X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Focaml%2Ftactics%2FproofEngineHelpers.ml;h=fd336910ea4a899e3d5fcdc15870bffd929afb12;hb=97c2d258a5c524eb5c4b85208899d80751a2c82f;hp=20e8341a6c90d987a401491902a26898f85f7818;hpb=180f30d039f1d2894c6a118ecee5549835127c72;p=helm.git

diff --git a/helm/ocaml/tactics/proofEngineHelpers.ml b/helm/ocaml/tactics/proofEngineHelpers.ml
index 20e8341a6..fd336910e 100644
--- a/helm/ocaml/tactics/proofEngineHelpers.ml
+++ b/helm/ocaml/tactics/proofEngineHelpers.ml
@@ -23,7 +23,7 @@
  * http://cs.unibo.it/helm/.
  *)
 
-exception Bad_pattern of string
+exception Bad_pattern of string Lazy.t
 
 let new_meta_of_proof ~proof:(_, metasenv, _, _) =
   CicMkImplicit.new_meta metasenv []
@@ -46,9 +46,10 @@ let subst_meta_in_proof proof meta term newmetasenv =
          List.map
           (function
               Some (n,Cic.Decl s) -> Some (n,Cic.Decl (subst_in s))
-            | Some (n,Cic.Def (s,None)) -> Some (n,Cic.Def ((subst_in s),None))
+            | Some (n,Cic.Def (s,None)) -> Some (n,Cic.Def (subst_in s,None))
             | None -> None
-            | Some (_,Cic.Def (_,Some _)) -> assert false
+            | Some (n,Cic.Def (bo,Some ty)) ->
+               Some (n,Cic.Def (subst_in bo,Some (subst_in ty)))
           ) canonical_context
         in
          i,canonical_context',(subst_in ty)
@@ -92,8 +93,9 @@ let subst_meta_and_metasenv_in_proof proof meta subst_in newmetasenv =
                  None -> None
                | Some (i,Cic.Decl t) -> Some (i,Cic.Decl (subst_in t))
                | Some (i,Cic.Def (t,None))  ->
-                  Some (i,Cic.Def ((subst_in t),None))
-               | Some (_,Cic.Def (_,Some _))  -> assert false
+                  Some (i,Cic.Def (subst_in t,None))
+               | Some (i,Cic.Def (bo,Some ty)) ->
+                  Some (i,Cic.Def (subst_in bo,Some (subst_in ty)))
              ) canonical_context
            in
             (m,canonical_context',subst_in ty)::i
@@ -111,147 +113,573 @@ let compare_metasenvs ~oldmetasenv ~newmetasenv =
 ;;
 
 (** finds the _pointers_ to subterms that are alpha-equivalent to wanted in t *)
-let find_subterms ~eq ~wanted t =
-  let rec find w t =
-    if eq w t then 
-      [t]
-    else
+let find_subterms ~subst ~metasenv ~ugraph ~wanted ~context t =
+  let rec find subst metasenv ugraph context w t =
+   try
+    let subst,metasenv,ugraph =
+     CicUnification.fo_unif_subst subst context metasenv w t ugraph
+    in
+      subst,metasenv,ugraph,[context,t]
+   with
+     CicUnification.UnificationFailure _
+   | CicUnification.Uncertain _ ->
       match t with
       | Cic.Sort _ 
-      | Cic.Rel _ -> []
+      | Cic.Rel _ -> subst,metasenv,ugraph,[]
       | Cic.Meta (_, ctx) -> 
           List.fold_left (
-            fun acc e -> 
+            fun (subst,metasenv,ugraph,acc) e -> 
               match e with 
-              | None -> acc 
-              | Some t -> find w t @ acc
-          ) [] ctx
-      | Cic.Lambda (_, t1, t2) 
-      | Cic.Prod (_, t1, t2) 
-      | Cic.LetIn (_, t1, t2) -> 
-          find w t1 @ find (CicSubstitution.lift 1 w) t2
+              | None -> subst,metasenv,ugraph,acc 
+              | Some t ->
+                 let subst,metasenv,ugraph,res =
+                  find subst metasenv ugraph context w t
+                 in
+                  subst,metasenv,ugraph, res @ acc
+          ) (subst,metasenv,ugraph,[]) ctx
+      | Cic.Lambda (name, t1, t2) 
+      | Cic.Prod (name, t1, t2) ->
+         let subst,metasenv,ugraph,rest1 =
+          find subst metasenv ugraph context w t1 in
+         let subst,metasenv,ugraph,rest2 =
+          find subst metasenv ugraph (Some (name, Cic.Decl t1)::context)
+           (CicSubstitution.lift 1 w) t2
+         in
+          subst,metasenv,ugraph,rest1 @ rest2
+      | Cic.LetIn (name, t1, t2) -> 
+         let subst,metasenv,ugraph,rest1 =
+          find subst metasenv ugraph context w t1 in
+         let subst,metasenv,ugraph,rest2 =
+          find subst metasenv ugraph (Some (name, Cic.Def (t1,None))::context)
+           (CicSubstitution.lift 1 w) t2
+         in
+          subst,metasenv,ugraph,rest1 @ rest2
       | Cic.Appl l -> 
-          List.fold_left (fun acc t -> find w t @ acc) [] l
-      | Cic.Cast (t, ty) -> find w t @ find w ty
+          List.fold_left
+           (fun (subst,metasenv,ugraph,acc) t ->
+             let subst,metasenv,ugraph,res =
+              find subst metasenv ugraph context w t
+             in
+              subst,metasenv,ugraph,res @ acc)
+           (subst,metasenv,ugraph,[]) l
+      | Cic.Cast (t, ty) ->
+         let subst,metasenv,ugraph,rest =
+          find subst metasenv ugraph context w t in
+         let subst,metasenv,ugraph,resty =
+          find subst metasenv ugraph context w ty
+         in
+          subst,metasenv,ugraph,rest @ resty
       | Cic.Implicit _ -> assert false
       | Cic.Const (_, esubst)
       | Cic.Var (_, esubst) 
       | Cic.MutInd (_, _, esubst) 
       | Cic.MutConstruct (_, _, _, esubst) -> 
-          List.fold_left (fun acc (_, t) -> find w t @ acc) [] esubst
+          List.fold_left
+           (fun (subst,metasenv,ugraph,acc) (_, t) ->
+             let subst,metasenv,ugraph,res =
+              find subst metasenv ugraph context w t
+             in
+              subst,metasenv,ugraph,res @ acc)
+           (subst,metasenv,ugraph,[]) esubst
       | Cic.MutCase (_, _, outty, indterm, patterns) -> 
-          find w outty @ find w indterm @ 
-            List.fold_left (fun acc p -> find w p @ acc) [] patterns
+         let subst,metasenv,ugraph,resoutty =
+          find subst metasenv ugraph context w outty in
+         let subst,metasenv,ugraph,resindterm =
+          find subst metasenv ugraph context w indterm in
+         let subst,metasenv,ugraph,respatterns =
+          List.fold_left
+           (fun (subst,metasenv,ugraph,acc) p ->
+             let subst,metaseng,ugraph,res =
+              find subst metasenv ugraph context w p
+             in
+              subst,metasenv,ugraph,res @ acc
+           ) (subst,metasenv,ugraph,[]) patterns
+         in
+          subst,metasenv,ugraph,resoutty @ resindterm @ respatterns
       | Cic.Fix (_, funl) -> 
+         let tys =
+          List.map (fun (n,_,ty,_) -> Some (Cic.Name n,(Cic.Decl ty))) funl
+         in
           List.fold_left (
-            fun acc (_, _, ty, bo) -> find w ty @ find w bo @ acc
-          ) [] funl
+            fun (subst,metasenv,ugraph,acc) (_, _, ty, bo) ->
+             let subst,metasenv,ugraph,resty =
+              find subst metasenv ugraph context w ty in
+             let subst,metasenv,ugraph,resbo =
+              find subst metasenv ugraph (tys @ context) w bo
+             in
+              subst,metasenv,ugraph, resty @ resbo @ acc
+          ) (subst,metasenv,ugraph,[]) funl
       | Cic.CoFix (_, funl) ->
+         let tys =
+          List.map (fun (n,ty,_) -> Some (Cic.Name n,(Cic.Decl ty))) funl
+         in
           List.fold_left (
-            fun acc (_, ty, bo) -> find w ty @ find w bo @ acc
-          ) [] funl
+            fun (subst,metasenv,ugraph,acc) (_, ty, bo) ->
+             let subst,metasenv,ugraph,resty =
+              find subst metasenv ugraph context w ty in
+             let subst,metasenv,ugraph,resbo =
+              find subst metasenv ugraph (tys @ context) w bo
+             in
+              subst,metasenv,ugraph, resty @ resbo @ acc
+          ) (subst,metasenv,ugraph,[]) funl
   in
-  find wanted t
+  find subst metasenv ugraph context wanted t
   
-let select ~term ~pattern =
-  let add_ctx i name entry =
-      (Some (name, entry)) :: i
+let select_in_term ~metasenv ~context ~ugraph ~term ~pattern:(wanted,where) =
+  let add_ctx context name entry =
+      (Some (name, entry)) :: context
+  in
+  let map2 error_msg f l1 l2 = 
+    try 
+      List.map2 f l1 l2 
+    with
+    | Invalid_argument _ -> raise (Bad_pattern (lazy error_msg))
   in
-  (* i is the number of binder traversed *) 
-  let rec aux i pattern term =
-    match (pattern, term) with
-    | Cic.Implicit (Some `Hole), t -> [i,t]
+  let rec aux context where term =
+    match (where, term) with
+    | Cic.Implicit (Some `Hole), t -> [context,t]
     | Cic.Implicit (Some `Type), t -> []
     | Cic.Implicit None,_ -> []
     | Cic.Meta (_, ctxt1), Cic.Meta (_, ctxt2) ->
         List.concat
-          (List.map2
+          (map2 "wrong number of argument in explicit substitution"
             (fun t1 t2 ->
-              (match (t1, t2) with Some t1, Some t2 -> aux i t1 t2 | _ -> []))
+              (match (t1, t2) with
+                  Some t1, Some t2 -> aux context t1 t2
+                | _ -> []))
             ctxt1 ctxt2)
-    | Cic.Cast (te1, ty1), Cic.Cast (te2, ty2) -> aux i te1 te2 @ aux i ty1 ty2
+    | Cic.Cast (te1, ty1), Cic.Cast (te2, ty2) ->
+       aux context te1 te2 @ aux context ty1 ty2
     | Cic.Prod (Cic.Anonymous, s1, t1), Cic.Prod (name, s2, t2)
     | Cic.Lambda (Cic.Anonymous, s1, t1), Cic.Lambda (name, s2, t2) ->
-        aux i s1 s2 @ aux (add_ctx i name (Cic.Decl s2)) t1 t2
+        aux context s1 s2 @ aux (add_ctx context name (Cic.Decl s2)) t1 t2
     | Cic.Prod (Cic.Name n1, s1, t1), 
       Cic.Prod ((Cic.Name n2) as name , s2, t2)
     | Cic.Lambda (Cic.Name n1, s1, t1), 
       Cic.Lambda ((Cic.Name n2) as name, s2, t2) when n1 = n2->
-        aux i s1 s2 @ aux (add_ctx i name (Cic.Decl s2)) t1 t2
+        aux context s1 s2 @ aux (add_ctx context name (Cic.Decl s2)) t1 t2
     | Cic.Prod (name1, s1, t1), Cic.Prod (name2, s2, t2)
     | Cic.Lambda (name1, s1, t1), Cic.Lambda (name2, s2, t2) -> []
     | Cic.LetIn (Cic.Anonymous, s1, t1), Cic.LetIn (name, s2, t2) -> 
-        aux i s1 s2 @ aux (add_ctx i name (Cic.Def (s2,None))) t1 t2
+        aux context s1 s2 @ aux (add_ctx context name (Cic.Def (s2,None))) t1 t2
     | Cic.LetIn (Cic.Name n1, s1, t1), 
       Cic.LetIn ((Cic.Name n2) as name, s2, t2) when n1 = n2-> 
-        aux i s1 s2 @ aux (add_ctx i name (Cic.Def (s2,None))) t1 t2
+        aux context s1 s2 @ aux (add_ctx context name (Cic.Def (s2,None))) t1 t2
     | Cic.LetIn (name1, s1, t1), Cic.LetIn (name2, s2, t2) -> []
-    | Cic.Appl terms1, Cic.Appl terms2 -> auxs i terms1 terms2
+    | Cic.Appl terms1, Cic.Appl terms2 -> auxs context terms1 terms2
     | Cic.Var (_, subst1), Cic.Var (_, subst2)
     | Cic.Const (_, subst1), Cic.Const (_, subst2)
     | Cic.MutInd (_, _, subst1), Cic.MutInd (_, _, subst2)
     | Cic.MutConstruct (_, _, _, subst1), Cic.MutConstruct (_, _, _, subst2) ->
-        auxs i (List.map snd subst1) (List.map snd subst2)
+        auxs context (List.map snd subst1) (List.map snd subst2)
     | Cic.MutCase (_, _, out1, t1, pat1), Cic.MutCase (_ , _, out2, t2, pat2) ->
-        aux i out1 out2 @ aux i t1 t2 @ auxs i pat1 pat2
+        aux context out1 out2 @ aux context t1 t2 @ auxs context pat1 pat2
     | Cic.Fix (_, funs1), Cic.Fix (_, funs2) ->
+       let tys =
+        List.map (fun (n,_,ty,_) -> Some (Cic.Name n,(Cic.Decl ty))) funs2
+       in
         List.concat
-          (List.map2
+          (map2 "wrong number of mutually recursive functions"
             (fun (_, _, ty1, bo1) (_, _, ty2, bo2) -> 
-              aux i ty1 ty2 @ aux i bo1 bo2)
+              aux context ty1 ty2 @ aux (tys @ context) bo1 bo2)
             funs1 funs2)
     | Cic.CoFix (_, funs1), Cic.CoFix (_, funs2) ->
+       let tys =
+        List.map (fun (n,ty,_) -> Some (Cic.Name n,(Cic.Decl ty))) funs2
+       in
         List.concat
-          (List.map2
-            (fun (_, ty1, bo1) (_, ty2, bo2) -> aux i ty1 ty2 @ aux i bo1 bo2)
+          (map2 "wrong number of mutually co-recursive functions"
+            (fun (_, ty1, bo1) (_, ty2, bo2) ->
+              aux context ty1 ty2 @ aux (tys @ context) bo1 bo2)
             funs1 funs2)
     | x,y -> 
         raise (Bad_pattern 
-                (Printf.sprintf "Pattern %s versus term %s" 
+                (lazy (Printf.sprintf "Pattern %s versus term %s" 
                   (CicPp.ppterm x)
-                  (CicPp.ppterm y)))
-  and auxs i terms1 terms2 =  (* as aux for list of terms *)
-    List.concat (List.map2 (fun t1 t2 -> aux i t1 t2) terms1 terms2)
+                  (CicPp.ppterm y))))
+  and auxs context terms1 terms2 =  (* as aux for list of terms *)
+    List.concat (map2 "wrong number of arguments in application"
+      (fun t1 t2 -> aux context t1 t2) terms1 terms2)
   in
-  aux [] pattern term
+   let context_len = List.length context in
+   let roots = aux context where term in
+    match wanted with
+       None -> [],metasenv,ugraph,roots
+     | Some wanted ->
+        let rec find_in_roots =
+         function
+            [] -> [],metasenv,ugraph,[]
+          | (context',where)::tl ->
+             let subst,metasenv,ugraph,tl' = find_in_roots tl in
+             let subst,metasenv,ugraph,found =
+              let wanted, metasenv, ugraph = wanted context' metasenv ugraph in
+               find_subterms ~subst ~metasenv ~ugraph ~wanted ~context:context'
+                where
+             in
+              subst,metasenv,ugraph,found @ tl'
+        in
+         find_in_roots roots
 
+(** create a pattern from a term and a list of subterms.
+* the pattern is granted to have a ? for every subterm that has no selected
+* subterms
+* @param equality equality function used while walking the term. Defaults to
+* physical equality (==) *)
 let pattern_of ?(equality=(==)) ~term terms =
   let (===) x y = equality x y in
+  let not_found = false, Cic.Implicit None in
   let rec aux t =
     match t with
-    | t when List.exists (fun t' -> t === t') terms -> Cic.Implicit (Some `Hole)
-    | Cic.Var (uri, subst) -> Cic.Var (uri, aux_subst subst)
+    | t when List.exists (fun t' -> t === t') terms ->
+       true,Cic.Implicit (Some `Hole)
+    | Cic.Var (uri, subst) ->
+       let b,subst = aux_subst subst in
+        if b then
+         true,Cic.Var (uri, subst)
+        else
+         not_found
     | Cic.Meta (i, ctxt) ->
-        let ctxt =
-          List.map (function None -> None | Some t -> Some (aux t)) ctxt
+        let b,ctxt =
+          List.fold_right
+           (fun e (b,ctxt) ->
+             match e with
+                None -> b,None::ctxt
+              | Some t -> let bt,t = aux t in b||bt ,Some t::ctxt
+           ) ctxt (false,[])
         in
-        Cic.Meta (i, ctxt)
-    | Cic.Cast (t, ty) -> Cic.Cast (aux t, aux ty)
-    | Cic.Prod (name, s, t) -> Cic.Prod (name, aux s, aux t)
-    | Cic.Lambda (name, s, t) -> Cic.Lambda (name, aux s, aux t)
-    | Cic.LetIn (name, s, t) -> Cic.LetIn (name, aux s, aux t)
-    | Cic.Appl terms -> Cic.Appl (List.map aux terms)
-    | Cic.Const (uri, subst) -> Cic.Const (uri, aux_subst subst)
-    | Cic.MutInd (uri, tyno, subst) -> Cic.MutInd (uri, tyno, aux_subst subst)
+         if b then
+          true,Cic.Meta (i, ctxt)
+         else
+          not_found
+    | Cic.Cast (te, ty) ->
+       let b1,te = aux te in
+       let b2,ty = aux ty in
+        if b1||b2 then true,Cic.Cast (te, ty)
+        else
+         not_found
+    | Cic.Prod (name, s, t) ->
+       let b1,s = aux s in
+       let b2,t = aux t in
+        if b1||b2 then
+         true, Cic.Prod (name, s, t)
+        else
+         not_found
+    | Cic.Lambda (name, s, t) ->
+       let b1,s = aux s in
+       let b2,t = aux t in
+        if b1||b2 then
+         true, Cic.Lambda (name, s, t)
+        else
+         not_found
+    | Cic.LetIn (name, s, t) ->
+       let b1,s = aux s in
+       let b2,t = aux t in
+        if b1||b2 then
+         true, Cic.LetIn (name, s, t)
+        else
+         not_found
+    | Cic.Appl terms ->
+       let b,terms =
+        List.fold_right
+         (fun t (b,terms) ->
+           let bt,t = aux t in
+            b||bt,t::terms
+         ) terms (false,[])
+       in
+        if b then
+         true,Cic.Appl terms
+        else
+         not_found
+    | Cic.Const (uri, subst) ->
+       let b,subst = aux_subst subst in
+        if b then
+         true, Cic.Const (uri, subst)
+        else
+         not_found
+    | Cic.MutInd (uri, tyno, subst) ->
+       let b,subst = aux_subst subst in
+        if b then
+         true, Cic.MutInd (uri, tyno, subst)
+        else
+         not_found
     | Cic.MutConstruct (uri, tyno, consno, subst) ->
-        Cic.MutConstruct (uri, tyno, consno, aux_subst subst)
+       let b,subst = aux_subst subst in
+        if b then
+         true, Cic.MutConstruct (uri, tyno, consno, subst)
+        else
+         not_found
     | Cic.MutCase (uri, tyno, outty, t, pat) ->
-        Cic.MutCase (uri, tyno, aux outty, aux t, List.map aux pat)
+       let b1,outty = aux outty in
+       let b2,t = aux t in
+       let b3,pat =
+        List.fold_right
+         (fun t (b,pat) ->
+           let bt,t = aux t in
+            bt||b,t::pat
+         ) pat (false,[])
+       in
+        if b1 || b2 || b3 then
+         true, Cic.MutCase (uri, tyno, outty, t, pat)
+        else
+         not_found
     | Cic.Fix (funno, funs) ->
-        let funs =
-          List.map (fun (name, i, ty, bo) -> (name, i, aux ty, aux bo)) funs
+        let b,funs =
+          List.fold_right
+           (fun (name, i, ty, bo) (b,funs) ->
+             let b1,ty = aux ty in
+             let b2,bo = aux bo in
+              b||b1||b2, (name, i, ty, bo)::funs) funs (false,[])
         in
-        Cic.Fix (funno, funs)
+         if b then
+          true, Cic.Fix (funno, funs)
+         else
+          not_found
     | Cic.CoFix (funno, funs) ->
-        let funs =
-          List.map (fun (name, ty, bo) -> (name, aux ty, aux bo)) funs
+        let b,funs =
+          List.fold_right
+           (fun (name, ty, bo) (b,funs) ->
+             let b1,ty = aux ty in
+             let b2,bo = aux bo in
+              b||b1||b2, (name, ty, bo)::funs) funs (false,[])
         in
-        Cic.CoFix (funno, funs)
+         if b then
+          true, Cic.CoFix (funno, funs)
+         else
+          not_found
     | Cic.Rel _
     | Cic.Sort _
-    | Cic.Implicit _ -> t
+    | Cic.Implicit _ -> not_found
   and aux_subst subst =
-    List.map (fun (uri, t) -> (uri, aux t)) subst
+    List.fold_right
+     (fun (uri, t) (b,subst) ->
+       let b1,t = aux t in
+        b||b1,(uri, t)::subst) subst (false,[])
   in
-  aux term
+   snd (aux term)
 
+exception Fail of string Lazy.t
+
+  (** select metasenv conjecture pattern
+  * select all subterms of [conjecture] matching [pattern].
+  * It returns the set of matched terms (that can be compared using physical
+  * equality to the subterms of [conjecture]) together with their contexts.
+  * The representation of the set mimics the ProofEngineTypes.pattern type:
+  * a list of hypothesis (names of) together with the list of its matched
+  * subterms (and their contexts) + the list of matched subterms of the
+  * with their context conclusion. Note: in the result the list of hypothesis
+  * has an entry for each entry in the context and in the same order.
+  * Of course the list of terms (with their context) associated to the
+  * hypothesis name may be empty. 
+  *
+  * @raise Bad_pattern
+  * *)
+  let select ~metasenv ~ugraph ~conjecture:(_,context,ty)
+       ~pattern:(what,hyp_patterns,goal_pattern)
+  =
+   let find_pattern_for name =
+     try Some (snd (List.find (fun (n, pat) -> Cic.Name n = name) hyp_patterns))
+     with Not_found -> None in
+   let subst,metasenv,ugraph,ty_terms =
+    select_in_term ~metasenv ~context ~ugraph ~term:ty
+     ~pattern:(what,goal_pattern) in
+   let context_len = List.length context in
+   let subst,metasenv,ugraph,context_terms =
+    let subst,metasenv,ugraph,res,_ =
+     (List.fold_right
+      (fun entry (subst,metasenv,ugraph,res,context) ->
+        match entry with
+          None -> subst,metasenv,ugraph,(None::res),(None::context)
+        | Some (name,Cic.Decl term) ->
+            (match find_pattern_for name with
+            | None ->
+               subst,metasenv,ugraph,((Some (`Decl []))::res),(entry::context)
+            | Some pat ->
+                let subst,metasenv,ugraph,terms =
+                 select_in_term ~metasenv ~context ~ugraph ~term
+                  ~pattern:(what,pat)
+                in
+                 subst,metasenv,ugraph,((Some (`Decl terms))::res),
+                  (entry::context))
+        | Some (name,Cic.Def (bo, ty)) ->
+            (match find_pattern_for name with
+            | None ->
+               let selected_ty=match ty with None -> None | Some _ -> Some [] in
+                subst,metasenv,ugraph,((Some (`Def ([],selected_ty)))::res),
+                 (entry::context)
+            | Some pat -> 
+                let subst,metasenv,ugraph,terms_bo =
+                 select_in_term ~metasenv ~context ~ugraph ~term:bo
+                  ~pattern:(what,pat) in
+                let subst,metasenv,ugraph,terms_ty =
+                 match ty with
+                    None -> subst,metasenv,ugraph,None
+                  | Some ty ->
+                     let subst,metasenv,ugraph,res =
+                      select_in_term ~metasenv ~context ~ugraph ~term:ty
+                       ~pattern:(what,pat)
+                     in
+                      subst,metasenv,ugraph,Some res
+                in
+                 subst,metasenv,ugraph,((Some (`Def (terms_bo,terms_ty)))::res),
+                  (entry::context))
+      ) context (subst,metasenv,ugraph,[],[]))
+    in
+     subst,metasenv,ugraph,res
+   in
+    subst,metasenv,ugraph,context_terms, ty_terms
+
+(** locate_in_term equality what where context
+* [what] must match a subterm of [where] according to [equality]
+* It returns the matched terms together with their contexts in [where]
+* [equality] defaults to physical equality
+* [context] must be the context of [where]
+*)
+let locate_in_term ?(equality=(fun _ -> (==))) what ~where context =
+  let add_ctx context name entry =
+      (Some (name, entry)) :: context in
+  let rec aux context where =
+   if equality context what where then [context,where]
+   else
+    match where with
+    | Cic.Implicit _
+    | Cic.Meta _
+    | Cic.Rel _
+    | Cic.Sort _
+    | Cic.Var _
+    | Cic.Const _
+    | Cic.MutInd _
+    | Cic.MutConstruct _ -> []
+    | Cic.Cast (te, ty) -> aux context te @ aux context ty
+    | Cic.Prod (name, s, t)
+    | Cic.Lambda (name, s, t) ->
+        aux context s @ aux (add_ctx context name (Cic.Decl s)) t
+    | Cic.LetIn (name, s, t) -> 
+        aux context s @ aux (add_ctx context name (Cic.Def (s,None))) t
+    | Cic.Appl tl -> auxs context tl
+    | Cic.MutCase (_, _, out, t, pat) ->
+        aux context out @ aux context t @ auxs context pat
+    | Cic.Fix (_, funs) ->
+       let tys =
+        List.map (fun (n,_,ty,_) -> Some (Cic.Name n,(Cic.Decl ty))) funs
+       in
+        List.concat
+          (List.map
+            (fun (_, _, ty, bo) -> 
+              aux context ty @ aux (tys @ context) bo)
+            funs)
+    | Cic.CoFix (_, funs) ->
+       let tys =
+        List.map (fun (n,ty,_) -> Some (Cic.Name n,(Cic.Decl ty))) funs
+       in
+        List.concat
+          (List.map
+            (fun (_, ty, bo) ->
+              aux context ty @ aux (tys @ context) bo)
+            funs)
+  and auxs context tl =  (* as aux for list of terms *)
+    List.concat (List.map (fun t -> aux context t) tl)
+  in
+   aux context where
+
+(** locate_in_conjecture equality what where context
+* [what] must match a subterm of [where] according to [equality]
+* It returns the matched terms together with their contexts in [where]
+* [equality] defaults to physical equality
+* [context] must be the context of [where]
+*)
+let locate_in_conjecture ?(equality=fun _ -> (==)) what (_,context,ty) =
+ let context,res =
+  List.fold_right
+   (fun entry (context,res) ->
+     match entry with
+        None -> entry::context, res
+      | Some (_, Cic.Decl ty) ->
+         let res = res @ locate_in_term what ~where:ty context in
+         let context' = entry::context in
+          context',res
+      | Some (_, Cic.Def (bo,ty)) ->
+         let res = res @ locate_in_term what ~where:bo context in
+         let res =
+          match ty with
+             None -> res
+           | Some ty ->
+              res @ locate_in_term what ~where:ty context in
+         let context' = entry::context in
+          context',res
+   ) context ([],[])
+ in
+  res @ locate_in_term what ~where:ty context
+
+(* saturate_term newmeta metasenv context ty goal_arity                       *)
+(* Given a type [ty] (a backbone), it returns its suffix of length            *)
+(* [goal_arity] head and a new metasenv in which there is new a META for each *)
+(* hypothesis, a list of arguments for the new applications and the index of  *)
+(* the last new META introduced. The nth argument in the list of arguments is *)
+(* just the nth new META.                                                     *)
+let saturate_term newmeta metasenv context ty goal_arity =
+ let module C = Cic in
+ let module S = CicSubstitution in
+ assert (goal_arity >= 0);
+  let rec aux newmeta ty =
+   match ty with
+      C.Cast (he,_) -> aux newmeta he
+(* CSC: patch to generate ?1 : ?2 : Type in place of ?1 : Type to simulate ?1 :< Type
+      (* If the expected type is a Type, then also Set is OK ==>
+      *  we accept any term of type Type *)
+      (*CSC: BUG HERE: in this way it is possible for the term of
+      * type Type to be different from a Sort!!! *)
+    | C.Prod (name,(C.Sort (C.Type _) as s),t) ->
+       (* TASSI: ask CSC if BUG HERE refers to the C.Cast or C.Propd case *)
+       let irl =
+         CicMkImplicit.identity_relocation_list_for_metavariable context
+       in
+        let newargument = C.Meta (newmeta+1,irl) in
+         let (res,newmetasenv,arguments,lastmeta) =
+          aux (newmeta + 2) (S.subst newargument t)
+         in
+          res,
+           (newmeta,[],s)::(newmeta+1,context,C.Meta (newmeta,[]))::newmetasenv,
+           newargument::arguments,lastmeta
+*)
+    | C.Prod (name,s,t) ->
+       let irl =
+         CicMkImplicit.identity_relocation_list_for_metavariable context
+       in
+        let newargument = C.Meta (newmeta,irl) in
+         let res,newmetasenv,arguments,lastmeta,prod_no =
+          aux (newmeta + 1) (S.subst newargument t)
+         in
+          if prod_no + 1 = goal_arity then
+           let head = CicReduction.normalize ~delta:false context ty in
+            head,[],[],lastmeta,goal_arity + 1
+          else
+           (** NORMALIZE RATIONALE 
+            * we normalize the target only NOW since we may be in this case:
+            * A1 -> A2 -> T where T = (\lambda x.A3 -> P) k  
+            * and we want a mesasenv with ?1:A1 and ?2:A2 and not
+            * ?1, ?2, ?3 (that is the one we whould get if we start from the
+            * beta-normalized A1 -> A2 -> A3 -> P **)
+           let s' = CicReduction.normalize ~delta:false context s in
+            res,(newmeta,context,s')::newmetasenv,newargument::arguments,
+             lastmeta,prod_no + 1
+    | t ->
+       let head = CicReduction.normalize ~delta:false context t in
+        match CicReduction.whd context head with
+           C.Prod _ as head' -> aux newmeta head'
+         | _ -> head,[],[],newmeta,0
+  in
+   (* WARNING: here we are using the invariant that above the most *)
+   (* recente new_meta() there are no used metas.                  *)
+   let res,newmetasenv,arguments,lastmeta,_ = aux newmeta ty in
+    res,metasenv @ newmetasenv,arguments,lastmeta
+
+let lookup_type metasenv context hyp =
+   let rec aux p = function
+      | Some (Cic.Name name, Cic.Decl t) :: _ when name = hyp -> p, t
+      | Some (Cic.Name name, Cic.Def (_, Some t)) :: _ when name = hyp -> p, t
+      | Some (Cic.Name name, Cic.Def (u, _)) :: tail when name = hyp ->
+         p, fst (CicTypeChecker.type_of_aux' metasenv tail u CicUniv.empty_ugraph)
+      | _ :: tail -> aux (succ p) tail
+      | [] -> raise (ProofEngineTypes.Fail (lazy "lookup_type: not premise in the current goal"))
+   in
+   aux 1 context