X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Focaml%2Fcic_unification%2FcicMetaSubst.ml;h=718951c68a579756e4c4bd1d0994c835d28e2bac;hb=4167cea65ca58897d1a3dbb81ff95de5074700cc;hp=54f13ed1191b87f8c9a505c6dffac48d18e53c75;hpb=de4ba26867714c8df37c5c02d649b5e8581f00b5;p=helm.git

diff --git a/helm/ocaml/cic_unification/cicMetaSubst.ml b/helm/ocaml/cic_unification/cicMetaSubst.ml
index 54f13ed11..718951c68 100644
--- a/helm/ocaml/cic_unification/cicMetaSubst.ml
+++ b/helm/ocaml/cic_unification/cicMetaSubst.ml
@@ -1,18 +1,359 @@
+(* Copyright (C) 2003, 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/.
+ *)
 
 open Printf
 
-exception AssertFailure of string
-exception MetaSubstFailure of string
+(* PROFILING *)
+(*
+let deref_counter = ref 0
+let apply_subst_context_counter = ref 0
+let apply_subst_metasenv_counter = ref 0
+let lift_counter = ref 0
+let subst_counter = ref 0
+let whd_counter = ref 0
+let are_convertible_counter = ref 0
+let metasenv_length = ref 0
+let context_length = ref 0
+let reset_counters () =
+ apply_subst_counter := 0;
+ apply_subst_context_counter := 0;
+ apply_subst_metasenv_counter := 0;
+ lift_counter := 0;
+ subst_counter := 0;
+ whd_counter := 0;
+ are_convertible_counter := 0;
+ metasenv_length := 0;
+ context_length := 0
+let print_counters () =
+  debug_print (lazy (Printf.sprintf
+"apply_subst: %d
+apply_subst_context: %d
+apply_subst_metasenv: %d
+lift: %d
+subst: %d
+whd: %d
+are_convertible: %d
+metasenv length: %d (avg = %.2f)
+context length: %d (avg = %.2f)
+"
+  !apply_subst_counter !apply_subst_context_counter
+  !apply_subst_metasenv_counter !lift_counter !subst_counter !whd_counter
+  !are_convertible_counter !metasenv_length
+  ((float !metasenv_length) /. (float !apply_subst_metasenv_counter))
+  !context_length
+  ((float !context_length) /. (float !apply_subst_context_counter))
+  ))*)
+
+
+
+exception MetaSubstFailure of string Lazy.t
+exception Uncertain of string Lazy.t
+exception AssertFailure of string Lazy.t
+exception DeliftingARelWouldCaptureAFreeVariable;;
+
+let debug_print = fun _ -> ()
+
+type substitution = (int * (Cic.context * Cic.term)) list
+
+(* 
+let rec deref subst =
+  let third _,_,a = a in
+  function
+      Cic.Meta(n,l) as t -> 
+	(try 
+	   deref subst
+	     (CicSubstitution.subst_meta 
+		l (third (CicUtil.lookup_subst n subst))) 
+	 with 
+	   CicUtil.Subst_not_found _ -> t)
+    | t -> t
+;;
+*)
+
+let lookup_subst = CicUtil.lookup_subst
+;;
 
-let debug_print = prerr_endline
 
-type substitution = (int * Cic.term) list
+(* clean_up_meta take a metasenv and a term and make every local context
+of each occurrence of a metavariable consistent with its canonical context, 
+with respect to the hidden hipothesis *)
+
+(*
+let clean_up_meta subst metasenv t =
+  let module C = Cic in
+  let rec aux t =
+  match t with
+      C.Rel _
+    | C.Sort _  -> t
+    | C.Implicit _ -> assert false
+    | C.Meta (n,l) as t ->
+        let cc =
+	  (try
+	     let (cc,_) = lookup_subst n subst in cc
+	   with CicUtil.Subst_not_found _ ->
+	     try
+	       let (_,cc,_) = CicUtil.lookup_meta n metasenv in cc
+             with CicUtil.Meta_not_found _ -> assert false) in
+	let l' = 
+          (try 
+	     List.map2
+	       (fun t1 t2 ->
+		  match t1,t2 with 
+		      None , _ -> None
+		    | _ , t -> t) cc l
+	   with 
+	       Invalid_argument _ -> assert false) in
+        C.Meta (n, l')
+    | C.Cast (te,ty) -> C.Cast (aux te, aux ty)
+    | C.Prod (name,so,dest) -> C.Prod (name, aux so, aux dest)
+    | C.Lambda (name,so,dest) -> C.Lambda (name, aux so, aux dest)
+    | C.LetIn (name,so,dest) -> C.LetIn (name, aux so, aux dest)
+    | C.Appl l -> C.Appl (List.map aux l)
+    | C.Var (uri,exp_named_subst) ->
+        let exp_named_subst' =
+          List.map (fun (uri,t) -> (uri, aux t)) exp_named_subst
+        in
+        C.Var (uri, exp_named_subst')
+    | C.Const (uri, exp_named_subst) ->
+        let exp_named_subst' =
+          List.map (fun (uri,t) -> (uri, aux t)) exp_named_subst
+        in
+        C.Const (uri, exp_named_subst')
+    | C.MutInd (uri,tyno,exp_named_subst) ->
+        let exp_named_subst' =
+          List.map (fun (uri,t) -> (uri, aux t)) exp_named_subst
+        in
+        C.MutInd (uri, tyno, exp_named_subst')
+    | C.MutConstruct (uri,tyno,consno,exp_named_subst) ->
+        let exp_named_subst' =
+          List.map (fun (uri,t) -> (uri, aux t)) exp_named_subst
+        in
+        C.MutConstruct (uri, tyno, consno, exp_named_subst')
+    | C.MutCase (uri,tyno,out,te,pl) ->
+        C.MutCase (uri, tyno, aux out, aux te, List.map aux pl)
+    | C.Fix (i,fl) ->
+       let fl' =
+         List.map
+          (fun (name,j,ty,bo) -> (name, j, aux ty, aux bo)) fl
+       in
+       C.Fix (i, fl')
+    | C.CoFix (i,fl) ->
+       let fl' =
+         List.map
+          (fun (name,ty,bo) -> (name, aux ty, aux bo)) fl
+       in
+       C.CoFix (i, fl')
+ in
+ aux t *)
+
+(*** Functions to apply a substitution ***)
+
+let apply_subst_gen ~appl_fun subst term =
+ let rec um_aux =
+  let module C = Cic in
+  let module S = CicSubstitution in 
+   function
+      C.Rel _ as t -> t
+    | C.Var (uri,exp_named_subst) ->
+       let exp_named_subst' =
+         List.map (fun (uri, t) -> (uri, um_aux t)) exp_named_subst
+       in
+       C.Var (uri, exp_named_subst')
+    | C.Meta (i, l) -> 
+        (try
+          let (_, t,_) = lookup_subst i subst in
+          um_aux (S.subst_meta l t)
+        with CicUtil.Subst_not_found _ -> 
+	  (* unconstrained variable, i.e. free in subst*)
+          let l' =
+            List.map (function None -> None | Some t -> Some (um_aux t)) l
+          in
+           C.Meta (i,l'))
+    | C.Sort _
+    | C.Implicit _ as t -> t
+    | C.Cast (te,ty) -> C.Cast (um_aux te, um_aux ty)
+    | C.Prod (n,s,t) -> C.Prod (n, um_aux s, um_aux t)
+    | C.Lambda (n,s,t) -> C.Lambda (n, um_aux s, um_aux t)
+    | C.LetIn (n,s,t) -> C.LetIn (n, um_aux s, um_aux t)
+    | C.Appl (hd :: tl) -> appl_fun um_aux hd tl
+    | C.Appl _ -> assert false
+    | C.Const (uri,exp_named_subst) ->
+       let exp_named_subst' =
+         List.map (fun (uri, t) -> (uri, um_aux t)) exp_named_subst
+       in
+       C.Const (uri, exp_named_subst')
+    | C.MutInd (uri,typeno,exp_named_subst) ->
+       let exp_named_subst' =
+         List.map (fun (uri, t) -> (uri, um_aux t)) exp_named_subst
+       in
+       C.MutInd (uri,typeno,exp_named_subst')
+    | C.MutConstruct (uri,typeno,consno,exp_named_subst) ->
+       let exp_named_subst' =
+         List.map (fun (uri, t) -> (uri, um_aux t)) exp_named_subst
+       in
+       C.MutConstruct (uri,typeno,consno,exp_named_subst')
+    | C.MutCase (sp,i,outty,t,pl) ->
+       let pl' = List.map um_aux pl in
+       C.MutCase (sp, i, um_aux outty, um_aux t, pl')
+    | C.Fix (i, fl) ->
+       let fl' =
+         List.map (fun (name, i, ty, bo) -> (name, i, um_aux ty, um_aux bo)) fl
+       in
+       C.Fix (i, fl')
+    | C.CoFix (i, fl) ->
+       let fl' =
+         List.map (fun (name, ty, bo) -> (name, um_aux ty, um_aux bo)) fl
+       in
+       C.CoFix (i, fl')
+ in
+ um_aux term
+;;
+
+let apply_subst =
+  let appl_fun um_aux he tl =
+    let tl' = List.map um_aux tl in
+    let t' =
+     match um_aux he with
+        Cic.Appl l -> Cic.Appl (l@tl')
+      | he' -> Cic.Appl (he'::tl')
+    in
+     begin
+      match he with
+         Cic.Meta (m,_) -> CicReduction.head_beta_reduce t'
+       | _ -> t'
+     end
+  in
+  fun s t ->
+(*     incr apply_subst_counter; *)
+    apply_subst_gen ~appl_fun s t
+;;
+
+let rec apply_subst_context subst context =
+(*
+  incr apply_subst_context_counter;
+  context_length := !context_length + List.length context;
+*)
+  List.fold_right
+    (fun item context ->
+      match item with
+      | Some (n, Cic.Decl t) ->
+          let t' = apply_subst subst t in
+          Some (n, Cic.Decl t') :: context
+      | Some (n, Cic.Def (t, ty)) ->
+          let ty' =
+            match ty with
+            | None -> None
+            | Some ty -> Some (apply_subst subst ty)
+          in
+          let t' = apply_subst subst t in
+          Some (n, Cic.Def (t', ty')) :: context
+      | None -> None :: context)
+    context []
+
+let apply_subst_metasenv subst metasenv =
+(*
+  incr apply_subst_metasenv_counter;
+  metasenv_length := !metasenv_length + List.length metasenv;
+*)
+  List.map
+    (fun (n, context, ty) ->
+      (n, apply_subst_context subst context, apply_subst subst ty))
+    (List.filter
+      (fun (i, _, _) -> not (List.mem_assoc i subst))
+      metasenv)
+
+(***** Pretty printing functions ******)
+
+let ppterm subst term = CicPp.ppterm (apply_subst subst term)
+
+let ppterm_in_name_context subst term name_context =
+ CicPp.pp (apply_subst subst term) name_context
+
+let ppterm_in_context subst term context =
+ let name_context =
+  List.map (function None -> None | Some (n,_) -> Some n) context
+ in
+  ppterm_in_name_context subst term name_context
+
+let ppcontext' ?(sep = "\n") subst context =
+ let separate s = if s = "" then "" else s ^ sep in
+  List.fold_right 
+   (fun context_entry (i,name_context) ->
+     match context_entry with
+        Some (n,Cic.Decl t) ->
+         sprintf "%s%s : %s" (separate i) (CicPp.ppname n)
+          (ppterm_in_name_context subst t name_context), (Some n)::name_context
+      | Some (n,Cic.Def (bo,ty)) ->
+         sprintf "%s%s : %s := %s" (separate i) (CicPp.ppname n)
+          (match ty with
+              None -> "_"
+            | Some ty -> ppterm_in_name_context subst ty name_context)
+          (ppterm_in_name_context subst bo name_context), (Some n)::name_context
+       | None ->
+          sprintf "%s_ :? _" (separate i), None::name_context
+    ) context ("",[])
+
+let ppsubst_unfolded subst =
+  String.concat "\n"
+    (List.map
+      (fun (idx, (c, t,_)) ->
+        let context,name_context = ppcontext' ~sep:"; " subst c in
+         sprintf "%s |- ?%d:= %s" context idx
+          (ppterm_in_name_context subst t name_context))
+       subst)
+(* 
+        Printf.sprintf "?%d := %s" idx (CicPp.ppterm term))
+      subst) *)
+;;
 
 let ppsubst subst =
   String.concat "\n"
     (List.map
-      (fun (idx, term) -> Printf.sprintf "?%d := %s" idx (CicPp.ppterm term))
-      subst)
+      (fun (idx, (c, t, _)) ->
+        let context,name_context = ppcontext' ~sep:"; " [] c in
+         sprintf "%s |- ?%d:= %s" context idx
+          (ppterm_in_name_context [] t name_context))
+       subst)
+;;
+
+let ppcontext ?sep subst context = fst (ppcontext' ?sep subst context)
+
+let ppmetasenv ?(sep = "\n") subst metasenv =
+  String.concat sep
+    (List.map
+      (fun (i, c, t) ->
+        let context,name_context = ppcontext' ~sep:"; " subst c in
+         sprintf "%s |- ?%d: %s" context i
+          (ppterm_in_name_context subst t name_context))
+      (List.filter
+        (fun (i, _, _) -> not (List.mem_assoc i subst))
+        metasenv))
+
+let tempi_type_of_aux_subst = ref 0.0;;
+let tempi_subst = ref 0.0;;
+let tempi_type_of_aux = ref 0.0;;
 
 (**** DELIFT ****)
 (* the delift function takes in input a metavariable index, an ordered list of
@@ -49,7 +390,7 @@ let rec force_does_not_occur subst to_be_restricted t =
       C.Rel r when List.mem (r - k) to_be_restricted -> raise Occur
     | C.Rel _
     | C.Sort _ as t -> t
-    | C.Implicit -> assert false
+    | C.Implicit _ -> assert false
     | C.Meta (n, l) ->
        (* we do not retrieve the term associated to ?n in subst since *)
        (* in this way we can restrict if something goes wrong         *)
@@ -122,7 +463,7 @@ let rec restrict subst to_be_restricted metasenv =
       (List.map
         (fun i ->
           try
-           match List.nth context i with
+           match List.nth context (i-1) with
            | None -> assert false
            | Some (n, _) -> CicPp.ppname n
           with
@@ -156,11 +497,11 @@ let rec restrict subst to_be_restricted metasenv =
     | [] -> [], to_be_restricted, []
     | hd::tl ->
         let more_to_be_restricted,restricted,tl' =
-         erase (i+1) to_be_restricted n tl
+          erase (i+1) to_be_restricted n tl
         in
         let restrict_me = List.mem i restricted in
         if restrict_me then
-         more_to_be_restricted, restricted, None:: tl'
+          more_to_be_restricted, restricted, None:: tl'
         else
           (try
             let more_to_be_restricted', hd' =
@@ -180,9 +521,9 @@ let rec restrict subst to_be_restricted metasenv =
           with Occur ->
             more_to_be_restricted, (i :: restricted), None :: tl')
   in
-  let (more_to_be_restricted, metasenv, subst) =
+  let (more_to_be_restricted, metasenv) =  (* restrict metasenv *)
     List.fold_right
-      (fun (n, context, t) (more, metasenv, subst) ->
+      (fun (n, context, t) (more, metasenv) ->
         let to_be_restricted =
           List.map snd (List.filter (fun (m, _) -> m = n) to_be_restricted)
         in
@@ -198,37 +539,69 @@ let rec restrict subst to_be_restricted metasenv =
             force_does_not_occur subst restricted t
           in
           let metasenv' = (n, context', t') :: metasenv in
-          (try
-            let s = List.assoc n subst in
-            try
-              let more_to_be_restricted'', s' =
-                force_does_not_occur subst restricted s
-              in
-              let subst' = (n, s') :: (List.remove_assoc n subst) in
-              let more =
-                more @ more_to_be_restricted @ more_to_be_restricted' @
-                  more_to_be_restricted''
-              in
-              (more, metasenv', subst')
-            with Occur ->
-              raise (MetaSubstFailure (sprintf
-                "Cannot restrict the context of the metavariable ?%d over the hypotheses %s since ?%d is already instantiated with %s and at least one of the hypotheses occurs in the substituted term"
-                n (names_of_context_indexes context to_be_restricted) n
-                (CicPp.ppterm s)))
-           with Not_found -> (more @ more_to_be_restricted @ more_to_be_restricted', metasenv', subst))
+          (more @ more_to_be_restricted @ more_to_be_restricted',
+          metasenv')
         with Occur ->
-          raise (MetaSubstFailure (sprintf
+          raise (MetaSubstFailure (lazy (sprintf
             "Cannot restrict the context of the metavariable ?%d over the hypotheses %s since metavariable's type depends on at least one of them"
-            n (names_of_context_indexes context to_be_restricted))))
-      metasenv ([], [], subst)
+	    n (names_of_context_indexes context to_be_restricted)))))
+      metasenv ([], [])
   in
-  match more_to_be_restricted with
+  let (more_to_be_restricted', subst) = (* restrict subst *)
+    List.fold_right
+      (* TODO: cambiare dopo l'aggiunta del ty *)
+      (fun (n, (context, term,ty)) (more, subst') ->
+        let to_be_restricted =
+          List.map snd (List.filter (fun (m, _) -> m = n) to_be_restricted)
+        in
+        (try
+          let (more_to_be_restricted, restricted, context') =
+           (* just an optimization *)
+            if to_be_restricted = [] then
+              [], [], context
+            else
+              erase 1 to_be_restricted n context
+          in
+          let more_to_be_restricted', term' =
+            force_does_not_occur subst restricted term
+          in
+          let more_to_be_restricted'', ty' =
+            force_does_not_occur subst restricted ty in
+          let subst' = (n, (context', term',ty')) :: subst' in
+          let more = 
+	    more @ more_to_be_restricted 
+	    @ more_to_be_restricted'@more_to_be_restricted'' in
+          (more, subst')
+        with Occur ->
+          let error_msg = lazy (sprintf
+            "Cannot restrict the context of the metavariable ?%d over the hypotheses %s since ?%d is already instantiated with %s and at least one of the hypotheses occurs in the substituted term"
+            n (names_of_context_indexes context to_be_restricted) n
+            (ppterm subst term))
+	  in 
+          (* DEBUG
+          debug_print (lazy error_msg);
+          debug_print (lazy ("metasenv = \n" ^ (ppmetasenv metasenv subst)));
+          debug_print (lazy ("subst = \n" ^ (ppsubst subst)));
+          debug_print (lazy ("context = \n" ^ (ppcontext subst context))); *)
+          raise (MetaSubstFailure error_msg))) 
+      subst ([], []) 
+  in
+  match more_to_be_restricted @ more_to_be_restricted' with
   | [] -> (metasenv, subst)
-  | _ -> restrict subst more_to_be_restricted metasenv
+  | l -> restrict subst l metasenv
 ;;
 
-(*CSC: maybe we should rename delift in abstract, as I did in my dissertation *)
+(*CSC: maybe we should rename delift in abstract, as I did in my dissertation *)(*Andrea: maybe not*)
+
 let delift n subst context metasenv l t =
+(* INVARIANT: we suppose that t is not another occurrence of Meta(n,_), 
+   otherwise the occur check does not make sense *)
+
+(*
+ debug_print (lazy ("sto deliftando il termine " ^ (CicPp.ppterm t) ^ " rispetto
+ al contesto locale " ^ (CicPp.ppterm (Cic.Meta(0,l)))));
+*)
+
  let module S = CicSubstitution in
   let l =
    let (_, canonical_context, _) = CicUtil.lookup_meta n metasenv in
@@ -248,54 +621,57 @@ let delift n subst context metasenv l t =
                     (*CSC: deliftato la regola per il LetIn                 *)
                     (*CSC: FALSO! La regola per il LetIn non lo fa          *)
          else
-          (match List.nth context (m-k-1) with
-            Some (_,C.Def (t,_)) ->
-             (*CSC: Hmmm. This bit of reduction is not in the spirit of    *)
-             (*CSC: first order unification. Does it help or does it harm? *)
-             deliftaux k (S.lift m t)
-          | Some (_,C.Decl t) ->
-             (*CSC: The following check seems to be wrong!             *)
-             (*CSC: B:Set |- ?2 : Set                                  *)
-             (*CSC: A:Set ; x:?2[A/B] |- ?1[x/A] =?= x                 *)
-             (*CSC: Why should I restrict ?2 over B? The instantiation *)
-             (*CSC: ?1 := A is perfectly reasonable and well-typed.    *)
-             (*CSC: Thus I comment out the following two lines that    *)
-             (*CSC: are the incriminated ones.                         *)
-             (*(* It may augment to_be_restricted *)
-               ignore (deliftaux k (S.lift m t)) ;*)
-             (*CSC: end of bug commented out                           *)
-             C.Rel ((position (m-k) l) + k)
-          | None -> raise (MetaSubstFailure "RelToHiddenHypothesis"))
+          (try
+            match List.nth context (m-k-1) with
+               Some (_,C.Def (t,_)) ->
+                (*CSC: Hmmm. This bit of reduction is not in the spirit of    *)
+                (*CSC: first order unification. Does it help or does it harm? *)
+                deliftaux k (S.lift m t)
+             | Some (_,C.Decl t) ->
+                C.Rel ((position (m-k) l) + k)
+             | None -> raise (MetaSubstFailure (lazy "RelToHiddenHypothesis"))
+           with
+            Failure _ ->
+             raise (MetaSubstFailure (lazy "Unbound variable found in deliftaux"))
+          )
      | C.Var (uri,exp_named_subst) ->
         let exp_named_subst' =
          List.map (function (uri,t) -> uri,deliftaux k t) exp_named_subst
         in
          C.Var (uri,exp_named_subst')
      | C.Meta (i, l1) as t -> 
-        if i = n then
-          raise (MetaSubstFailure (sprintf
-            "Cannot unify the metavariable ?%d with a term that has as subterm %s in which the same metavariable occurs (occur check)"
-            i (CicPp.ppterm t)))
-        else
-         (* I do not consider the term associated to ?i in subst since *)
-         (* in this way I can restrict if something goes wrong.        *)
-          let rec deliftl j =
-           function
-              [] -> []
-            | None::tl -> None::(deliftl (j+1) tl)
-            | (Some t)::tl ->
-               let l1' = (deliftl (j+1) tl) in
-                try
-                 Some (deliftaux k t)::l1'
-                with
-                   NotInTheList
-                 | MetaSubstFailure _ ->
-                    to_be_restricted := (i,j)::!to_be_restricted ; None::l1'
-          in
-           let l' = deliftl 1 l1 in
-            C.Meta(i,l')
+         (try
+           let (_,t,_) = CicUtil.lookup_subst i subst in
+             deliftaux k (CicSubstitution.subst_meta l1 t)
+         with CicUtil.Subst_not_found _ ->
+           (* see the top level invariant *)
+           if (i = n) then 
+            raise (MetaSubstFailure (lazy (sprintf
+              "Cannot unify the metavariable ?%d with a term that has as subterm %s in which the same metavariable occurs (occur check)"
+              i (ppterm subst t))))
+          else
+            begin
+           (* I do not consider the term associated to ?i in subst since *)
+           (* in this way I can restrict if something goes wrong.        *)
+              let rec deliftl j =
+                function
+                    [] -> []
+                  | None::tl -> None::(deliftl (j+1) tl)
+                  | (Some t)::tl ->
+                      let l1' = (deliftl (j+1) tl) in
+                        try
+                          Some (deliftaux k t)::l1'
+                        with
+                            NotInTheList
+                          | MetaSubstFailure _ ->
+                              to_be_restricted := 
+                              (i,j)::!to_be_restricted ; None::l1'
+              in
+              let l' = deliftl 1 l1 in
+                C.Meta(i,l')
+            end)
      | C.Sort _ as t -> t
-     | C.Implicit as t -> t
+     | C.Implicit _ as t -> t
      | C.Cast (te,ty) -> C.Cast (deliftaux k te, deliftaux k ty)
      | C.Prod (n,s,t) -> C.Prod (n, deliftaux k s, deliftaux (k+1) t)
      | C.Lambda (n,s,t) -> C.Lambda (n, deliftaux k s, deliftaux (k+1) t)
@@ -346,259 +722,175 @@ let delift n subst context metasenv l t =
       (* The reason is that our delift function is weaker than first  *)
       (* order (in the sense of alpha-conversion). See comment above  *)
       (* related to the delift function.                              *)
-debug_print "!!!!!!!!!!! First Order UnificationFailure, but maybe it could have been successful even in a first order setting (no conversion, only alpha convertibility)! Please, implement a better delift function !!!!!!!!!!!!!!!!" ;
-      raise (MetaSubstFailure (sprintf
+(* debug_print (lazy "First Order UnificationFailure during delift") ;
+debug_print(lazy (sprintf
+        "Error trying to abstract %s over [%s]: the algorithm only tried to abstract over bound variables"
+        (ppterm subst t)
+        (String.concat "; "
+          (List.map
+            (function Some t -> ppterm subst t | None -> "_") l
+          )))); *)
+      raise (Uncertain (lazy (sprintf
         "Error trying to abstract %s over [%s]: the algorithm only tried to abstract over bound variables"
-        (CicPp.ppterm t)
+        (ppterm subst t)
         (String.concat "; "
           (List.map
-            (function Some t -> CicPp.ppterm t | None -> "_")
-            l))))
+            (function Some t -> ppterm subst t | None -> "_")
+            l)))))
    in
    let (metasenv, subst) = restrict subst !to_be_restricted metasenv in
     res, metasenv, subst
 ;;
 
-(**** END OF DELIFT ****)
-
-let apply_subst_gen ~appl_fun subst term =
- let rec um_aux =
+(* delifts a term t of n levels strating from k, that is changes (Rel m)
+ * to (Rel (m - n)) when m > (k + n). if k <= m < k + n delift fails
+ *)
+let delift_rels_from subst metasenv k n =
+ let rec liftaux subst metasenv k =
   let module C = Cic in
-  let module S = CicSubstitution in 
    function
-      C.Rel _ as t -> t
-    | C.Var _  as t -> t
-    | C.Meta (i, l) -> 
+      C.Rel m ->
+       if m < k then
+        C.Rel m, subst, metasenv
+       else if m < k + n then
+         raise DeliftingARelWouldCaptureAFreeVariable
+       else
+        C.Rel (m - n), subst, metasenv
+    | C.Var (uri,exp_named_subst) ->
+       let exp_named_subst',subst,metasenv = 
+        List.fold_right
+         (fun (uri,t) (l,subst,metasenv) ->
+           let t',subst,metasenv = liftaux subst metasenv k t in
+            (uri,t')::l,subst,metasenv) exp_named_subst ([],subst,metasenv)
+       in
+        C.Var (uri,exp_named_subst'),subst,metasenv
+    | C.Meta (i,l) ->
         (try
-          let t = List.assoc i subst in
-          um_aux (S.lift_meta l t)
-        with Not_found -> (* not constrained variable, i.e. free in subst*)
-          let l' =
-            List.map (function None -> None | Some t -> Some (um_aux t)) l
-          in
-           C.Meta (i,l'))
-    | C.Sort _ as t -> t
-    | C.Implicit -> assert false
-    | C.Cast (te,ty) -> C.Cast (um_aux te, um_aux ty)
-    | C.Prod (n,s,t) -> C.Prod (n, um_aux s, um_aux t)
-    | C.Lambda (n,s,t) -> C.Lambda (n, um_aux s, um_aux t)
-    | C.LetIn (n,s,t) -> C.LetIn (n, um_aux s, um_aux t)
-    | C.Appl (hd :: tl) -> appl_fun um_aux hd tl
-    | C.Appl _ -> assert false
+          let (_, t,_) = lookup_subst i subst in
+           liftaux subst metasenv k (CicSubstitution.subst_meta l t)
+         with CicUtil.Subst_not_found _ -> 
+          let l',to_be_restricted,subst,metasenv =
+           let rec aux con l subst metasenv =
+            match l with
+               [] -> [],[],subst,metasenv
+             | he::tl ->
+                let tl',to_be_restricted,subst,metasenv =
+                 aux (con + 1) tl subst metasenv in
+                let he',more_to_be_restricted,subst,metasenv =
+                 match he with
+                    None -> None,[],subst,metasenv
+                  | Some t ->
+                     try
+                      let t',subst,metasenv = liftaux subst metasenv k t in
+                       Some t',[],subst,metasenv
+                     with
+                      DeliftingARelWouldCaptureAFreeVariable ->
+                       None,[i,con],subst,metasenv
+                in
+                 he'::tl',more_to_be_restricted@to_be_restricted,subst,metasenv
+           in
+            aux 1 l subst metasenv in
+          let metasenv,subst = restrict subst to_be_restricted metasenv in
+           C.Meta(i,l'),subst,metasenv)
+    | C.Sort _ as t -> t,subst,metasenv
+    | C.Implicit _ as t -> t,subst,metasenv
+    | C.Cast (te,ty) ->
+       let te',subst,metasenv = liftaux subst metasenv k te in
+       let ty',subst,metasenv = liftaux subst metasenv k ty in
+        C.Cast (te',ty'),subst,metasenv
+    | C.Prod (n,s,t) ->
+       let s',subst,metasenv = liftaux subst metasenv k s in
+       let t',subst,metasenv = liftaux subst metasenv (k+1) t in
+        C.Prod (n,s',t'),subst,metasenv
+    | C.Lambda (n,s,t) ->
+       let s',subst,metasenv = liftaux subst metasenv k s in
+       let t',subst,metasenv = liftaux subst metasenv (k+1) t in
+        C.Lambda (n,s',t'),subst,metasenv
+    | C.LetIn (n,s,t) ->
+       let s',subst,metasenv = liftaux subst metasenv k s in
+       let t',subst,metasenv = liftaux subst metasenv (k+1) t in
+        C.LetIn (n,s',t'),subst,metasenv
+    | C.Appl l ->
+       let l',subst,metasenv =
+        List.fold_right
+         (fun t (l,subst,metasenv) ->
+           let t',subst,metasenv = liftaux subst metasenv k t in
+            t'::l,subst,metasenv) l ([],subst,metasenv) in
+       C.Appl l',subst,metasenv
     | C.Const (uri,exp_named_subst) ->
-       let exp_named_subst' =
-         List.map (fun (uri, t) -> (uri, um_aux t)) exp_named_subst
+       let exp_named_subst',subst,metasenv = 
+        List.fold_right
+         (fun (uri,t) (l,subst,metasenv) ->
+           let t',subst,metasenv = liftaux subst metasenv k t in
+            (uri,t')::l,subst,metasenv) exp_named_subst ([],subst,metasenv)
        in
-       C.Const (uri, exp_named_subst')
-    | C.MutInd (uri,typeno,exp_named_subst) ->
-       let exp_named_subst' =
-         List.map (fun (uri, t) -> (uri, um_aux t)) exp_named_subst
+        C.Const (uri,exp_named_subst'),subst,metasenv
+    | C.MutInd (uri,tyno,exp_named_subst) ->
+       let exp_named_subst',subst,metasenv = 
+        List.fold_right
+         (fun (uri,t) (l,subst,metasenv) ->
+           let t',subst,metasenv = liftaux subst metasenv k t in
+            (uri,t')::l,subst,metasenv) exp_named_subst ([],subst,metasenv)
        in
-       C.MutInd (uri,typeno,exp_named_subst')
-    | C.MutConstruct (uri,typeno,consno,exp_named_subst) ->
-       let exp_named_subst' =
-         List.map (fun (uri, t) -> (uri, um_aux t)) exp_named_subst
+        C.MutInd (uri,tyno,exp_named_subst'),subst,metasenv
+    | C.MutConstruct (uri,tyno,consno,exp_named_subst) ->
+       let exp_named_subst',subst,metasenv = 
+        List.fold_right
+         (fun (uri,t) (l,subst,metasenv) ->
+           let t',subst,metasenv = liftaux subst metasenv k t in
+            (uri,t')::l,subst,metasenv) exp_named_subst ([],subst,metasenv)
        in
-       C.MutConstruct (uri,typeno,consno,exp_named_subst')
+        C.MutConstruct (uri,tyno,consno,exp_named_subst'),subst,metasenv
     | C.MutCase (sp,i,outty,t,pl) ->
-       let pl' = List.map um_aux pl in
-       C.MutCase (sp, i, um_aux outty, um_aux t, pl')
+       let outty',subst,metasenv = liftaux subst metasenv k outty in
+       let t',subst,metasenv = liftaux subst metasenv k t in
+       let pl',subst,metasenv =
+        List.fold_right
+         (fun t (l,subst,metasenv) ->
+           let t',subst,metasenv = liftaux subst metasenv k t in
+            t'::l,subst,metasenv) pl ([],subst,metasenv)
+       in
+        C.MutCase (sp,i,outty',t',pl'),subst,metasenv
     | C.Fix (i, fl) ->
-       let fl' =
-         List.map (fun (name, i, ty, bo) -> (name, i, um_aux ty, um_aux bo)) fl
+       let len = List.length fl in
+       let liftedfl,subst,metasenv =
+        List.fold_right
+         (fun (name, i, ty, bo) (l,subst,metasenv) ->
+           let ty',subst,metasenv = liftaux subst metasenv k ty in
+           let bo',subst,metasenv = liftaux subst metasenv (k+len) bo in
+            (name,i,ty',bo')::l,subst,metasenv
+         ) fl ([],subst,metasenv)
        in
-       C.Fix (i, fl')
+        C.Fix (i, liftedfl),subst,metasenv
     | C.CoFix (i, fl) ->
-       let fl' =
-         List.map (fun (name, ty, bo) -> (name, um_aux ty, um_aux bo)) fl
+       let len = List.length fl in
+       let liftedfl,subst,metasenv =
+        List.fold_right
+         (fun (name, ty, bo) (l,subst,metasenv) ->
+           let ty',subst,metasenv = liftaux subst metasenv k ty in
+           let bo',subst,metasenv = liftaux subst metasenv (k+len) bo in
+            (name,ty',bo')::l,subst,metasenv
+         ) fl ([],subst,metasenv)
        in
-       C.CoFix (i, fl')
+        C.CoFix (i, liftedfl),subst,metasenv
  in
- um_aux term
+  liftaux subst metasenv k
 
-let apply_subst =
-  let appl_fun um_aux he tl =
-    let tl' = List.map um_aux tl in
-      begin
-       match um_aux he with
-          Cic.Appl l -> Cic.Appl (l@tl')
-        | he' -> Cic.Appl (he'::tl')
-      end
-  in
-  apply_subst_gen ~appl_fun
-
-let ppterm subst term = CicPp.ppterm (apply_subst subst term)
-
-(* apply_subst_reducing subst (Some (mtr,reductions_no)) t              *)
-(* performs as (apply_subst subst t) until it finds an application of   *)
-(* (META [meta_to_reduce]) that, once unwinding is performed, creates   *)
-(* a new beta-redex; in this case up to [reductions_no] consecutive     *)
-(* beta-reductions are performed.                                       *)
-(* Hint: this function is usually called when [reductions_no]           *)
-(*  eta-expansions have been performed and the head of the new          *)
-(*  application has been unified with (META [meta_to_reduce]):          *)
-(*  during the unwinding the eta-expansions are undone.                 *)
-
-let apply_subst_reducing meta_to_reduce =
-  let appl_fun um_aux he tl =
-    let tl' = List.map um_aux tl in
-    let t' =
-     match um_aux he with
-        Cic.Appl l -> Cic.Appl (l@tl')
-      | he' -> Cic.Appl (he'::tl')
-    in
-     begin
-      match meta_to_reduce, he with
-         Some (mtr,reductions_no), Cic.Meta (m,_) when m = mtr ->
-          let rec beta_reduce =
-           function
-              (n,(Cic.Appl (Cic.Lambda (_,_,t)::he'::tl'))) when n > 0 ->
-                let he'' = CicSubstitution.subst he' t in
-                 if tl' = [] then
-                  he''
-                 else
-                  beta_reduce (n-1,Cic.Appl(he''::tl'))
-            | (_,t) -> t
-          in
-           beta_reduce (reductions_no,t')
-       | _,_ -> t'
-     end
-  in
-  apply_subst_gen ~appl_fun
-
-let rec apply_subst_context subst context =
-  List.fold_right
-    (fun item context ->
-      match item with
-      | Some (n, Cic.Decl t) ->
-          let t' = apply_subst subst t in
-          Some (n, Cic.Decl t') :: context
-      | Some (n, Cic.Def (t, ty)) ->
-          let ty' =
-            match ty with
-            | None -> None
-            | Some ty -> Some (apply_subst subst ty)
-          in
-          let t' = apply_subst subst t in
-          Some (n, Cic.Def (t', ty')) :: context
-      | None -> None :: context)
-    context []
-
-let apply_subst_metasenv subst metasenv =
-  List.map
-    (fun (n, context, ty) ->
-      (n, apply_subst_context subst context, apply_subst subst ty))
-    (List.filter
-      (fun (i, _, _) -> not (List.exists (fun (j, _) -> (j = i)) subst))
-      metasenv)
-
-let ppterm subst term = CicPp.ppterm (apply_subst subst term)
-
-let ppterm_in_context subst term name_context =
- CicPp.pp (apply_subst subst term) name_context
-
-let ppcontext' ?(sep = "\n") subst context =
- let separate s = if s = "" then "" else s ^ sep in
-  List.fold_right 
-   (fun context_entry (i,name_context) ->
-     match context_entry with
-        Some (n,Cic.Decl t) ->
-         sprintf "%s%s : %s" (separate i) (CicPp.ppname n)
-          (ppterm_in_context subst t name_context), (Some n)::name_context
-      | Some (n,Cic.Def (bo,ty)) ->
-         sprintf "%s%s : %s := %s" (separate i) (CicPp.ppname n)
-          (match ty with
-              None -> "_"
-            | Some ty -> ppterm_in_context subst ty name_context)
-          (ppterm_in_context subst bo name_context), (Some n)::name_context
-       | None ->
-          sprintf "%s_ :? _" (separate i), None::name_context
-    ) context ("",[])
+let delift_rels subst metasenv n t =
+  delift_rels_from subst metasenv 1 n t
+ 
 
-let ppcontext ?sep subst context = fst (ppcontext' ?sep subst context)
+(**** END OF DELIFT ****)
 
-let ppmetasenv ?(sep = "\n") metasenv subst =
-  String.concat sep
-    (List.map
-      (fun (i, c, t) ->
-        let context,name_context = ppcontext' ~sep:"; " subst c in
-         sprintf "%s |- ?%d: %s" context i
-          (ppterm_in_context subst t name_context))
-      (List.filter
-        (fun (i, _, _) -> not (List.exists (fun (j, _) -> (j = i)) subst))
-        metasenv))
 
-(* UNWIND THE MGU INSIDE THE MGU *)
-(*
-let unwind_subst metasenv subst =
-  List.fold_left
-   (fun (unwinded,metasenv) (i,_) ->
-     let (_,canonical_context,_) = CicUtil.lookup_meta i metasenv in
-     let identity_relocation_list =
-      CicMkImplicit.identity_relocation_list_for_metavariable canonical_context
-     in
-      let (_,metasenv',subst') =
-       unwind metasenv subst unwinded (Cic.Meta (i,identity_relocation_list))
-      in
-       subst',metasenv'
-   ) ([],metasenv) subst
-*)
+(** {2 Format-like pretty printers} *)
 
-(* From now on we recreate a kernel abstraction where substitutions are part of
- * the calculus *)
-
-let lift subst n term =
-  let term = apply_subst subst term in
-  try
-    CicSubstitution.lift n term
-  with e ->
-    raise (MetaSubstFailure ("Lift failure: " ^ Printexc.to_string e))
-
-let subst subst t1 t2 =
-  let t1 = apply_subst subst t1 in
-  let t2 = apply_subst subst t2 in
-  try
-    CicSubstitution.subst t1 t2
-  with e ->
-    raise (MetaSubstFailure ("Subst failure: " ^ Printexc.to_string e))
-
-let whd subst context term =
-  let term = apply_subst subst term in
-  let context = apply_subst_context subst context in
-  try
-    CicReduction.whd context term
-  with e ->
-    raise (MetaSubstFailure ("Weak head reduction failure: " ^
-      Printexc.to_string e))
-
-let are_convertible subst context t1 t2 =
-  let context = apply_subst_context subst context in
-  let t1 = apply_subst subst t1 in
-  let t2 = apply_subst subst t2 in
-  CicReduction.are_convertible context t1 t2
+let fpp_gen ppf s =
+  Format.pp_print_string ppf s;
+  Format.pp_print_newline ppf ();
+  Format.pp_print_flush ppf ()
 
-let tempi_type_of_aux_subst = ref 0.0;;
-let tempi_type_of_aux = ref 0.0;;
+let fppsubst ppf subst = fpp_gen ppf (ppsubst subst)
+let fppterm ppf term = fpp_gen ppf (CicPp.ppterm term)
+let fppmetasenv ppf metasenv = fpp_gen ppf (ppmetasenv [] metasenv)
 
-let type_of_aux' metasenv subst context term =
-let time1 = Unix.gettimeofday () in
-  let term = apply_subst subst term in
-  let context = apply_subst_context subst context in
-  let metasenv =
-    List.map
-      (fun (i, c, t) -> (i, apply_subst_context subst c, apply_subst subst t))
-      (List.filter
-        (fun (i, _, _) -> not (List.exists (fun (j, _) -> (j = i)) subst))
-        metasenv)
-  in
-let time2 = Unix.gettimeofday () in
-let res =
-  try
-    CicTypeChecker.type_of_aux' metasenv context term
-  with CicTypeChecker.TypeCheckerFailure msg ->
-    raise (MetaSubstFailure ("Type checker failure: " ^ msg))
-in
-let time3 = Unix.gettimeofday () in
- tempi_type_of_aux_subst := !tempi_type_of_aux_subst +. time3 -. time1 ; 
- tempi_type_of_aux := !tempi_type_of_aux +. time2 -. time1 ; 
- res