--- /dev/null
+(* Copyright (C) 2002, HELM Team.
+ *
+ * This file is part of HELM, an Hypertextual, Electronic
+ * Library of Mathematics, developed at the Computer Science
+ * Department, University of Bologna, Italy.
+ *
+ * HELM is free software; you can redistribute it and/or
+ * modify it under the terms of the GNU General Public License
+ * as published by the Free Software Foundation; either version 2
+ * of the License, or (at your option) any later version.
+ *
+ * HELM is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with HELM; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place - Suite 330, Boston,
+ * MA 02111-1307, USA.
+ *
+ * For details, see the HELM World-Wide-Web page,
+ * http://cs.unibo.it/helm/.
+ *)
+
+open AutoTypes;;
+open AutoCache;;
+
+let debug = false;;
+let debug_print s =
+ if debug then prerr_endline (Lazy.force s);;
+
+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 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
+;;
+
+let lambda_close ?prefix_name t menv ctx =
+ let t = 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,List.length menv) ctx
+;;
+
+(* functions for retrieving theorems *)
+
+exception FillingFailure of AutoCache.cache * int
+
+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.empty_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 maxm _ _ cache _ _ _ _ = [],cache,maxm ;;
+
+
+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.empty_ugraph
+ in
+ let b, _ =
+ CicReduction.are_convertible ~metasenv context
+ sort (Cic.Sort Cic.Prop) u
+ in
+ if b 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 universe cache t =
+ 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.empty_ugraph
+ in
+ let consts = MetadataConstraints.constants_of ty in
+ let b = MetadataConstraints.UriManagerSet.subset consts signature in
+ if b then b
+ else
+ let ty' = unfold context ty in
+ let consts' = MetadataConstraints.constants_of ty' in
+ MetadataConstraints.UriManagerSet.subset consts' signature
+ 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 universe cache fake_eq in
+ if dont_filter then candidates
+ else
+ let candidates = List.filter not_default_eq_term candidates in
+ List.filter (only signature context metasenv) candidates
+
+let build_equality bag head args proof newmetas maxmeta =
+ 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 e = Equality.mk_equality bag (w, proof, stat, newmetas) in
+ (* to clean the local context of metas *)
+ Equality.fix_metas bag maxmeta e
+ | _ -> assert false
+;;
+
+let partition_unit_equalities context metasenv newmeta bag equations =
+ List.fold_left
+ (fun (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
+ units,(t,ty)::other,maxmeta
+ else
+ match is_unit_equation context metasenv maxmeta ty with
+ | Some (args,metasenv,newmetas,head,newmeta') ->
+ let maxmeta,equality =
+ build_equality bag head args t newmetas newmeta' in
+ equality::units,other,maxmeta
+ | None ->
+ units,(t,ty)::other,maxmeta)
+ ([],[],newmeta) equations
+
+let empty_tables =
+ (Saturation.make_active [],
+ Saturation.make_passive [],
+ Equality.mk_equality_bag)
+
+let init_cache_and_tables
+ ?dbd use_library paramod use_context dont_filter universe (proof, goal)
+=
+ (* the local cache in initially empty *)
+ let cache = AutoCache.cache_empty in
+ let _, metasenv, _subst,_, _, _ = proof in
+ let signature = MetadataQuery.signature_of metasenv goal in
+ let newmeta = CicMkImplicit.new_meta metasenv [] in
+ let _,context,_ = CicUtil.lookup_meta goal metasenv in
+ let ct = if use_context then find_context_theorems context metasenv else [] in
+ debug_print
+ (lazy ("ho trovato nel contesto " ^ (string_of_int (List.length ct))));
+ let lt =
+ match use_library, dbd with
+ | true, Some dbd -> find_library_theorems dbd metasenv goal
+ | _ -> []
+ in
+ debug_print
+ (lazy ("ho trovato nella libreria " ^ (string_of_int (List.length lt))));
+ let cache = cache_add_list cache context (ct@lt) in
+ let equations =
+ retrieve_equations dont_filter signature universe cache context metasenv
+ 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'
+ metasenv context t CicUniv.empty_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 units, other_equalities, newmeta =
+ partition_unit_equalities context metasenv newmeta bag eqs_and_types
+ in
+ (* SIMPLIFICATION STEP
+ let equalities =
+ let env = (metasenv, context, CicUniv.empty_ugraph) in
+ let eq_uri = HExtlib.unopt (LibraryObjects.eq_URI()) in
+ Saturation.simplify_equalities bag eq_uri env units
+ in
+ *)
+ let passive = Saturation.make_passive units in
+ let no = List.length units in
+ let active = Saturation.make_active [] in
+ let active,passive,newmeta =
+ if paramod then active,passive,newmeta
+ else
+ Saturation.pump_actives
+ context bag newmeta active passive (no+1) infinity
+ in
+ (active,passive,bag),cache,newmeta
+
+let fill_hypothesis context metasenv oldnewmeta term tables (universe:Universe.universe) cache auto fast =
+ 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.empty_ugraph
+ in
+ let b, _ =
+ CicReduction.are_convertible ~metasenv context
+ sort (Cic.Sort Cic.Prop) u
+ in
+ if b then Some i else None
+ | _ -> assert false)
+ args
+ in
+ let results,cache,newmeta =
+ if propositional_args = [] then
+ let newmetas = List.filter (fun (i,_,_) -> i >= oldnewmeta) metasenv in
+ [args,metasenv,newmetas,head,newmeta],cache,newmeta
+ 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 newmeta tables universe cache context metasenv propositional_args flags with
+ | [],cache,newmeta -> raise (FillingFailure (cache,newmeta))
+ | substs,cache,newmeta ->
+ List.map
+ (fun subst ->
+ let metasenv =
+ CicMetaSubst.apply_subst_metasenv subst metasenv
+ in
+ let head = CicMetaSubst.apply_subst subst head in
+ let newmetas =
+ List.filter (fun (i,_,_) ->i >= oldnewmeta) metasenv
+ in
+ let args = List.map (CicMetaSubst.apply_subst subst) args in
+ let newm = CicMkImplicit.new_meta metasenv subst in
+ args,metasenv,newmetas,head,max newm newmeta)
+ substs, cache, newmeta
+ in
+ results,cache,newmeta
+
+let build_equalities auto context metasenv tables universe cache newmeta equations =
+ List.fold_left
+ (fun (facts,cache,newmeta) (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,newmeta =
+ fill_hypothesis context metasenv newmeta ty tables universe cache auto true
+ in
+ let (active,passive,bag) = tables in
+ let eqs,bag,newmeta =
+ List.fold_left
+ (fun (acc,bag,newmeta) (args,metasenv,newmetas,head,newmeta') ->
+ let maxmeta,equality =
+ build_equality bag head args t newmetas newmeta'
+ in
+ equality::acc,bag,maxmeta)
+ ([],bag,newmeta) saturated
+ in
+ (eqs@facts, cache, newmeta)
+ with FillingFailure (cache,newmeta) ->
+ (* if filling hypothesis fails we add the equation to
+ the cache *)
+ (facts,cache,newmeta)
+ )
+ ([],cache,newmeta) equations
+
+let close_more tables maxmeta context status auto universe cache =
+ let (active,passive,bag) = tables in
+ let proof, goalno = status in
+ let _, metasenv,_subst,_,_, _ = proof in
+ let signature = MetadataQuery.signature_of metasenv goalno 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.empty_ugraph in
+ (* retrieve_equations could also return flexible terms *)
+ if is_an_equality ty then Some(t,ty) else None)
+ equations in
+ let units, cache, maxm =
+ build_equalities auto context metasenv tables universe cache maxmeta eqs_and_types in
+ debug_print (lazy (">>>>>>> gained from a new context saturation >>>>>>>>>" ^
+ string_of_int maxm));
+ List.iter
+ (fun e -> debug_print (lazy (Equality.string_of_equality e)))
+ units;
+ debug_print (lazy ">>>>>>>>>>>>>>>>>>>>>>");
+ let passive = Saturation.add_to_passive units passive in
+ let no = List.length units in
+ debug_print (lazy ("No = " ^ (string_of_int no)));
+ let active,passive,newmeta =
+ Saturation.pump_actives context bag maxm active passive (no+1) infinity
+ in
+ (active,passive,bag),cache,newmeta
+
+let find_context_equalities
+ maxmeta bag 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
+ let newmeta = max (ProofEngineHelpers.new_meta_of_proof ~proof) maxmeta 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 cache index newmeta = function
+ | [] -> [], newmeta,cache
+ | (Some (_, C.Decl (term)))::tl ->
+ debug_print
+ (lazy
+ (Printf.sprintf "Examining: %d (%s)" index (CicPp.ppterm term)));
+ let do_find 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,newmeta =
+ fill_hypothesis context metasenv newmeta term
+ empty_tables universe cache default_auto false
+ in
+ let eqs,newmeta =
+ List.fold_left
+ (fun (acc,newmeta) (args,metasenv,newmetas,head,newmeta') ->
+ let newmeta, equality =
+ build_equality
+ bag head args (Cic.Rel index) newmetas (max newmeta newmeta')
+ in
+ equality::acc, newmeta + 1)
+ ([],newmeta) saturated
+ in
+ eqs, newmeta, cache
+ with FillingFailure (cache,newmeta) ->
+ [],newmeta,cache)
+ | C.Appl [C.MutInd (uri, _, _); ty; t1; t2]
+ when LibraryObjects.is_eq_URI uri ->
+ let term = S.lift index term in
+ let newmeta, e =
+ build_equality bag term [] (Cic.Rel index) [] newmeta
+ in
+ [e], (newmeta+1),cache
+ | _ -> [], newmeta, cache
+ in
+ let eqs, newmeta, cache = do_find context term in
+ let rest, newmeta,cache = aux cache (index+1) newmeta tl in
+ List.map (fun x -> index,x) eqs @ rest, newmeta, cache
+ | _::tl ->
+ aux cache (index+1) newmeta tl
+ in
+ let il, maxm, cache =
+ aux cache 1 newmeta context
+ in
+ let indexes, equalities = List.split il in
+ indexes, equalities, maxm, 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 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;
+ }
+
+let universe_of_params metasenv context universe tl =
+ if tl = [] then universe else
+ let tys =
+ List.map
+ (fun term ->
+ fst (CicTypeChecker.type_of_aux' metasenv context term
+ CicUniv.oblivion_ugraph))
+ tl
+ in
+ Universe.index_list Universe.empty context (List.combine tl tys)
+;;
+
+
+(***************** applyS *******************)
+
+let new_metasenv_and_unify_and_t
+ dbd flags universe proof goal ?tables newmeta' metasenv'
+ 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 proof',oldmetasenv =
+ let (puri,metasenv,_subst,pbo,pty, attrs) = proof in
+ (puri,newmetasenv,_subst,pbo,pty, attrs),metasenv
+ in
+ let goal_for_paramod =
+ match LibraryObjects.eq_URI () with
+ | Some uri ->
+ Cic.Appl [Cic.MutInd (uri,0,[]); Cic.Sort Cic.Prop; consthead; ty]
+ | None -> raise (ProofEngineTypes.Fail (lazy "No equality defined"))
+ in
+ let newmeta = CicMkImplicit.new_meta newmetasenv (*subst*) [] in
+ let metasenv_for_paramod = (newmeta,context,goal_for_paramod)::newmetasenv in
+ let proof'' =
+ let uri,_,_subst,p,ty, attrs = proof' in
+ uri,metasenv_for_paramod,_subst,p,ty, attrs
+ in
+ let irl = CicMkImplicit.identity_relocation_list_for_metavariable context in
+ 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
+ match
+ let (active, passive,bag), cache, maxmeta =
+ init_cache_and_tables ~dbd flags.use_library true true false universe
+ (proof'''',newmeta)
+ in
+ Saturation.given_clause bag maxmeta (proof'''',newmeta) active passive
+ max_int max_int flags.timeout
+ with
+ | None, _,_,_ ->
+ raise (ProofEngineTypes.Fail (lazy ("FIXME: propaga le tabelle")))
+ | Some (_,proof''''',_), active,passive,_ ->
+ proof''''',
+ ProofEngineHelpers.compare_metasenvs ~oldmetasenv
+ ~newmetasenv:(let _,m,_subst,_,_, _ = proof''''' in m), active, passive
+;;
+
+let rec count_prods context ty =
+ match CicReduction.whd context ty with
+ Cic.Prod (n,s,t) -> 1 + count_prods (Some (n,Cic.Decl s)::context) t
+ | _ -> 0
+
+let apply_smart
+ ~dbd ~term ~subst ~universe ?tables ~params:(univ,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 flags = flags_of_params params ~for_applyS:true () in
+ let universe = universe_of_params metasenv context universe univ 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' context term' CicUniv.empty_ugraph
+ in
+ let termty = CicSubstitution.subst_vars exp_named_subst_diff termty in
+ let goal_arity = count_prods context ty in
+ let proof, gl, active, passive =
+ new_metasenv_and_unify_and_t dbd flags universe proof goal ?tables
+ newmeta' metasenv' context term' ty termty goal_arity
+ in
+ proof, gl, active, passive
+;;
+
+(****************** AUTO ********************)
+
+let mk_irl ctx = CicMkImplicit.identity_relocation_list_for_metavariable ctx;;
+let ugraph = CicUniv.empty_ugraph;;
+let typeof = CicTypeChecker.type_of_aux';;
+let ppterm ctx t =
+ let names = List.map (function None -> None | Some (x,_) -> Some x) ctx in
+ CicPp.pp t names
+;;
+let is_in_prop context subst metasenv ty =
+ let sort,u = typeof ~subst metasenv context ty CicUniv.empty_ugraph in
+ fst (CicReduction.are_convertible context sort (Cic.Sort Cic.Prop) u)
+;;
+
+let assert_proof_is_valid proof metasenv context goalty =
+ if debug then
+ begin
+ let ty,u = typeof metasenv context proof CicUniv.empty_ugraph in
+ let b,_ = CicReduction.are_convertible context ty goalty u in
+ if not b then
+ begin
+ let names =
+ List.map (function None -> None | Some (x,_) -> Some x) context
+ in
+ debug_print (lazy ("PROOF:" ^ CicPp.pp proof names));
+ debug_print (lazy ("PROOFTY:" ^ CicPp.pp ty names));
+ debug_print (lazy ("GOAL:" ^ CicPp.pp goalty names));
+ debug_print (lazy ("MENV:" ^ CicMetaSubst.ppmetasenv [] metasenv));
+ end;
+ assert b
+ end
+ else ()
+;;
+
+let assert_subst_are_disjoint subst subst' =
+ if debug then
+ assert(List.for_all
+ (fun (i,_) -> List.for_all (fun (j,_) -> i<>j) subst')
+ subst)
+ else ()
+;;
+
+let split_goals_in_prop metasenv subst gl =
+ List.partition
+ (fun g ->
+ let _,context,ty = CicUtil.lookup_meta g metasenv in
+ try
+ let sort,u = typeof ~subst metasenv context ty ugraph in
+ let b,_ =
+ CicReduction.are_convertible
+ ~subst ~metasenv context sort (Cic.Sort Cic.Prop) u in
+ b
+ with
+ | CicTypeChecker.AssertFailure s
+ | CicTypeChecker.TypeCheckerFailure s ->
+ debug_print
+ (lazy ("NON TIPA" ^ ppterm context (CicMetaSubst.apply_subst subst ty)));
+ debug_print s;
+ false)
+ (* FIXME... they should type! *)
+ gl
+;;
+
+let split_goals_with_metas metasenv subst gl =
+ List.partition
+ (fun g ->
+ let _,context,ty = CicUtil.lookup_meta g metasenv in
+ let ty = CicMetaSubst.apply_subst subst ty in
+ CicUtil.is_meta_closed ty)
+ gl
+;;
+
+let order_new_goals metasenv subst open_goals ppterm =
+ let prop,rest = split_goals_in_prop metasenv subst open_goals in
+ let closed_prop, open_prop = split_goals_with_metas metasenv subst prop in
+ let open_goals =
+ (List.map (fun x -> x,P) (closed_prop @ open_prop))
+ @
+ (List.map (fun x -> x,T) rest)
+ in
+ let tys =
+ List.map
+ (fun (i,sort) ->
+ let _,_,ty = CicUtil.lookup_meta i metasenv in i,ty,sort) open_goals
+ in
+ debug_print (lazy (" OPEN: "^
+ String.concat "\n"
+ (List.map
+ (function
+ | (i,t,P) -> string_of_int i ^ ":"^ppterm t^ "Prop"
+ | (i,t,T) -> string_of_int i ^ ":"^ppterm t^ "Type")
+ tys)));
+ open_goals
+;;
+
+let is_an_equational_goal = function
+ | Cic.Appl [Cic.MutInd(u,_,_);_;_;_] when LibraryObjects.is_eq_URI u -> true
+ | _ -> false
+;;
+
+(*
+let prop = function (_,depth,P) -> depth < 9 | _ -> false;;
+*)
+
+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
+ (*
+ let msg="Not an equational goal.\nYou cant use the paramodulation flag"in
+ raise (ProofEngineTypes.Fail (lazy msg))
+ *)
+ in
+ (flags.use_paramod && is_an_equational_goal goalty) ||
+ (flags.use_only_paramod && ensure_equational goalty)
+;;
+(*
+let cache_add_success sort cache k v =
+ if sort = P then cache_add_success cache k v else cache_remove_underinspection
+ cache k
+;;
+*)
+
+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
+type cache = AutoCache.cache
+type tables =
+ Saturation.active_table * Saturation.passive_table * Equality.equality_bag
+
+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, maxmeta *)
+ | Proved of menv * subst * elem list * tables * cache * int
+ | Gaveup of tables * cache * int
+
+
+(* 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) list) list *
+ (int * Cic.term * int) list * Cic.term 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 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
+;;
+
+(* Works if there is no dependency over proofs *)
+let is_a_green_cut goalty =
+ CicUtil.is_meta_closed goalty
+;;
+let rec first_s = function
+ | (D _)::tl -> first_s tl
+ | (S (g,k,c,s))::tl -> Some ((g,k,c,s),tl)
+ | [] -> None
+;;
+let list_union l1 l2 =
+ (* TODO ottimizzare compare *)
+ HExtlib.list_uniq (List.sort compare (l1 @ l1))
+;;
+let eat_head todo id fl orlist =
+ let rec aux acc = function
+ | [] -> [], acc
+ | (m, s, _, _, todo1, fl1)::tl as orlist ->
+ let rec aux1 todo1 =
+ match first_s todo1 with
+ | None -> orlist, acc
+ | Some (((gno,_,_),_,_,_), todo11) ->
+ (* TODO confronto tra todo da ottimizzare *)
+ if gno = id && todo11 = todo then
+ aux (list_union fl1 acc) tl
+ else
+ aux1 todo11
+ in
+ aux1 todo1
+ in
+ aux fl orlist
+;;
+let close_proof p ty menv context =
+ let metas =
+ List.map fst (CicUtil.metas_of_term p @ CicUtil.metas_of_term ty)
+ in
+ let menv = List.filter (fun (i,_,_) -> List.exists ((=)i) metas) menv in
+ naif_closure p menv context
+;;
+(* XXX capire bene quando aggiungere alla cache *)
+let add_to_cache_and_del_from_orlist_if_green_cut
+ g s m cache key todo orlist fl ctx size minsize
+=
+ let cache = cache_remove_underinspection cache key in
+ (* prima per fare la irl usavamo il contesto vero e proprio e non quello
+ * canonico! XXX *)
+ match calculate_closed_goal_ty g s with
+ | None -> assert false
+ | Some (canonical_ctx , gty) ->
+ let goalno,depth,sort = g in
+ let irl = mk_irl canonical_ctx in
+ let goal = Cic.Meta(goalno, irl) in
+ let proof = CicMetaSubst.apply_subst s goal in
+ let green_proof, closed_proof =
+ let b = is_a_green_cut proof in
+ if not b then
+ b, (* close_proof proof gty m ctx *) proof
+ else
+ b, proof
+ in
+ debug_print (lazy ("TENTATIVE CACHE: " ^ CicPp.ppterm key));
+ if is_a_green_cut key then
+ (* if the initia goal was closed, we cut alternatives *)
+ let _ = debug_print (lazy ("MANGIO: " ^ string_of_int goalno)) in
+ let orlist, fl = eat_head todo goalno fl orlist in
+ let cache =
+ if size < minsize then
+ (debug_print (lazy ("NO CACHE: 2 (size <= minsize)"));cache)
+ else
+ (* if the proof is closed we cache it *)
+ if green_proof then cache_add_success cache key proof
+ else (* cache_add_success cache key closed_proof *)
+ (debug_print (lazy ("NO CACHE: (no gree proof)"));cache)
+ in
+ cache, orlist, fl, true
+ else
+ let cache =
+ debug_print (lazy ("TENTATIVE CACHE: " ^ CicPp.ppterm gty));
+ if size < minsize then
+ (debug_print (lazy ("NO CACHE: (size <= minsize)")); cache) else
+ (* if the substituted goal and the proof are closed we cache it *)
+ if is_a_green_cut gty then
+ if green_proof then cache_add_success cache gty proof
+ else (* cache_add_success cache gty closed_proof *)
+ (debug_print (lazy ("NO CACHE: (no green proof (gty))"));cache)
+ else (*
+ try
+ let ty, _ =
+ CicTypeChecker.type_of_aux' ~subst:s
+ m ctx closed_proof CicUniv.oblivion_ugraph
+ in
+ if is_a_green_cut ty then
+ cache_add_success cache ty closed_proof
+ else cache
+ with
+ | CicTypeChecker.TypeCheckerFailure _ ->*)
+ (debug_print (lazy ("NO CACHE: (no green gty )"));cache)
+ in
+ cache, orlist, fl, false
+;;
+let close_failures (fl : fail list) (cache : cache) =
+ List.fold_left
+ (fun cache ((gno,depth,_),gty) ->
+ debug_print (lazy ("FAIL: INDUCED: " ^ string_of_int gno));
+ cache_add_failure cache gty depth)
+ cache fl
+;;
+let put_in_subst subst metasenv (goalno,_,_) canonical_ctx t ty =
+ let entry = goalno, (canonical_ctx, t,ty) in
+ assert_subst_are_disjoint subst [entry];
+ let subst = entry :: subst in
+ let metasenv = CicMetaSubst.apply_subst_metasenv subst metasenv in
+ subst, metasenv
+;;
+let mk_fake_proof metasenv subst (goalno,_,_) goalty context =
+ None,metasenv,subst ,Cic.Meta(goalno,mk_irl context),goalty, []
+;;
+let equational_case
+ tables maxm cache depth fake_proof goalno goalty subst context
+ flags
+=
+ let active,passive,bag = tables in
+ let ppterm = ppterm context in
+ let status = (fake_proof,goalno) in
+ if flags.use_only_paramod then
+ begin
+ debug_print (lazy ("PARAMODULATION SU: " ^
+ string_of_int goalno ^ " " ^ ppterm goalty ));
+ let goal_steps, saturation_steps, timeout =
+ max_int,max_int,flags.timeout
+ in
+ match
+ Saturation.given_clause bag maxm status active passive
+ goal_steps saturation_steps timeout
+ with
+ | None, active, passive, maxmeta ->
+ [], (active,passive,bag), cache, maxmeta, flags
+ | Some(subst',(_,metasenv,_subst,proof,_, _),open_goals),active,
+ passive,maxmeta ->
+ assert_subst_are_disjoint subst subst';
+ let subst = subst@subst' in
+ let open_goals =
+ order_new_goals metasenv subst open_goals ppterm
+ in
+ let open_goals =
+ List.map (fun (x,sort) -> x,depth-1,sort) open_goals
+ in
+ incr candidate_no;
+ [(!candidate_no,proof),metasenv,subst,open_goals],
+ (active,passive,bag),
+ cache, maxmeta, flags
+ end
+ else
+ begin
+ debug_print
+ (lazy
+ ("SUBSUMPTION SU: " ^ string_of_int goalno ^ " " ^ ppterm goalty));
+ let res, maxmeta =
+ Saturation.all_subsumed bag maxm status active passive
+ in
+ assert (maxmeta >= maxm);
+ let res' =
+ List.map
+ (fun (subst',(_,metasenv,_subst,proof,_, _),open_goals) ->
+ assert_subst_are_disjoint subst subst';
+ let subst = subst@subst' in
+ let open_goals =
+ order_new_goals metasenv subst open_goals ppterm
+ in
+ let open_goals =
+ List.map (fun (x,sort) -> x,depth-1,sort) open_goals
+ in
+ incr candidate_no;
+ (!candidate_no,proof),metasenv,subst,open_goals)
+ res
+ in
+ res', (active,passive,bag), cache, maxmeta, flags
+ end
+;;
+
+let try_candidate
+ goalty tables maxm subst fake_proof goalno depth context cand
+=
+ let ppterm = ppterm context in
+ try
+ let subst,((_,metasenv,_,_,_,_), open_goals),maxmeta =
+ (PrimitiveTactics.apply_with_subst ~subst ~maxmeta:maxm ~term:cand)
+ (fake_proof,goalno)
+ in
+ debug_print (lazy (" OK: " ^ ppterm cand));
+ let metasenv = CicRefine.pack_coercion_metasenv metasenv in
+ let open_goals = order_new_goals metasenv subst open_goals ppterm in
+ let open_goals = List.map (fun (x,sort) -> x,depth-1,sort) open_goals in
+ incr candidate_no;
+ Some ((!candidate_no,cand),metasenv,subst,open_goals), tables , maxmeta
+ with
+ | ProofEngineTypes.Fail s -> None,tables, maxm
+ | CicUnification.Uncertain s -> None,tables, maxm
+;;
+
+let sort_new_elems =
+ List.sort (fun (_,_,_,l1) (_,_,_,l2) ->
+ List.length (prop_only l1) - List.length (prop_only l2))
+;;
+
+let applicative_case
+ tables maxm depth subst fake_proof goalno goalty metasenv context universe
+ cache
+=
+ let candidates = get_candidates universe cache goalty in
+ let tables, elems, maxm =
+ List.fold_left
+ (fun (tables,elems,maxm) cand ->
+ match
+ try_candidate goalty
+ tables maxm subst fake_proof goalno depth context cand
+ with
+ | None, tables,maxm -> tables,elems, maxm
+ | Some x, tables, maxm -> tables,x::elems, maxm)
+ (tables,[],maxm) candidates
+ in
+ let elems = sort_new_elems elems in
+ elems, tables, cache, maxm
+;;
+
+let equational_and_applicative_case
+ universe flags m s g gty tables cache maxm context
+=
+ let goalno, depth, sort = g in
+ let fake_proof = mk_fake_proof m s g gty context in
+ if is_equational_case gty flags then
+ let elems,tables,cache,maxm1, flags =
+ equational_case tables maxm cache
+ depth fake_proof goalno gty s context flags
+ in
+ let maxm = maxm1 in
+ let more_elems, tables, cache, maxm1 =
+ if flags.use_only_paramod then
+ [],tables, cache, maxm
+ else
+ applicative_case
+ tables maxm depth s fake_proof goalno
+ gty m context universe cache
+ in
+ let maxm = maxm1 in
+ elems@more_elems, tables, cache, maxm, flags
+ else
+ let elems, tables, cache, maxm =
+ applicative_case tables maxm depth s fake_proof goalno
+ gty m context universe cache
+ in
+ elems, tables, cache, maxm, flags
+;;
+let rec condition_for_hint i = function
+ | [] -> false
+ | S (_,_,(j,_),_):: tl -> j <> i (* && condition_for_hint i tl *)
+ | _::tl -> condition_for_hint i tl
+;;
+let remove_s_from_fl (id,_,_) (fl : fail list) =
+ let rec aux = function
+ | [] -> []
+ | ((id1,_,_),_)::tl when id = id1 -> tl
+ | hd::tl -> hd :: aux tl
+ in
+ aux fl
+;;
+
+let prunable_for_size flags s m todo =
+ let rec aux b = function
+ | (S _)::tl -> aux b tl
+ | (D (_,_,T))::tl -> aux b tl
+ | (D g)::tl ->
+ (match calculate_goal_ty g s m with
+ | None -> aux b tl
+ | Some (canonical_ctx, gty) ->
+ let gsize, _ =
+ Utils.weight_of_term
+ ~consider_metas:false ~count_metas_occurrences:true gty in
+ let newb = b || gsize > flags.maxgoalsizefactor in
+ aux newb tl)
+ | [] -> b
+ in
+ aux false todo
+
+(*
+let prunable ty todo =
+ let rec aux b = function
+ | (S(_,k,_,_))::tl -> aux (b || Equality.meta_convertibility k ty) tl
+ | (D (_,_,T))::tl -> aux b tl
+ | D _::_ -> false
+ | [] -> b
+ in
+ aux false todo
+;;
+*)
+
+let prunable menv subst ty todo =
+ let rec aux = function
+ | (S(_,k,_,_))::tl ->
+ (match Equality.meta_convertibility_subst k ty menv with
+ | None -> aux tl
+ | Some variant ->
+ no_progress variant tl (* || aux tl*))
+ | (D (_,_,T))::tl -> aux tl
+ | _ -> false
+ and no_progress variant = function
+ | [] -> (*prerr_endline "++++++++++++++++++++++++ no_progress";*) true
+ | D ((n,_,P) as g)::tl ->
+ (match calculate_goal_ty g subst menv with
+ | None -> no_progress variant tl
+ | Some (_, gty) ->
+ (match calculate_goal_ty g variant menv with
+ | None -> assert false
+ | Some (_, gty') ->
+ if gty = gty' then
+ no_progress variant tl
+ else false))
+ | _::tl -> no_progress variant tl
+ in
+ aux todo
+
+;;
+let condition_for_prune_hint prune (m, s, size, don, todo, fl) =
+ let s =
+ HExtlib.filter_map (function S (_,_,(c,_),_) -> Some c | _ -> None) todo
+ in
+ List.for_all (fun i -> List.for_all (fun j -> i<>j) prune) s
+;;
+let filter_prune_hint l =
+ let prune = !prune_hint in
+ prune_hint := []; (* possible race... *)
+ if prune = [] then l
+ else List.filter (condition_for_prune_hint prune) l
+;;
+let auto_main tables maxm context flags universe cache elems =
+ auto_context := context;
+ let rec aux tables maxm flags cache (elems : status) =
+(* pp_status context elems; *)
+(* DEBUGGING CODE: uncomment these two lines to stop execution at each iteration
+ auto_status := elems;
+ check_pause ();
+*)
+ let elems = filter_prune_hint elems in
+ match elems with
+ | (m, s, size, don, todo, fl)::orlist when !hint <> None ->
+ (match !hint with
+ | Some i when condition_for_hint i todo ->
+ aux tables maxm flags cache orlist
+ | _ ->
+ hint := None;
+ aux tables maxm flags cache elems)
+ | [] ->
+ (* complete failure *)
+ Gaveup (tables, cache, maxm)
+ | (m, s, _, _, [],_)::orlist ->
+ (* complete success *)
+ Proved (m, s, orlist, tables, cache, maxm)
+ | (m, s, size, don, (D (_,_,T))::todo, fl)::orlist
+ when not flags.AutoTypes.do_types ->
+ (* skip since not Prop, don't even check if closed by side-effect *)
+ aux tables maxm flags cache ((m, s, size, don, todo, fl)::orlist)
+ | (m, s, size, don, (S(g, key, c,minsize) as op)::todo, fl)::orlist ->
+ (* partial success, cache g and go on *)
+ let cache, orlist, fl, sibling_pruned =
+ add_to_cache_and_del_from_orlist_if_green_cut
+ g s m cache key todo orlist fl context size minsize
+ in
+ debug_print (lazy (AutoCache.cache_print context cache));
+ let fl = remove_s_from_fl g fl in
+ let don = if sibling_pruned then don else op::don in
+ aux tables maxm flags cache ((m, s, size, don, todo, fl)::orlist)
+ | (m, s, size, don, todo, fl)::orlist
+ when List.length(prop_only (d_goals todo)) > flags.maxwidth ->
+ debug_print (lazy ("FAIL: WIDTH"));
+ (* too many goals in and generated by last th *)
+ let cache = close_failures fl cache in
+ aux tables maxm flags cache orlist
+ | (m, s, size, don, todo, fl)::orlist when size > flags.maxsize ->
+ debug_print
+ (lazy ("FAIL: SIZE: "^string_of_int size ^
+ " > " ^ string_of_int flags.maxsize ));
+ (* we already have a too large proof term *)
+ let cache = close_failures fl cache in
+ aux tables maxm flags cache orlist
+ | _ when Unix.gettimeofday () > flags.timeout ->
+ (* timeout *)
+ debug_print (lazy ("FAIL: TIMEOUT"));
+ Gaveup (tables, cache, maxm)
+ | (m, s, size, don, (D (gno,depth,_ as g))::todo, fl)::orlist as status ->
+ (* attack g *)
+ match calculate_goal_ty g s m with
+ | None ->
+ (* closed by side effect *)
+ debug_print (lazy ("SUCCESS: SIDE EFFECT: " ^ string_of_int gno));
+ aux tables maxm flags cache ((m,s,size,don,todo, fl)::orlist)
+ | Some (canonical_ctx, gty) ->
+ let gsize, _ =
+ Utils.weight_of_term ~consider_metas:false ~count_metas_occurrences:true gty
+ in
+ if gsize > flags.maxgoalsizefactor then
+ (debug_print (lazy ("FAIL: SIZE: goal: "^string_of_int gsize));
+ aux tables maxm flags cache orlist)
+ else if prunable_for_size flags s m todo then
+ (debug_print (lazy ("POTO at depth: "^(string_of_int depth)));
+ aux tables maxm flags cache orlist)
+ else
+ (* still to be proved *)
+ (debug_print (lazy ("EXAMINE: "^CicPp.ppterm gty));
+ match cache_examine cache gty with
+ | Failed_in d when d >= depth ->
+ (* fail depth *)
+ debug_print (lazy ("FAIL: DEPTH (cache): "^string_of_int gno));
+ let cache = close_failures fl cache in
+ aux tables maxm flags cache orlist
+ | UnderInspection ->
+ (* fail loop *)
+ debug_print (lazy ("FAIL: LOOP: " ^ string_of_int gno));
+ let cache = close_failures fl cache in
+ aux tables maxm flags cache orlist
+ | Succeded t ->
+ debug_print (lazy ("SUCCESS: CACHE HIT: " ^ string_of_int gno));
+ let s, m = put_in_subst s m g canonical_ctx t gty in
+ aux tables maxm flags cache ((m, s, size, don,todo, fl)::orlist)
+ | Notfound
+ | Failed_in _ when depth > 0 ->
+ ( (* more depth or is the first time we see the goal *)
+ if prunable m s gty todo then
+ (debug_print (lazy(
+ "FAIL: LOOP: one father is equal"));
+ aux tables maxm flags cache orlist)
+ else
+ let cache = cache_add_underinspection cache gty depth in
+ auto_status := status;
+ check_pause ();
+ debug_print
+ (lazy ("INSPECTING: " ^
+ string_of_int gno ^ "("^ string_of_int size ^ "): "^
+ CicPp.ppterm gty));
+ (* elems are possible computations for proving gty *)
+ let elems, tables, cache, maxm, flags =
+ equational_and_applicative_case
+ universe flags m s g gty tables cache maxm context
+ in
+ if elems = [] then
+ (* this goal has failed *)
+ let cache = close_failures ((g,gty)::fl) cache in
+ aux tables maxm flags cache orlist
+ else
+ (* elems = (cand,m,s,gl) *)
+ let size_gl l = List.length
+ (List.filter (function (_,_,P) -> true | _ -> false) l)
+ in
+ let elems =
+ let inj_gl gl = List.map (fun g -> D g) gl in
+ let rec map = function
+ | [] -> assert false
+ | (cand,m,s,gl)::[] ->
+ (* in the last one we add the failure *)
+ let todo =
+ inj_gl gl @ (S(g,gty,cand,size+1))::todo
+ in
+ (* we are the last in OR, we fail on g and
+ * also on all failures implied by g *)
+ (m,s, size + size_gl gl, don, todo, (g,gty)::fl)
+ :: orlist
+ | (cand,m,s,gl)::tl ->
+ (* we add the S step after gl and before todo *)
+ let todo =
+ inj_gl gl @ (S(g,gty,cand,size+1))::todo
+ in
+ (* since we are not the last in OR, we do not
+ * imply failures *)
+ (m,s, size + size_gl gl, don, todo, []) :: map tl
+ in
+ map elems
+ in
+ aux tables maxm flags cache elems)
+ | _ ->
+ (* no more depth *)
+ debug_print (lazy ("FAIL: DEPTH: " ^ string_of_int gno));
+ let cache = close_failures fl cache in
+ aux tables maxm flags cache orlist)
+ in
+ (aux tables maxm flags cache elems : auto_result)
+;;
+
+
+let
+ auto_all_solutions maxm tables universe cache context metasenv gl flags
+=
+ let goals = order_new_goals metasenv [] gl CicPp.ppterm in
+ let goals =
+ List.map
+ (fun (x,s) -> D (x,flags.maxdepth,s)) goals
+ in
+ let elems = [metasenv,[],1,[],goals,[]] in
+ let rec aux tables maxm solutions cache elems flags =
+ match auto_main tables maxm context flags universe cache elems with
+ | Gaveup (tables,cache,maxm) ->
+ solutions,cache,maxm
+ | Proved (metasenv,subst,others,tables,cache,maxm) ->
+ if Unix.gettimeofday () > flags.timeout then
+ ((subst,metasenv)::solutions), cache, maxm
+ else
+ aux tables maxm ((subst,metasenv)::solutions) cache others flags
+ in
+ let rc = aux tables maxm [] cache elems flags in
+ match rc with
+ | [],cache,maxm -> [],cache,maxm
+ | solutions,cache,maxm ->
+ let solutions =
+ HExtlib.filter_map
+ (fun (subst,newmetasenv) ->
+ let opened =
+ ProofEngineHelpers.compare_metasenvs ~oldmetasenv:metasenv ~newmetasenv
+ in
+ if opened = [] then Some subst else None)
+ solutions
+ in
+ solutions,cache,maxm
+;;
+
+(* }}} ****************** AUTO ***************)
+
+let auto flags metasenv tables universe cache context metasenv gl =
+ let initial_time = Unix.gettimeofday() in
+ let goals = order_new_goals metasenv [] gl CicPp.ppterm in
+ let goals = List.map (fun (x,s) -> D(x,flags.maxdepth,s)) goals in
+ let elems = [metasenv,[],1,[],goals,[]] in
+ match auto_main tables 0 context flags universe cache elems with
+ | Proved (metasenv,subst,_, tables,cache,_) ->
+ debug_print(lazy
+ ("TIME:"^string_of_float(Unix.gettimeofday()-.initial_time)));
+ Some (subst,metasenv), cache
+ | Gaveup (tables,cache,maxm) ->
+ debug_print(lazy
+ ("TIME:"^string_of_float(Unix.gettimeofday()-.initial_time)));
+ None,cache
+;;
+
+let applyS_tac ~dbd ~term ~params ~universe =
+ ProofEngineTypes.mk_tactic
+ (fun status ->
+ try
+ let proof, gl,_,_ =
+ apply_smart ~dbd ~term ~subst:[] ~params ~universe status
+ in
+ proof, gl
+ with
+ | CicUnification.UnificationFailure msg
+ | CicTypeChecker.TypeCheckerFailure msg ->
+ raise (ProofEngineTypes.Fail msg))
+
+let auto_tac ~(dbd:HSql.dbd) ~params:(univ,params) ~universe (proof, goal) =
+ let _,metasenv,_subst,_,_, _ = proof in
+ let _,context,goalty = CicUtil.lookup_meta goal metasenv in
+ let universe = universe_of_params metasenv context universe univ in
+ let flags = flags_of_params params () in
+ let use_library = flags.use_library in
+ let tables,cache,newmeta =
+ init_cache_and_tables ~dbd use_library flags.use_only_paramod true
+ false universe (proof, goal) in
+ let tables,cache,newmeta =
+ if flags.close_more then
+ close_more
+ tables newmeta context (proof, goal)
+ auto_all_solutions universe cache
+ else tables,cache,newmeta in
+ let initial_time = Unix.gettimeofday() in
+ let (_,oldmetasenv,_subst,_,_, _) = proof in
+ hint := None;
+ let elem =
+ metasenv,[],1,[],[D (goal,flags.maxdepth,P)],[]
+ in
+ match auto_main tables newmeta context flags universe cache [elem] with
+ | Proved (metasenv,subst,_, tables,cache,_) ->
+ (*prerr_endline
+ ("TIME:"^string_of_float(Unix.gettimeofday()-.initial_time));*)
+ let proof,metasenv =
+ ProofEngineHelpers.subst_meta_and_metasenv_in_proof
+ proof goal subst metasenv
+ in
+ let opened =
+ ProofEngineHelpers.compare_metasenvs ~oldmetasenv
+ ~newmetasenv:metasenv
+ in
+ proof,opened
+ | Gaveup (tables,cache,maxm) ->
+ debug_print
+ (lazy ("TIME:"^
+ string_of_float(Unix.gettimeofday()-.initial_time)));
+ raise (ProofEngineTypes.Fail (lazy "Auto gave up"))
+;;
+
+let auto_tac ~dbd ~params ~universe =
+ ProofEngineTypes.mk_tactic (auto_tac ~params ~dbd ~universe);;
+
+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_tac ~universe ~params:(univ,params) (proof,goal as status)=
+ let _,metasenv,_subst,_,_,_ = proof in
+ let _,context,ty = CicUtil.lookup_meta goal metasenv in
+ let steps = int_of_string (string params "steps" "1") in
+ let universe = universe_of_params metasenv context universe univ in
+ let eq_uri = eq_of_goal ty in
+ let (active,passive,bag), cache, maxm =
+ (* we take the whole universe (no signature filtering) *)
+ init_cache_and_tables false true false true universe (proof,goal)
+ in
+ let initgoal = [], metasenv, ty in
+ let table =
+ let equalities = (Saturation.list_of_passive passive) in
+ (* we demodulate using both actives passives *)
+ List.fold_left (fun tbl eq -> Indexing.index tbl eq) (snd active) equalities
+ in
+ let env = metasenv,context,CicUniv.empty_ugraph in
+ match Indexing.solve_demodulating bag env table initgoal steps with
+ | Some (proof, metasenv, newty) ->
+ let refl =
+ match newty with
+ | Cic.Appl[Cic.MutInd _;eq_ty;left;_] ->
+ Equality.Exact (Equality.refl_proof eq_uri eq_ty left)
+ | _ -> assert false
+ in
+ let proofterm,_ =
+ Equality.build_goal_proof
+ bag eq_uri proof refl newty [] context metasenv
+ in
+ ProofEngineTypes.apply_tactic
+ (PrimitiveTactics.apply_tac ~term:proofterm) status
+ | None ->
+ raise
+ (ProofEngineTypes.Fail (lazy
+ ("Unable to solve with " ^ string_of_int steps ^ " demodulations")))
+;;
+let solve_rewrite_tac ~params ~universe () =
+ ProofEngineTypes.mk_tactic (solve_rewrite_tac ~universe ~params)
+;;
+
+(* DEMODULATE *)
+let demodulate_tac ~dbd ~universe ~params:(univ, params) (proof,goal)=
+ let curi,metasenv,_subst,pbo,pty, attrs = proof in
+ let metano,context,ty = CicUtil.lookup_meta goal metasenv in
+ let universe = universe_of_params metasenv context universe univ in
+ let irl = CicMkImplicit.identity_relocation_list_for_metavariable context in
+ let initgoal = [], metasenv, ty in
+ let eq_uri = eq_of_goal ty in
+ let (active,passive,bag), cache, maxm =
+ init_cache_and_tables
+ ~dbd false true true false universe (proof,goal)
+ in
+ let equalities = (Saturation.list_of_passive passive) in
+ (* we demodulate using both actives passives *)
+ 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
+ (metasenv,context,CicUniv.empty_ugraph) table initgoal
+ in
+ if changed then
+ begin
+ let opengoal = Equality.Exact (Cic.Meta(maxm,irl)) in
+ let proofterm,_ =
+ Equality.build_goal_proof bag
+ eq_uri newproof opengoal ty [] context metasenv
+ in
+ let extended_metasenv = (maxm,context,newty)::metasenv in
+ let extended_status =
+ (curi,extended_metasenv,_subst,pbo,pty, attrs),goal in
+ let (status,newgoals) =
+ ProofEngineTypes.apply_tactic
+ (PrimitiveTactics.apply_tac ~term:proofterm)
+ extended_status in
+ (status,maxm::newgoals)
+ 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*)
+;;
+
+let demodulate_tac ~dbd ~params ~universe =
+ ProofEngineTypes.mk_tactic (demodulate_tac ~dbd ~params ~universe);;
+
+let pp_proofterm = Equality.pp_proofterm;;
+
+let revision = "$Revision$";;
+let size_and_depth context metasenv t = 100, 100
projects / helm.git / blobdiff