+++ /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/.
- *)
-
-(* $Id$ *)
-
-module C = Cic
-module U = UriManager
-module PET = ProofEngineTypes
-module PER = ProofEngineReduction
-module PEH = ProofEngineHelpers
-module PESR = ProofEngineStructuralRules
-module P = PrimitiveTactics
-module T = Tacticals
-module R = CicReduction
-module S = CicSubstitution
-module TC = CicTypeChecker
-module LO = LibraryObjects
-module DTI = DoubleTypeInference
-module HEL = HExtlib
-
-let rec rewrite ~direction ~pattern:(wanted,hyps_pat,concl_pat) equality status=
- assert (wanted = None); (* this should be checked syntactically *)
- let proof,goal = status in
- let curi, metasenv, subst, pbo, pty, attrs = proof in
- let (metano,context,gty) = CicUtil.lookup_meta goal metasenv in
- match hyps_pat with
- he::(_::_ as tl) ->
- PET.apply_tactic
- (T.then_
- (PET.mk_tactic (rewrite ~direction
- ~pattern:(None,[he],None) equality))
- (PET.mk_tactic (rewrite ~direction
- ~pattern:(None,tl,concl_pat) (S.lift 1 equality)))
- ) status
- | [_] as hyps_pat when concl_pat <> None ->
- PET.apply_tactic
- (T.then_
- (PET.mk_tactic (rewrite ~direction
- ~pattern:(None,hyps_pat,None) equality))
- (PET.mk_tactic (rewrite ~direction
- ~pattern:(None,[],concl_pat) (S.lift 1 equality)))
- ) status
- | _ ->
- let arg,dir2,tac,concl_pat,gty =
- match hyps_pat with
- [] -> None,true,(fun ~term _ -> P.exact_tac term),concl_pat,gty
- | [name,pat] ->
- let arg,gty = ProofEngineHelpers.find_hyp name context in
- let dummy = "dummy" in
- Some arg,false,
- (fun ~term typ ->
- T.seq
- ~tactics:
- [PESR.rename [name] [dummy];
- P.letin_tac
- ~mk_fresh_name_callback:(fun _ _ _ ~typ -> Cic.Name name) term;
- PESR.clearbody name;
- ReductionTactics.change_tac
- ~pattern:
- (None,[name,Cic.Implicit (Some `Hole)], None)
- (ProofEngineTypes.const_lazy_term typ);
- PESR.clear [dummy]
- ]),
- Some pat,gty
- | _::_ -> assert false
- in
- let gsort,_ =
- CicTypeChecker.type_of_aux'
- metasenv ~subst context gty CicUniv.oblivion_ugraph
- 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 ~subst context equality
- CicUniv.oblivion_ugraph in
- let (ty_eq,metasenv',arguments,fresh_meta) =
- TermUtil.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 =
- match gsort with
- C.Sort C.Prop ->
- if_right_to_left dir2
- LibraryObjects.eq_ind_URI LibraryObjects.eq_ind_r_URI
- | C.Sort C.Set ->
- if_right_to_left dir2
- LibraryObjects.eq_rec_URI LibraryObjects.eq_rec_r_URI
- | _ ->
- if_right_to_left dir2
- LibraryObjects.eq_rect_URI LibraryObjects.eq_rect_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 = S.lift 1 t1x in
- let lifted_gty = S.lift 1 gty in
- let lifted_conjecture =
- metano,(Some (fresh_name,Cic.Decl ty))::context,lifted_gty in
- let lifted_pattern =
- let lifted_concl_pat =
- match concl_pat with
- | None -> None
- | Some term -> Some (S.lift 1 term) in
- Some (fun c m u ->
- let distance = pred (List.length c - List.length context) in
- S.lift distance lifted_t1, m, u),[],lifted_concl_pat
- in
- let subst,metasenv',ugraph,_,selected_terms_with_context =
- ProofEngineHelpers.select
- ~metasenv:metasenv' ~subst ~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 ty = CicMetaSubst.apply_subst subst ty in
- let pbo = lazy (CicMetaSubst.apply_subst subst (Lazy.force pbo)) in
- let pty = CicMetaSubst.apply_subst subst pty 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
- if lifted_gty = abstr_gty then
- raise (ProofEngineTypes.Fail (lazy "nothing to do"));
- 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 fresh_meta = CicMkImplicit.new_meta metasenv' subst in
- let gty' = S.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' = S.subst t1 abstr_gty in
- metasenv',arg,gty'
- in
- let exact_proof =
- C.Appl [eq_ind ; ty ; t2 ; pred ; arg ; t1 ;equality]
- in
- try
- let (proof',goals) =
- PET.apply_tactic (tac ~term:exact_proof newtyp)
- ((curi,metasenv',subst,pbo,pty, attrs),goal)
- in
- let goals =
- goals@(ProofEngineHelpers.compare_metasenvs ~oldmetasenv:metasenv
- ~newmetasenv:metasenv')
- in
- (proof',goals)
- with (* FG: this should be PET.Fail _ *)
- TC.TypeCheckerFailure m ->
- let msg = lazy ("rewrite: "^ Lazy.force m) in
- raise (PET.Fail msg)
-;;
-
-let rewrite_tac ~direction ~pattern equality names =
- let _, hyps_pat, _ = pattern in
- let froms = List.map fst hyps_pat in
- let start = PET.mk_tactic (rewrite ~direction ~pattern equality) in
- let continuation = PESR.rename ~froms ~tos:names in
- if names = [] then start else T.then_ ~start ~continuation
-;;
-
-let rewrite_simpl_tac ~direction ~pattern equality names =
- T.then_
- ~start:(rewrite_tac ~direction ~pattern equality names)
- ~continuation:
- (ReductionTactics.simpl_tac
- ~pattern:(ProofEngineTypes.conclusion_pattern None))
-
-let replace_tac ~(pattern: ProofEngineTypes.lazy_pattern) ~with_what =
- let replace_tac ~(pattern: ProofEngineTypes.lazy_pattern) ~with_what status =
- let _wanted, hyps_pat, concl_pat = pattern in
- let (proof, goal) = status in
- let uri,metasenv,subst,pbo,pty, attrs = proof in
- let (_,context,ty) as conjecture = CicUtil.lookup_meta goal metasenv in
- assert (hyps_pat = []); (*CSC: not implemented yet *)
- let eq_URI =
- match LibraryObjects.eq_URI () with
- Some uri -> uri
- | None -> raise (ProofEngineTypes.Fail (lazy "You need to register the default equality first. Please use the \"default\" command"))
- in
- let context_len = List.length context in
- let subst,metasenv,u,_,selected_terms_with_context =
- ProofEngineHelpers.select ~subst ~metasenv ~ugraph:CicUniv.oblivion_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 = lazy (CicMetaSubst.apply_subst subst (Lazy.force pbo)) in
- let pty = CicMetaSubst.apply_subst subst pty in
- let status = (uri,metasenv,subst,pbo,pty, attrs),goal in
- let ty_of_with_what,u =
- CicTypeChecker.type_of_aux'
- metasenv ~subst context with_what CicUniv.oblivion_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 ~subst context t_in_context
- CicUniv.oblivion_ugraph in
- let b,u = CicReduction.are_convertible ~metasenv ~subst 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,[],Some 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 : ProofEngineTypes.status) =
- match whats with
- [] -> ProofEngineTypes.apply_tactic T.id_tac status
- | (what,lazy_pattern)::tl ->
- let what = S.lift n what in
- let with_what = S.lift n with_what in
- let ty_of_with_what = S.lift n ty_of_with_what in
- ProofEngineTypes.apply_tactic
- (T.thens
- ~start:(
- P.cut_tac
- (C.Appl [
- (C.MutInd (eq_URI, 0, [])) ;
- ty_of_with_what ;
- what ;
- with_what]))
- ~continuations:[
- T.then_
- ~start:(
- rewrite_tac
- ~direction:`LeftToRight ~pattern:lazy_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 hyps =
- try
- match List.hd context with
- Some (Cic.Name name,_) -> [name]
- | _ -> assert false
- with (Failure "hd") -> assert false
- in
- ProofEngineTypes.apply_tactic
- (PESR.clear ~hyps) 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 : ProofEngineTypes.status)
- in
- ProofEngineTypes.mk_tactic (replace_tac ~pattern ~with_what)
-;;
-
-
-(* All these tacs do is applying the right constructor/theorem *)
-
-let reflexivity_tac =
- IntroductionTactics.constructor_tac ~n:1
-;;
-
-let symmetry_tac =
- let symmetry_tac (proof, goal) =
- 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 LibraryObjects.is_eq_URI uri ->
- ProofEngineTypes.apply_tactic
- (PrimitiveTactics.apply_tac
- ~term:(C.Const (LibraryObjects.sym_eq_URI uri, [])))
- (proof,goal)
-
- | _ -> raise (ProofEngineTypes.Fail (lazy "Symmetry failed"))
- in
- ProofEngineTypes.mk_tactic symmetry_tac
-;;
-
-let transitivity_tac ~term =
- let transitivity_tac ~term status =
- let (proof, goal) = status 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 LibraryObjects.is_eq_URI uri ->
- ProofEngineTypes.apply_tactic
- (T.thens
- ~start:(PrimitiveTactics.apply_tac
- ~term: (C.Const (LibraryObjects.trans_eq_URI uri, [])))
- ~continuations:
- [PrimitiveTactics.exact_tac ~term ; T.id_tac ; T.id_tac])
- status
-
- | _ -> raise (ProofEngineTypes.Fail (lazy "Transitivity failed"))
- in
- ProofEngineTypes.mk_tactic (transitivity_tac ~term)
-;;
-
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