X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=components%2Ftactics%2FproofEngineHelpers.ml;fp=components%2Ftactics%2FproofEngineHelpers.ml;h=7d223a4437b4d9fe232032315b9ec8c933a17a6a;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/.
+ *)
+
+(* $Id$ *)
+
+exception Bad_pattern of string Lazy.t
+
+let new_meta_of_proof ~proof:(_, metasenv, _, _, _, _) =
+  CicMkImplicit.new_meta metasenv []
+
+let subst_meta_in_proof proof meta term newmetasenv =
+ let uri,metasenv,initial_subst,bo,ty, attrs = proof in
+   (* empty context is ok for term since it wont be used by apply_subst *)
+   (* hack: since we do not know the context and the type of term, we
+      create a substitution with cc =[] and type = Implicit; they will be
+      in  any case dropped by apply_subst, but it would be better to rewrite
+      the code. Cannot we just use apply_subst_metasenv, etc. ?? *)
+  let subst_in = CicMetaSubst.apply_subst [meta,([], term,Cic.Implicit None)] in
+   let metasenv' =
+    newmetasenv @ (List.filter (function (m,_,_) -> m <> meta) metasenv)
+   in
+    let metasenv'' =
+     List.map
+      (function i,canonical_context,ty ->
+        let canonical_context' =
+         List.map
+          (function
+              Some (n,Cic.Decl s) -> Some (n,Cic.Decl (subst_in s))
+            | None -> None
+            | Some (n,Cic.Def (bo,ty)) ->
+               Some (n,Cic.Def (subst_in bo,subst_in ty))
+          ) canonical_context
+        in
+         i,canonical_context',(subst_in ty)
+      ) metasenv'
+    in
+     let bo' = subst_in bo in
+     (* Metavariables can appear also in the *statement* of the theorem
+      * since the parser does not reject as statements terms with
+      * metavariable therein *)
+     let ty' = subst_in ty in
+      let newproof = uri,metasenv'',initial_subst,bo',ty', attrs in
+       (newproof, metasenv'')
+
+(*CSC: commento vecchio *)
+(* refine_meta_with_brand_new_metasenv meta term subst_in newmetasenv     *)
+(* This (heavy) function must be called when a tactic can instantiate old *)
+(* metavariables (i.e. existential variables). It substitues the metasenv *)
+(* of the proof with the result of removing [meta] from the domain of     *)
+(* [newmetasenv]. Then it replaces Cic.Meta [meta] with [term] everywhere *)
+(* in the current proof. Finally it applies [apply_subst_replacing] to    *)
+(*  current proof.                                                        *)
+(*CSC: A questo punto perche' passare un bo' gia' istantiato, se tanto poi *)
+(*CSC: ci ripasso sopra apply_subst!!!                                     *)
+(*CSC: Attenzione! Ora questa funzione applica anche [subst_in] a *)
+(*CSC: [newmetasenv].                                             *)
+let subst_meta_and_metasenv_in_proof proof meta subst newmetasenv =
+ let (uri,_,initial_subst,bo,ty, attrs) = proof in
+  let subst_in = CicMetaSubst.apply_subst subst in
+  let bo' = subst_in bo in
+  (* Metavariables can appear also in the *statement* of the theorem
+   * since the parser does not reject as statements terms with
+   * metavariable therein *)
+  let ty' = subst_in ty in
+  let metasenv' =
+   List.fold_right
+    (fun metasenv_entry i ->
+      match metasenv_entry with
+         (m,canonical_context,ty) when m <> meta ->
+           let canonical_context' =
+            List.map
+             (function
+                 None -> None
+               | Some (i,Cic.Decl t) -> Some (i,Cic.Decl (subst_in t))
+               | Some (i,Cic.Def (bo,ty)) ->
+                  Some (i,Cic.Def (subst_in bo,subst_in ty))
+             ) canonical_context
+           in
+            (m,canonical_context',subst_in ty)::i
+       | _ -> i
+    ) newmetasenv []
+  in
+  (* qui da capire se per la fase transitoria si fa initial_subst @ subst
+   * oppure subst *)
+   let newproof = uri,metasenv',subst,bo',ty', attrs in
+    (newproof, metasenv')
+
+let compare_metasenvs ~oldmetasenv ~newmetasenv =
+ List.map (function (i,_,_) -> i)
+  (List.filter
+   (function (i,_,_) ->
+     not (List.exists (fun (j,_,_) -> i=j) oldmetasenv)) newmetasenv)
+;;
+
+(** finds the _pointers_ to subterms that are alpha-equivalent to wanted in t *)
+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 _ -> subst,metasenv,ugraph,[]
+      | Cic.Meta (_, ctx) -> 
+          List.fold_left (
+            fun (subst,metasenv,ugraph,acc) e -> 
+              match e with 
+              | 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, t3) -> 
+         let subst,metasenv,ugraph,rest1 =
+          find subst metasenv ugraph context w t1 in
+         let subst,metasenv,ugraph,rest2 =
+          find subst metasenv ugraph context w t2 in
+         let subst,metasenv,ugraph,rest3 =
+          find subst metasenv ugraph (Some (name, Cic.Def (t1,t2))::context)
+           (CicSubstitution.lift 1 w) t3
+         in
+          subst,metasenv,ugraph,rest1 @ rest2 @ rest3
+      | Cic.Appl l -> 
+          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 (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) -> 
+         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 (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 (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 subst metasenv ugraph context wanted t
+  
+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
+  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
+          (map2 "wrong number of argument in explicit substitution"
+            (fun 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 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 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 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, ty1, t1), Cic.LetIn (name, s2, ty2, t2) -> 
+        aux context s1 s2 @
+        aux context ty1 ty2 @
+        aux (add_ctx context name (Cic.Def (s2,ty2))) t1 t2
+    | Cic.LetIn (Cic.Name n1, s1, ty1, t1), 
+      Cic.LetIn ((Cic.Name n2) as name, s2, ty2, t2) when n1 = n2-> 
+        aux context s1 s2 @
+        aux context ty1 ty2 @
+        aux (add_ctx context name (Cic.Def (s2,ty2))) t1 t2
+    | Cic.LetIn (name1, s1, ty1, t1), Cic.LetIn (name2, s2, ty2, t2) -> []
+    | 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 context (List.map snd subst1) (List.map snd subst2)
+    | Cic.MutCase (_, _, out1, t1, pat1), Cic.MutCase (_ , _, out2, t2, 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
+          (map2 "wrong number of mutually recursive functions"
+            (fun (_, _, ty1, bo1) (_, _, ty2, 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
+          (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 
+                (lazy (Printf.sprintf "Pattern %s versus term %s" 
+                  (CicPp.ppterm x)
+                  (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
+   let roots =
+     match where with
+     | None -> []
+     | Some where -> 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 ->
+       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 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
+         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 (_, s, t) ->
+       let b1,s = aux s in
+       let b2,t = aux t in
+        if b1||b2 then
+         true, Cic.Prod (Cic.Anonymous, s, t)
+        else
+         not_found
+    | Cic.Lambda (_, s, t) ->
+       let b1,s = aux s in
+       let b2,t = aux t in
+        if b1||b2 then
+         true, Cic.Lambda (Cic.Anonymous, s, t)
+        else
+         not_found
+    | Cic.LetIn (_, s, ty, t) ->
+       let b1,s = aux s in
+       let b2,ty = aux ty in
+       let b3,t = aux t in
+        if b1||b2||b3 then
+         true, Cic.LetIn (Cic.Anonymous, s, ty, 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) ->
+       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) ->
+       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 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
+         if b then
+          true, Cic.Fix (funno, funs)
+         else
+          not_found
+    | Cic.CoFix (funno, 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
+         if b then
+          true, Cic.CoFix (funno, funs)
+         else
+          not_found
+    | Cic.Rel _
+    | Cic.Sort _
+    | Cic.Implicit _ -> not_found
+  and aux_subst subst =
+    List.fold_right
+     (fun (uri, t) (b,subst) ->
+       let b1,t = aux t in
+        b||b1,(uri, t)::subst) subst (false,[])
+  in
+   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: (Cic.term, Cic.lazy_term) ProofEngineTypes.pattern)
+  =
+   let what, hyp_patterns, goal_pattern = pattern in
+   let find_pattern_for name =
+     try Some (snd (List.find (fun (n, pat) -> Cic.Name n = name) hyp_patterns))
+     with Not_found -> None in
+   (* Multiple hypotheses with the same name can be in the context.
+      In this case we need to pick the last one, but we will perform
+      a fold_right on the context. Thus we pre-process hyp_patterns. *)
+   let full_hyp_pattern =
+    let rec aux blacklist =
+     function
+        [] -> []
+      | None::tl -> None::aux blacklist tl
+      | Some (name,_)::tl ->
+         if List.mem name blacklist then
+          None::aux blacklist tl
+         else
+          find_pattern_for name::aux (name::blacklist) tl
+    in
+     aux [] context
+   in
+   let subst,metasenv,ugraph,ty_terms =
+    select_in_term ~metasenv ~context ~ugraph ~term:ty
+     ~pattern:(what,goal_pattern) in
+   let subst,metasenv,ugraph,context_terms =
+    let subst,metasenv,ugraph,res,_ =
+     (List.fold_right
+      (fun (pattern,entry) (subst,metasenv,ugraph,res,context) ->
+        match entry with
+          None -> subst,metasenv,ugraph,None::res,None::context
+        | Some (name,Cic.Decl term) ->
+            (match pattern 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, Some pat)
+                in
+                 subst,metasenv,ugraph,((Some (`Decl terms))::res),
+                  (entry::context))
+        | Some (name,Cic.Def (bo, ty)) ->
+            (match pattern with
+            | None ->
+               let selected_ty = [] 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, Some pat) in
+                let subst,metasenv,ugraph,terms_ty =
+                 let subst,metasenv,ugraph,res =
+                  select_in_term ~metasenv ~context ~ugraph ~term:ty
+                   ~pattern:(what, Some pat)
+                 in
+                  subst,metasenv,ugraph,res
+                in
+                 subst,metasenv,ugraph,((Some (`Def (terms_bo,terms_ty)))::res),
+                  (entry::context))
+      ) (List.combine full_hyp_pattern 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, ty, t) -> 
+        aux context s @
+        aux context ty @
+        aux (add_ctx context name (Cic.Def (s,ty))) 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 = 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
+
+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 (_,t)) :: _ when name = hyp -> p, t
+      | _ :: tail -> aux (succ p) tail
+      | [] -> raise (ProofEngineTypes.Fail (lazy "lookup_type: not premise in the current goal"))
+   in
+   aux 1 context
+
+(* FG: **********************************************************************)
+
+let get_name context index =
+   try match List.nth context (pred index) with
+      | Some (Cic.Name name, _)     -> Some name
+      | _                           -> None
+   with Invalid_argument "List.nth" -> None
+
+let get_rel context name =
+   let rec aux i = function
+      | []                                      -> None
+      | Some (Cic.Name s, _) :: _ when s = name -> Some (Cic.Rel i)
+      | _ :: tl                                 -> aux (succ i) tl
+   in
+   aux 1 context
+
+let split_with_whd (c, t) =
+   let add s v c = Some (s, Cic.Decl v) :: c in
+   let rec aux whd a n c = function
+      | Cic.Prod (s, v, t)  -> aux false ((c, v) :: a) (succ n) (add s v c) t
+      | v when whd          -> (c, v) :: a, n
+      | v                   -> aux true a n c (CicReduction.whd c v)
+    in
+    aux false [] 0 c t
+
+let split_with_normalize (c, t) =
+   let add s v c = Some (s, Cic.Decl v) :: c in
+   let rec aux a n c = function
+      | Cic.Prod (s, v, t)  -> aux ((c, v) :: a) (succ n) (add s v c) t
+      | v                   -> (c, v) :: a, n
+    in
+    aux [] 0 c (CicReduction.normalize c t)
+
+  (* menv sorting *)
+module OT = 
+  struct 
+    type t = Cic.conjecture
+    let compare (i,_,_) (j,_,_) = Pervasives.compare i j
+  end
+module MS = HTopoSort.Make(OT)
+let relations_of_menv m c =
+  let i, ctx, ty = c in
+  let m = List.filter (fun (j,_,_) -> j <> i) m in
+  let m_ty = List.map fst (CicUtil.metas_of_term ty) in
+  let m_ctx = 
+    List.flatten
+      (List.map 
+        (function 
+         | None -> []
+         | Some (_,Cic.Decl t) ->
+             List.map fst (CicUtil.metas_of_term ty)
+         | Some (_,Cic.Def (t,ty)) -> 
+             List.map fst (CicUtil.metas_of_term ty) @
+             List.map fst (CicUtil.metas_of_term t))
+        ctx)
+  in
+  let metas = HExtlib.list_uniq (List.sort compare (m_ty @ m_ctx)) in
+  List.filter (fun (i,_,_) -> List.exists ((=) i) metas) m
+;;
+let sort_metasenv (m : Cic.metasenv) =
+  (MS.topological_sort m (relations_of_menv m) : Cic.metasenv)
+;;