X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=components%2Ftactics%2FequalityTactics.ml;fp=components%2Ftactics%2FequalityTactics.ml;h=72a63571cef7221ae211360b5d44f58ba36a2f20;hp=0000000000000000000000000000000000000000;hb=f61af501fb4608cc4fb062a0864c774e677f0d76;hpb=58ae1809c352e71e7b5530dc41e2bfc834e1aef1

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+(* 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_tac ~direction ~pattern:(wanted,hyps_pat,concl_pat) equality =
+ let _rewrite_tac 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
+  let gsort,_ =
+   CicTypeChecker.type_of_aux' metasenv context gty CicUniv.oblivion_ugraph in
+  match hyps_pat with
+     he::(_::_ as tl) ->
+       PET.apply_tactic
+        (T.then_
+          (rewrite_tac ~direction
+           ~pattern:(None,[he],None) equality)
+          (rewrite_tac ~direction ~pattern:(None,tl,concl_pat)
+            (S.lift 1 equality))
+        ) status
+   | [_] as hyps_pat when concl_pat <> None ->
+       PET.apply_tactic
+        (T.then_
+          (rewrite_tac ~direction
+           ~pattern:(None,hyps_pat,None) equality)
+          (rewrite_tac ~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 rec find_hyp n =
+       function
+          [] -> assert false
+        | Some (Cic.Name s,Cic.Decl ty)::_ when name = s ->
+           Cic.Rel n, S.lift n ty
+        | Some (Cic.Name s,Cic.Def _)::_ when name = s -> 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 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 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) =
+   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' ~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 = CicMetaSubst.apply_subst subst 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 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 _ -> 
+      let msg = lazy "rewrite: nothing to rewrite" in
+      raise (PET.Fail msg)
+ in    
+  PET.mk_tactic _rewrite_tac 
+
+let rewrite_tac ~direction ~pattern equality names =
+   let _, hyps_pat, _ = pattern in 
+   let froms = List.map fst hyps_pat in
+   let start = rewrite_tac ~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 ~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,_subst,pbo,pty, attrs),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,[],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,_subst,_,_, _ = 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,_subst,_,_, _) = 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,_subst,_,_, _) = 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)
+;;
+