X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=components%2Ftactics%2Fauto.ml;fp=components%2Ftactics%2Fauto.ml;h=41ea1e5e44386f35ec74959a6784bdfb0a095deb;hp=0000000000000000000000000000000000000000;hb=f61af501fb4608cc4fb062a0864c774e677f0d76;hpb=58ae1809c352e71e7b5530dc41e2bfc834e1aef1 diff --git a/components/tactics/auto.ml b/components/tactics/auto.ml new file mode 100644 index 000000000..41ea1e5e4 --- /dev/null +++ b/components/tactics/auto.ml @@ -0,0 +1,1715 @@ +(* 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