+let is_an_equational_goal = function
+ | Cic.Appl [Cic.MutInd(u,_,_);_;_;_] when LibraryObjects.is_eq_URI u -> true
+ | _ -> false
+;;
+
+type auto_params = Cic.term list * (string * string) list
+
+let elems = ref [] ;;
+
+(* closing a term w.r.t. its metavariables
+ very naif version: it does not take dependencies properly into account *)
+
+let naif_closure ?(prefix_name="xxx_") t metasenv context =
+ let in_term t (i,_,_) =
+ List.exists (fun (j,_) -> j=i) (CicUtil.metas_of_term t)
+ in
+ let metasenv = List.filter (in_term t) metasenv in
+ let metasenv = ProofEngineHelpers.sort_metasenv metasenv in
+ let n = List.length metasenv in
+ let what = List.map (fun (i,cc,ty) -> Cic.Meta(i,[])) metasenv in
+ let _,with_what =
+ List.fold_left
+ (fun (i,acc) (_,cc,ty) -> (i-1,Cic.Rel i::acc))
+ (n,[]) metasenv
+ in
+ let t = CicSubstitution.lift n t in
+ let body =
+ ProofEngineReduction.replace_lifting
+ ~equality:(fun c t1 t2 ->
+ match t1,t2 with
+ | Cic.Meta(i,_),Cic.Meta(j,_) -> i = j
+ | _ -> false)
+ ~context ~what ~with_what ~where:t
+ in
+ let _, t =
+ List.fold_left
+ (fun (n,t) (_,cc,ty) ->
+ n-1, Cic.Lambda(Cic.Name (prefix_name^string_of_int n),
+ CicSubstitution.lift n ty,t))
+ (n-1,body) metasenv
+ in
+ t, List.length metasenv
+;;
+
+let lambda_close ?prefix_name t menv ctx =
+ let t, num_lambdas = naif_closure ?prefix_name t menv ctx in
+ List.fold_left
+ (fun (t,i) -> function
+ | None -> CicSubstitution.subst (Cic.Implicit None) t,i (* delift *)
+ | Some (name, Cic.Decl ty) -> Cic.Lambda (name, ty, t),i+1
+ | Some (name, Cic.Def (bo, ty)) -> Cic.LetIn (name, bo, ty, t),i+1)
+ (t,num_lambdas) ctx
+;;
+
+(* functions for retrieving theorems *)
+
+
+exception FillingFailure of AutoCache.cache * AutomationCache.tables
+
+let rec unfold context = function
+ | Cic.Prod(name,s,t) ->
+ let t' = unfold ((Some (name,Cic.Decl s))::context) t in
+ Cic.Prod(name,s,t')
+ | t -> ProofEngineReduction.unfold context t
+
+let find_library_theorems dbd proof goal =
+ let univ = MetadataQuery.universe_of_goal ~dbd false proof goal in
+ let terms = List.map CicUtil.term_of_uri univ in
+ List.map
+ (fun t ->
+ (t,fst(CicTypeChecker.type_of_aux' [] [] t CicUniv.oblivion_ugraph)))
+ terms
+
+let find_context_theorems context metasenv =
+ let l,_ =
+ List.fold_left
+ (fun (res,i) ctxentry ->
+ match ctxentry with
+ | Some (_,Cic.Decl t) ->
+ (Cic.Rel i, CicSubstitution.lift i t)::res,i+1
+ | Some (_,Cic.Def (_,t)) ->
+ (Cic.Rel i, CicSubstitution.lift i t)::res,i+1
+ | None -> res,i+1)
+ ([],1) context
+ in l
+
+let rec is_an_equality = function
+ | Cic.Appl [Cic.MutInd (uri, _, _); _; _; _]
+ when (LibraryObjects.is_eq_URI uri) -> true
+ | Cic.Prod (_, _, t) -> is_an_equality t
+ | _ -> false
+;;
+
+let partition_equalities =
+ List.partition (fun (_,ty) -> is_an_equality ty)
+
+
+let default_auto tables _ cache _ _ _ _ = [],cache,tables ;;
+
+(* giusto per provare che succede
+let is_unit_equation context metasenv oldnewmeta term =
+ let head, metasenv, args, newmeta =
+ TermUtil.saturate_term oldnewmeta metasenv context term 0
+ in
+ let newmetas =
+ List.filter (fun (i,_,_) -> i >= oldnewmeta) metasenv
+ in
+ Some (args,metasenv,newmetas,head,newmeta) *)
+
+let is_unit_equation context metasenv oldnewmeta term =
+ let head, metasenv, args, newmeta =
+ TermUtil.saturate_term oldnewmeta metasenv context term 0
+ in
+ let propositional_args =
+ HExtlib.filter_map
+ (function
+ | Cic.Meta(i,_) ->
+ let _,_,mt = CicUtil.lookup_meta i metasenv in
+ let sort,u =
+ CicTypeChecker.type_of_aux' metasenv context mt
+ CicUniv.oblivion_ugraph
+ in
+ if is_propositional context sort then Some i else None
+ | _ -> assert false)
+ args
+ in
+ if propositional_args = [] then
+ let newmetas =
+ List.filter (fun (i,_,_) -> i >= oldnewmeta) metasenv
+ in
+ Some (args,metasenv,newmetas,head,newmeta)
+ else None
+;;
+
+let get_candidates skip_trie_filtering universe cache t =
+ let t = if skip_trie_filtering then Cic.Meta(0,[]) else t in
+ let candidates=
+ (Universe.get_candidates universe t)@(AutoCache.get_candidates cache t)
+ in
+ let debug_msg =
+ (lazy ("candidates for " ^ (CicPp.ppterm t) ^ " = " ^
+ (String.concat "\n" (List.map CicPp.ppterm candidates)))) in
+ debug_print debug_msg;
+ candidates
+;;
+
+let only signature context metasenv t =
+ try
+ let ty,_ =
+ CicTypeChecker.type_of_aux' metasenv context t CicUniv.oblivion_ugraph
+ in
+ let consts = MetadataConstraints.constants_of ty in
+ let b = MetadataConstraints.UriManagerSet.subset consts signature in
+(* if b then (prerr_endline ("keeping " ^ (CicPp.ppterm t)); b) *)
+ if b then b
+ else
+ let ty' = unfold context ty in
+ let consts' = MetadataConstraints.constants_of ty' in
+ let b = MetadataConstraints.UriManagerSet.subset consts' signature in
+(*
+ if not b then prerr_endline ("filtering " ^ (CicPp.ppterm t))
+ else prerr_endline ("keeping " ^ (CicPp.ppterm t));
+*)
+ b
+ with
+ | CicTypeChecker.TypeCheckerFailure _ -> assert false
+ | ProofEngineTypes.Fail _ -> false (* unfold may fail *)
+;;
+
+let not_default_eq_term t =
+ try
+ let uri = CicUtil.uri_of_term t in
+ not (LibraryObjects.in_eq_URIs uri)
+ with Invalid_argument _ -> true
+
+let retrieve_equations dont_filter signature universe cache context metasenv =
+ match LibraryObjects.eq_URI() with
+ | None -> []
+ | Some eq_uri ->
+ let eq_uri = UriManager.strip_xpointer eq_uri in
+ let fake= Cic.Meta(-1,[]) in
+ let fake_eq = Cic.Appl [Cic.MutInd (eq_uri,0, []);fake;fake;fake] in
+ let candidates = get_candidates false universe cache fake_eq in
+ if dont_filter then candidates
+ else let eq_uri = UriManager.uri_of_uriref eq_uri 0 None in
+ (* let candidates = List.filter not_default_eq_term candidates in *)
+ List.filter
+ (only (MetadataConstraints.UriManagerSet.add eq_uri signature)
+ context metasenv) candidates
+
+let build_equality bag head args proof newmetas =
+ match head with
+ | Cic.Appl [Cic.MutInd (uri, _, _); ty; t1; t2] ->
+ let p =
+ if args = [] then proof else Cic.Appl (proof::args)
+ in
+ let o = !Utils.compare_terms t1 t2 in
+ let stat = (ty,t1,t2,o) in
+ (* let w = compute_equality_weight stat in *)
+ let w = 0 in
+ let proof = Equality.Exact p in
+ let bag, e = Equality.mk_equality bag (w, proof, stat, newmetas) in
+ (* to clean the local context of metas *)
+ Equality.fix_metas bag e
+ | _ -> assert false
+;;
+
+let partition_unit_equalities context metasenv newmeta bag equations =
+ List.fold_left
+ (fun (bag,units,other,maxmeta)(t,ty) ->
+ if not (CicUtil.is_meta_closed t && CicUtil.is_meta_closed ty) then
+ let _ =
+ HLog.warn
+ ("Skipping " ^ CicMetaSubst.ppterm_in_context ~metasenv [] t context
+ ^ " since it is not meta closed")
+ in
+ bag, units,(t,ty)::other,maxmeta
+ else
+ match is_unit_equation context metasenv maxmeta ty with
+ | Some (args,metasenv,newmetas,head,newmeta') ->
+ let bag, equality =
+ build_equality bag head args t newmetas in
+ bag, equality::units,other,maxmeta
+ | None ->
+ bag, units,(t,ty)::other,maxmeta)
+ (bag,[],[],newmeta) equations
+;;
+
+let init_cache_and_tables
+ ?dbd ~use_library ~use_context
+ automation_cache restricted_univ (proof, goal)
+=
+ let _, metasenv, subst, _, _, _ = proof in
+ let _,context,_ = CicUtil.lookup_meta goal metasenv in
+ let add_list_to_tables metasenv subst automation_cache ct =
+ List.fold_left
+ (fun automation_cache (t,_) ->
+ AutomationCache.add_term_to_active automation_cache
+ metasenv subst context t None)
+ automation_cache ct
+ in
+ if restricted_univ = [] then
+ let ct =
+ if use_context then find_context_theorems context metasenv else []
+ in
+ let lt =
+ match use_library, dbd with
+ | true, Some dbd -> find_library_theorems dbd metasenv goal
+ | _ -> []
+ in
+ let cache = AutoCache.cache_empty in
+ let cache = cache_add_list cache context (ct@lt) in
+ let automation_cache =
+ add_list_to_tables metasenv subst automation_cache ct
+ in
+(* AutomationCache.pp_cache automation_cache; *)
+ automation_cache.AutomationCache.univ,
+ automation_cache.AutomationCache.tables,
+ cache
+ else
+ let t_ty =
+ List.map
+ (fun t ->
+ let ty, _ = CicTypeChecker.type_of_aux'
+ metasenv ~subst:[] context t CicUniv.oblivion_ugraph
+ in
+ t, ty)
+ restricted_univ
+ in
+ (* let automation_cache = AutomationCache.empty () in *)
+ let automation_cache =
+ let universe = Universe.empty in
+ let universe =
+ Universe.index_list universe context t_ty
+ in
+ { automation_cache with AutomationCache.univ = universe }
+ in
+ let ct =
+ if use_context then find_context_theorems context metasenv else t_ty
+ in
+ let automation_cache =
+ add_list_to_tables metasenv subst automation_cache ct
+ in
+ (* AutomationCache.pp_cache automation_cache; *)
+ automation_cache.AutomationCache.univ,
+ automation_cache.AutomationCache.tables,
+ cache_empty
+;;
+
+let fill_hypothesis context metasenv subst term tables (universe:Universe.universe) cache auto fast =
+ let actives, passives, bag = tables in
+ let bag, head, metasenv, args =
+ Equality.saturate_term bag metasenv subst context term
+ in
+ let tables = actives, passives, bag in
+ let propositional_args =
+ HExtlib.filter_map
+ (function
+ | Cic.Meta(i,_) ->
+ let _,_,mt = CicUtil.lookup_meta i metasenv in
+ let sort,u =
+ CicTypeChecker.type_of_aux' metasenv context mt
+ CicUniv.oblivion_ugraph
+ in
+ if is_propositional context sort then Some i else None
+ | _ -> assert false)
+ args
+ in
+ let results,cache,tables =
+ if propositional_args = [] then
+ let _,_,bag = tables in
+ let newmetas = Equality.filter_metasenv_gt_maxmeta bag metasenv in
+ [args,metasenv,newmetas,head],cache,tables
+ else
+ (*
+ let proof =
+ None,metasenv,term,term (* term non e' significativo *)
+ in *)
+ let flags =
+ if fast then
+ {AutoTypes.default_flags() with
+ AutoTypes.timeout = Unix.gettimeofday() +. 1.0;
+ maxwidth = 2;maxdepth = 2;
+ use_paramod=true;use_only_paramod=false}
+ else
+ {AutoTypes.default_flags() with
+ AutoTypes.timeout = Unix.gettimeofday() +. 1.0;
+ maxwidth = 2;maxdepth = 4;
+ use_paramod=true;use_only_paramod=false}
+ in
+ match auto tables universe cache context metasenv propositional_args flags with
+ | [],cache,tables -> raise (FillingFailure (cache,tables))
+ | substs,cache,tables ->
+ let actives, passaives, bag = tables in
+ let bag, res =
+ List.fold_right
+ (fun subst (bag,acc) ->
+ let metasenv =
+ CicMetaSubst.apply_subst_metasenv subst metasenv
+ in
+ let head = CicMetaSubst.apply_subst subst head in
+ let newmetas = Equality.filter_metasenv_gt_maxmeta bag metasenv in
+ let args = List.map (CicMetaSubst.apply_subst subst) args in
+ let newm = CicMkImplicit.new_meta metasenv subst in
+ let bag = Equality.push_maxmeta bag newm in
+ bag, ((args,metasenv,newmetas,head) :: acc))
+ substs (bag,[])
+ in
+ let tables = actives, passives, bag in
+ res, cache, tables
+ in
+ results,cache,tables
+;;
+
+let build_equalities auto context metasenv subst tables universe cache equations =
+ List.fold_left
+ (fun (tables,facts,cache) (t,ty) ->
+ (* in any case we add the equation to the cache *)
+ let cache = AutoCache.cache_add_list cache context [(t,ty)] in
+ try
+ let saturated, cache, tables =
+ fill_hypothesis context metasenv subst ty tables universe cache auto true
+ in
+ let eqs, tables =
+ List.fold_left
+ (fun (acc, tables) (args,metasenv,newmetas,head) ->
+ let actives, passives, bag = tables in
+ let bag, equality =
+ build_equality bag head args t newmetas
+ in
+ let tables = actives, passives, bag in
+ equality::acc,tables)
+ ([],tables) saturated
+ in
+ (tables, eqs@facts, cache)
+ with FillingFailure (cache,tables) ->
+ (* if filling hypothesis fails we add the equation to
+ the cache *)
+ (tables,facts,cache)
+ )
+ (tables,[],cache) equations
+
+let close_more tables context status auto signature universe cache =
+ let proof, goalno = status in
+ let _, metasenv,subst,_,_, _ = proof in
+ let equations =
+ retrieve_equations false signature universe cache context metasenv
+ in
+ let eqs_and_types =
+ HExtlib.filter_map
+ (fun t ->
+ let ty,_ =
+ CicTypeChecker.type_of_aux' metasenv context t
+ CicUniv.oblivion_ugraph in
+ (* retrieve_equations could also return flexible terms *)
+ if is_an_equality ty then Some(t,ty) else None)
+ equations in
+ let tables, units, cache =
+ build_equalities auto context metasenv subst tables universe cache eqs_and_types
+ in
+ let active,passive,bag = tables in
+ let passive = Saturation.add_to_passive units passive in
+ let no = List.length units in
+ let active, passive, bag =
+ Saturation.pump_actives context bag active passive (no+1) infinity
+ in
+ (active,passive,bag), cache
+;;
+
+let find_context_equalities dbd tables context proof (universe:Universe.universe) cache
+=
+ let module C = Cic in
+ let module S = CicSubstitution in
+ let module T = CicTypeChecker in
+ let _,metasenv,subst,_,_, _ = proof in
+ (* if use_auto is true, we try to close the hypothesis of equational
+ statements using auto; a naif, and probably wrong approach *)
+ let rec aux tables cache index = function
+ | [] -> tables, [], cache
+ | (Some (_, C.Decl (term)))::tl ->
+ debug_print
+ (lazy
+ (Printf.sprintf "Examining: %d (%s)" index (CicPp.ppterm term)));
+ let do_find tables context term =
+ match term with
+ | C.Prod (name, s, t) when is_an_equality t ->
+ (try
+ let term = S.lift index term in
+ let saturated, cache, tables =
+ fill_hypothesis context metasenv subst term
+ tables universe cache default_auto false
+ in
+ let actives, passives, bag = tables in
+ let bag,eqs =
+ List.fold_left
+ (fun (bag,acc) (args,metasenv,newmetas,head) ->
+ let bag, equality =
+ build_equality bag head args (Cic.Rel index) newmetas
+ in
+ bag, equality::acc)
+ (bag,[]) saturated
+ in
+ let tables = actives, passives, bag in
+ tables, eqs, cache
+ with FillingFailure (cache,tables) ->
+ tables, [], cache)
+ | C.Appl [C.MutInd (uri, _, _); ty; t1; t2]
+ when LibraryObjects.is_eq_URI uri ->
+ let term = S.lift index term in
+ let actives, passives, bag = tables in
+ let bag, e =
+ build_equality bag term [] (Cic.Rel index) []
+ in
+ let tables = actives, passives, bag in
+ tables, [e], cache
+ | _ -> tables, [], cache
+ in
+ let tables, eqs, cache = do_find tables context term in
+ let tables, rest, cache = aux tables cache (index+1) tl in
+ tables, List.map (fun x -> index,x) eqs @ rest, cache
+ | _::tl ->
+ aux tables cache (index+1) tl
+ in
+ let tables, il, cache = aux tables cache 1 context in
+ let indexes, equalities = List.split il in
+ tables, indexes, equalities, cache
+;;
+
+(********** PARAMETERS PASSING ***************)
+
+let bool params name default =
+ try
+ let s = List.assoc name params in
+ if s = "" || s = "1" || s = "true" || s = "yes" || s = "on" then true
+ else if s = "0" || s = "false" || s = "no" || s= "off" then false
+ else
+ let msg = "Unrecognized value for parameter "^name^"\n" in
+ let msg = msg^"Accepted values are 1,true,yes,on and 0,false,no,off" in
+ raise (ProofEngineTypes.Fail (lazy msg))
+ with Not_found -> default
+;;
+
+let string params name default =
+ try List.assoc name params with
+ | Not_found -> default
+;;
+
+let int params name default =
+ try int_of_string (List.assoc name params) with
+ | Not_found -> default
+ | Failure _ ->
+ raise (ProofEngineTypes.Fail (lazy (name ^ " must be an integer")))
+;;
+
+let flags_of_params params ?(for_applyS=false) () =
+ let int = int params in
+ let bool = bool params in
+ let close_more = bool "close_more" false in
+ let use_paramod = bool "use_paramod" true in
+ let skip_trie_filtering = bool "skip_trie_filtering" false in
+ let skip_context = bool "skip_context" false in
+ let use_only_paramod =
+ if for_applyS then true else bool "paramodulation" false in
+ let use_library = bool "library"
+ ((AutoTypes.default_flags()).AutoTypes.use_library) in
+ let depth = int "depth" ((AutoTypes.default_flags()).AutoTypes.maxdepth) in
+ let width = int "width" ((AutoTypes.default_flags()).AutoTypes.maxwidth) in
+ let size = int "size" ((AutoTypes.default_flags()).AutoTypes.maxsize) in
+ let gsize = int "gsize" ((AutoTypes.default_flags()).AutoTypes.maxgoalsizefactor) in
+ let do_type = bool "type" false in
+ let timeout = int "timeout" 0 in
+ { AutoTypes.maxdepth =
+ if use_only_paramod then 2 else depth;
+ AutoTypes.maxwidth = width;
+ AutoTypes.maxsize = size;
+ AutoTypes.timeout =
+ if timeout = 0 then
+ if for_applyS then Unix.gettimeofday () +. 30.0
+ else
+ infinity
+ else
+ Unix.gettimeofday() +. (float_of_int timeout);
+ AutoTypes.use_library = use_library;
+ AutoTypes.use_paramod = use_paramod;
+ AutoTypes.use_only_paramod = use_only_paramod;
+ AutoTypes.close_more = close_more;
+ AutoTypes.dont_cache_failures = false;
+ AutoTypes.maxgoalsizefactor = gsize;
+ AutoTypes.do_types = do_type;
+ AutoTypes.skip_trie_filtering = skip_trie_filtering;
+ AutoTypes.skip_context = skip_context;
+ }
+
+
+let eq_of_goal = function
+ | Cic.Appl [Cic.MutInd(uri,0,_);_;_;_] when LibraryObjects.is_eq_URI uri ->
+ uri
+ | _ -> raise (ProofEngineTypes.Fail (lazy ("The goal is not an equality ")))
+;;
+
+(* performs steps of rewrite with the universe, obtaining if possible
+ * a trivial goal *)
+let solve_rewrite ~automation_cache ~params:(univ,params) (proof,goal)=
+ let steps = int_of_string (string params "steps" "4") in
+ let use_context = bool params "use_context" true in
+ let universe, tables, cache =
+ init_cache_and_tables ~use_library:false ~use_context
+ automation_cache univ (proof,goal)
+ in
+ let actives, passives, bag = tables in
+ let pa,metasenv,subst,pb,pc,pd = proof in
+ let _,context,ty = CicUtil.lookup_meta goal metasenv in
+ let metasenv = CicMetaSubst.apply_subst_metasenv subst metasenv in
+ let context = CicMetaSubst.apply_subst_context subst context in
+ let ty = CicMetaSubst.apply_subst subst ty in
+ let eq_uri = eq_of_goal ty in
+ let initgoal = [], metasenv, ty in
+ let table =
+ let equalities = (Saturation.list_of_passive passives) in
+ List.fold_left (fun tbl eq -> Indexing.index tbl eq) (snd actives) equalities
+ in
+ let env = metasenv,context,CicUniv.oblivion_ugraph in
+ debug_print (lazy ("demod to solve: " ^ CicPp.ppterm ty));
+ match Indexing.solve_demodulating bag env table initgoal steps with
+ | Some (bag, gproof, metasenv, sub_subst, proof) ->
+ let subst_candidates,extra_infos =
+ List.split
+ (HExtlib.filter_map
+ (fun (i,c,_) ->
+ if i <> goal && c = context then Some (i,(c,ty)) else None)
+ metasenv)
+ in
+ let proofterm,proto_subst =
+ let proof = Equality.add_subst sub_subst proof in
+ Equality.build_goal_proof
+ bag eq_uri gproof proof ty subst_candidates context metasenv
+ in
+ let proofterm = Subst.apply_subst sub_subst proofterm in
+ let extrasubst =
+ HExtlib.filter_map
+ (fun (i,((c,ty),t)) ->
+ match t with
+ | Cic.Meta (j,_) when i=j -> None
+ | _ -> Some (i,(c,t,ty)))
+ (List.combine subst_candidates
+ (List.combine extra_infos proto_subst))
+ in
+ let subst = subst @ extrasubst in
+ let metasenv = CicMetaSubst.apply_subst_metasenv subst metasenv in
+ let proofterm, _, metasenv,subst, _ =
+ CicRefine.type_of metasenv subst context proofterm
+ CicUniv.oblivion_ugraph
+ in
+ let status = (pa,metasenv,subst,pb,pc,pd), goal in
+ ProofEngineTypes.apply_tactic
+ (PrimitiveTactics.apply_tac ~term:proofterm) status
+ | None ->
+ raise
+ (ProofEngineTypes.Fail (lazy
+ ("Unable to solve with " ^ string_of_int steps ^ " demodulations")))
+;;
+
+(* Demodulate thorem *)
+let open_type ty bo =
+ let rec open_type_aux context ty k args =
+ match ty with
+ | Cic.Prod (n,s,t) ->
+ let n' =
+ FreshNamesGenerator.mk_fresh_name [] context n ~typ:s ~subst:[] in
+ let entry = match n' with
+ | Cic.Name _ -> Some (n',(Cic.Decl s))
+ | Cic.Anonymous -> None
+ in
+ open_type_aux (entry::context) t (k+1) ((Cic.Rel k)::args)
+ | Cic.LetIn (n,s,sty,t) ->
+ let entry = Some (n,(Cic.Def (s,sty)))
+ in
+ open_type_aux (entry::context) t (k+1) args
+ | _ -> context, ty, args
+ in
+ let context, ty, args = open_type_aux [] ty 1 [] in
+ match args with
+ | [] -> context, ty, bo
+ | _ -> context, ty, Cic.Appl (bo::args)
+;;
+
+let rec close_type bo ty context =
+ match context with
+ | [] -> assert_proof_is_valid bo [] [] ty; (bo,ty)
+ | Some (n,(Cic.Decl s))::tl ->
+ close_type (Cic.Lambda (n,s,bo)) (Cic.Prod (n,s,ty)) tl
+ | Some (n,(Cic.Def (s,sty)))::tl ->
+ close_type (Cic.LetIn (n,s,sty,bo)) (Cic.LetIn (n,s,sty,ty)) tl
+ | _ -> assert false
+;;
+
+let is_subsumed univ context ty =
+ let candidates = Universe.get_candidates univ ty in
+ List.fold_left
+ (fun res cand ->
+ match res with
+ | Some found -> Some found
+ | None ->
+ try
+ let mk_irl =
+ CicMkImplicit.identity_relocation_list_for_metavariable in
+ let metasenv = [(0,context,ty)] in
+ let fake_proof =
+ None,metasenv,[] , (lazy (Cic.Meta(0,mk_irl context))),ty,[]
+ in
+ let (_,metasenv,subst,_,_,_), open_goals =
+ ProofEngineTypes.apply_tactic
+ (PrimitiveTactics.apply_tac ~term:cand)
+ (fake_proof,0)
+ in
+ let prop_goals, other =
+ split_goals_in_prop metasenv subst open_goals
+ in
+ if prop_goals = [] then Some cand else None
+ with
+ | ProofEngineTypes.Fail s -> None
+ | CicUnification.Uncertain s -> None
+ ) None candidates
+;;
+
+let demodulate_theorem ~automation_cache uri =
+ let eq_uri =
+ match LibraryObjects.eq_URI () with
+ | Some (uri) -> uri
+ | None -> raise (ProofEngineTypes.Fail (lazy "equality not declared")) in
+ let obj,_ = CicEnvironment.get_cooked_obj CicUniv.empty_ugraph uri
+ in
+ let context,ty,bo =
+ match obj with
+ | Cic.Constant(n, _, ty ,_, _) -> open_type ty (Cic.Const(uri,[]))
+ | _ -> raise (ProofEngineTypes.Fail (lazy "not a theorem"))
+ in
+ if CicUtil.is_closed ty then
+ raise (ProofEngineTypes.Fail (lazy ("closed term: dangerous reduction")));
+ let initgoal = [], [], ty in
+ (* compute the signature *)
+ let signature =
+ let ty_set = MetadataConstraints.constants_of ty in
+ let hyp_set = MetadataQuery.signature_of_hypothesis context [] in
+ let set = MetadataConstraints.UriManagerSet.union ty_set hyp_set in
+ MetadataQuery.close_with_types set [] context
+ in
+ (* retrieve equations from the universe universe *)
+ (* XXX automation_cache *)
+ let universe = automation_cache.AutomationCache.univ in
+ let equations =
+ retrieve_equations true signature universe AutoCache.cache_empty context []
+ in
+ debug_print
+ (lazy ("ho trovato equazioni n. "^(string_of_int (List.length equations))));
+ let eqs_and_types =
+ HExtlib.filter_map
+ (fun t ->
+ let ty,_ =
+ CicTypeChecker.type_of_aux' [] context t CicUniv.oblivion_ugraph
+ in
+ (* retrieve_equations could also return flexible terms *)
+ if is_an_equality ty then Some(t,ty)
+ else
+ try
+ let ty' = unfold context ty in
+ if is_an_equality ty' then Some(t,ty') else None
+ with ProofEngineTypes.Fail _ -> None)
+ equations
+ in
+ let bag = Equality.mk_equality_bag () in
+
+ let bag, units, _, newmeta =
+ partition_unit_equalities context [] (CicMkImplicit.new_meta [] []) bag eqs_and_types
+ in
+ let table =
+ List.fold_left
+ (fun tbl eq -> Indexing.index tbl eq)
+ Indexing.empty units
+ in
+ let changed,(newproof,newmetasenv, newty) =
+ Indexing.demod bag
+ ([],context,CicUniv.oblivion_ugraph) table initgoal in
+ if changed then
+ begin
+ let oldproof = Equality.Exact bo in
+ let proofterm,_ =
+ Equality.build_goal_proof (~contextualize:false) (~forward:true) bag
+ eq_uri newproof oldproof ty [] context newmetasenv
+ in
+ if newmetasenv <> [] then
+ raise (ProofEngineTypes.Fail (lazy ("metasenv not empty")))
+ else
+ begin
+ assert_proof_is_valid proofterm newmetasenv context newty;
+ match is_subsumed universe context newty with
+ | Some t -> raise
+ (ProofEngineTypes.Fail (lazy ("subsumed by " ^ CicPp.ppterm t)))
+ | None -> close_type proofterm newty context
+ end
+ end
+ else (* if newty = ty then *)
+ raise (ProofEngineTypes.Fail (lazy "no progress"))
+ (*else ProofEngineTypes.apply_tactic
+ (ReductionTactics.simpl_tac
+ ~pattern:(ProofEngineTypes.conclusion_pattern None)) initialstatus*)
+;;
+
+
+(* NEW DEMODULATE *)
+let demodulate ~dbd ~automation_cache ~params:(univ, params) (proof,goal)=
+ let universe, tables, cache =
+ init_cache_and_tables
+ ~dbd ~use_library:false ~use_context:true
+ automation_cache univ (proof,goal)
+ in
+ let eq_uri =
+ match LibraryObjects.eq_URI () with
+ | Some (uri) -> uri
+ | None -> raise (ProofEngineTypes.Fail (lazy "equality not declared")) in
+ let active, passive, bag = tables in
+ let curi,metasenv,subst,pbo,pty, attrs = proof in
+ let metano,context,ty = CicUtil.lookup_meta goal metasenv in
+ let irl = CicMkImplicit.identity_relocation_list_for_metavariable context in
+ let initgoal = [], metasenv, ty in
+ let equalities = (Saturation.list_of_passive passive) in
+ (* we demodulate using both actives passives *)
+ let env = metasenv,context,CicUniv.empty_ugraph in
+ debug_print (lazy ("PASSIVES:" ^ string_of_int(List.length equalities)));
+ List.iter (fun e -> debug_print (lazy (Equality.string_of_equality ~env e)))
+ equalities;
+ let table =
+ List.fold_left
+ (fun tbl eq -> Indexing.index tbl eq)
+ (snd active) equalities
+ in
+ let changed,(newproof,newmetasenv, newty) =
+ (* Indexing.demodulation_goal bag *)
+ Indexing.demod bag
+ (metasenv,context,CicUniv.oblivion_ugraph) table initgoal
+ in
+ if changed then
+ begin
+ let maxm = CicMkImplicit.new_meta metasenv subst in
+ let opengoal = Equality.Exact (Cic.Meta(maxm,irl)) in
+ let subst_candidates = List.map (fun (i,_,_) -> i) metasenv in
+ let subst_candidates = List.filter (fun x-> x <> goal) subst_candidates in
+ let proofterm, proto_subst =
+ Equality.build_goal_proof (~contextualize:false) bag
+ eq_uri newproof opengoal ty subst_candidates context metasenv
+ in
+ (* XXX understan what to do with proto subst *)
+ let metasenv = (maxm,context,newty)::metasenv in
+ let proofterm, _, metasenv, subst, _ =
+ CicRefine.type_of metasenv subst context proofterm
+ CicUniv.oblivion_ugraph
+ in
+ let extended_status = (curi,metasenv,subst,pbo,pty, attrs),goal in
+ let proof,gl =
+ ProofEngineTypes.apply_tactic
+ (PrimitiveTactics.apply_tac ~term:proofterm) extended_status
+ in
+ proof,maxm::gl
+ end
+ else
+ raise (ProofEngineTypes.Fail (lazy "no progress"))
+;;
+
+let demodulate_tac ~dbd ~params:(_,flags as params) ~automation_cache =
+ ProofEngineTypes.mk_tactic
+ (fun status ->
+ let all = bool flags "all" false in
+ if all then
+ solve_rewrite ~params ~automation_cache status
+ else
+ demodulate ~dbd ~params ~automation_cache status)
+;;
+(***************** applyS *******************)
+
+let apply_smart_aux
+ dbd automation_cache params proof goal newmeta' metasenv' subst
+ context term' ty termty goal_arity
+=
+ let consthead,newmetasenv,arguments,_ =
+ TermUtil.saturate_term newmeta' metasenv' context termty goal_arity in
+ let term'' =
+ match arguments with
+ | [] -> term'
+ | _ -> Cic.Appl (term'::arguments)
+ in
+ let consthead =
+ let rec aux t = function
+ | [] ->
+ let t = CicReduction.normalize ~delta:false context t in
+ (match t, ty with
+ | Cic.Appl (hd1::_), Cic.Appl (hd2::_) when hd1 <> hd2 ->
+ let t = ProofEngineReduction.unfold context t in
+ (match t with
+ | Cic.Appl (hd1'::_) when hd1' = hd2 -> t
+ | _ -> raise (ProofEngineTypes.Fail (lazy "incompatible head")))
+ | _ -> t)
+ | arg :: tl ->
+ match CicReduction.whd context t with
+ | Cic.Prod (_,_,tgt) ->
+ aux (CicSubstitution.subst arg tgt) tl
+ | _ -> assert false
+ in
+ aux termty arguments
+ in
+ let goal_for_paramod =
+ match LibraryObjects.eq_URI () with
+ | Some uri ->
+ Cic.Appl [Cic.MutInd (uri,0,[]); Cic.Implicit (Some `Type); consthead; ty]
+ | None -> raise (ProofEngineTypes.Fail (lazy "No equality defined"))
+ in
+ try
+ let goal_for_paramod, _, newmetasenv, subst, _ =
+ CicRefine.type_of newmetasenv subst context goal_for_paramod
+ CicUniv.oblivion_ugraph
+ in
+ let newmeta = CicMkImplicit.new_meta newmetasenv subst in
+ let metasenv_for_paramod = (newmeta,context,goal_for_paramod)::newmetasenv in
+ let proof'' =
+ let uri,_,_,p,ty, attrs = proof in
+ uri,metasenv_for_paramod,subst,p,ty, attrs
+ in
+ let irl = CicMkImplicit.identity_relocation_list_for_metavariable context in
+(*
+ prerr_endline ("------ prima di rewrite su ------ " ^ string_of_int goal);
+ prerr_endline ("menv:\n"^CicMetaSubst.ppmetasenv [] metasenv_for_paramod);
+ prerr_endline ("subst:\n"^CicMetaSubst.ppsubst
+ ~metasenv:(metasenv_for_paramod)
+ subst);
+*)
+
+ let (proof''',goals) =
+ ProofEngineTypes.apply_tactic
+ (EqualityTactics.rewrite_tac ~direction:`RightToLeft
+ ~pattern:(ProofEngineTypes.conclusion_pattern None)
+ (Cic.Meta(newmeta,irl)) []) (proof'',goal)
+ in
+ let goal = match goals with [g] -> g | _ -> assert false in
+ let proof'''', _ =
+ ProofEngineTypes.apply_tactic
+ (PrimitiveTactics.apply_tac term'')
+ (proof''',goal)
+ in
+
+
+ let (_,m,_,_,_,_ as p) =
+ let pu,metasenv,subst,proof,px,py = proof'''' in
+ let metasenv = CicMetaSubst.apply_subst_metasenv subst metasenv in
+ let proof'''' = pu,metasenv,subst,proof,px,py in
+ let univ, params = params in
+ let use_context = bool params "use_context" true in
+ let universe, (active,passive,bag), cache =
+ init_cache_and_tables ~use_library:false ~use_context
+ automation_cache univ (proof'''',newmeta)
+ in
+ match
+ Saturation.solve_narrowing bag (proof'''',newmeta) active passive
+ 2 (*0 infinity*)
+ with
+ | None, active, passive, bag ->
+ raise (ProofEngineTypes.Fail (lazy ("paramod fails")))
+ | Some(subst',(pu,metasenv,_,proof,px, py),open_goals),active,
+ passive,bag ->
+ assert_subst_are_disjoint subst subst';
+ let subst = subst@subst' in
+ pu,metasenv,subst,proof,px,py
+ in
+
+(*
+ let (_,m,_,_,_,_ as p),_ =
+ solve_rewrite ~params ~automation_cache (proof'''',newmeta)
+ in
+*)
+
+ let open_goals =
+ ProofEngineHelpers.compare_metasenvs ~oldmetasenv:metasenv' ~newmetasenv:m
+ in
+ p, open_goals
+ with
+ CicRefine.RefineFailure msg ->
+ raise (ProofEngineTypes.Fail msg)
+;;
+
+let apply_smart
+ ~dbd ~term ~automation_cache ~params (proof, goal)
+=
+ let module T = CicTypeChecker in
+ let module R = CicReduction in
+ let module C = Cic in
+ let (_,metasenv,subst,_,_, _) = proof in
+ let metano,context,ty = CicUtil.lookup_meta goal metasenv in
+ let newmeta = CicMkImplicit.new_meta metasenv subst in
+ let exp_named_subst_diff,newmeta',newmetasenvfragment,term' =
+ match term with
+ C.Var (uri,exp_named_subst) ->
+ let newmeta',newmetasenvfragment,exp_named_subst',exp_named_subst_diff =
+ PrimitiveTactics.generalize_exp_named_subst_with_fresh_metas context newmeta uri
+ exp_named_subst
+ in
+ exp_named_subst_diff,newmeta',newmetasenvfragment,
+ C.Var (uri,exp_named_subst')
+ | C.Const (uri,exp_named_subst) ->
+ let newmeta',newmetasenvfragment,exp_named_subst',exp_named_subst_diff =
+ PrimitiveTactics.generalize_exp_named_subst_with_fresh_metas context newmeta uri
+ exp_named_subst
+ in
+ exp_named_subst_diff,newmeta',newmetasenvfragment,
+ C.Const (uri,exp_named_subst')
+ | C.MutInd (uri,tyno,exp_named_subst) ->
+ let newmeta',newmetasenvfragment,exp_named_subst',exp_named_subst_diff =
+ PrimitiveTactics.generalize_exp_named_subst_with_fresh_metas context newmeta uri
+ exp_named_subst
+ in
+ exp_named_subst_diff,newmeta',newmetasenvfragment,
+ C.MutInd (uri,tyno,exp_named_subst')
+ | C.MutConstruct (uri,tyno,consno,exp_named_subst) ->
+ let newmeta',newmetasenvfragment,exp_named_subst',exp_named_subst_diff =
+ PrimitiveTactics.generalize_exp_named_subst_with_fresh_metas context newmeta uri
+ exp_named_subst
+ in
+ exp_named_subst_diff,newmeta',newmetasenvfragment,
+ C.MutConstruct (uri,tyno,consno,exp_named_subst')
+ | _ -> [],newmeta,[],term
+ in
+ let metasenv' = metasenv@newmetasenvfragment in
+ let termty,_ =
+ CicTypeChecker.type_of_aux'
+ metasenv' ~subst context term' CicUniv.oblivion_ugraph
+ in
+ let termty = CicSubstitution.subst_vars exp_named_subst_diff termty in
+ let goal_arity =
+ let rec count_prods context ty =
+ match CicReduction.whd ~subst context ty with
+ | Cic.Prod (n,s,t) -> 1 + count_prods (Some (n,Cic.Decl s)::context) t
+ | _ -> 0
+ in
+ count_prods context ty
+ in
+ apply_smart_aux dbd automation_cache params proof goal
+ newmeta' metasenv' subst context term' ty termty goal_arity
+;;
+
+let applyS_tac ~dbd ~term ~params ~automation_cache =
+ ProofEngineTypes.mk_tactic
+ (fun status ->
+ try
+ apply_smart ~dbd ~term ~params ~automation_cache status
+ with
+ | CicUnification.UnificationFailure msg
+ | CicTypeChecker.TypeCheckerFailure msg ->
+ raise (ProofEngineTypes.Fail msg))
+;;
+
+
+(****************** AUTO ********************)
+
+let calculate_timeout flags =
+ if flags.timeout = 0. then
+ (debug_print (lazy "AUTO WITH NO TIMEOUT");
+ {flags with timeout = infinity})
+ else
+ flags
+;;
+let is_equational_case goalty flags =
+ let ensure_equational t =
+ if is_an_equational_goal t then true
+ else false
+ in
+ (flags.use_paramod && is_an_equational_goal goalty) ||
+ (flags.use_only_paramod && ensure_equational goalty)
+;;
+
+type menv = Cic.metasenv
+type subst = Cic.substitution
+type goal = ProofEngineTypes.goal * int * AutoTypes.sort
+let candidate_no = ref 0;;
+type candidate = int * Cic.term Lazy.t
+type cache = AutoCache.cache
+
+type fail =
+ (* the goal (mainly for depth) and key of the goal *)
+ goal * AutoCache.cache_key
+type op =
+ (* goal has to be proved *)
+ | D of goal
+ (* goal has to be cached as a success obtained using candidate as the first
+ * step *)
+ | S of goal * AutoCache.cache_key * candidate * int
+type elem =
+ (* menv, subst, size, operations done (only S), operations to do, failures to cache if any op fails *)
+ menv * subst * int * op list * op list * fail list
+type status =
+ (* list of computations that may lead to the solution: all op list will
+ * end with the same (S(g,_)) *)
+ elem list
+type auto_result =
+ (* menv, subst, alternatives, tables, cache *)
+ | Proved of menv * subst * elem list * AutomationCache.tables * cache
+ | Gaveup of AutomationCache.tables * cache
+
+
+(* the status exported to the external observer *)
+type auto_status =
+ (* context, (goal,candidate) list, and_list, history *)
+ Cic.context * (int * Cic.term * bool * int * (int * Cic.term Lazy.t) list) list *
+ (int * Cic.term * int) list * Cic.term Lazy.t list
+
+let d_prefix l =
+ let rec aux acc = function
+ | (D g)::tl -> aux (acc@[g]) tl
+ | _ -> acc
+ in
+ aux [] l
+;;
+let prop_only l =
+ List.filter (function (_,_,P) -> true | _ -> false) l
+;;
+
+let d_goals l =
+ let rec aux acc = function
+ | (D g)::tl -> aux (acc@[g]) tl
+ | (S _)::tl -> aux acc tl
+ | [] -> acc
+ in
+ aux [] l
+;;
+
+let calculate_goal_ty (goalno,_,_) s m =
+ try
+ let _,cc,goalty = CicUtil.lookup_meta goalno m in
+ (* XXX applicare la subst al contesto? *)
+ Some (cc, CicMetaSubst.apply_subst s goalty)
+ with CicUtil.Meta_not_found i when i = goalno -> None
+;;
+
+let calculate_closed_goal_ty (goalno,_,_) s =
+ try
+ let cc,_,goalty = List.assoc goalno s in
+ (* XXX applicare la subst al contesto? *)
+ Some (cc, CicMetaSubst.apply_subst s goalty)
+ with Not_found ->
+ None
+;;
+
+let pp_status ctx status =
+ if debug then
+ let names = Utils.names_of_context ctx in
+ let pp x =
+ let x =
+ ProofEngineReduction.replace
+ ~equality:(fun a b -> match b with Cic.Meta _ -> true | _ -> false)
+ ~what:[Cic.Rel 1] ~with_what:[Cic.Implicit None] ~where:x
+ in
+ CicPp.pp x names
+ in
+ let string_of_do m s (gi,_,_ as g) d =
+ match calculate_goal_ty g s m with
+ | Some (_,gty) -> Printf.sprintf "D(%d, %s, %d)" gi (pp gty) d
+ | None -> Printf.sprintf "D(%d, _, %d)" gi d
+ in
+ let string_of_s m su k (ci,ct) gi =
+ Printf.sprintf "S(%d, %s, %s, %d)" gi (pp k) (pp (Lazy.force ct)) ci
+ in
+ let string_of_ol m su l =
+ String.concat " | "
+ (List.map
+ (function
+ | D (g,d,s) -> string_of_do m su (g,d,s) d
+ | S ((gi,_,_),k,c,_) -> string_of_s m su k c gi)
+ l)
+ in
+ let string_of_fl m s fl =
+ String.concat " | "
+ (List.map (fun ((i,_,_),ty) ->
+ Printf.sprintf "(%d, %s)" i (pp ty)) fl)
+ in
+ let rec aux = function
+ | [] -> ()
+ | (m,s,_,_,ol,fl)::tl ->
+ Printf.eprintf "< [%s] ;;; [%s]>\n"
+ (string_of_ol m s ol) (string_of_fl m s fl);
+ aux tl
+ in
+ Printf.eprintf "-------------------------- status -------------------\n";
+ aux status;
+ Printf.eprintf "-----------------------------------------------------\n";
+;;
+
+let auto_status = ref [] ;;
+let auto_context = ref [];;
+let in_pause = ref false;;
+let pause b = in_pause := b;;
+let cond = Condition.create ();;
+let mutex = Mutex.create ();;
+let hint = ref None;;
+let prune_hint = ref [];;
+
+let step _ = Condition.signal cond;;
+let give_hint n = hint := Some n;;
+let give_prune_hint hint =
+ prune_hint := hint :: !prune_hint
+;;
+
+let check_pause _ =
+ if !in_pause then
+ begin
+ Mutex.lock mutex;
+ Condition.wait cond mutex;
+ Mutex.unlock mutex
+ end
+;;
+
+let get_auto_status _ =
+ let status = !auto_status in
+ let and_list,elems,last =
+ match status with
+ | [] -> [],[],[]
+ | (m,s,_,don,gl,fail)::tl ->
+ let and_list =
+ HExtlib.filter_map
+ (fun (id,d,_ as g) ->
+ match calculate_goal_ty g s m with
+ | Some (_,x) -> Some (id,x,d) | None -> None)
+ (d_goals gl)
+ in
+ let rows =
+ (* these are the S goalsin the or list *)
+ let orlist =
+ List.map
+ (fun (m,s,_,don,gl,fail) ->
+ HExtlib.filter_map
+ (function S (g,k,c,_) -> Some (g,k,c) | _ -> None)
+ (List.rev don @ gl))
+ status
+ in
+ (* this function eats id from a list l::[id,x] returning x, l *)
+ let eat_tail_if_eq id l =
+ let rec aux (s, l) = function
+ | [] -> s, l
+ | ((id1,_,_),k1,c)::tl when id = id1 ->
+ (match s with
+ | None -> aux (Some c,l) tl
+ | Some _ -> assert false)
+ | ((id1,_,_),k1,c as e)::tl -> aux (s, e::l) tl
+ in
+ let c, l = aux (None, []) l in
+ c, List.rev l
+ in
+ let eat_in_parallel id l =
+ let rec aux (b,eaten, new_l as acc) l =
+ match l with
+ | [] -> acc
+ | l::tl ->
+ match eat_tail_if_eq id l with
+ | None, l -> aux (b@[false], eaten, new_l@[l]) tl
+ | Some t,l -> aux (b@[true],eaten@[t], new_l@[l]) tl
+ in
+ aux ([],[],[]) l
+ in
+ let rec eat_all rows l =
+ match l with
+ | [] -> rows
+ | elem::or_list ->
+ match List.rev elem with
+ | ((to_eat,depth,_),k,_)::next_lunch ->
+ let b, eaten, l = eat_in_parallel to_eat l in
+ let eaten = HExtlib.list_uniq eaten in
+ let eaten = List.rev eaten in
+ let b = true (* List.hd (List.rev b) *) in
+ let rows = rows @ [to_eat,k,b,depth,eaten] in
+ eat_all rows l
+ | [] -> eat_all rows or_list
+ in
+ eat_all [] (List.rev orlist)
+ in
+ let history =
+ HExtlib.filter_map
+ (function (S (_,_,(_,c),_)) -> Some c | _ -> None)
+ gl
+ in
+(* let rows = List.filter (fun (_,l) -> l <> []) rows in *)
+ and_list, rows, history
+ in
+ !auto_context, elems, and_list, last