factorization of rewrite.

now the tactic also does a beta reduction step
(behaving as expected)

diff --git a/helm/ocaml/tactics/equalityTactics.ml b/helm/ocaml/tactics/equalityTactics.ml
index 718a1bac21cb8902daf6f7519a038cfea1fee2b7..52ea4054de21ae6c0b2d1525f36398c114517e6e 100644 (file)
--- 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 =