with - | Zneg y' -> compOpp (Coq_Pos.compare x' y') - | _ -> Lt) - - (** val leb : z -> z -> bool **) - - let leb x y = - match compare x y with - | Gt -> false - | _ -> true - - (** val ltb : z -> z -> bool **) - - let ltb x y = - match compare x y with - | Lt -> true - | _ -> false - - (** val gtb : z -> z -> bool **) - - let gtb x y = - match compare x y with - | Gt -> true - | _ -> false - - (** val max : z -> z -> z **) - - let max n0 m = - match compare n0 m with - | Lt -> m - | _ -> n0 - - (** val abs : z -> z **) - - let abs = function - | Zneg p -> Zpos p - | x -> x - - (** val to_N : z -> n **) - - let to_N = function - | Zpos p -> Npos p - | _ -> N0 - - (** val pos_div_eucl : positive -> z -> z * z **) - - let rec pos_div_eucl a b = - match a with - | XI a' -> - let q0,r = pos_div_eucl a' b in - let r' = add (mul (Zpos (XO XH)) r) (Zpos XH) in - if ltb r' b - then (mul (Zpos (XO XH)) q0),r' - else (add (mul (Zpos (XO XH)) q0) (Zpos XH)),(sub r' b) - | XO a' -> - let q0,r = pos_div_eucl a' b in - let r' = mul (Zpos (XO XH)) r in - if ltb r' b - then (mul (Zpos (XO XH)) q0),r' - else (add (mul (Zpos (XO XH)) q0) (Zpos XH)),(sub r' b) - | XH -> if leb (Zpos (XO XH)) b then Z0,(Zpos XH) else (Zpos XH),Z0 - - (** val div_eucl : z -> z -> z * z **) - - let div_eucl a b = - match a with - | Z0 -> Z0,Z0 - | Zpos a' -> - (match b with - | Z0 -> Z0,Z0 - | Zpos _ -> pos_div_eucl a' b - | Zneg b' -> - let q0,r = pos_div_eucl a' (Zpos b') in - (match r with - | Z0 -> (opp q0),Z0 - | _ -> (opp (add q0 (Zpos XH))),(add b r))) - | Zneg a' -> - (match b with - | Z0 -> Z0,Z0 - | Zpos _ -> - let q0,r = pos_div_eucl a' b in - (match r with - | Z0 -> (opp q0),Z0 - | _ -> (opp (add q0 (Zpos XH))),(sub b r)) - | Zneg b' -> let q0,r = pos_div_eucl a' (Zpos b') in q0,(opp r)) - - (** val div : z -> z -> z **) - - let div a b = - let q0,_ = div_eucl a b in q0 - - (** val gcd : z -> z -> z **) - - let gcd a b = - match a with - | Z0 -> abs b - | Zpos a0 -> - (match b with - | Z0 -> abs a - | Zpos b0 -> Zpos (Coq_Pos.gcd a0 b0) - | Zneg b0 -> Zpos (Coq_Pos.gcd a0 b0)) - | Zneg a0 -> - (match b with - | Z0 -> abs a - | Zpos b0 -> Zpos (Coq_Pos.gcd a0 b0) - | Zneg b0 -> Zpos (Coq_Pos.gcd a0 b0)) - end - -(** val zeq_bool : z -> z -> bool **) - -let zeq_bool x y = - match Z.compare x y with - | Eq -> true - | _ -> false - -type 'c pol = -| Pc of 'c -| Pinj of positive * 'c pol -| PX of 'c pol * positive * 'c pol - -(** val p0 : 'a1 -> 'a1 pol **) - -let p0 cO = - Pc cO - -(** val p1 : 'a1 -> 'a1 pol **) - -let p1 cI = - Pc cI - -(** val peq : ('a1 -> 'a1 -> bool) -> 'a1 pol -> 'a1 pol -> bool **) - -let rec peq ceqb p p' = - match p with - | Pc c -> - (match p' with - | Pc c' -> ceqb c c' - | _ -> false) - | Pinj (j, q0) -> - (match p' with - | Pinj (j', q') -> - (match Coq_Pos.compare j j' with - | Eq -> peq ceqb q0 q' - | _ -> false) - | _ -> false) - | PX (p2, i, q0) -> - (match p' with - | PX (p'0, i', q') -> - (match Coq_Pos.compare i i' with - | Eq -> if peq ceqb p2 p'0 then peq ceqb q0 q' else false - | _ -> false) - | _ -> false) - -(** val mkPinj : positive -> 'a1 pol -> 'a1 pol **) - -let mkPinj j p = match p with -| Pc _ -> p -| Pinj (j', q0) -> Pinj ((Coq_Pos.add j j'), q0) -| PX (_, _, _) -> Pinj (j, p) - -(** val mkPinj_pred : positive -> 'a1 pol -> 'a1 pol **) - -let mkPinj_pred j p = - match j with - | XI j0 -> Pinj ((XO j0), p) - | XO j0 -> Pinj ((Coq_Pos.pred_double j0), p) - | XH -> p - -(** val mkPX : - 'a1 -> ('a1 -> 'a1 -> bool) -> 'a1 pol -> positive -> 'a1 pol -> 'a1 - pol **) - -let mkPX cO ceqb p i q0 = - match p with - | Pc c -> if ceqb c cO then mkPinj XH q0 else PX (p, i, q0) - | Pinj (_, _) -> PX (p, i, q0) - | PX (p', i', q') -> - if peq ceqb q' (p0 cO) - then PX (p', (Coq_Pos.add i' i), q0) - else PX (p, i, q0) - -(** val mkXi : 'a1 -> 'a1 -> positive -> 'a1 pol **) - -let mkXi cO cI i = - PX ((p1 cI), i, (p0 cO)) - -(** val mkX : 'a1 -> 'a1 -> 'a1 pol **) - -let mkX cO cI = - mkXi cO cI XH - -(** val popp : ('a1 -> 'a1) -> 'a1 pol -> 'a1 pol **) - -let rec popp copp = function -| Pc c -> Pc (copp c) -| Pinj (j, q0) -> Pinj (j, (popp copp q0)) -| PX (p2, i, q0) -> PX ((popp copp p2), i, (popp copp q0)) - -(** val paddC : ('a1 -> 'a1 -> 'a1) -> 'a1 pol -> 'a1 -> 'a1 pol **) - -let rec paddC cadd p c = - match p with - | Pc c1 -> Pc (cadd c1 c) - | Pinj (j, q0) -> Pinj (j, (paddC cadd q0 c)) - | PX (p2, i, q0) -> PX (p2, i, (paddC cadd q0 c)) - -(** val psubC : ('a1 -> 'a1 -> 'a1) -> 'a1 pol -> 'a1 -> 'a1 pol **) - -let rec psubC csub p c = - match p with - | Pc c1 -> Pc (csub c1 c) - | Pinj (j, q0) -> Pinj (j, (psubC csub q0 c)) - | PX (p2, i, q0) -> PX (p2, i, (psubC csub q0 c)) - -(** val paddI : - ('a1 -> 'a1 -> 'a1) -> ('a1 pol -> 'a1 pol -> 'a1 pol) -> 'a1 pol -> - positive -> 'a1 pol -> 'a1 pol **) - -let rec paddI cadd pop q0 j = function -| Pc c -> mkPinj j (paddC cadd q0 c) -| Pinj (j', q') -> - (match Z.pos_sub j' j with - | Z0 -> mkPinj j (pop q' q0) - | Zpos k -> mkPinj j (pop (Pinj (k, q')) q0) - | Zneg k -> mkPinj j' (paddI cadd pop q0 k q')) -| PX (p2, i, q') -> - (match j with - | XI j0 -> PX (p2, i, (paddI cadd pop q0 (XO j0) q')) - | XO j0 -> PX (p2, i, (paddI cadd pop q0 (Coq_Pos.pred_double j0) q')) - | XH -> PX (p2, i, (pop q' q0))) - -(** val psubI : - ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1) -> ('a1 pol -> 'a1 pol -> 'a1 pol) - -> 'a1 pol -> positive -> 'a1 pol -> 'a1 pol **) - -let rec psubI cadd copp pop q0 j = function -| Pc c -> mkPinj j (paddC cadd (popp copp q0) c) -| Pinj (j', q') -> - (match Z.pos_sub j' j with - | Z0 -> mkPinj j (pop q' q0) - | Zpos k -> mkPinj j (pop (Pinj (k, q')) q0) - | Zneg k -> mkPinj j' (psubI cadd copp pop q0 k q')) -| PX (p2, i, q') -> - (match j with - | XI j0 -> PX (p2, i, (psubI cadd copp pop q0 (XO j0) q')) - | XO j0 -> - PX (p2, i, (psubI cadd copp pop q0 (Coq_Pos.pred_double j0) q')) - | XH -> PX (p2, i, (pop q' q0))) - -(** val paddX : - 'a1 -> ('a1 -> 'a1 -> bool) -> ('a1 pol -> 'a1 pol -> 'a1 pol) -> 'a1 - pol -> positive -> 'a1 pol -> 'a1 pol **) - -let rec paddX cO ceqb pop p' i' p = match p with -| Pc _ -> PX (p', i', p) -| Pinj (j, q') -> - (match j with - | XI j0 -> PX (p', i', (Pinj ((XO j0), q'))) - | XO j0 -> PX (p', i', (Pinj ((Coq_Pos.pred_double j0), q'))) - | XH -> PX (p', i', q')) -| PX (p2, i, q') -> - (match Z.pos_sub i i' with - | Z0 -> mkPX cO ceqb (pop p2 p') i q' - | Zpos k -> mkPX cO ceqb (pop (PX (p2, k, (p0 cO))) p') i' q' - | Zneg k -> mkPX cO ceqb (paddX cO ceqb pop p' k p2) i q') - -(** val psubX : - 'a1 -> ('a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> ('a1 pol -> 'a1 pol -> - 'a1 pol) -> 'a1 pol -> positive -> 'a1 pol -> 'a1 pol **) - -let rec psubX cO copp ceqb pop p' i' p = match p with -| Pc _ -> PX ((popp copp p'), i', p) -| Pinj (j, q') -> - (match j with - | XI j0 -> PX ((popp copp p'), i', (Pinj ((XO j0), q'))) - | XO j0 -> - PX ((popp copp p'), i', (Pinj ((Coq_Pos.pred_double j0), q'))) - | XH -> PX ((popp copp p'), i', q')) -| PX (p2, i, q') -> - (match Z.pos_sub i i' with - | Z0 -> mkPX cO ceqb (pop p2 p') i q' - | Zpos k -> mkPX cO ceqb (pop (PX (p2, k, (p0 cO))) p') i' q' - | Zneg k -> mkPX cO ceqb (psubX cO copp ceqb pop p' k p2) i q') - -(** val padd : - 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 pol -> 'a1 - pol -> 'a1 pol **) - -let rec padd cO cadd ceqb p = function -| Pc c' -> paddC cadd p c' -| Pinj (j', q') -> paddI cadd (padd cO cadd ceqb) q' j' p -| PX (p'0, i', q') -> - (match p with - | Pc c -> PX (p'0, i', (paddC cadd q' c)) - | Pinj (j, q0) -> - (match j with - | XI j0 -> PX (p'0, i', (padd cO cadd ceqb (Pinj ((XO j0), q0)) q')) - | XO j0 -> - PX (p'0, i', - (padd cO cadd ceqb (Pinj ((Coq_Pos.pred_double j0), q0)) q')) - | XH -> PX (p'0, i', (padd cO cadd ceqb q0 q'))) - | PX (p2, i, q0) -> - (match Z.pos_sub i i' with - | Z0 -> - mkPX cO ceqb (padd cO cadd ceqb p2 p'0) i - (padd cO cadd ceqb q0 q') - | Zpos k -> - mkPX cO ceqb (padd cO cadd ceqb (PX (p2, k, (p0 cO))) p'0) i' - (padd cO cadd ceqb q0 q') - | Zneg k -> - mkPX cO ceqb (paddX cO ceqb (padd cO cadd ceqb) p'0 k p2) i - (padd cO cadd ceqb q0 q'))) - -(** val psub : - 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1) -> - ('a1 -> 'a1 -> bool) -> 'a1 pol -> 'a1 pol -> 'a1 pol **) - -let rec psub cO cadd csub copp ceqb p = function -| Pc c' -> psubC csub p c' -| Pinj (j', q') -> psubI cadd copp (psub cO cadd csub copp ceqb) q' j' p -| PX (p'0, i', q') -> - (match p with - | Pc c -> PX ((popp copp p'0), i', (paddC cadd (popp copp q') c)) - | Pinj (j, q0) -> - (match j with - | XI j0 -> - PX ((popp copp p'0), i', - (psub cO cadd csub copp ceqb (Pinj ((XO j0), q0)) q')) - | XO j0 -> - PX ((popp copp p'0), i', - (psub cO cadd csub copp ceqb (Pinj ((Coq_Pos.pred_double j0), - q0)) q')) - | XH -> - PX ((popp copp p'0), i', (psub cO cadd csub copp ceqb q0 q'))) - | PX (p2, i, q0) -> - (match Z.pos_sub i i' with - | Z0 -> - mkPX cO ceqb (psub cO cadd csub copp ceqb p2 p'0) i - (psub cO cadd csub copp ceqb q0 q') - | Zpos k -> - mkPX cO ceqb - (psub cO cadd csub copp ceqb (PX (p2, k, (p0 cO))) p'0) i' - (psub cO cadd csub copp ceqb q0 q') - | Zneg k -> - mkPX cO ceqb - (psubX cO copp ceqb (psub cO cadd csub copp ceqb) p'0 k p2) i - (psub cO cadd csub copp ceqb q0 q'))) - -(** val pmulC_aux : - 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 pol -> 'a1 - -> 'a1 pol **) - -let rec pmulC_aux cO cmul ceqb p c = - match p with - | Pc c' -> Pc (cmul c' c) - | Pinj (j, q0) -> mkPinj j (pmulC_aux cO cmul ceqb q0 c) - | PX (p2, i, q0) -> - mkPX cO ceqb (pmulC_aux cO cmul ceqb p2 c) i - (pmulC_aux cO cmul ceqb q0 c) - -(** val pmulC : - 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 pol - -> 'a1 -> 'a1 pol **) - -let pmulC cO cI cmul ceqb p c = - if ceqb c cO - then p0 cO - else if ceqb c cI then p else pmulC_aux cO cmul ceqb p c - -(** val pmulI : - 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> ('a1 pol - -> 'a1 pol -> 'a1 pol) -> 'a1 pol -> positive -> 'a1 pol -> 'a1 pol **) - -let rec pmulI cO cI cmul ceqb pmul0 q0 j = function -| Pc c -> mkPinj j (pmulC cO cI cmul ceqb q0 c) -| Pinj (j', q') -> - (match Z.pos_sub j' j with - | Z0 -> mkPinj j (pmul0 q' q0) - | Zpos k -> mkPinj j (pmul0 (Pinj (k, q')) q0) - | Zneg k -> mkPinj j' (pmulI cO cI cmul ceqb pmul0 q0 k q')) -| PX (p', i', q') -> - (match j with - | XI j' -> - mkPX cO ceqb (pmulI cO cI cmul ceqb pmul0 q0 j p') i' - (pmulI cO cI cmul ceqb pmul0 q0 (XO j') q') - | XO j' -> - mkPX cO ceqb (pmulI cO cI cmul ceqb pmul0 q0 j p') i' - (pmulI cO cI cmul ceqb pmul0 q0 (Coq_Pos.pred_double j') q') - | XH -> - mkPX cO ceqb (pmulI cO cI cmul ceqb pmul0 q0 XH p') i' (pmul0 q' q0)) - -(** val pmul : - 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> - 'a1 -> bool) -> 'a1 pol -> 'a1 pol -> 'a1 pol **) - -let rec pmul cO cI cadd cmul ceqb p p'' = match p'' with -| Pc c -> pmulC cO cI cmul ceqb p c -| Pinj (j', q') -> - pmulI cO cI cmul ceqb (pmul cO cI cadd cmul ceqb) q' j' p -| PX (p', i', q') -> - (match p with - | Pc c -> pmulC cO cI cmul ceqb p'' c - | Pinj (j, q0) -> - let qQ' = - match j with - | XI j0 -> pmul cO cI cadd cmul ceqb (Pinj ((XO j0), q0)) q' - | XO j0 -> - pmul cO cI cadd cmul ceqb (Pinj ((Coq_Pos.pred_double j0), q0)) - q' - | XH -> pmul cO cI cadd cmul ceqb q0 q' - in - mkPX cO ceqb (pmul cO cI cadd cmul ceqb p p') i' qQ' - | PX (p2, i, q0) -> - let qQ' = pmul cO cI cadd cmul ceqb q0 q' in - let pQ' = pmulI cO cI cmul ceqb (pmul cO cI cadd cmul ceqb) q' XH p2 - in - let qP' = pmul cO cI cadd cmul ceqb (mkPinj XH q0) p' in - let pP' = pmul cO cI cadd cmul ceqb p2 p' in - padd cO cadd ceqb - (mkPX cO ceqb (padd cO cadd ceqb (mkPX cO ceqb pP' i (p0 cO)) qP') - i' (p0 cO)) (mkPX cO ceqb pQ' i qQ')) - -(** val psquare : - 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> - 'a1 -> bool) -> 'a1 pol -> 'a1 pol **) - -let rec psquare cO cI cadd cmul ceqb = function -| Pc c -> Pc (cmul c c) -| Pinj (j, q0) -> Pinj (j, (psquare cO cI cadd cmul ceqb q0)) -| PX (p2, i, q0) -> - let twoPQ = - pmul cO cI cadd cmul ceqb p2 - (mkPinj XH (pmulC cO cI cmul ceqb q0 (cadd cI cI))) - in - let q2 = psquare cO cI cadd cmul ceqb q0 in - let p3 = psquare cO cI cadd cmul ceqb p2 in - mkPX cO ceqb (padd cO cadd ceqb (mkPX cO ceqb p3 i (p0 cO)) twoPQ) i q2 - -type 'c pExpr = -| PEc of 'c -| PEX of positive -| PEadd of 'c pExpr * 'c pExpr -| PEsub of 'c pExpr * 'c pExpr -| PEmul of 'c pExpr * 'c pExpr -| PEopp of 'c pExpr -| PEpow of 'c pExpr * n - -(** val mk_X : 'a1 -> 'a1 -> positive -> 'a1 pol **) - -let mk_X cO cI j = - mkPinj_pred j (mkX cO cI) - -(** val ppow_pos : - 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> - 'a1 -> bool) -> ('a1 pol -> 'a1 pol) -> 'a1 pol -> 'a1 pol -> positive - -> 'a1 pol **) - -let rec ppow_pos cO cI cadd cmul ceqb subst_l res p = function -| XI p3 -> - subst_l - (pmul cO cI cadd cmul ceqb - (ppow_pos cO cI cadd cmul ceqb subst_l - (ppow_pos cO cI cadd cmul ceqb subst_l res p p3) p p3) p) -| XO p3 -> - ppow_pos cO cI cadd cmul ceqb subst_l - (ppow_pos cO cI cadd cmul ceqb subst_l res p p3) p p3 -| XH -> subst_l (pmul cO cI cadd cmul ceqb res p) - -(** val ppow_N : - 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> - 'a1 -> bool) -> ('a1 pol -> 'a1 pol) -> 'a1 pol -> n -> 'a1 pol **) - -let ppow_N cO cI cadd cmul ceqb subst_l p = function -| N0 -> p1 cI -| Npos p2 -> ppow_pos cO cI cadd cmul ceqb subst_l (p1 cI) p p2 - -(** val norm_aux : - 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> - 'a1 -> 'a1) -> ('a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 pExpr -> - 'a1 pol **) - -let rec norm_aux cO cI cadd cmul csub copp ceqb = function -| PEc c -> Pc c -| PEX j -> mk_X cO cI j -| PEadd (pe1, pe2) -> - (match pe1 with - | PEopp pe3 -> - psub cO cadd csub copp ceqb - (norm_aux cO cI cadd cmul csub copp ceqb pe2) - (norm_aux cO cI cadd cmul csub copp ceqb pe3) - | _ -> - (match pe2 with - | PEopp pe3 -> - psub cO cadd csub copp ceqb - (norm_aux cO cI cadd cmul csub copp ceqb pe1) - (norm_aux cO cI cadd cmul csub copp ceqb pe3) - | _ -> - padd cO cadd ceqb (norm_aux cO cI cadd cmul csub copp ceqb pe1) - (norm_aux cO cI cadd cmul csub copp ceqb pe2))) -| PEsub (pe1, pe2) -> - psub cO cadd csub copp ceqb - (norm_aux cO cI cadd cmul csub copp ceqb pe1) - (norm_aux cO cI cadd cmul csub copp ceqb pe2) -| PEmul (pe1, pe2) -> - pmul cO cI cadd cmul ceqb (norm_aux cO cI cadd cmul csub copp ceqb pe1) - (norm_aux cO cI cadd cmul csub copp ceqb pe2) -| PEopp pe1 -> popp copp (norm_aux cO cI cadd cmul csub copp ceqb pe1) -| PEpow (pe1, n0) -> - ppow_N cO cI cadd cmul ceqb (fun p -> p) - (norm_aux cO cI cadd cmul csub copp ceqb pe1) n0 - -type 'a bFormula = -| TT -| FF -| X -| A of 'a -| Cj of 'a bFormula * 'a bFormula -| D of 'a bFormula * 'a bFormula -| N of 'a bFormula -| I of 'a bFormula * 'a bFormula - -(** val map_bformula : ('a1 -> 'a2) -> 'a1 bFormula -> 'a2 bFormula **) - -let rec map_bformula fct = function -| TT -> TT -| FF -> FF -| X -> X -| A a -> A (fct a) -| Cj (f1, f2) -> Cj ((map_bformula fct f1), (map_bformula fct f2)) -| D (f1, f2) -> D ((map_bformula fct f1), (map_bformula fct f2)) -| N f0 -> N (map_bformula fct f0) -| I (f1, f2) -> I ((map_bformula fct f1), (map_bformula fct f2)) - -type 'x clause = 'x list - -type 'x cnf = 'x clause list - -(** val tt : 'a1 cnf **) - -let tt = - [] - -(** val ff : 'a1 cnf **) - -let ff = - []::[] - -(** val add_term : - ('a1 -> bool) -> ('a1 -> 'a1 -> 'a1 option) -> 'a1 -> 'a1 clause -> - 'a1 clause option **) - -let rec add_term unsat deduce t0 = function -| [] -> - (match deduce t0 t0 with - | Some u -> if unsat u then None else Some (t0::[]) - | None -> Some (t0::[])) -| t'::cl0 -> - (match deduce t0 t' with - | Some u -> - if unsat u - then None - else (match add_term unsat deduce t0 cl0 with - | Some cl' -> Some (t'::cl') - | None -> None) - | None -> - (match add_term unsat deduce t0 cl0 with - | Some cl' -> Some (t'::cl') - | None -> None)) - -(** val or_clause : - ('a1 -> bool) -> ('a1 -> 'a1 -> 'a1 option) -> 'a1 clause -> 'a1 - clause -> 'a1 clause option **) - -let rec or_clause unsat deduce cl1 cl2 = - match cl1 with - | [] -> Some cl2 - | t0::cl -> - (match add_term unsat deduce t0 cl2 with - | Some cl' -> or_clause unsat deduce cl cl' - | None -> None) - -(** val or_clause_cnf : - ('a1 -> bool) -> ('a1 -> 'a1 -> 'a1 option) -> 'a1 clause -> 'a1 cnf - -> 'a1 cnf **) - -let or_clause_cnf unsat deduce t0 f = - fold_right (fun e acc -> - match or_clause unsat deduce t0 e with - | Some cl -> cl::acc - | None -> acc) [] f - -(** val or_cnf : - ('a1 -> bool) -> ('a1 -> 'a1 -> 'a1 option) -> 'a1 cnf -> 'a1 cnf -> - 'a1 cnf **) - -let rec or_cnf unsat deduce f f' = - match f with - | [] -> tt - | e::rst -> - app (or_cnf unsat deduce rst f') (or_clause_cnf unsat deduce e f') - -(** val and_cnf : 'a1 cnf -> 'a1 cnf -> 'a1 cnf **) - -let and_cnf f1 f2 = - app f1 f2 - -(** val xcnf : - ('a2 -> bool) -> ('a2 -> 'a2 -> 'a2 option) -> ('a1 -> 'a2 cnf) -> - ('a1 -> 'a2 cnf) -> bool -> 'a1 bFormula -> 'a2 cnf **) - -let rec xcnf unsat deduce normalise0 negate0 pol0 = function -| TT -> if pol0 then tt else ff -| FF -> if pol0 then ff else tt -| X -> ff -| A x -> if pol0 then normalise0 x else negate0 x -| Cj (e1, e2) -> - if pol0 - then and_cnf (xcnf unsat deduce normalise0 negate0 pol0 e1) - (xcnf unsat deduce normalise0 negate0 pol0 e2) - else or_cnf unsat deduce (xcnf unsat deduce normalise0 negate0 pol0 e1) - (xcnf unsat deduce normalise0 negate0 pol0 e2) -| D (e1, e2) -> - if pol0 - then or_cnf unsat deduce (xcnf unsat deduce normalise0 negate0 pol0 e1) - (xcnf unsat deduce normalise0 negate0 pol0 e2) - else and_cnf (xcnf unsat deduce normalise0 negate0 pol0 e1) - (xcnf unsat deduce normalise0 negate0 pol0 e2) -| N e -> xcnf unsat deduce normalise0 negate0 (negb pol0) e -| I (e1, e2) -> - if pol0 - then or_cnf unsat deduce - (xcnf unsat deduce normalise0 negate0 (negb pol0) e1) - (xcnf unsat deduce normalise0 negate0 pol0 e2) - else and_cnf (xcnf unsat deduce normalise0 negate0 (negb pol0) e1) - (xcnf unsat deduce normalise0 negate0 pol0 e2) - -(** val cnf_checker : - ('a1 list -> 'a2 -> bool) -> 'a1 cnf -> 'a2 list -> bool **) - -let rec cnf_checker checker f l = - match f with - | [] -> true - | e::f0 -> - (match l with - | [] -> false - | c::l0 -> if checker e c then cnf_checker checker f0 l0 else false) - -(** val tauto_checker : - ('a2 -> bool) -> ('a2 -> 'a2 -> 'a2 option) -> ('a1 -> 'a2 cnf) -> - ('a1 -> 'a2 cnf) -> ('a2 list -> 'a3 -> bool) -> 'a1 bFormula -> 'a3 - list -> bool **) - -let tauto_checker unsat deduce normalise0 negate0 checker f w = - cnf_checker checker (xcnf unsat deduce normalise0 negate0 true f) w - -(** val cneqb : ('a1 -> 'a1 -> bool) -> 'a1 -> 'a1 -> bool **) - -let cneqb ceqb x y = - negb (ceqb x y) - -(** val cltb : - ('a1 -> 'a1 -> bool) -> ('a1 -> 'a1 -> bool) -> 'a1 -> 'a1 -> bool **) - -let cltb ceqb cleb x y = - (&&) (cleb x y) (cneqb ceqb x y) - -type 'c polC = 'c pol - -type op1 = -| Equal -| NonEqual -| Strict -| NonStrict - -type 'c nFormula = 'c polC * op1 - -(** val opMult : op1 -> op1 -> op1 option **) - -let opMult o o' = - match o with - | Equal -> Some Equal - | NonEqual -> - (match o' with - | Equal -> Some Equal - | NonEqual -> Some NonEqual - | _ -> None) - | Strict -> - (match o' with - | NonEqual -> None - | _ -> Some o') - | NonStrict -> - (match o' with - | Equal -> Some Equal - | NonEqual -> None - | _ -> Some NonStrict) - -(** val opAdd : op1 -> op1 -> op1 option **) - -let opAdd o o' = - match o with - | Equal -> Some o' - | NonEqual -> - (match o' with - | Equal -> Some NonEqual - | _ -> None) - | Strict -> - (match o' with - | NonEqual -> None - | _ -> Some Strict) - | NonStrict -> - (match o' with - | Equal -> Some NonStrict - | NonEqual -> None - | x -> Some x) - -type 'c psatz = -| PsatzIn of nat -| PsatzSquare of 'c polC -| PsatzMulC of 'c polC * 'c psatz -| PsatzMulE of 'c psatz * 'c psatz -| PsatzAdd of 'c psatz * 'c psatz -| PsatzC of 'c -| PsatzZ - -(** val map_option : ('a1 -> 'a2 option) -> 'a1 option -> 'a2 option **) - -let map_option f = function -| Some x -> f x -| None -> None - -(** val map_option2 : - ('a1 -> 'a2 -> 'a3 option) -> 'a1 option -> 'a2 option -> 'a3 option **) - -let map_option2 f o o' = - match o with - | Some x -> - (match o' with - | Some x' -> f x x' - | None -> None) - | None -> None - -(** val pexpr_times_nformula : - 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> - 'a1 -> bool) -> 'a1 polC -> 'a1 nFormula -> 'a1 nFormula option **) - -let pexpr_times_nformula cO cI cplus ctimes ceqb e = function -| ef,o -> - (match o with - | Equal -> Some ((pmul cO cI cplus ctimes ceqb e ef),Equal) - | _ -> None) - -(** val nformula_times_nformula : - 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> - 'a1 -> bool) -> 'a1 nFormula -> 'a1 nFormula -> 'a1 nFormula option **) - -let nformula_times_nformula cO cI cplus ctimes ceqb f1 f2 = - let e1,o1 = f1 in - let e2,o2 = f2 in - map_option (fun x -> Some ((pmul cO cI cplus ctimes ceqb e1 e2),x)) - (opMult o1 o2) - -(** val nformula_plus_nformula : - 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 nFormula -> - 'a1 nFormula -> 'a1 nFormula option **) - -let nformula_plus_nformula cO cplus ceqb f1 f2 = - let e1,o1 = f1 in - let e2,o2 = f2 in - map_option (fun x -> Some ((padd cO cplus ceqb e1 e2),x)) (opAdd o1 o2) - -(** val eval_Psatz : - 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> - 'a1 -> bool) -> ('a1 -> 'a1 -> bool) -> 'a1 nFormula list -> 'a1 psatz - -> 'a1 nFormula option **) - -let rec eval_Psatz cO cI cplus ctimes ceqb cleb l = function -| PsatzIn n0 -> Some (nth n0 l ((Pc cO),Equal)) -| PsatzSquare e0 -> Some ((psquare cO cI cplus ctimes ceqb e0),NonStrict) -| PsatzMulC (re, e0) -> - map_option (pexpr_times_nformula cO cI cplus ctimes ceqb re) - (eval_Psatz cO cI cplus ctimes ceqb cleb l e0) -| PsatzMulE (f1, f2) -> - map_option2 (nformula_times_nformula cO cI cplus ctimes ceqb) - (eval_Psatz cO cI cplus ctimes ceqb cleb l f1) - (eval_Psatz cO cI cplus ctimes ceqb cleb l f2) -| PsatzAdd (f1, f2) -> - map_option2 (nformula_plus_nformula cO cplus ceqb) - (eval_Psatz cO cI cplus ctimes ceqb cleb l f1) - (eval_Psatz cO cI cplus ctimes ceqb cleb l f2) -| PsatzC c -> if cltb ceqb cleb cO c then Some ((Pc c),Strict) else None -| PsatzZ -> Some ((Pc cO),Equal) - -(** val check_inconsistent : - 'a1 -> ('a1 -> 'a1 -> bool) -> ('a1 -> 'a1 -> bool) -> 'a1 nFormula -> - bool **) - -let check_inconsistent cO ceqb cleb = function -| e,op -> - (match e with - | Pc c -> - (match op with - | Equal -> cneqb ceqb c cO - | NonEqual -> ceqb c cO - | Strict -> cleb c cO - | NonStrict -> cltb ceqb cleb c cO) - | _ -> false) - -(** val check_normalised_formulas : - 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> - 'a1 -> bool) -> ('a1 -> 'a1 -> bool) -> 'a1 nFormula list -> 'a1 psatz - -> bool **) - -let check_normalised_formulas cO cI cplus ctimes ceqb cleb l cm = - match eval_Psatz cO cI cplus ctimes ceqb cleb l cm with - | Some f -> check_inconsistent cO ceqb cleb f - | None -> false - -type op2 = -| OpEq -| OpNEq -| OpLe -| OpGe -| OpLt -| OpGt - -type 't formula = { flhs : 't pExpr; fop : op2; frhs : 't pExpr } - -(** val norm : - 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> - 'a1 -> 'a1) -> ('a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 pExpr -> - 'a1 pol **) - -let norm cO cI cplus ctimes cminus copp ceqb = - norm_aux cO cI cplus ctimes cminus copp ceqb - -(** val psub0 : - 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1) -> - ('a1 -> 'a1 -> bool) -> 'a1 pol -> 'a1 pol -> 'a1 pol **) - -let psub0 cO cplus cminus copp ceqb = - psub cO cplus cminus copp ceqb - -(** val padd0 : - 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 pol -> 'a1 - pol -> 'a1 pol **) - -let padd0 cO cplus ceqb = - padd cO cplus ceqb - -(** val xnormalise : - 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> - 'a1 -> 'a1) -> ('a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 formula -> - 'a1 nFormula list **) - -let xnormalise cO cI cplus ctimes cminus copp ceqb t0 = - let { flhs = lhs; fop = o; frhs = rhs } = t0 in - let lhs0 = norm cO cI cplus ctimes cminus copp ceqb lhs in - let rhs0 = norm cO cI cplus ctimes cminus copp ceqb rhs in - (match o with - | OpEq -> - ((psub0 cO cplus cminus copp ceqb lhs0 rhs0),Strict)::(((psub0 cO - cplus - cminus copp - ceqb rhs0 - lhs0),Strict)::[]) - | OpNEq -> ((psub0 cO cplus cminus copp ceqb lhs0 rhs0),Equal)::[] - | OpLe -> ((psub0 cO cplus cminus copp ceqb lhs0 rhs0),Strict)::[] - | OpGe -> ((psub0 cO cplus cminus copp ceqb rhs0 lhs0),Strict)::[] - | OpLt -> ((psub0 cO cplus cminus copp ceqb lhs0 rhs0),NonStrict)::[] - | OpGt -> ((psub0 cO cplus cminus copp ceqb rhs0 lhs0),NonStrict)::[]) - -(** val cnf_normalise : - 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> - 'a1 -> 'a1) -> ('a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 formula -> - 'a1 nFormula cnf **) - -let cnf_normalise cO cI cplus ctimes cminus copp ceqb t0 = - map (fun x -> x::[]) (xnormalise cO cI cplus ctimes cminus copp ceqb t0) - -(** val xnegate : - 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> - 'a1 -> 'a1) -> ('a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 formula -> - 'a1 nFormula list **) - -let xnegate cO cI cplus ctimes cminus copp ceqb t0 = - let { flhs = lhs; fop = o; frhs = rhs } = t0 in - let lhs0 = norm cO cI cplus ctimes cminus copp ceqb lhs in - let rhs0 = norm cO cI cplus ctimes cminus copp ceqb rhs in - (match o with - | OpEq -> ((psub0 cO cplus cminus copp ceqb lhs0 rhs0),Equal)::[] - | OpNEq -> - ((psub0 cO cplus cminus copp ceqb lhs0 rhs0),Strict)::(((psub0 cO - cplus - cminus copp - ceqb rhs0 - lhs0),Strict)::[]) - | OpLe -> ((psub0 cO cplus cminus copp ceqb rhs0 lhs0),NonStrict)::[] - | OpGe -> ((psub0 cO cplus cminus copp ceqb lhs0 rhs0),NonStrict)::[] - | OpLt -> ((psub0 cO cplus cminus copp ceqb rhs0 lhs0),Strict)::[] - | OpGt -> ((psub0 cO cplus cminus copp ceqb lhs0 rhs0),Strict)::[]) - -(** val cnf_negate : - 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> - 'a1 -> 'a1) -> ('a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 formula -> - 'a1 nFormula cnf **) - -let cnf_negate cO cI cplus ctimes cminus copp ceqb t0 = - map (fun x -> x::[]) (xnegate cO cI cplus ctimes cminus copp ceqb t0) - -(** val xdenorm : positive -> 'a1 pol -> 'a1 pExpr **) - -let rec xdenorm jmp = function -| Pc c -> PEc c -| Pinj (j, p2) -> xdenorm (Coq_Pos.add j jmp) p2 -| PX (p2, j, q0) -> - PEadd ((PEmul ((xdenorm jmp p2), (PEpow ((PEX jmp), (Npos j))))), - (xdenorm (Coq_Pos.succ jmp) q0)) - -(** val denorm : 'a1 pol -> 'a1 pExpr **) - -let denorm p = - xdenorm XH p - -(** val map_PExpr : ('a2 -> 'a1) -> 'a2 pExpr -> 'a1 pExpr **) - -let rec map_PExpr c_of_S = function -| PEc c -> PEc (c_of_S c) -| PEX p -> PEX p -| PEadd (e1, e2) -> PEadd ((map_PExpr c_of_S e1), (map_PExpr c_of_S e2)) -| PEsub (e1, e2) -> PEsub ((map_PExpr c_of_S e1), (map_PExpr c_of_S e2)) -| PEmul (e1, e2) -> PEmul ((map_PExpr c_of_S e1), (map_PExpr c_of_S e2)) -| PEopp e0 -> PEopp (map_PExpr c_of_S e0) -| PEpow (e0, n0) -> PEpow ((map_PExpr c_of_S e0), n0) - -(** val map_Formula : ('a2 -> 'a1) -> 'a2 formula -> 'a1 formula **) - -let map_Formula c_of_S f = - let { flhs = l; fop = o; frhs = r } = f in - { flhs = (map_PExpr c_of_S l); fop = o; frhs = (map_PExpr c_of_S r) } - -(** val simpl_cone : - 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 psatz - -> 'a1 psatz **) - -let simpl_cone cO cI ctimes ceqb e = match e with -| PsatzSquare t0 -> - (match t0 with - | Pc c -> if ceqb cO c then PsatzZ else PsatzC (ctimes c c) - | _ -> PsatzSquare t0) -| PsatzMulE (t1, t2) -> - (match t1 with - | PsatzMulE (x, x0) -> - (match x with - | PsatzC p2 -> - (match t2 with - | PsatzC c -> PsatzMulE ((PsatzC (ctimes c p2)), x0) - | PsatzZ -> PsatzZ - | _ -> e) - | _ -> - (match x0 with - | PsatzC p2 -> - (match t2 with - | PsatzC c -> PsatzMulE ((PsatzC (ctimes c p2)), x) - | PsatzZ -> PsatzZ - | _ -> e) - | _ -> - (match t2 with - | PsatzC c -> if ceqb cI c then t1 else PsatzMulE (t1, t2) - | PsatzZ -> PsatzZ - | _ -> e))) - | PsatzC c -> - (match t2 with - | PsatzMulE (x, x0) -> - (match x with - | PsatzC p2 -> PsatzMulE ((PsatzC (ctimes c p2)), x0) - | _ -> - (match x0 with - | PsatzC p2 -> PsatzMulE ((PsatzC (ctimes c p2)), x) - | _ -> if ceqb cI c then t2 else PsatzMulE (t1, t2))) - | PsatzAdd (y, z0) -> - PsatzAdd ((PsatzMulE ((PsatzC c), y)), (PsatzMulE ((PsatzC c), - z0))) - | PsatzC c0 -> PsatzC (ctimes c c0) - | PsatzZ -> PsatzZ - | _ -> if ceqb cI c then t2 else PsatzMulE (t1, t2)) - | PsatzZ -> PsatzZ - | _ -> - (match t2 with - | PsatzC c -> if ceqb cI c then t1 else PsatzMulE (t1, t2) - | PsatzZ -> PsatzZ - | _ -> e)) -| PsatzAdd (t1, t2) -> - (match t1 with - | PsatzZ -> t2 - | _ -> - (match t2 with - | PsatzZ -> t1 - | _ -> PsatzAdd (t1, t2))) -| _ -> e - -type q = { qnum : z; qden : positive } - -(** val qnum : q -> z **) - -let qnum x = x.qnum - -(** val qden : q -> positive **) - -let qden x = x.qden - -(** val qeq_bool : q -> q -> bool **) - -let qeq_bool x y = - zeq_bool (Z.mul x.qnum (Zpos y.qden)) (Z.mul y.qnum (Zpos x.qden)) - -(** val qle_bool : q -> q -> bool **) - -let qle_bool x y = - Z.leb (Z.mul x.qnum (Zpos y.qden)) (Z.mul y.qnum (Zpos x.qden)) - -(** val qplus : q -> q -> q **) - -let qplus x y = - { qnum = - (Z.add (Z.mul x.qnum (Zpos y.qden)) (Z.mul y.qnum (Zpos x.qden))); - qden = (Coq_Pos.mul x.qden y.qden) } - -(** val qmult : q -> q -> q **) - -let qmult x y = - { qnum = (Z.mul x.qnum y.qnum); qden = (Coq_Pos.mul x.qden y.qden) } - -(** val qopp : q -> q **) - -let qopp x = - { qnum = (Z.opp x.qnum); qden = x.qden } - -(** val qminus : q -> q -> q **) - -let qminus x y = - qplus x (qopp y) - -(** val qinv : q -> q **) - -let qinv x = - match x.qnum with - | Z0 -> { qnum = Z0; qden = XH } - | Zpos p -> { qnum = (Zpos x.qden); qden = p } - | Zneg p -> { qnum = (Zneg x.qden); qden = p } - -(** val qpower_positive : q -> positive -> q **) - -let qpower_positive = - pow_pos qmult - -(** val qpower : q -> z -> q **) - -let qpower q0 = function -| Z0 -> { qnum = (Zpos XH); qden = XH } -| Zpos p -> qpower_positive q0 p -| Zneg p -> qinv (qpower_positive q0 p) - -type 'a t = -| Empty -| Leaf of 'a -| Node of 'a t * 'a * 'a t - -(** val find : 'a1 -> 'a1 t -> positive -> 'a1 **) - -let rec find default vm p = - match vm with - | Empty -> default - | Leaf i -> i - | Node (l, e, r) -> - (match p with - | XI p2 -> find default r p2 - | XO p2 -> find default l p2 - | XH -> e) - -(** val singleton : 'a1 -> positive -> 'a1 -> 'a1 t **) - -let rec singleton default x v = - match x with - | XI p -> Node (Empty, default, (singleton default p v)) - | XO p -> Node ((singleton default p v), default, Empty) - | XH -> Leaf v - -(** val vm_add : 'a1 -> positive -> 'a1 -> 'a1 t -> 'a1 t **) - -let rec vm_add default x v = function -| Empty -> singleton default x v -| Leaf vl -> - (match x with - | XI p -> Node (Empty, vl, (singleton default p v)) - | XO p -> Node ((singleton default p v), vl, Empty) - | XH -> Leaf v) -| Node (l, o, r) -> - (match x with - | XI p -> Node (l, o, (vm_add default p v r)) - | XO p -> Node ((vm_add default p v l), o, r) - | XH -> Node (l, v, r)) - -type zWitness = z psatz - -(** val zWeakChecker : z nFormula list -> z psatz -> bool **) - -let zWeakChecker = - check_normalised_formulas Z0 (Zpos XH) Z.add Z.mul zeq_bool Z.leb - -(** val psub1 : z pol -> z pol -> z pol **) - -let psub1 = - psub0 Z0 Z.add Z.sub Z.opp zeq_bool - -(** val padd1 : z pol -> z pol -> z pol **) - -let padd1 = - padd0 Z0 Z.add zeq_bool - -(** val norm0 : z pExpr -> z pol **) - -let norm0 = - norm Z0 (Zpos XH) Z.add Z.mul Z.sub Z.opp zeq_bool - -(** val xnormalise0 : z formula -> z nFormula list **) - -let xnormalise0 t0 = - let { flhs = lhs; fop = o; frhs = rhs } = t0 in - let lhs0 = norm0 lhs in - let rhs0 = norm0 rhs in - (match o with - | OpEq -> - ((psub1 lhs0 (padd1 rhs0 (Pc (Zpos XH)))),NonStrict)::(((psub1 rhs0 - (padd1 lhs0 - (Pc (Zpos - XH)))),NonStrict)::[]) - | OpNEq -> ((psub1 lhs0 rhs0),Equal)::[] - | OpLe -> ((psub1 lhs0 (padd1 rhs0 (Pc (Zpos XH)))),NonStrict)::[] - | OpGe -> ((psub1 rhs0 (padd1 lhs0 (Pc (Zpos XH)))),NonStrict)::[] - | OpLt -> ((psub1 lhs0 rhs0),NonStrict)::[] - | OpGt -> ((psub1 rhs0 lhs0),NonStrict)::[]) - -(** val normalise : z formula -> z nFormula cnf **) - -let normalise t0 = - map (fun x -> x::[]) (xnormalise0 t0) - -(** val xnegate0 : z formula -> z nFormula list **) - -let xnegate0 t0 = - let { flhs = lhs; fop = o; frhs = rhs } = t0 in - let lhs0 = norm0 lhs in - let rhs0 = norm0 rhs in - (match o with - | OpEq -> ((psub1 lhs0 rhs0),Equal)::[] - | OpNEq -> - ((psub1 lhs0 (padd1 rhs0 (Pc (Zpos XH)))),NonStrict)::(((psub1 rhs0 - (padd1 lhs0 - (Pc (Zpos - XH)))),NonStrict)::[]) - | OpLe -> ((psub1 rhs0 lhs0),NonStrict)::[] - | OpGe -> ((psub1 lhs0 rhs0),NonStrict)::[] - | OpLt -> ((psub1 rhs0 (padd1 lhs0 (Pc (Zpos XH)))),NonStrict)::[] - | OpGt -> ((psub1 lhs0 (padd1 rhs0 (Pc (Zpos XH)))),NonStrict)::[]) - -(** val negate : z formula -> z nFormula cnf **) - -let negate t0 = - map (fun x -> x::[]) (xnegate0 t0) - -(** val zunsat : z nFormula -> bool **) - -let zunsat = - check_inconsistent Z0 zeq_bool Z.leb - -(** val zdeduce : z nFormula -> z nFormula -> z nFormula option **) - -let zdeduce = - nformula_plus_nformula Z0 Z.add zeq_bool - -(** val ceiling : z -> z -> z **) - -let ceiling a b = - let q0,r = Z.div_eucl a b in - (match r with - | Z0 -> q0 - | _ -> Z.add q0 (Zpos XH)) - -type zArithProof = -| DoneProof -| RatProof of zWitness * zArithProof -| CutProof of zWitness * zArithProof -| EnumProof of zWitness * zWitness * zArithProof list - -(** val zgcdM : z -> z -> z **) - -let zgcdM x y = - Z.max (Z.gcd x y) (Zpos XH) - -(** val zgcd_pol : z polC -> z * z **) - -let rec zgcd_pol = function -| Pc c -> Z0,c -| Pinj (_, p2) -> zgcd_pol p2 -| PX (p2, _, q0) -> - let g1,c1 = zgcd_pol p2 in - let g2,c2 = zgcd_pol q0 in (zgcdM (zgcdM g1 c1) g2),c2 - -(** val zdiv_pol : z polC -> z -> z polC **) - -let rec zdiv_pol p x = - match p with - | Pc c -> Pc (Z.div c x) - | Pinj (j, p2) -> Pinj (j, (zdiv_pol p2 x)) - | PX (p2, j, q0) -> PX ((zdiv_pol p2 x), j, (zdiv_pol q0 x)) - -(** val makeCuttingPlane : z polC -> z polC * z **) - -let makeCuttingPlane p = - let g,c = zgcd_pol p in - if Z.gtb g Z0 - then (zdiv_pol (psubC Z.sub p c) g),(Z.opp (ceiling (Z.opp c) g)) - else p,Z0 - -(** val genCuttingPlane : z nFormula -> ((z polC * z) * op1) option **) - -let genCuttingPlane = function -| e,op -> - (match op with - | Equal -> - let g,c = zgcd_pol e in - if (&&) (Z.gtb g Z0) - ((&&) (negb (zeq_bool c Z0)) (negb (zeq_bool (Z.gcd g c) g))) - then None - else Some ((makeCuttingPlane e),Equal) - | NonEqual -> Some ((e,Z0),op) - | Strict -> - Some ((makeCuttingPlane (psubC Z.sub e (Zpos XH))),NonStrict) - | NonStrict -> Some ((makeCuttingPlane e),NonStrict)) - -(** val nformula_of_cutting_plane : ((z polC * z) * op1) -> z nFormula **) - -let nformula_of_cutting_plane = function -| e_z,o -> let e,z0 = e_z in (padd1 e (Pc z0)),o - -(** val is_pol_Z0 : z polC -> bool **) - -let is_pol_Z0 = function -| Pc z0 -> - (match z0 with - | Z0 -> true - | _ -> false) -| _ -> false - -(** val eval_Psatz0 : z nFormula list -> zWitness -> z nFormula option **) - -let eval_Psatz0 = - eval_Psatz Z0 (Zpos XH) Z.add Z.mul zeq_bool Z.leb - -(** val valid_cut_sign : op1 -> bool **) - -let valid_cut_sign = function -| Equal -> true -| NonStrict -> true -| _ -> false - -(** val zChecker : z nFormula list -> zArithProof -> bool **) - -let rec zChecker l = function -| DoneProof -> false -| RatProof (w, pf0) -> - (match eval_Psatz0 l w with - | Some f -> if zunsat f then true else zChecker (f::l) pf0 - | None -> false) -| CutProof (w, pf0) -> - (match eval_Psatz0 l w with - | Some f -> - (match genCuttingPlane f with - | Some cp -> zChecker ((nformula_of_cutting_plane cp)::l) pf0 - | None -> true) - | None -> false) -| EnumProof (w1, w2, pf0) -> - (match eval_Psatz0 l w1 with - | Some f1 -> - (match eval_Psatz0 l w2 with - | Some f2 -> - (match genCuttingPlane f1 with - | Some p -> - let p2,op3 = p in - let e1,z1 = p2 in - (match genCuttingPlane f2 with - | Some p3 -> - let p4,op4 = p3 in - let e2,z2 = p4 in - if (&&) ((&&) (valid_cut_sign op3) (valid_cut_sign op4)) - (is_pol_Z0 (padd1 e1 e2)) - then let rec label pfs lb ub = - match pfs with - | [] -> Z.gtb lb ub - | pf1::rsr -> - (&&) (zChecker (((psub1 e1 (Pc lb)),Equal)::l) pf1) - (label rsr (Z.add lb (Zpos XH)) ub) - in label pf0 (Z.opp z1) z2 - else false - | None -> true) - | None -> true) - | None -> false) - | None -> false) - -(** val zTautoChecker : z formula bFormula -> zArithProof list -> bool **) - -let zTautoChecker f w = - tauto_checker zunsat zdeduce normalise negate zChecker f w - -type qWitness = q psatz - -(** val qWeakChecker : q nFormula list -> q psatz -> bool **) - -let qWeakChecker = - check_normalised_formulas { qnum = Z0; qden = XH } { qnum = (Zpos XH); - qden = XH } qplus qmult qeq_bool qle_bool - -(** val qnormalise : q formula -> q nFormula cnf **) - -let qnormalise = - cnf_normalise { qnum = Z0; qden = XH } { qnum = (Zpos XH); qden = XH } - qplus qmult qminus qopp qeq_bool - -(** val qnegate : q formula -> q nFormula cnf **) - -let qnegate = - cnf_negate { qnum = Z0; qden = XH } { qnum = (Zpos XH); qden = XH } - qplus qmult qminus qopp qeq_bool - -(** val qunsat : q nFormula -> bool **) - -let qunsat = - check_inconsistent { qnum = Z0; qden = XH } qeq_bool qle_bool - -(** val qdeduce : q nFormula -> q nFormula -> q nFormula option **) - -let qdeduce = - nformula_plus_nformula { qnum = Z0; qden = XH } qplus qeq_bool - -(** val qTautoChecker : q formula bFormula -> qWitness list -> bool **) - -let qTautoChecker f w = - tauto_checker qunsat qdeduce qnormalise qnegate qWeakChecker f w - -type rcst = -| C0 -| C1 -| CQ of q -| CZ of z -| CPlus of rcst * rcst -| CMinus of rcst * rcst -| CMult of rcst * rcst -| CInv of rcst -| COpp of rcst - -(** val q_of_Rcst : rcst -> q **) - -let rec q_of_Rcst = function -| C0 -> { qnum = Z0; qden = XH } -| C1 -> { qnum = (Zpos XH); qden = XH } -| CQ q0 -> q0 -| CZ z0 -> { qnum = z0; qden = XH } -| CPlus (r1, r2) -> qplus (q_of_Rcst r1) (q_of_Rcst r2) -| CMinus (r1, r2) -> qminus (q_of_Rcst r1) (q_of_Rcst r2) -| CMult (r1, r2) -> qmult (q_of_Rcst r1) (q_of_Rcst r2) -| CInv r0 -> qinv (q_of_Rcst r0) -| COpp r0 -> qopp (q_of_Rcst r0) - -type rWitness = q psatz - -(** val rWeakChecker : q nFormula list -> q psatz -> bool **) - -let rWeakChecker = - check_normalised_formulas { qnum = Z0; qden = XH } { qnum = (Zpos XH); - qden = XH } qplus qmult qeq_bool qle_bool - -(** val rnormalise : q formula -> q nFormula cnf **) - -let rnormalise = - cnf_normalise { qnum = Z0; qden = XH } { qnum = (Zpos XH); qden = XH } - qplus qmult qminus qopp qeq_bool - -(** val rnegate : q formula -> q nFormula cnf **) - -let rnegate = - cnf_negate { qnum = Z0; qden = XH } { qnum = (Zpos XH); qden = XH } - qplus qmult qminus qopp qeq_bool - -(** val runsat : q nFormula -> bool **) - -let runsat = - check_inconsistent { qnum = Z0; qden = XH } qeq_bool qle_bool - -(** val rdeduce : q nFormula -> q nFormula -> q nFormula option **) - -let rdeduce = - nformula_plus_nformula { qnum = Z0; qden = XH } qplus qeq_bool - -(** val rTautoChecker : rcst formula bFormula -> rWitness list -> bool **) - -let rTautoChecker f w = - tauto_checker runsat rdeduce rnormalise rnegate rWeakChecker - (map_bformula (map_Formula q_of_Rcst) f) w diff --git a/plugins/micromega/micromega.mli b/plugins/micromega/micromega.mli deleted file mode 100644 index beb042f49d..0000000000 --- a/plugins/micromega/micromega.mli +++ /dev/null @@ -1,522 +0,0 @@ -val negb : bool -> bool - -type nat = -| O -| S of nat - -val app : 'a1 list -> 'a1 list -> 'a1 list - -type comparison = -| Eq -| Lt -| Gt - -val compOpp : comparison -> comparison - -val add : nat -> nat -> nat - -type positive = -| XI of positive -| XO of positive -| XH - -type n = -| N0 -| Npos of positive - -type z = -| Z0 -| Zpos of positive -| Zneg of positive - -module Pos : - sig - type mask = - | IsNul - | IsPos of positive - | IsNeg - end - -module Coq_Pos : - sig - val succ : positive -> positive - - val add : positive -> positive -> positive - - val add_carry : positive -> positive -> positive - - val pred_double : positive -> positive - - type mask = Pos.mask = - | IsNul - | IsPos of positive - | IsNeg - - val succ_double_mask : mask -> mask - - val double_mask : mask -> mask - - val double_pred_mask : positive -> mask - - val sub_mask : positive -> positive -> mask - - val sub_mask_carry : positive -> positive -> mask - - val sub : positive -> positive -> positive - - val mul : positive -> positive -> positive - - val size_nat : positive -> nat - - val compare_cont : comparison -> positive -> positive -> comparison - - val compare : positive -> positive -> comparison - - val gcdn : nat -> positive -> positive -> positive - - val gcd : positive -> positive -> positive - - val of_succ_nat : nat -> positive - end - -module N : - sig - val of_nat : nat -> n - end - -val pow_pos : ('a1 -> 'a1 -> 'a1) -> 'a1 -> positive -> 'a1 - -val nth : nat -> 'a1 list -> 'a1 -> 'a1 - -val map : ('a1 -> 'a2) -> 'a1 list -> 'a2 list - -val fold_right : ('a2 -> 'a1 -> 'a1) -> 'a1 -> 'a2 list -> 'a1 - -module Z : - sig - val double : z -> z - - val succ_double : z -> z - - val pred_double : z -> z - - val pos_sub : positive -> positive -> z - - val add : z -> z -> z - - val opp : z -> z - - val sub : z -> z -> z - - val mul : z -> z -> z - - val compare : z -> z -> comparison - - val leb : z -> z -> bool - - val ltb : z -> z -> bool - - val gtb : z -> z -> bool - - val max : z -> z -> z - - val abs : z -> z - - val to_N : z -> n - - val pos_div_eucl : positive -> z -> z * z - - val div_eucl : z -> z -> z * z - - val div : z -> z -> z - - val gcd : z -> z -> z - end - -val zeq_bool : z -> z -> bool - -type 'c pol = -| Pc of 'c -| Pinj of positive * 'c pol -| PX of 'c pol * positive * 'c pol - -val p0 : 'a1 -> 'a1 pol - -val p1 : 'a1 -> 'a1 pol - -val peq : ('a1 -> 'a1 -> bool) -> 'a1 pol -> 'a1 pol -> bool - -val mkPinj : positive -> 'a1 pol -> 'a1 pol - -val mkPinj_pred : positive -> 'a1 pol -> 'a1 pol - -val mkPX : - 'a1 -> ('a1 -> 'a1 -> bool) -> 'a1 pol -> positive -> 'a1 pol -> 'a1 pol - -val mkXi : 'a1 -> 'a1 -> positive -> 'a1 pol - -val mkX : 'a1 -> 'a1 -> 'a1 pol - -val popp : ('a1 -> 'a1) -> 'a1 pol -> 'a1 pol - -val paddC : ('a1 -> 'a1 -> 'a1) -> 'a1 pol -> 'a1 -> 'a1 pol - -val psubC : ('a1 -> 'a1 -> 'a1) -> 'a1 pol -> 'a1 -> 'a1 pol - -val paddI : - ('a1 -> 'a1 -> 'a1) -> ('a1 pol -> 'a1 pol -> 'a1 pol) -> 'a1 pol -> - positive -> 'a1 pol -> 'a1 pol - -val psubI : - ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1) -> ('a1 pol -> 'a1 pol -> 'a1 pol) - -> 'a1 pol -> positive -> 'a1 pol -> 'a1 pol - -val paddX : - 'a1 -> ('a1 -> 'a1 -> bool) -> ('a1 pol -> 'a1 pol -> 'a1 pol) -> 'a1 - pol -> positive -> 'a1 pol -> 'a1 pol - -val psubX : - 'a1 -> ('a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> ('a1 pol -> 'a1 pol -> - 'a1 pol) -> 'a1 pol -> positive -> 'a1 pol -> 'a1 pol - -val padd : - 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 pol -> 'a1 pol - -> 'a1 pol - -val psub : - 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1) -> - ('a1 -> 'a1 -> bool) -> 'a1 pol -> 'a1 pol -> 'a1 pol - -val pmulC_aux : - 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 pol -> 'a1 -> - 'a1 pol - -val pmulC : - 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 pol -> - 'a1 -> 'a1 pol - -val pmulI : - 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> ('a1 pol -> - 'a1 pol -> 'a1 pol) -> 'a1 pol -> positive -> 'a1 pol -> 'a1 pol - -val pmul : - 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 - -> bool) -> 'a1 pol -> 'a1 pol -> 'a1 pol - -val psquare : - 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 - -> bool) -> 'a1 pol -> 'a1 pol - -type 'c pExpr = -| PEc of 'c -| PEX of positive -| PEadd of 'c pExpr * 'c pExpr -| PEsub of 'c pExpr * 'c pExpr -| PEmul of 'c pExpr * 'c pExpr -| PEopp of 'c pExpr -| PEpow of 'c pExpr * n - -val mk_X : 'a1 -> 'a1 -> positive -> 'a1 pol - -val ppow_pos : - 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 - -> bool) -> ('a1 pol -> 'a1 pol) -> 'a1 pol -> 'a1 pol -> positive -> - 'a1 pol - -val ppow_N : - 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 - -> bool) -> ('a1 pol -> 'a1 pol) -> 'a1 pol -> n -> 'a1 pol - -val norm_aux : - 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 - -> 'a1) -> ('a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 pExpr -> 'a1 pol - -type 'a bFormula = -| TT -| FF -| X -| A of 'a -| Cj of 'a bFormula * 'a bFormula -| D of 'a bFormula * 'a bFormula -| N of 'a bFormula -| I of 'a bFormula * 'a bFormula - -val map_bformula : ('a1 -> 'a2) -> 'a1 bFormula -> 'a2 bFormula - -type 'x clause = 'x list - -type 'x cnf = 'x clause list - -val tt : 'a1 cnf - -val ff : 'a1 cnf - -val add_term : - ('a1 -> bool) -> ('a1 -> 'a1 -> 'a1 option) -> 'a1 -> 'a1 clause -> 'a1 - clause option - -val or_clause : - ('a1 -> bool) -> ('a1 -> 'a1 -> 'a1 option) -> 'a1 clause -> 'a1 clause - -> 'a1 clause option - -val or_clause_cnf : - ('a1 -> bool) -> ('a1 -> 'a1 -> 'a1 option) -> 'a1 clause -> 'a1 cnf -> - 'a1 cnf - -val or_cnf : - ('a1 -> bool) -> ('a1 -> 'a1 -> 'a1 option) -> 'a1 cnf -> 'a1 cnf -> 'a1 - cnf - -val and_cnf : 'a1 cnf -> 'a1 cnf -> 'a1 cnf - -val xcnf : - ('a2 -> bool) -> ('a2 -> 'a2 -> 'a2 option) -> ('a1 -> 'a2 cnf) -> ('a1 - -> 'a2 cnf) -> bool -> 'a1 bFormula -> 'a2 cnf - -val cnf_checker : ('a1 list -> 'a2 -> bool) -> 'a1 cnf -> 'a2 list -> bool - -val tauto_checker : - ('a2 -> bool) -> ('a2 -> 'a2 -> 'a2 option) -> ('a1 -> 'a2 cnf) -> ('a1 - -> 'a2 cnf) -> ('a2 list -> 'a3 -> bool) -> 'a1 bFormula -> 'a3 list -> - bool - -val cneqb : ('a1 -> 'a1 -> bool) -> 'a1 -> 'a1 -> bool - -val cltb : - ('a1 -> 'a1 -> bool) -> ('a1 -> 'a1 -> bool) -> 'a1 -> 'a1 -> bool - -type 'c polC = 'c pol - -type op1 = -| Equal -| NonEqual -| Strict -| NonStrict - -type 'c nFormula = 'c polC * op1 - -val opMult : op1 -> op1 -> op1 option - -val opAdd : op1 -> op1 -> op1 option - -type 'c psatz = -| PsatzIn of nat -| PsatzSquare of 'c polC -| PsatzMulC of 'c polC * 'c psatz -| PsatzMulE of 'c psatz * 'c psatz -| PsatzAdd of 'c psatz * 'c psatz -| PsatzC of 'c -| PsatzZ - -val map_option : ('a1 -> 'a2 option) -> 'a1 option -> 'a2 option - -val map_option2 : - ('a1 -> 'a2 -> 'a3 option) -> 'a1 option -> 'a2 option -> 'a3 option - -val pexpr_times_nformula : - 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 - -> bool) -> 'a1 polC -> 'a1 nFormula -> 'a1 nFormula option - -val nformula_times_nformula : - 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 - -> bool) -> 'a1 nFormula -> 'a1 nFormula -> 'a1 nFormula option - -val nformula_plus_nformula : - 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 nFormula -> - 'a1 nFormula -> 'a1 nFormula option - -val eval_Psatz : - 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 - -> bool) -> ('a1 -> 'a1 -> bool) -> 'a1 nFormula list -> 'a1 psatz -> - 'a1 nFormula option - -val check_inconsistent : - 'a1 -> ('a1 -> 'a1 -> bool) -> ('a1 -> 'a1 -> bool) -> 'a1 nFormula -> - bool - -val check_normalised_formulas : - 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 - -> bool) -> ('a1 -> 'a1 -> bool) -> 'a1 nFormula list -> 'a1 psatz -> - bool - -type op2 = -| OpEq -| OpNEq -| OpLe -| OpGe -| OpLt -| OpGt - -type 't formula = { flhs : 't pExpr; fop : op2; frhs : 't pExpr } - -val norm : - 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 - -> 'a1) -> ('a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 pExpr -> 'a1 pol - -val psub0 : - 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1) -> - ('a1 -> 'a1 -> bool) -> 'a1 pol -> 'a1 pol -> 'a1 pol - -val padd0 : - 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 pol -> 'a1 pol - -> 'a1 pol - -val xnormalise : - 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 - -> 'a1) -> ('a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 formula -> 'a1 - nFormula list - -val cnf_normalise : - 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 - -> 'a1) -> ('a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 formula -> 'a1 - nFormula cnf - -val xnegate : - 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 - -> 'a1) -> ('a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 formula -> 'a1 - nFormula list - -val cnf_negate : - 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 - -> 'a1) -> ('a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 formula -> 'a1 - nFormula cnf - -val xdenorm : positive -> 'a1 pol -> 'a1 pExpr - -val denorm : 'a1 pol -> 'a1 pExpr - -val map_PExpr : ('a2 -> 'a1) -> 'a2 pExpr -> 'a1 pExpr - -val map_Formula : ('a2 -> 'a1) -> 'a2 formula -> 'a1 formula - -val simpl_cone : - 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 psatz - -> 'a1 psatz - -type q = { qnum : z; qden : positive } - -val qnum : q -> z - -val qden : q -> positive - -val qeq_bool : q -> q -> bool - -val qle_bool : q -> q -> bool - -val qplus : q -> q -> q - -val qmult : q -> q -> q - -val qopp : q -> q - -val qminus : q -> q -> q - -val qinv : q -> q - -val qpower_positive : q -> positive -> q - -val qpower : q -> z -> q - -type 'a t = -| Empty -| Leaf of 'a -| Node of 'a t * 'a * 'a t - -val find : 'a1 -> 'a1 t -> positive -> 'a1 - -val singleton : 'a1 -> positive -> 'a1 -> 'a1 t - -val vm_add : 'a1 -> positive -> 'a1 -> 'a1 t -> 'a1 t - -type zWitness = z psatz - -val zWeakChecker : z nFormula list -> z psatz -> bool - -val psub1 : z pol -> z pol -> z pol - -val padd1 : z pol -> z pol -> z pol - -val norm0 : z pExpr -> z pol - -val xnormalise0 : z formula -> z nFormula list - -val normalise : z formula -> z nFormula cnf - -val xnegate0 : z formula -> z nFormula list - -val negate : z formula -> z nFormula cnf - -val zunsat : z nFormula -> bool - -val zdeduce : z nFormula -> z nFormula -> z nFormula option - -val ceiling : z -> z -> z - -type zArithProof = -| DoneProof -| RatProof of zWitness * zArithProof -| CutProof of zWitness * zArithProof -| EnumProof of zWitness * zWitness * zArithProof list - -val zgcdM : z -> z -> z - -val zgcd_pol : z polC -> z * z - -val zdiv_pol : z polC -> z -> z polC - -val makeCuttingPlane : z polC -> z polC * z - -val genCuttingPlane : z nFormula -> ((z polC * z) * op1) option - -val nformula_of_cutting_plane : ((z polC * z) * op1) -> z nFormula - -val is_pol_Z0 : z polC -> bool - -val eval_Psatz0 : z nFormula list -> zWitness -> z nFormula option - -val valid_cut_sign : op1 -> bool - -val zChecker : z nFormula list -> zArithProof -> bool - -val zTautoChecker : z formula bFormula -> zArithProof list -> bool - -type qWitness = q psatz - -val qWeakChecker : q nFormula list -> q psatz -> bool - -val qnormalise : q formula -> q nFormula cnf - -val qnegate : q formula -> q nFormula cnf - -val qunsat : q nFormula -> bool - -val qdeduce : q nFormula -> q nFormula -> q nFormula option - -val qTautoChecker : q formula bFormula -> qWitness list -> bool - -type rcst = -| C0 -| C1 -| CQ of q -| CZ of z -| CPlus of rcst * rcst -| CMinus of rcst * rcst -| CMult of rcst * rcst -| CInv of rcst -| COpp of rcst - -val q_of_Rcst : rcst -> q - -type rWitness = q psatz - -val rWeakChecker : q nFormula list -> q psatz -> bool - -val rnormalise : q formula -> q nFormula cnf - -val rnegate : q formula -> q nFormula cnf - -val runsat : q nFormula -> bool - -val rdeduce : q nFormula -> q nFormula -> q nFormula option - -val rTautoChecker : rcst formula bFormula -> rWitness list -> bool diff --git a/plugins/micromega/vo.itarget b/plugins/micromega/vo.itarget index c9009ea4de..a555d5ba17 100644 --- a/plugins/micromega/vo.itarget +++ b/plugins/micromega/vo.itarget @@ -1,3 +1,4 @@ +MExtraction.vo EnvRing.vo Env.vo OrderedRing.vo diff --git a/plugins/omega/coq_omega.ml b/plugins/omega/coq_omega.ml index ee748567b8..d7408e88ec 100644 --- a/plugins/omega/coq_omega.ml +++ b/plugins/omega/coq_omega.ml @@ -39,10 +39,10 @@ open OmegaSolver let elim_id id = Proofview.Goal.enter { enter = begin fun gl -> - simplest_elim (Tacmach.New.pf_global id gl) + simplest_elim (mkVar id) end } let resolve_id id = Proofview.Goal.enter { enter = begin fun gl -> - apply (Tacmach.New.pf_global id gl) + apply (mkVar id) end } let timing timer_name f arg = f arg diff --git a/plugins/quote/quote.ml b/plugins/quote/quote.ml index 7412de1e80..ba8356b525 100644 --- a/plugins/quote/quote.ml +++ b/plugins/quote/quote.ml @@ -456,39 +456,56 @@ let quote_terms env sigma ivs lc = term. Ring for example needs that, but Ring doesn't use Quote yet. *) +let pf_constrs_of_globals l = + let rec aux l acc = + match l with + [] -> Proofview.tclUNIT (List.rev acc) + | hd :: tl -> + Tacticals.New.pf_constr_of_global hd >>= fun g -> aux tl (g :: acc) + in aux l [] + let quote f lid = - Proofview.Goal.nf_enter { enter = begin fun gl -> - let env = Proofview.Goal.env gl in - let sigma = Tacmach.New.project gl in - let f = Tacmach.New.pf_global f gl in - let cl = List.map (fun id -> EConstr.to_constr sigma (Tacmach.New.pf_global id gl)) lid in - let ivs = compute_ivs f cl gl in - let concl = Proofview.Goal.concl gl in - let quoted_terms = quote_terms env sigma ivs [concl] in - let (p, vm) = match quoted_terms with + Proofview.Goal.enter { enter = begin fun gl -> + let fg = Tacmach.New.pf_global f gl in + let clg = List.map (fun id -> Tacmach.New.pf_global id gl) lid in + Tacticals.New.pf_constr_of_global fg >>= fun f -> + pf_constrs_of_globals clg >>= fun cl -> + Proofview.Goal.nf_enter { enter = begin fun gl -> + let env = Proofview.Goal.env gl in + let sigma = Tacmach.New.project gl in + let ivs = compute_ivs f (List.map (EConstr.to_constr sigma) cl) gl in + let concl = Proofview.Goal.concl gl in + let quoted_terms = quote_terms env sigma ivs [concl] in + let (p, vm) = match quoted_terms with | [p], vm -> (p,vm) | _ -> assert false - in - match ivs.variable_lhs with - | None -> Tactics.convert_concl (mkApp (f, [| p |])) DEFAULTcast - | Some _ -> Tactics.convert_concl (mkApp (f, [| vm; p |])) DEFAULTcast + in + match ivs.variable_lhs with + | None -> Tactics.convert_concl (mkApp (f, [| p |])) DEFAULTcast + | Some _ -> Tactics.convert_concl (mkApp (f, [| vm; p |])) DEFAULTcast + end } end } let gen_quote cont c f lid = - Proofview.Goal.nf_enter { enter = begin fun gl -> - let env = Proofview.Goal.env gl in - let sigma = Tacmach.New.project gl in - let f = Tacmach.New.pf_global f gl in - let cl = List.map (fun id -> EConstr.to_constr sigma (Tacmach.New.pf_global id gl)) lid in - let ivs = compute_ivs f cl gl in - let quoted_terms = quote_terms env sigma ivs [c] in - let (p, vm) = match quoted_terms with - | [p], vm -> (p,vm) - | _ -> assert false - in - match ivs.variable_lhs with - | None -> cont (mkApp (f, [| p |])) - | Some _ -> cont (mkApp (f, [| vm; p |])) + Proofview.Goal.enter { enter = begin fun gl -> + let fg = Tacmach.New.pf_global f gl in + let clg = List.map (fun id -> Tacmach.New.pf_global id gl) lid in + Tacticals.New.pf_constr_of_global fg >>= fun f -> + pf_constrs_of_globals clg >>= fun cl -> + Proofview.Goal.nf_enter { enter = begin fun gl -> + let env = Proofview.Goal.env gl in + let sigma = Tacmach.New.project gl in + let cl = List.map (EConstr.to_constr sigma) cl in + let ivs = compute_ivs f cl gl in + let quoted_terms = quote_terms env sigma ivs [c] in + let (p, vm) = match quoted_terms with + | [p], vm -> (p,vm) + | _ -> assert false + in + match ivs.variable_lhs with + | None -> cont (mkApp (f, [| p |])) + | Some _ -> cont (mkApp (f, [| vm; p |])) + end } end } (*i |