X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Focaml%2Ftactics%2FequalityTactics.ml;h=7ed946170b5e36e018304c7062a033f96a4cb20c;hb=4167cea65ca58897d1a3dbb81ff95de5074700cc;hp=232911450400654bed1c31db192f100e4303f0f1;hpb=b3bfd6b249600b15552c890306a635aee30c2a74;p=helm.git diff --git a/helm/ocaml/tactics/equalityTactics.ml b/helm/ocaml/tactics/equalityTactics.ml index 232911450..7ed946170 100644 --- a/helm/ocaml/tactics/equalityTactics.ml +++ b/helm/ocaml/tactics/equalityTactics.ml @@ -22,148 +22,283 @@ * For details, see the HELM World-Wide-Web page, * http://cs.unibo.it/helm/. *) - - -let rewrite_tac ~term:equality ~status:(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]) - ~status:((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 ~status:(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'') - 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]) - ~status:((curi,metasenv',pbo,pty),goal) - in - assert (List.length goals = 0) ; - (proof',[fresh_meta]) - -;; - - -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 rec rewrite_tac ~direction ~pattern equality = + let _rewrite_tac ~direction ~pattern:(wanted,hyps_pat,concl_pat) equality status + = + 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 + assert (wanted = None); (* this should be checked syntactically *) + let proof,goal = status in + let curi, metasenv, pbo, pty = proof in + let (metano,context,gty) as conjecture = CicUtil.lookup_meta goal metasenv in + match hyps_pat with + he::(_::_ as tl) -> + PET.apply_tactic + (Tacticals.then_ + (rewrite_tac ~direction + ~pattern:(None,[he],Cic.Implicit None) equality) + (rewrite_tac ~direction ~pattern:(None,tl,concl_pat) equality) + ) status + | [_] as hyps_pat when concl_pat <> Cic.Implicit None -> + PET.apply_tactic + (Tacticals.then_ + (rewrite_tac ~direction + ~pattern:(None,hyps_pat,Cic.Implicit None) equality) + (rewrite_tac ~direction ~pattern:(None,[],concl_pat) equality) + ) status + | _ -> + let arg,dir2,tac,concl_pat,gty = + match hyps_pat with + [] -> None,true,(fun ~term _ -> PT.exact_tac term),concl_pat,gty + | [name,pat] -> + let rec find_hyp n = + function + [] -> assert false + | Some (Cic.Name s,Cic.Decl ty)::_ when name = s -> + Cic.Rel n, CicSubstitution.lift n ty + | Some (Cic.Name s,Cic.Def _)::_ -> assert false (*CSC: not implemented yet! But does this make any sense?*) + | _::tl -> find_hyp (n+1) tl + in + let arg,gty = find_hyp 1 context in + let last_hyp_name_of_status (proof,goal) = + let curi, metasenv, pbo, pty = proof in + let metano,context,gty = CicUtil.lookup_meta goal metasenv in + match context with + (Some (Cic.Name s,_))::_ -> s + | _ -> assert false + in + let dummy = "dummy" in + Some arg,false, + (fun ~term typ -> + Tacticals.seq + ~tactics: + [ProofEngineStructuralRules.rename name dummy; + PT.letin_tac + ~mk_fresh_name_callback:(fun _ _ _ ~typ -> Cic.Name name) term; + ProofEngineStructuralRules.clearbody name; + ReductionTactics.change_tac + ~pattern: + (None,[name,Cic.Implicit (Some `Hole)],Cic.Implicit None) + (ProofEngineTypes.const_lazy_term typ); + ProofEngineStructuralRules.clear dummy + ]), + pat,gty + | _::_ -> assert false + in + let if_right_to_left do_not_change a b = + match direction with + | `RightToLeft -> if do_not_change then a else b + | `LeftToRight -> if do_not_change then b else a + in + let ty_eq,ugraph = + CicTypeChecker.type_of_aux' metasenv context equality + CicUniv.empty_ugraph in + let (ty_eq,metasenv',arguments,fresh_meta) = + ProofEngineHelpers.saturate_term + (ProofEngineHelpers.new_meta_of_proof proof) metasenv context ty_eq 0 in + let equality = + if List.length arguments = 0 then + equality + else + C.Appl (equality :: arguments) in + (* t1x is t2 if we are rewriting in an hypothesis *) + let eq_ind, ty, t1, t2, t1x = + match ty_eq with + | C.Appl [C.MutInd (uri, 0, []); ty; t1; t2] + when LibraryObjects.is_eq_URI uri -> + let ind_uri = + if_right_to_left dir2 + LibraryObjects.eq_ind_URI LibraryObjects.eq_ind_r_URI + in + let eq_ind = C.Const (ind_uri uri,[]) in + if dir2 then + if_right_to_left true (eq_ind,ty,t2,t1,t2) (eq_ind,ty,t1,t2,t1) + else + if_right_to_left true (eq_ind,ty,t1,t2,t2) (eq_ind,ty,t2,t1,t1) + | _ -> raise (PET.Fail (lazy "Rewrite: argument is not a proof of an equality")) in + (* now we always do as if direction was `LeftToRight *) + let fresh_name = + FreshNamesGenerator.mk_fresh_name + ~subst:[] metasenv' context C.Anonymous ~typ:ty in + let lifted_t1 = CicSubstitution.lift 1 t1x in + let lifted_gty = CicSubstitution.lift 1 gty in + let lifted_conjecture = + metano,(Some (fresh_name,Cic.Decl ty))::context,lifted_gty in + let lifted_pattern = + Some (fun _ m u -> lifted_t1, m, u),[],CicSubstitution.lift 1 concl_pat + in + let subst,metasenv',ugraph,_,selected_terms_with_context = + ProofEngineHelpers.select + ~metasenv:metasenv' ~ugraph ~conjecture:lifted_conjecture + ~pattern:lifted_pattern in + let metasenv' = CicMetaSubst.apply_subst_metasenv subst metasenv' in + let what,with_what = + (* Note: Rel 1 does not live in the context context_of_t *) + (* The replace_lifting_csc 0 function will take care of lifting it *) + (* to context_of_t *) + List.fold_right + (fun (context_of_t,t) (l1,l2) -> t::l1, Cic.Rel 1::l2) + selected_terms_with_context ([],[]) in + let t1 = CicMetaSubst.apply_subst subst t1 in + let t2 = CicMetaSubst.apply_subst subst t2 in + let equality = CicMetaSubst.apply_subst subst equality in + let abstr_gty = + ProofEngineReduction.replace_lifting_csc 0 + ~equality:(==) ~what ~with_what:with_what ~where:lifted_gty in + let abstr_gty = CicMetaSubst.apply_subst subst abstr_gty in + let pred = C.Lambda (fresh_name, ty, abstr_gty) in + (* The argument is either a meta if we are rewriting in the conclusion + or the hypothesis if we are rewriting in an hypothesis *) + let metasenv',arg,newtyp = + match arg with + None -> + let gty' = CicSubstitution.subst t2 abstr_gty in + let irl = + CicMkImplicit.identity_relocation_list_for_metavariable context in + let metasenv' = (fresh_meta,context,gty')::metasenv' in + metasenv', C.Meta (fresh_meta,irl), Cic.Rel (-1) (* dummy term, never used *) + | Some arg -> + let gty' = CicSubstitution.subst t1 abstr_gty in + metasenv,arg,gty' + in + let exact_proof = + C.Appl [eq_ind ; ty ; t2 ; pred ; arg ; t1 ;equality] + in + let (proof',goals) = + PET.apply_tactic + (tac ~term:exact_proof newtyp) ((curi,metasenv',pbo,pty),goal) + in + let goals = + goals@(ProofEngineHelpers.compare_metasenvs ~oldmetasenv:metasenv + ~newmetasenv:metasenv') + in + (proof',goals) + in + ProofEngineTypes.mk_tactic (_rewrite_tac ~direction ~pattern equality) + + +let rewrite_simpl_tac ~direction ~pattern equality = + let rewrite_simpl_tac ~direction ~pattern equality status = + ProofEngineTypes.apply_tactic + (Tacticals.then_ + ~start:(rewrite_tac ~direction ~pattern equality) + ~continuation: + (ReductionTactics.simpl_tac + ~pattern:(ProofEngineTypes.conclusion_pattern None))) + status + in + ProofEngineTypes.mk_tactic (rewrite_simpl_tac ~direction ~pattern equality) ;; - -let replace_tac ~what ~with_what ~status:((proof, goal) as status) = +let replace_tac ~pattern ~with_what = + let replace_tac ~pattern:(wanted,hyps_pat,concl_pat) ~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 ; + let uri,metasenv,pbo,pty = proof in + let (_,context,ty) as conjecture = CicUtil.lookup_meta goal metasenv in + assert (hyps_pat = []); (*CSC: not implemented yet *) + let context_len = List.length context in + let subst,metasenv,u,_,selected_terms_with_context = + ProofEngineHelpers.select ~metasenv ~ugraph:CicUniv.empty_ugraph + ~conjecture ~pattern in + let metasenv = CicMetaSubst.apply_subst_metasenv subst metasenv in + let with_what, metasenv, u = with_what context metasenv u in + let with_what = CicMetaSubst.apply_subst subst with_what in + let pbo = CicMetaSubst.apply_subst subst pbo in + let pty = CicMetaSubst.apply_subst subst pty in + let status = (uri,metasenv,pbo,pty),goal in + let ty_of_with_what,u = + CicTypeChecker.type_of_aux' + metasenv context with_what CicUniv.empty_ugraph in + let whats = + match selected_terms_with_context with + [] -> raise (ProofEngineTypes.Fail (lazy "Replace: no term selected")) + | l -> + List.map + (fun (context_of_t,t) -> + let t_in_context = + try + let context_of_t_len = List.length context_of_t in + if context_of_t_len = context_len then t + else + (let t_in_context,subst,metasenv' = + CicMetaSubst.delift_rels [] metasenv + (context_of_t_len - context_len) t + in + assert (subst = []); + assert (metasenv = metasenv'); + t_in_context) + with + CicMetaSubst.DeliftingARelWouldCaptureAFreeVariable -> + (*CSC: we could implement something stronger by completely changing + the semantics of the tactic *) + raise (ProofEngineTypes.Fail + (lazy "Replace: one of the selected terms is not closed")) in + let ty_of_t_in_context,u = (* TASSI: FIXME *) + CicTypeChecker.type_of_aux' metasenv context t_in_context + CicUniv.empty_ugraph in + let b,u = CicReduction.are_convertible ~metasenv context + ty_of_with_what ty_of_t_in_context u in + if b then + let concl_pat_for_t = ProofEngineHelpers.pattern_of ~term:ty [t] in + let pattern_for_t = None,[],concl_pat_for_t in + t_in_context,pattern_for_t + else + raise + (ProofEngineTypes.Fail + (lazy "Replace: one of the selected terms and the term to be replaced with have not convertible types")) + ) l in + let rec aux n whats status = + match whats with + [] -> ProofEngineTypes.apply_tactic T.id_tac status + | (what,pattern)::tl -> + let what = CicSubstitution.lift n what in + let with_what = CicSubstitution.lift n with_what in + let ty_of_with_what = CicSubstitution.lift n ty_of_with_what in + ProofEngineTypes.apply_tactic + (T.thens + ~start:( + P.cut_tac + (C.Appl [ + (C.MutInd (LibraryObjects.eq_URI (), 0, [])) ; + ty_of_with_what ; 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") + ~continuations:[ + T.then_ + ~start:( + rewrite_tac ~direction:`LeftToRight ~pattern (C.Rel 1)) + ~continuation:( + T.then_ + ~start:( + ProofEngineTypes.mk_tactic + (function ((proof,goal) as status) -> + let _,metasenv,_,_ = proof in + let _,context,_ = CicUtil.lookup_meta goal metasenv in + let hyp = + try + match List.hd context with + Some (Cic.Name name,_) -> name + | _ -> assert false + with (Failure "hd") -> assert false + in + ProofEngineTypes.apply_tactic + (ProofEngineStructuralRules.clear ~hyp) status)) + ~continuation:(aux_tac (n + 1) tl)); + T.id_tac]) + status + and aux_tac n tl = ProofEngineTypes.mk_tactic (aux n tl) in + aux 0 whats status + in + ProofEngineTypes.mk_tactic (replace_tac ~pattern ~with_what) ;; @@ -173,23 +308,29 @@ let reflexivity_tac = IntroductionTactics.constructor_tac ~n:1 ;; - -let symmetry_tac ~status:(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 ~status:(proof,goal) - ~term: (C.Const (HelmLibraryObjects.Logic.sym_eq_URI, [])) + (C.Appl [(C.MutInd (uri, 0, [])); _; _; _]) + when LibraryObjects.is_eq_URI uri -> + ProofEngineTypes.apply_tactic + (PrimitiveTactics.apply_tac + ~term: (C.Const (LibraryObjects.sym_eq_URI uri, []))) + (proof,goal) - | _ -> raise (ProofEngineTypes.Fail "Symmetry failed") + | _ -> raise (ProofEngineTypes.Fail (lazy "Symmetry failed")) + in + ProofEngineTypes.mk_tactic symmetry_tac ;; - -let transitivity_tac ~term ~status:((proof, goal) as 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 let module U = UriManager in @@ -197,15 +338,19 @@ let transitivity_tac ~term ~status:((proof, goal) as 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 LibraryObjects.is_eq_URI uri -> + ProofEngineTypes.apply_tactic + (T.thens ~start:(PrimitiveTactics.apply_tac - ~term: (C.Const (HelmLibraryObjects.Logic.trans_eq_URI, []))) + ~term: (C.Const (LibraryObjects.trans_eq_URI uri, []))) ~continuations: - [PrimitiveTactics.exact_tac ~term ; T.id_tac ; T.id_tac] - ~status + [PrimitiveTactics.exact_tac ~term ; T.id_tac ; T.id_tac]) + status - | _ -> raise (ProofEngineTypes.Fail "Transitivity failed") + | _ -> raise (ProofEngineTypes.Fail (lazy "Transitivity failed")) + in + ProofEngineTypes.mk_tactic (transitivity_tac ~term) ;;