From 6bc368145d8f865d5af3de857ea882f66649f705 Mon Sep 17 00:00:00 2001 From: Enrico Tassi Date: Fri, 6 May 2005 10:12:16 +0000 Subject: [PATCH] factorization of rewrite. now the tactic also does a beta reduction step (behaving as expected) --- helm/ocaml/tactics/equalityTactics.ml | 165 ++++++++++---------------- 1 file changed, 63 insertions(+), 102 deletions(-) diff --git a/helm/ocaml/tactics/equalityTactics.ml b/helm/ocaml/tactics/equalityTactics.ml index 718a1bac2..52ea4054d 100644 --- a/helm/ocaml/tactics/equalityTactics.ml +++ b/helm/ocaml/tactics/equalityTactics.ml @@ -23,57 +23,66 @@ * http://cs.unibo.it/helm/. *) -let rewrite_tac ~term:equality = - 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 ty_eq,_ = - CicTypeChecker.type_of_aux' metasenv context equality - CicUniv.empty_ugraph in - let eq_ind_r,ty,t1,t2 = - match ty_eq 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 ~subst:[] metasenv context C.Anonymous ~typ: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 rewrite ~term:equality ?(direction=`Left) (proof,goal) = + let module C = Cic in + let module U = UriManager in + let module PET = ProofEngineTypes 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 gty'' = + ProofEngineReduction.replace_lifting + ~equality:ProofEngineReduction.alpha_equivalence + ~what:[t1'] ~with_what:[C.Rel 1] ~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 (proof',goals) = - ProofEngineTypes.apply_tactic - (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_tac ~term = + let rewrite_tac ~term status = + rewrite ~term ~direction:`Right status in - ProofEngineTypes.mk_tactic (rewrite_tac ~term:equality) -;; - + ProofEngineTypes.mk_tactic (rewrite_tac ~term) let rewrite_simpl_tac ~term = let rewrite_simpl_tac ~term status = @@ -87,59 +96,11 @@ let rewrite_simpl_tac ~term = ProofEngineTypes.mk_tactic (rewrite_simpl_tac ~term) ;; - -let rewrite_back_tac ~term:equality = - let rewrite_back_tac 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 ty_eq,_ = - CicTypeChecker.type_of_aux' metasenv context equality - CicUniv.empty_ugraph in - let eq_ind_r,ty,t1,t2 = - match ty_eq 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 ~subst:[] metasenv context C.Anonymous ~typ: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) = - ProofEngineTypes.apply_tactic - (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]) - in - ProofEngineTypes.mk_tactic (rewrite_back_tac equality) -;; - +let rewrite_back_tac ~term = + let rewrite_back_tac ~term status = + rewrite ~term ~direction:`Left status + in + ProofEngineTypes.mk_tactic (rewrite_back_tac ~term) let rewrite_back_simpl_tac ~term = let rewrite_back_simpl_tac ~term status = -- 2.39.2