X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fcomponents%2Ftactics%2Fauto.ml;h=4cd6bf62ff477db6033aafcd9eeb9e82871fbbe8;hb=57e3de08d963ff08d671c639c0e9990368b86f20;hp=2db8cc0014ec1d468b60df2872caff898fba9c57;hpb=2eaee49a7ff3ed74598a0db84ce4dbc5bca92380;p=helm.git diff --git a/helm/software/components/tactics/auto.ml b/helm/software/components/tactics/auto.ml index 2db8cc001..4cd6bf62f 100644 --- a/helm/software/components/tactics/auto.ml +++ b/helm/software/components/tactics/auto.ml @@ -26,65 +26,460 @@ open AutoTypes;; open AutoCache;; -let debug_print s = () (* prerr_endline s;; *) +let debug = false;; +let debug_print s = + if debug then prerr_endline (Lazy.force s);; -(* {{{ *********** local given_clause wrapper ***********) +let elems = ref [] ;; -let given_clause dbd ?tables maxm ?auto cache subst flags smart_flag status = - let active,passive,bag,cache,maxmeta,goal_steps,saturation_steps,timeout = - match tables with - | None -> - (* first time, do a huge saturation *) - let bag, equalities, cache, maxmeta = - Saturation.find_equalities dbd status ?auto smart_flag cache - in - let passive = Saturation.make_passive equalities in - let active = Saturation.make_active [] in - let goal_steps, saturation_steps, timeout = - if flags.use_only_paramod then max_int,max_int,flags.timeout - else 82, 82, infinity - in - let maxm = max maxm maxmeta in - active,passive,bag,cache,maxm,goal_steps,saturation_steps,timeout - | Some (active,passive,bag,oldcache) -> - (* saturate a bit more if cache cahnged *) - let bag, equalities, cache, maxm = - if cache_size oldcache <> cache_size cache then - Saturation.saturate_more - bag active maxm status smart_flag ?auto cache - else - bag, [], cache, maxm - in - let minsteps = List.length equalities in - let passive = Saturation.add_to_passive equalities passive in - let goal_steps, saturation_steps, timeout = - if flags.use_only_paramod then max_int,max_int,flags.timeout - else max 80 minsteps, minsteps, infinity - in - active,passive,bag,cache,maxm,goal_steps,saturation_steps,timeout +(* 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 -> function + | None -> CicSubstitution.subst (Cic.Implicit None) t (* delift *) + | Some (name, Cic.Decl ty) -> Cic.Lambda (name, ty, t) + | Some (name, Cic.Def (bo, _)) -> Cic.LetIn (name, bo, t)) + t 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 (_,Some t)) -> + (Cic.Rel i, CicSubstitution.lift i t)::res,i+1 + | Some (_,Cic.Def (_,None)) -> + let t = Cic.Rel i in + let ty,_ = + CicTypeChecker.type_of_aux' + metasenv context t CicUniv.empty_ugraph + in + (t,ty)::res,i+1 + | _ -> 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 res,actives,passives,maxmeta = - Saturation.given_clause bag maxmeta status active passive - goal_steps saturation_steps timeout + 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 - res,actives,passives,bag,cache,maxmeta + 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 t = + try + let ty,_ = CicTypeChecker.type_of_aux' [] 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 + try + let ty' = unfold context ty in + let consts' = MetadataConstraints.constants_of ty' in + MetadataConstraints.UriManagerSet.subset consts' signature + with _-> false + with _ -> false +;; + +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 signature universe cache context= + 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 + (* defaults eq uris are built-in in auto *) + let candidates = List.filter not_default_eq_term candidates in + let candidates = List.filter (only signature context) candidates in + List.iter (fun t -> debug_print (lazy (CicPp.ppterm t))) candidates; + 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) -> + 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 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 = find_context_theorems context metasenv in + debug_print + (lazy ("ho trovato nel contesto " ^ (string_of_int (List.length ct)))); + let lt = + if use_library then + find_library_theorems dbd metasenv goal + else [] 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 signature universe cache context in + debug_print + (lazy ("ho trovato equazioni n. "^(string_of_int (List.length equations)))); + let eqs_and_types = + HExtlib.filter_map + (fun t -> + let ty,_ = + CicTypeChecker.type_of_aux' 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 _ -> None) (* catturare l'eccezione giusta di unfold *) + 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 + (* let env = (metasenv, context, CicUniv.empty_ugraph) in + let equalities = + let eq_uri = + match LibraryObjects.eq_URI() with + | None ->assert false + | Some eq_uri -> 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 signature universe cache context 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 +;; -(* {{{ **************** applyS *******************) +(***************** applyS *******************) let new_metasenv_and_unify_and_t - dbd proof goal ?tables newmeta' metasenv' context term' ty termty goal_arity + dbd flags universe proof goal ?tables newmeta' metasenv' + context term' ty termty goal_arity = let (consthead,newmetasenv,arguments,_) = - ProofEngineHelpers.saturate_term newmeta' metasenv' context termty goal_arity in + 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,pbo,pty) = proof in - (puri,newmetasenv,pbo,pty),metasenv + 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 @@ -94,32 +489,38 @@ let new_metasenv_and_unify_and_t in let newmeta = CicMkImplicit.new_meta newmetasenv (*subst*) [] in let metasenv_for_paramod = (newmeta,context,goal_for_paramod)::newmetasenv in - let proof'' = let uri,_,p,ty = proof' in uri,metasenv_for_paramod,p,ty 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))) + (Cic.Meta(newmeta,irl)) []) (proof'',goal) in let goal = match goals with [g] -> g | _ -> assert false in - let subst, (proof'''', _), _ = - PrimitiveTactics.apply_with_subst ~term:term'' ~subst:[] (proof''',goal) + let proof'''', _ = + ProofEngineTypes.apply_tactic + (PrimitiveTactics.apply_tac term'') + (proof''',goal) in match - let cache, flags = cache_empty, default_flags() in - let flags = - {flags with use_only_paramod=true;timeout=Unix.gettimeofday() +. 30.0} + let (active, passive,bag), cache, maxmeta = + init_cache_and_tables dbd flags.use_library true universe + (proof'''',newmeta) in - given_clause dbd ?tables 0 cache [] flags true (proof'''',newmeta) + Saturation.given_clause bag maxmeta (proof'''',newmeta) active passive + max_int max_int flags.timeout with - | None, active, passive, bag,_,_ -> + | None, _,_,_ -> raise (ProofEngineTypes.Fail (lazy ("FIXME: propaga le tabelle"))) - | Some (_,proof''''',_), active, passive,bag,_,_ -> - subst,proof''''', + | Some (_,proof''''',_), active,passive,_ -> + proof''''', ProofEngineHelpers.compare_metasenvs ~oldmetasenv - ~newmetasenv:(let _,m,_,_ = proof''''' in m), active, passive + ~newmetasenv:(let _,m,_subst,_,_, _ = proof''''' in m), active, passive ;; let rec count_prods context ty = @@ -127,11 +528,11 @@ let rec count_prods context ty = Cic.Prod (n,s,t) -> 1 + count_prods (Some (n,Cic.Decl s)::context) t | _ -> 0 -let apply_smart ~dbd ~term ~subst ?tables (proof, goal) = +let apply_smart ~dbd ~term ~subst ~universe ?tables flags (proof, goal) = let module T = CicTypeChecker in let module R = CicReduction in let module C = Cic in - let (_,metasenv,_,_) = proof in + let (_,metasenv,_subst,_,_, _) = proof in let metano,context,ty = CicUtil.lookup_meta goal metasenv in let newmeta = CicMkImplicit.new_meta metasenv subst in let exp_named_subst_diff,newmeta',newmetasenvfragment,term' = @@ -172,16 +573,14 @@ let apply_smart ~dbd ~term ~subst ?tables (proof, goal) = in let termty = CicSubstitution.subst_vars exp_named_subst_diff termty in let goal_arity = count_prods context ty in - let subst, proof, gl, active, passive = - new_metasenv_and_unify_and_t dbd proof goal ?tables + 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 - subst, proof, gl, active, passive + proof, gl, active, passive ;; -(* }}} **************** applyS **************) - -(* {{{ ***************** AUTO ********************) +(****************** AUTO ********************) let mk_irl ctx = CicMkImplicit.identity_relocation_list_for_metavariable ctx;; let ugraph = CicUniv.empty_ugraph;; @@ -192,30 +591,35 @@ let ppterm ctx t = ;; 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 (Cic.Sort Cic.Prop) sort u) + fst (CicReduction.are_convertible context sort (Cic.Sort Cic.Prop) u) ;; + let assert_proof_is_valid proof metasenv context goalty = - 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 + if debug then begin - let names = - List.map (function None -> None | Some (x,_) -> Some x) context - in - prerr_endline ("PROOF:" ^ CicPp.pp proof names); - prerr_endline ("PROOFTY:" ^ CicPp.pp ty names); - prerr_endline ("GOAL:" ^ CicPp.pp goalty names); - prerr_endline ("METASENV:" ^ CicMetaSubst.ppmetasenv [] metasenv); - end; - assert b + 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' = - assert(List.for_all - (fun (i,_) -> List.for_all (fun (j,_) -> i<>j) subst') - subst) -;; -let sort_new_elems = - List.sort (fun (_,_,l1) (_,_,l2) -> List.length l1 - List.length l2) + 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 = @@ -224,12 +628,16 @@ let split_goals_in_prop metasenv subst gl = let _,context,ty = CicUtil.lookup_meta g metasenv in try let sort,u = typeof ~subst metasenv context ty ugraph in - fst (CicReduction.are_convertible context (Cic.Sort Cic.Prop) sort u) + 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 (ppterm context (CicMetaSubst.apply_subst subst ty)); - debug_print (Lazy.force s); + debug_print + (lazy ("NON TIPA" ^ ppterm context (CicMetaSubst.apply_subst subst ty))); + debug_print s; false) (* FIXME... they should type! *) gl @@ -246,7 +654,7 @@ let split_goals_with_metas metasenv subst gl = let order_new_goals metasenv subst open_goals ppterm = let prop,rest = split_goals_in_prop metasenv subst open_goals in - let open_prop,closed_prop = split_goals_with_metas metasenv subst prop 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)) @ @@ -254,12 +662,16 @@ let order_new_goals metasenv subst open_goals ppterm = in let tys = List.map - (fun (i,_) -> - let _,_,ty = CicUtil.lookup_meta i metasenv in i,ty) open_goals + (fun (i,sort) -> + let _,_,ty = CicUtil.lookup_meta i metasenv in i,ty,sort) open_goals in - debug_print (" OPEN: "^ - String.concat " " - (List.map (fun (i,t) -> string_of_int i ^":"^ppterm t) tys)); + 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 ;; @@ -268,276 +680,1095 @@ let is_an_equational_goal = function | _ -> 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 + assert (sort = P); + 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 - dbd tables maxm ?auto cache depth fake_proof goalno goalty subst context + tables maxm cache depth fake_proof goalno goalty subst context flags = + let active,passive,bag = tables in let ppterm = ppterm context in - prerr_endline ("PARAMOD SU: " ^ string_of_int goalno ^ " " ^ ppterm goalty ); - prerr_endline ""; - prerr_endline (cache_print context cache); - prerr_endline ""; - match - given_clause dbd ?tables maxm ?auto cache subst flags false (fake_proof,goalno) - with - | None, active,passive, bag, cache, maxmeta -> - let tables = Some (active,passive,bag,cache) in - None, tables, cache, maxmeta - | Some(subst',(_,metasenv,proof,_),open_goals),active,passive,bag,cache,maxmeta -> - let tables = Some (active,passive,bag,cache) in - 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 - Some [metasenv,subst,open_goals], tables, cache, maxmeta + 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 dbd tables maxm subst fake_proof goalno depth context cand + 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 - ~maxmeta:maxm ~term:cand ~subst (fake_proof,goalno) + let subst,((_,metasenv,_,_,_,_), open_goals),maxmeta = + (PrimitiveTactics.apply_with_subst ~subst ~maxmeta:maxm ~term:cand) + (fake_proof,goalno) in - debug_print (" OK: " ^ ppterm cand); - assert (maxmeta >= maxm); - (*FIXME:sicuro che posso @?*) - assert_subst_are_disjoint subst subst'; - let subst = subst@subst' 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 - Some (metasenv,subst,open_goals), tables , maxmeta - with ProofEngineTypes.Fail s -> - (*debug_print(" KO: "^Lazy.force s);*)None,tables, maxm + 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 l1 - List.length l2) +(* List.sort (fun (_,_,_,l2) (_,_,_,l1) -> List.length l1 - List.length l2) *) ;; let applicative_case - dbd tables maxm depth subst fake_proof goalno goalty metasenv context cache + tables maxm depth subst fake_proof goalno goalty metasenv context universe + cache = - let candidates = get_candidates cache goalty in + let candidates = get_candidates universe cache goalty in let tables, elems, maxm = List.fold_left (fun (tables,elems,maxm) cand -> match try_candidate goalty - dbd tables maxm subst fake_proof goalno depth context cand + 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 + elems, tables, cache, maxm ;; -(* Works if there is no dependency over proofs *) -let is_a_green_cut goalty = - CicUtil.is_meta_closed goalty +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 prop = function (_,_,P) -> true | _ -> false;; -let calculate_timeout flags = - if flags.timeout = 0. then - (prerr_endline "AUTO WITH NO TIMEOUT";{flags with timeout = infinity}) - else - 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 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)) - *) +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 - (flags.use_paramod && is_an_equational_goal goalty) || - (flags.use_only_paramod && ensure_equational goalty) + 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 cache_add_success sort cache k v = - if sort = P then cache_add_success cache k v else cache -;; - -let rec auto_main dbd tables maxm context flags elems cache = - let callback_for_paramod maxm flags proof commonctx cache l = - let flags = {flags with use_paramod = false;dont_cache_failures=true} in - let _,metasenv,_,_ = proof in - let oldmetasenv = metasenv in - match - auto_all_solutions - dbd tables maxm cache commonctx metasenv l flags - with - | [],cache,maxm -> [],cache,maxm - | solutions,cache,maxm -> - let solutions = - HExtlib.filter_map - (fun (subst,newmetasenv) -> - let opened = - ProofEngineHelpers.compare_metasenvs ~oldmetasenv ~newmetasenv - in - if opened = [] then Some subst else None) - solutions - in - solutions,cache,maxm +*) + +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 - let flags = calculate_timeout flags in - let ppterm = ppterm context in - let irl = mk_irl context in - let rec aux tables maxm cache = function (* elems in OR *) - | [] -> Fail "no more steps can be done", tables, cache, maxm - (*COMPLETE FAILURE*) - | (metasenv,subst,[])::tl -> - Success (metasenv,subst,tl), tables, cache,maxm (* solution::cont *) - | (metasenv,subst,goals)::tl when - List.length (List.filter prop goals) > flags.maxwidth -> - debug_print (" FAILURE(width): " ^ string_of_int (List.length goals)); - aux tables maxm cache tl (* FAILURE (width) *) - | (metasenv,subst,((goalno,depth,sort) as elem)::gl)::tl -> - if Unix.gettimeofday() > flags.timeout then - Fail "timeout",tables,cache,maxm - else - try - let _,cc,goalty = CicUtil.lookup_meta goalno metasenv in - debug_print ("INSPECTING " ^ string_of_int goalno^ ":"^ppterm goalty); - if sort = T && tl <> [] then (* FIXME!!!! *) - (debug_print (" FAILURE(not in prop)"); - aux tables maxm cache tl (* FAILURE (not in prop) *)) - else - match aux_single tables maxm cache metasenv subst elem goalty cc with - | Fail s, tables, cache, maxm' -> - assert(maxm' >= maxm);let maxm = maxm' in - debug_print - (" FAIL "^s^": "^string_of_int goalno^":"^ppterm goalty); - let cache = - if flags.dont_cache_failures then - cache_remove_underinspection cache goalty - else cache_add_failure cache goalty depth - in - aux tables maxm cache tl - | Success (metasenv,subst,others), tables, cache, maxm' -> - assert(maxm' >= maxm);let maxm = maxm' in - (* others are alternatives in OR *) - try - let goal = Cic.Meta(goalno,irl) in - let proof = CicMetaSubst.apply_subst subst goal in - debug_print ("DONE: " ^ ppterm goalty^" with: "^ppterm proof); - if is_a_green_cut goalty then - (assert_proof_is_valid proof metasenv context goalty; - let cache = cache_add_success sort cache goalty proof in - aux tables maxm cache ((metasenv,subst,gl)::tl)) - else - (let goalty = CicMetaSubst.apply_subst subst goalty in - assert_proof_is_valid proof metasenv context goalty; - let cache = - if is_a_green_cut goalty then - cache_add_success sort cache goalty proof - else - cache - in - let others = - List.map - (fun (metasenv,subst,goals) -> (metasenv,subst,goals@gl)) - others - in - aux tables maxm cache ((metasenv,subst,gl)::others@tl)) - with CicUtil.Meta_not_found i when i = goalno -> - assert false - with CicUtil.Meta_not_found i when i = goalno -> - (* goalno was closed by sideeffect *) - debug_print ("Goal "^string_of_int goalno^" closed by sideeffect"); - aux tables maxm cache ((metasenv,subst,gl)::tl) - and aux_single tables maxm cache metasenv subst (goalno, depth, _) goalty cc = - let goalty = CicMetaSubst.apply_subst subst goalty in -(* else if not (is_in_prop context subst metasenv goalty) then Fail,cache *) - (* FAILURE (euristic cut) *) - match cache_examine cache goalty with - | Failed_in d when d >= depth -> - Fail ("depth " ^ string_of_int d ^ ">=" ^ string_of_int depth), - tables,cache,maxm(*FAILURE(depth)*) - | Succeded t -> - assert(List.for_all (fun (i,_) -> i <> goalno) subst); - let entry = goalno, (cc, t,goalty) in - assert_subst_are_disjoint subst [entry]; - let subst = entry :: subst in - let metasenv = CicMetaSubst.apply_subst_metasenv subst metasenv in - debug_print (" CACHE HIT!"); - Success (metasenv, subst, []), tables, cache, maxm - | UnderInspection -> Fail "looping",tables,cache, maxm - | Notfound - | Failed_in _ when depth > 0 -> (* we have more depth now *) - let cache = cache_add_underinspection cache goalty depth in - let fake_proof = None,metasenv,Cic.Meta(goalno,irl),goalty in - let elems, tables, cache, maxm = - if is_equational_case goalty flags then - match - equational_case dbd tables maxm - ~auto:callback_for_paramod cache - depth fake_proof goalno goalty subst context flags - with - | Some elems, tables, cache, maxm -> - elems, tables, cache, maxm (* manca cache *) - | None, tables,cache,maxm -> - applicative_case dbd tables maxm depth subst fake_proof goalno - goalty metasenv context cache - else - applicative_case dbd tables maxm depth subst fake_proof goalno - goalty metasenv context cache + 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 -> + (* 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 - aux tables maxm cache elems - | _ -> Fail "??",tables,cache,maxm + 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,P 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 + (prerr_endline ("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 cache elems + (aux tables maxm flags cache elems : auto_result) +;; + -and - auto_all_solutions dbd tables maxm cache context metasenv gl flags +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) -> x,flags.maxdepth,s) goals in - let elems = [metasenv,[],goals] 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 dbd tables maxm context flags elems cache with - | Fail s,tables,cache,maxm ->prerr_endline s; solutions,cache,maxm - | Success (metasenv,subst,others),tables,cache,maxm -> + 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 - prerr_endline "fine auto all solutions"; - rc + 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_all_solutions dbd cache context metasenv gl flags = - let solutions, cache, _ = - auto_all_solutions dbd None 0 cache context metasenv gl flags - in - solutions, cache -;; - -let auto dbd cache context metasenv gl flags = +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) -> x,flags.maxdepth,s) goals in - let elems = [metasenv,[],goals] in - match auto_main dbd None 0 context flags elems cache with - | Success (metasenv,subst,_), tables,cache,_ -> - prerr_endline("TIME:"^string_of_float(Unix.gettimeofday()-.initial_time)); + 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 - | Fail s,tables,cache,maxm -> None,cache + | Gaveup (tables,cache,maxm) -> + debug_print(lazy + ("TIME:"^string_of_float(Unix.gettimeofday()-.initial_time))); + None,cache ;; -let applyS_tac ~dbd ~term = +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 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; + } + +let applyS_tac ~dbd ~term ~params ~universe = ProofEngineTypes.mk_tactic (fun status -> try - let _, proof, gl,_,_ = apply_smart ~dbd ~term ~subst:[] status in - proof, gl + let proof, gl,_,_ = + apply_smart ~dbd ~term ~subst:[] ~universe + (flags_of_params params ~for_applyS:true ()) status + in + proof, gl with | CicUnification.UnificationFailure msg | CicTypeChecker.TypeCheckerFailure msg -> raise (ProofEngineTypes.Fail msg)) +(* SUPERPOSITION *) + +(* Syntax: + * auto superposition target = NAME + * [table = NAME_LIST] [demod_table = NAME_LIST] [subterms_only] + * + * - if table is omitted no superposition will be performed + * - if demod_table is omitted no demodulation will be prformed + * - subterms_only is passed to Indexing.superposition_right + * + * lists are coded using _ (example: H_H1_H2) + *) + +let eq_and_ty_of_goal = function + | Cic.Appl [Cic.MutInd(uri,0,_);t;_;_] when LibraryObjects.is_eq_URI uri -> + uri,t + | _ -> raise (ProofEngineTypes.Fail (lazy ("The goal is not an equality "))) +;; + +let rec find_in_ctx i name = function + | [] -> raise (ProofEngineTypes.Fail (lazy ("Hypothesis not found: " ^ name))) + | Some (Cic.Name name', _)::tl when name = name' -> i + | _::tl -> find_in_ctx (i+1) name tl +;; + +let rec position_of i x = function + | [] -> assert false + | j::tl when j <> x -> position_of (i+1) x tl + | _ -> i +;; + + +let superposition_tac ~target ~table ~subterms_only ~demod_table status = + Saturation.reset_refs(); + let proof,goalno = status in + let curi,metasenv,_subst,pbo,pty, attrs = proof in + let metano,context,ty = CicUtil.lookup_meta goalno metasenv in + let eq_uri,tty = eq_and_ty_of_goal ty in + let env = (metasenv, context, CicUniv.empty_ugraph) in + let names = Utils.names_of_context context in + let bag = Equality.mk_equality_bag () in + let eq_index, equalities, maxm,cache = + find_context_equalities 0 bag context proof Universe.empty AutoCache.cache_empty + in + let eq_what = + let what = find_in_ctx 1 target context in + List.nth equalities (position_of 0 what eq_index) + in + let eq_other = + if table <> "" then + let other = + let others = Str.split (Str.regexp "_") table in + List.map (fun other -> find_in_ctx 1 other context) others + in + List.map + (fun other -> List.nth equalities (position_of 0 other eq_index)) + other + else + [] + in + let index = List.fold_left Indexing.index Indexing.empty eq_other in + let maxm, eql = + if table = "" then maxm,[eq_what] else + Indexing.superposition_right bag + ~subterms_only eq_uri maxm env index eq_what + in + debug_print (lazy ("Superposition right:")); + debug_print (lazy ("\n eq: " ^ Equality.string_of_equality eq_what ~env)); + debug_print (lazy ("\n table: ")); + List.iter + (fun e -> + debug_print (lazy (" " ^ Equality.string_of_equality e ~env))) eq_other; + debug_print (lazy ("\n result: ")); + List.iter (fun e -> debug_print (lazy (Equality.string_of_equality e ~env))) eql; + debug_print (lazy ("\n result (cut&paste): ")); + List.iter + (fun e -> + let t = Equality.term_of_equality eq_uri e in + debug_print (lazy (CicPp.pp t names))) + eql; + debug_print (lazy ("\n result proofs: ")); + List.iter (fun e -> + debug_print (lazy (let _,p,_,_,_ = Equality.open_equality e in + let s = match p with Equality.Exact _ -> Subst.empty_subst | Equality.Step (s,_) -> s in + Subst.ppsubst s ^ "\n" ^ + CicPp.pp (Equality.build_proof_term bag eq_uri [] 0 p) names))) eql; + if demod_table <> "" then + begin + let eql = + if eql = [] then [eq_what] else eql + in + let demod = + let demod = Str.split (Str.regexp "_") demod_table in + List.map (fun other -> find_in_ctx 1 other context) demod + in + let eq_demod = + List.map + (fun demod -> List.nth equalities (position_of 0 demod eq_index)) + demod + in + let table = List.fold_left Indexing.index Indexing.empty eq_demod in + let maxm,eql = + List.fold_left + (fun (maxm,acc) e -> + let maxm,eq = + Indexing.demodulation_equality bag eq_uri maxm env table e + in + maxm,eq::acc) + (maxm,[]) eql + in + let eql = List.rev eql in + debug_print (lazy ("\n result [demod]: ")); + List.iter + (fun e -> debug_print (lazy (Equality.string_of_equality e ~env))) eql; + debug_print (lazy ("\n result [demod] (cut&paste): ")); + List.iter + (fun e -> + let t = Equality.term_of_equality eq_uri e in + debug_print (lazy (CicPp.pp t names))) + eql; + end; + proof,[goalno] +;; + +let auto_tac ~(dbd:HSql.dbd) ~params ~universe (proof, goal) = + (* argument parsing *) + let string = string params in + let bool = bool params in + (* hacks to debug paramod *) + let superposition = bool "superposition" false in + let target = string "target" "" in + let table = string "table" "" in + let subterms_only = bool "subterms_only" false in + let demod_table = string "demod_table" "" in + match superposition with + | true -> + (* this is the ugly hack to debug paramod *) + superposition_tac + ~target ~table ~subterms_only ~demod_table (proof,goal) + | false -> + (* this is the real auto *) + let _,metasenv,_subst,_,_, _ = proof in + let _,context,goalty = CicUtil.lookup_meta goal metasenv in + let flags = flags_of_params params () in + (* just for testing *) + let use_library = flags.use_library in + let tables,cache,newmeta = + init_cache_and_tables dbd use_library flags.use_only_paramod + 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 "))) +;; + +(* DEMODULATE *) +let demodulate_tac ~dbd ~universe (proof,goal)= + let curi,metasenv,_subst,pbo,pty, attrs = proof in + let metano,context,ty = CicUtil.lookup_meta goal metasenv in + let irl = CicMkImplicit.identity_relocation_list_for_metavariable context in + let initgoal = [], [], ty in + let eq_uri = eq_of_goal ty in + let (active,passive,bag), cache, maxm = + init_cache_and_tables dbd false true 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 ~universe = + ProofEngineTypes.mk_tactic (demodulate_tac ~dbd ~universe);; + +let pp_proofterm = Equality.pp_proofterm;; + +let revision = "$Revision$";; +let size_and_depth context metasenv t = 100, 100