X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Focaml%2Ftactics%2FequalityTactics.ml;h=b9db6f705777eb9ae7acb09bace47a5cc6b1857c;hb=bbe7741f3bbaacb93f2876c018dace82f5e929b8;hp=0e9f72b0f96b73d65ea5644a85dbdceda93913d6;hpb=a6fc115fd7d4cfba94a43f001f4c27322d3db1a8;p=helm.git diff --git a/helm/ocaml/tactics/equalityTactics.ml b/helm/ocaml/tactics/equalityTactics.ml index 0e9f72b0f..b9db6f705 100644 --- a/helm/ocaml/tactics/equalityTactics.ml +++ b/helm/ocaml/tactics/equalityTactics.ml @@ -22,149 +22,165 @@ * For details, see the HELM World-Wide-Web page, * http://cs.unibo.it/helm/. *) + - -let rewrite_tac ~term:equality (proof,goal) = - let module C = Cic in - let module U = UriManager in - let curi,metasenv,pbo,pty = proof in - let metano,context,gty = CicUtil.lookup_meta goal metasenv in - let eq_ind_r,ty,t1,t2 = - match CicTypeChecker.type_of_aux' metasenv context equality with - C.Appl [C.MutInd (uri,0,[]) ; ty ; t1 ; t2] - when U.eq uri HelmLibraryObjects.Logic.eq_URI -> - let eq_ind_r = - C.Const - (HelmLibraryObjects.Logic.eq_ind_r_URI,[]) - in - eq_ind_r,ty,t1,t2 - | _ -> - raise - (ProofEngineTypes.Fail - "Rewrite: the argument is not a proof of an equality") - in - let pred = - let gty' = CicSubstitution.lift 1 gty in - let t1' = CicSubstitution.lift 1 t1 in - let gty'' = - ProofEngineReduction.replace_lifting - ~equality:ProofEngineReduction.alpha_equivalence - ~what:[t1'] ~with_what:[C.Rel 1] ~where:gty' - in - C.Lambda - (FreshNamesGenerator.mk_fresh_name metasenv context C.Anonymous ty, - ty, gty'') - in - let fresh_meta = ProofEngineHelpers.new_meta_of_proof proof in - let irl = CicMkImplicit.identity_relocation_list_for_metavariable context in - let metasenv' = (fresh_meta,context,C.Appl [pred ; t2])::metasenv in - - let (proof',goals) = - PrimitiveTactics.exact_tac - ~term:(C.Appl - [eq_ind_r ; ty ; t2 ; pred ; C.Meta (fresh_meta,irl) ; t1 ;equality]) - ((curi,metasenv',pbo,pty),goal) - in - assert (List.length goals = 0) ; - (proof',[fresh_meta]) -;; - - -let rewrite_simpl_tac ~term status = - Tacticals.then_ - ~start:(rewrite_tac ~term) - ~continuation: - (ReductionTactics.simpl_tac ~also_in_hypotheses:false ~terms:None) - status -;; - - -let rewrite_back_tac ~term:equality (proof,goal) = - let module C = Cic in - let module U = UriManager in - let curi,metasenv,pbo,pty = proof in - let metano,context,gty = CicUtil.lookup_meta goal metasenv in - let eq_ind_r,ty,t1,t2 = - match CicTypeChecker.type_of_aux' metasenv context equality with - C.Appl [C.MutInd (uri,0,[]) ; ty ; t1 ; t2] - when U.eq uri HelmLibraryObjects.Logic.eq_URI -> - let eq_ind_r = - C.Const (HelmLibraryObjects.Logic.eq_ind_URI,[]) - in - eq_ind_r,ty,t2,t1 - | _ -> - raise - (ProofEngineTypes.Fail - "Rewrite: the argument is not a proof of an equality") - in - let pred = - let gty' = CicSubstitution.lift 1 gty in - let t1' = CicSubstitution.lift 1 t1 in - let gty'' = - ProofEngineReduction.replace_lifting - ~equality:ProofEngineReduction.alpha_equivalence - ~what:[t1'] ~with_what:[C.Rel 1] ~where:gty' - in - C.Lambda - (FreshNamesGenerator.mk_fresh_name metasenv context C.Anonymous ty, - ty, gty'') +let rewrite ~term:equality ?where ?(direction=`Left) (proof,goal) = + let module C = Cic in + let module U = UriManager in + let module PET = ProofEngineTypes in + let module PER = ProofEngineReduction in + let module PEH = ProofEngineHelpers in + let module PT = PrimitiveTactics in + let module HLO = HelmLibraryObjects in + let if_left a b = + match direction with + | `Right -> b + | `Left -> a + in + let curi, metasenv, pbo, pty = proof in + let metano, context, gty = CicUtil.lookup_meta goal metasenv in + let eq_uri = HLO.Logic.eq_URI in + let ty_eq,_ = + CicTypeChecker.type_of_aux' metasenv context equality + CicUniv.empty_ugraph + in + let eq_ind, ty, t1, t2 = + match ty_eq with + | C.Appl [C.MutInd (uri, 0, []); ty; t1; t2] when U.eq uri eq_uri -> + let eq_ind = + C.Const (if_left HLO.Logic.eq_ind_URI HLO.Logic.eq_ind_r_URI,[]) + in + if_left (eq_ind, ty, t2, t1) (eq_ind, ty, t1, t2) + | _ -> raise (PET.Fail "Rewrite: argument is not a proof of an equality") + in + (* now we always do as if direction was `Left *) + let gty' = CicSubstitution.lift 1 gty in + let t1' = CicSubstitution.lift 1 t1 in + let eq_kind, what = + match where with + | None + | Some ([], None) -> + PER.alpha_equivalence, [t1'] + | Some (hp_paths, goal_path) -> + assert (hp_paths = []); + match goal_path with + | None -> assert false (* (==), [t1'] *) + | Some path -> + let roots = ProofEngineHelpers.select ~term:gty' ~pattern:path in + let subterms = + List.fold_left ( + fun acc (i, r) -> + let wanted = CicSubstitution.lift (List.length i) t1' in + PEH.find_subterms ~eq:PER.alpha_equivalence ~wanted r @ acc + ) [] roots + in + (==), subterms + in + let with_what = + let rec aux = function + | 0 -> [] + | n -> C.Rel 1 :: aux (n-1) in - let fresh_meta = ProofEngineHelpers.new_meta_of_proof proof in - let irl = - CicMkImplicit.identity_relocation_list_for_metavariable context in - let metasenv' = (fresh_meta,context,C.Appl [pred ; t2])::metasenv in - - let (proof',goals) = - PrimitiveTactics.exact_tac - ~term:(C.Appl - [eq_ind_r ; ty ; t2 ; pred ; C.Meta (fresh_meta,irl) ; t1 ;equality]) - ((curi,metasenv',pbo,pty),goal) - in - assert (List.length goals = 0) ; - (proof',[fresh_meta]) - + aux (List.length what) + in + let gty'' = + ProofEngineReduction.replace_lifting_csc 0 + ~equality:eq_kind ~what ~with_what ~where:gty' + in + let gty_red = CicSubstitution.subst t2 gty'' in + let fresh_meta = ProofEngineHelpers.new_meta_of_proof proof in + let irl =CicMkImplicit.identity_relocation_list_for_metavariable context in + let metasenv' = (fresh_meta,context,gty_red)::metasenv in + let fresh_name = + FreshNamesGenerator.mk_fresh_name + ~subst:[] metasenv context C.Anonymous ~typ:ty + in + let pred = C.Lambda (fresh_name, ty, gty'') in + let exact_proof = + C.Appl [eq_ind ; ty ; t2 ; pred ; C.Meta (fresh_meta,irl) ; t1 ;equality] + in + let (proof',goals) = + PET.apply_tactic + (PT.exact_tac ~term:exact_proof) ((curi,metasenv',pbo,pty),goal) + in + assert (List.length goals = 0) ; + (proof',[fresh_meta]) + + +let rewrite_tac ?where ~term () = + let rewrite_tac ?where ~term status = + rewrite ?where ~term ~direction:`Right status + in + ProofEngineTypes.mk_tactic (rewrite_tac ?where ~term) + +let rewrite_simpl_tac ?where ~term () = + let rewrite_simpl_tac ?where ~term status = + ProofEngineTypes.apply_tactic + (Tacticals.then_ + ~start:(rewrite_tac ?where ~term ()) + ~continuation: + (ReductionTactics.simpl_tac ~pattern:ProofEngineTypes.goal_pattern)) + status + in + ProofEngineTypes.mk_tactic (rewrite_simpl_tac ~term) ;; - -let rewrite_back_simpl_tac ~term status = - Tacticals.then_ - ~start:(rewrite_back_tac ~term) - ~continuation: - (ReductionTactics.simpl_tac ~also_in_hypotheses:false ~terms:None) - status +let rewrite_back_tac ?where ~term () = + let rewrite_back_tac ?where ~term status = + rewrite ?where ~term ~direction:`Left status + in + ProofEngineTypes.mk_tactic (rewrite_back_tac ?where ~term) + +let rewrite_back_simpl_tac ?where ~term () = + let rewrite_back_simpl_tac ?where ~term status = + ProofEngineTypes.apply_tactic + (Tacticals.then_ + ~start:(rewrite_back_tac ?where ~term ()) + ~continuation: + (ReductionTactics.simpl_tac ~pattern:ProofEngineTypes.goal_pattern)) + status + in + ProofEngineTypes.mk_tactic (rewrite_back_simpl_tac ~term) ;; - -let replace_tac ~what ~with_what status = +let replace_tac ~pattern ~with_what = +(* + let replace_tac ~pattern ~with_what status = let (proof, goal) = status in let module C = Cic in let module U = UriManager in let module P = PrimitiveTactics in let module T = Tacticals in - let _,metasenv,_,_ = proof in - let _,context,_ = CicUtil.lookup_meta goal metasenv in - let wty = CicTypeChecker.type_of_aux' metasenv context what in - try - if (wty = (CicTypeChecker.type_of_aux' metasenv context with_what)) - then - T.thens - ~start:( - P.cut_tac - (C.Appl [ - (C.MutInd (HelmLibraryObjects.Logic.eq_URI, 0, [])) ; - wty ; - what ; - with_what])) - ~continuations:[ - T.then_ - ~start:(rewrite_simpl_tac ~term:(C.Rel 1)) - ~continuation:( - ProofEngineStructuralRules.clear - ~hyp:(List.hd context)) ; - T.id_tac] + let _,metasenv,_,_ = proof in + let _,context,_ = CicUtil.lookup_meta goal metasenv in + let wty,u = (* TASSI: FIXME *) + CicTypeChecker.type_of_aux' metasenv context what CicUniv.empty_ugraph in + let wwty,_ = CicTypeChecker.type_of_aux' metasenv context with_what u in + try + if (wty = wwty) then + ProofEngineTypes.apply_tactic + (T.thens + ~start:( + P.cut_tac + (C.Appl [ + (C.MutInd (HelmLibraryObjects.Logic.eq_URI, 0, [])) ; + wty ; + what ; + with_what])) + ~continuations:[ + + T.then_ ~start:(rewrite_simpl_tac ~term:(C.Rel 1) ()) + ~continuation:( + ProofEngineStructuralRules.clear + ~hyp:(List.hd context)) ; + T.id_tac]) status - else raise (ProofEngineTypes.Fail "Replace: terms not replaceable") - with (Failure "hd") -> raise (ProofEngineTypes.Fail "Replace: empty context") + else raise (ProofEngineTypes.Fail "Replace: terms not replaceable") + with (Failure "hd") -> + raise (ProofEngineTypes.Fail "Replace: empty context") + in + ProofEngineTypes.mk_tactic (replace_tac ~what ~with_what) +*) assert false ;; @@ -174,23 +190,28 @@ let reflexivity_tac = IntroductionTactics.constructor_tac ~n:1 ;; - -let symmetry_tac (proof, goal) = +let symmetry_tac = + let symmetry_tac (proof, goal) = let module C = Cic in let module R = CicReduction in let module U = UriManager in let (_,metasenv,_,_) = proof in let metano,context,ty = CicUtil.lookup_meta goal metasenv in match (R.whd context ty) with - (C.Appl [(C.MutInd (uri, 0, [])); _; _; _]) when (U.eq uri HelmLibraryObjects.Logic.eq_URI) -> - PrimitiveTactics.apply_tac (proof,goal) - ~term: (C.Const (HelmLibraryObjects.Logic.sym_eq_URI, [])) + (C.Appl [(C.MutInd (uri, 0, [])); _; _; _]) + when (U.eq uri HelmLibraryObjects.Logic.eq_URI) -> + ProofEngineTypes.apply_tactic + (PrimitiveTactics.apply_tac + ~term: (C.Const (HelmLibraryObjects.Logic.sym_eq_URI, []))) + (proof,goal) | _ -> raise (ProofEngineTypes.Fail "Symmetry failed") + in + ProofEngineTypes.mk_tactic symmetry_tac ;; - -let transitivity_tac ~term status = +let transitivity_tac ~term = + let transitivity_tac ~term status = let (proof, goal) = status in let module C = Cic in let module R = CicReduction in @@ -199,15 +220,19 @@ let transitivity_tac ~term status = let (_,metasenv,_,_) = proof in let metano,context,ty = CicUtil.lookup_meta goal metasenv in match (R.whd context ty) with - (C.Appl [(C.MutInd (uri, 0, [])); _; _; _]) when (uri = HelmLibraryObjects.Logic.eq_URI) -> - T.thens + (C.Appl [(C.MutInd (uri, 0, [])); _; _; _]) + when (uri = HelmLibraryObjects.Logic.eq_URI) -> + ProofEngineTypes.apply_tactic + (T.thens ~start:(PrimitiveTactics.apply_tac ~term: (C.Const (HelmLibraryObjects.Logic.trans_eq_URI, []))) ~continuations: - [PrimitiveTactics.exact_tac ~term ; T.id_tac ; T.id_tac] + [PrimitiveTactics.exact_tac ~term ; T.id_tac ; T.id_tac]) status | _ -> raise (ProofEngineTypes.Fail "Transitivity failed") + in + ProofEngineTypes.mk_tactic (transitivity_tac ~term) ;;