+++ /dev/null
-(* Copyright (C) 2002, HELM Team.
- *
- * This file is part of HELM, an Hypertextual, Electronic
- * Library of Mathematics, developed at the Computer Science
- * Department, University of Bologna, Italy.
- *
- * HELM is free software; you can redistribute it and/or
- * modify it under the terms of the GNU General Public License
- * as published by the Free Software Foundation; either version 2
- * of the License, or (at your option) any later version.
- *
- * HELM is distributed in the hope that it will be useful,
- * but WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
- * GNU General Public License for more details.
- *
- * You should have received a copy of the GNU General Public License
- * along with HELM; if not, write to the Free Software
- * Foundation, Inc., 59 Temple Place - Suite 330, Boston,
- * MA 02111-1307, USA.
- *
- * For details, see the HELM World-Wide-Web page,
- * http://cs.unibo.it/helm/.
- *)
-
-
-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'')
- 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_back_simpl_tac ~term status =
- Tacticals.then_
- ~start:(rewrite_back_tac ~term)
- ~continuation:
- (ReductionTactics.simpl_tac ~also_in_hypotheses:false ~terms:None)
- status
-;;
-
-
-let replace_tac ~what ~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]
- status
- else raise (ProofEngineTypes.Fail "Replace: terms not replaceable")
- with (Failure "hd") -> raise (ProofEngineTypes.Fail "Replace: empty context")
-;;
-
-
-(* All these tacs do is applying the right constructor/theorem *)
-
-let reflexivity_tac =
- IntroductionTactics.constructor_tac ~n:1
-;;
-
-
-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, []))
-
- | _ -> raise (ProofEngineTypes.Fail "Symmetry failed")
-;;
-
-
-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
- let module T = Tacticals 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 (uri = HelmLibraryObjects.Logic.eq_URI) ->
- 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]
- status
-
- | _ -> raise (ProofEngineTypes.Fail "Transitivity failed")
-;;
-
-
projects / helm.git / blobdiff