X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=components%2Fng_kernel%2FnCicReduction.ml;fp=components%2Fng_kernel%2FnCicReduction.ml;h=db19c9c9617dd13d237c99bb941daa19ed351d87;hp=0000000000000000000000000000000000000000;hb=f61af501fb4608cc4fb062a0864c774e677f0d76;hpb=58ae1809c352e71e7b5530dc41e2bfc834e1aef1

diff --git a/components/ng_kernel/nCicReduction.ml b/components/ng_kernel/nCicReduction.ml
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+++ b/components/ng_kernel/nCicReduction.ml
@@ -0,0 +1,620 @@
+(*
+    ||M||  This file is part of HELM, an Hypertextual, Electronic        
+    ||A||  Library of Mathematics, developed at the Computer Science     
+    ||T||  Department, University of Bologna, Italy.                     
+    ||I||                                                                
+    ||T||  HELM is free software; you can redistribute it and/or         
+    ||A||  modify it under the terms of the GNU General Public License   
+    \   /  version 2 or (at your option) any later version.      
+     \ /   This software is distributed as is, NO WARRANTY.     
+      V_______________________________________________________________ *)
+
+(* $Id$ *)
+
+(* TODO unify exceptions *)
+
+exception WrongUriToInductiveDefinition;;
+exception Impossible of int;;
+exception ReferenceToConstant;;
+exception ReferenceToVariable;;
+exception ReferenceToCurrentProof;;
+exception ReferenceToInductiveDefinition;;
+
+let debug = false
+let profile = false
+let debug_print s = if debug then prerr_endline (Lazy.force s)
+
+let fdebug = ref 1;;
+let debug t env s =
+ let rec debug_aux t i =
+  let module C = Cic in
+  let module U = UriManager in
+   CicPp.ppobj (C.Variable ("DEBUG", None, t, [], [])) ^ "\n" ^ i
+ in
+  if !fdebug = 0 then
+   debug_print (lazy (s ^ "\n" ^ List.fold_right debug_aux (t::env) ""))
+;;
+
+module type Strategy =
+ sig
+  type stack_term
+  type env_term
+  type config = int * env_term list * NCic.term * stack_term list
+  val to_env :
+   reduce: (config -> config) ->
+   unwind: (config -> NCic.term) ->
+   config -> env_term
+  val from_stack : stack_term -> config
+  val from_stack_list_for_unwind :
+   unwind: (config -> NCic.term) ->
+   stack_term list -> NCic.term list
+  val from_env : env_term -> config
+  val from_env_for_unwind :
+   unwind: (config -> NCic.term) ->
+   env_term -> NCic.term
+  val stack_to_env :
+   reduce: (config -> config) ->
+   unwind: (config -> NCic.term) ->
+   stack_term -> env_term
+  val compute_to_env :
+   reduce: (config -> config) ->
+   unwind: (config -> NCic.term) ->
+   int -> env_term list -> 
+    NCic.term -> env_term
+  val compute_to_stack :
+   reduce: (config -> config) ->
+   unwind: (config -> NCic.term) ->
+   config -> stack_term
+ end
+;;
+
+module CallByValueByNameForUnwind' =
+ struct
+  type config = int * env_term list * NCic.term * stack_term list
+  and stack_term = config lazy_t * NCic.term lazy_t (* cbv, cbn *)
+  and env_term = config lazy_t * NCic.term lazy_t (* cbv, cbn *)
+  let to_env ~reduce ~unwind c = lazy (reduce c),lazy (unwind c)
+  let from_stack (c,_) = Lazy.force c
+  let from_stack_list_for_unwind ~unwind:_ l = 
+   List.map (function (_,c) -> Lazy.force c) l
+  let from_env (c,_) = Lazy.force c
+  let from_env_for_unwind ~unwind:_ (_,c) = Lazy.force c
+  let stack_to_env ~reduce:_ ~unwind:_ config = config
+  let compute_to_env ~reduce ~unwind k e t =
+   lazy (reduce (k,e,t,[])), lazy (unwind (k,e,t,[]))
+  let compute_to_stack ~reduce ~unwind config = 
+   lazy (reduce config), lazy (unwind config)
+ end
+;;
+
+
+(* {{{ module CallByValueByNameForUnwind =
+ struct
+  type config = int * env_term list * ens_term Cic.explicit_named_substitution * Cic.term * stack_term list
+  and stack_term = config
+  and env_term = config * config (* cbv, cbn *)
+  and ens_term = config * config (* cbv, cbn *)
+
+  let to_env c = c,c
+  let to_ens c = c,c
+  let from_stack config = config
+  let from_stack_list_for_unwind ~unwind l = List.map unwind l
+  let from_env (c,_) = c
+  let from_ens (c,_) = c
+  let from_env_for_unwind ~unwind (_,c) = unwind c
+  let from_ens_for_unwind ~unwind (_,c) = unwind c
+  let stack_to_env ~reduce ~unwind config = reduce config, (0,[],[],unwind config,[])
+  let compute_to_env ~reduce ~unwind k e ens t = (k,e,ens,t,[]), (k,e,ens,t,[])
+  let compute_to_stack ~reduce ~unwind config = config
+ end
+;;
+
+
+(* Old Machine *)
+module CallByNameStrategy =
+ struct
+  type stack_term = Cic.term
+  type env_term = Cic.term
+  type ens_term = Cic.term
+  type config = int * env_term list * ens_term Cic.explicit_named_substitution * Cic.term * stack_term list
+  let to_env v = v
+  let to_ens v = v
+  let from_stack ~unwind v = v
+  let from_stack_list ~unwind l = l
+  let from_env v = v
+  let from_ens v = v
+  let from_env_for_unwind ~unwind v = v
+  let from_ens_for_unwind ~unwind v = v
+  let stack_to_env ~reduce ~unwind v = v
+  let compute_to_stack ~reduce ~unwind k e ens t = unwind k e ens t
+  let compute_to_env ~reduce ~unwind k e ens t = unwind k e ens t
+ end
+;;
+
+module CallByNameStrategy =
+ struct
+  type config = int * env_term list * ens_term Cic.explicit_named_substitution * Cic.term * stack_term list
+  and stack_term = config
+  and env_term = config
+  and ens_term = config
+
+  let to_env c = c
+  let to_ens c = c
+  let from_stack config = config
+  let from_stack_list_for_unwind ~unwind l = List.map unwind l
+  let from_env c = c
+  let from_ens c = c
+  let from_env_for_unwind ~unwind c = unwind c
+  let from_ens_for_unwind ~unwind c = unwind c
+  let stack_to_env ~reduce ~unwind config = 0,[],[],unwind config,[]
+  let compute_to_env ~reduce ~unwind k e ens t = k,e,ens,t,[]
+  let compute_to_stack ~reduce ~unwind config = config
+ end
+;;
+
+module CallByValueStrategy =
+ struct
+  type stack_term = Cic.term
+  type env_term = Cic.term
+  type ens_term = Cic.term
+  type config = int * env_term list * ens_term Cic.explicit_named_substitution * Cic.term * stack_term list
+  let to_env v = v
+  let to_ens v = v
+  let from_stack ~unwind v = v
+  let from_stack_list ~unwind l = l
+  let from_env v = v
+  let from_ens v = v
+  let from_env_for_unwind ~unwind v = v
+  let from_ens_for_unwind ~unwind v = v
+  let stack_to_env ~reduce ~unwind v = v
+  let compute_to_stack ~reduce ~unwind k e ens t = reduce (k,e,ens,t,[])
+  let compute_to_env ~reduce ~unwind k e ens t = reduce (k,e,ens,t,[])
+ end
+;;
+
+module CallByValueStrategyByNameOnConstants =
+ struct
+  type stack_term = Cic.term
+  type env_term = Cic.term
+  type ens_term = Cic.term
+  type config = int * env_term list * ens_term Cic.explicit_named_substitution * Cic.term * stack_term list
+  let to_env v = v
+  let to_ens v = v
+  let from_stack ~unwind v = v
+  let from_stack_list ~unwind l = l
+  let from_env v = v
+  let from_ens v = v
+  let from_env_for_unwind ~unwind v = v
+  let from_ens_for_unwind ~unwind v = v
+  let stack_to_env ~reduce ~unwind v = v
+  let compute_to_stack ~reduce ~unwind k e ens =
+   function
+      Cic.Const _ as t -> unwind k e ens t    
+    | t -> reduce (k,e,ens,t,[])
+  let compute_to_env ~reduce ~unwind k e ens =
+   function
+      Cic.Const _ as t -> unwind k e ens t    
+    | t -> reduce (k,e,ens,t,[])
+ end
+;;
+
+module LazyCallByValueStrategy =
+ struct
+  type stack_term = Cic.term lazy_t
+  type env_term = Cic.term lazy_t
+  type ens_term = Cic.term lazy_t
+  type config = int * env_term list * ens_term Cic.explicit_named_substitution * Cic.term * stack_term list
+  let to_env v = lazy v
+  let to_ens v = lazy v
+  let from_stack ~unwind v = Lazy.force v
+  let from_stack_list ~unwind l = List.map (from_stack ~unwind) l
+  let from_env v = Lazy.force v
+  let from_ens v = Lazy.force v
+  let from_env_for_unwind ~unwind v = Lazy.force v
+  let from_ens_for_unwind ~unwind v = Lazy.force v
+  let stack_to_env ~reduce ~unwind v = v
+  let compute_to_stack ~reduce ~unwind k e ens t = lazy (reduce (k,e,ens,t,[]))
+  let compute_to_env ~reduce ~unwind k e ens t = lazy (reduce (k,e,ens,t,[]))
+ end
+;;
+
+module LazyCallByValueStrategyByNameOnConstants =
+ struct
+  type stack_term = Cic.term lazy_t
+  type env_term = Cic.term lazy_t
+  type ens_term = Cic.term lazy_t
+  type config = int * env_term list * ens_term Cic.explicit_named_substitution * Cic.term * stack_term list
+  let to_env v = lazy v
+  let to_ens v = lazy v
+  let from_stack ~unwind v = Lazy.force v
+  let from_stack_list ~unwind l = List.map (from_stack ~unwind) l
+  let from_env v = Lazy.force v
+  let from_ens v = Lazy.force v
+  let from_env_for_unwind ~unwind v = Lazy.force v
+  let from_ens_for_unwind ~unwind v = Lazy.force v
+  let stack_to_env ~reduce ~unwind v = v
+  let compute_to_stack ~reduce ~unwind k e ens t =
+   lazy (
+    match t with
+       Cic.Const _ as t -> unwind k e ens t    
+     | t -> reduce (k,e,ens,t,[]))
+  let compute_to_env ~reduce ~unwind k e ens t =
+   lazy (
+    match t with
+       Cic.Const _ as t -> unwind k e ens t    
+     | t -> reduce (k,e,ens,t,[]))
+ end
+;;
+
+module LazyCallByNameStrategy =
+ struct
+  type stack_term = Cic.term lazy_t
+  type env_term = Cic.term lazy_t
+  type ens_term = Cic.term lazy_t
+  type config = int * env_term list * ens_term Cic.explicit_named_substitution * Cic.term * stack_term list
+  let to_env v = lazy v
+  let to_ens v = lazy v
+  let from_stack ~unwind v = Lazy.force v
+  let from_stack_list ~unwind l = List.map (from_stack ~unwind) l
+  let from_env v = Lazy.force v
+  let from_ens v = Lazy.force v
+  let from_env_for_unwind ~unwind v = Lazy.force v
+  let from_ens_for_unwind ~unwind v = Lazy.force v
+  let stack_to_env ~reduce ~unwind v = v
+  let compute_to_stack ~reduce ~unwind k e ens t = lazy (unwind k e ens t)
+  let compute_to_env ~reduce ~unwind k e ens t = lazy (unwind k e ens t)
+ end
+;;
+
+module
+ LazyCallByValueByNameOnConstantsWhenFromStack_ByNameStrategyWhenFromEnvOrEns
+=
+ struct
+  type stack_term = reduce:bool -> Cic.term
+  type env_term = reduce:bool -> Cic.term
+  type ens_term = reduce:bool -> Cic.term
+  type config = int * env_term list * ens_term Cic.explicit_named_substitution * Cic.term * stack_term list
+  let to_env v =
+   let value = lazy v in
+    fun ~reduce -> Lazy.force value
+  let to_ens v =
+   let value = lazy v in
+    fun ~reduce -> Lazy.force value
+  let from_stack ~unwind v = (v ~reduce:false)
+  let from_stack_list ~unwind l = List.map (from_stack ~unwind) l
+  let from_env v = (v ~reduce:true)
+  let from_ens v = (v ~reduce:true)
+  let from_env_for_unwind ~unwind v = (v ~reduce:true)
+  let from_ens_for_unwind ~unwind v = (v ~reduce:true)
+  let stack_to_env ~reduce ~unwind v = v
+  let compute_to_stack ~reduce ~unwind k e ens t =
+   let svalue =
+     lazy (
+      match t with
+         Cic.Const _ as t -> unwind k e ens t    
+       | t -> reduce (k,e,ens,t,[])
+     ) in
+   let lvalue =
+    lazy (unwind k e ens t)
+   in
+    fun ~reduce ->
+     if reduce then Lazy.force svalue else Lazy.force lvalue
+  let compute_to_env ~reduce ~unwind k e ens t =
+   let svalue =
+     lazy (
+      match t with
+         Cic.Const _ as t -> unwind k e ens t    
+       | t -> reduce (k,e,ens,t,[])
+     ) in
+   let lvalue =
+    lazy (unwind k e ens t)
+   in
+    fun ~reduce ->
+     if reduce then Lazy.force svalue else Lazy.force lvalue
+ end
+;;
+
+module ClosuresOnStackByValueFromEnvOrEnsStrategy =
+ struct
+  type config = int * env_term list * ens_term Cic.explicit_named_substitution * Cic.term * stack_term list
+  and stack_term = config
+  and env_term = config
+  and ens_term = config
+
+  let to_env config = config
+  let to_ens config = config
+  let from_stack config = config
+  let from_stack_list_for_unwind ~unwind l = List.map unwind l
+  let from_env v = v
+  let from_ens v = v
+  let from_env_for_unwind ~unwind config = unwind config
+  let from_ens_for_unwind ~unwind config = unwind config
+  let stack_to_env ~reduce ~unwind config = reduce config
+  let compute_to_env ~reduce ~unwind k e ens t = (k,e,ens,t,[])
+  let compute_to_stack ~reduce ~unwind config = config
+ end
+;;
+
+module ClosuresOnStackByValueFromEnvOrEnsByNameOnConstantsStrategy =
+ struct
+  type stack_term =
+   int * Cic.term list * Cic.term Cic.explicit_named_substitution * Cic.term
+  type env_term = Cic.term
+  type ens_term = Cic.term
+  type config = int * env_term list * ens_term Cic.explicit_named_substitution * Cic.term * stack_term list
+  let to_env v = v
+  let to_ens v = v
+  let from_stack ~unwind (k,e,ens,t) = unwind k e ens t
+  let from_stack_list ~unwind l = List.map (from_stack ~unwind) l
+  let from_env v = v
+  let from_ens v = v
+  let from_env_for_unwind ~unwind v = v
+  let from_ens_for_unwind ~unwind v = v
+  let stack_to_env ~reduce ~unwind (k,e,ens,t) =
+   match t with
+      Cic.Const _ as t -> unwind k e ens t    
+    | t -> reduce (k,e,ens,t,[])
+  let compute_to_env ~reduce ~unwind k e ens t =
+   unwind k e ens t
+  let compute_to_stack ~reduce ~unwind k e ens t = (k,e,ens,t)
+ end
+;;
+
+}}} *)
+
+module Reduction(RS : Strategy) =
+ struct
+  type env = RS.env_term list
+  type stack = RS.stack_term list
+  type config = int * env * NCic.term * stack
+
+  let rec unwind (k,e,t,s) =
+    let t = 
+      if k = 0 then t 
+      else 
+        NCicSubstitution.psubst ~avoid_beta_redexes:true  
+          true 0 (RS.from_env_for_unwind ~unwind) e t
+    in
+    if s = [] then t 
+    else NCic.Appl(t::(RS.from_stack_list_for_unwind ~unwind s))
+  ;;
+
+  let list_nth l n = try List.nth l n with Failure _ -> assert false;;
+  let rec replace i s t =
+    match i,s with
+    |  0,_::tl -> t::tl
+    | n,he::tl -> he::(replace (n - 1) tl t)
+    | _,_ -> assert false
+  ;;
+
+  let rec reduce ~delta ?(subst = []) context : config -> config = 
+   let rec aux = function
+     | k, e, NCic.Rel n, s when n <= k ->
+        let k',e',t',s' = RS.from_env (list_nth e (n-1)) in
+        aux (k',e',t',s'@s)
+     | k, _, NCic.Rel n, s as config (* when n > k *) ->
+        (match List.nth context (n - 1 - k) with
+        | (_,NCic.Decl _) -> config
+        | (_,NCic.Def (x,_)) -> aux (0,[],NCicSubstitution.lift (n - k) x,s))
+     | (k, e, NCic.Meta (n,l), s) as config ->
+        (try 
+           let _,_, term,_ = NCicUtils.lookup_subst n subst in
+           aux (k, e, NCicSubstitution.subst_meta l term,s)
+         with  NCicUtils.Subst_not_found _ -> config)
+     | (_, _, NCic.Sort _, _) as config -> config
+     | (_, _, NCic.Implicit _, _) -> assert false
+     | (_, _, NCic.Prod _, _) as config -> config
+     | (_, _, NCic.Lambda _, []) as config -> config
+     | (k, e, NCic.Lambda (_,_,t), p::s) ->
+         aux (k+1, (RS.stack_to_env ~reduce:aux ~unwind p)::e, t,s)
+     | (k, e, NCic.LetIn (_,_,m,t), s) ->
+        let m' = RS.compute_to_env ~reduce:aux ~unwind k e m in
+         aux (k+1, m'::e, t, s)
+     | (_, _, NCic.Appl [], _) -> assert false
+     | (k, e, NCic.Appl (he::tl), s) ->
+        let tl' =
+         List.map (fun t->RS.compute_to_stack ~reduce:aux ~unwind (k,e,t,[])) tl
+        in
+         aux (k, e, he, tl' @ s)
+     | (_, _, NCic.Const
+            (NReference.Ref (_,_,NReference.Def) as refer), s) as config ->
+         let _,_,body,_,_,height = NCicEnvironment.get_checked_def refer in
+         if delta > height then config else aux (0, [], body, s) 
+     | (_, _, NCic.Const (NReference.Ref 
+               (_,_,NReference.Fix (fixno,recindex)) as refer),s) as config ->
+        let fixes,_, height = NCicEnvironment.get_checked_fixes refer in
+        if delta > height then config else
+        (match
+          try Some (RS.from_stack (List.nth s recindex))
+          with Failure _ -> None
+        with 
+        | None -> config
+        | Some recparam ->
+           match reduce ~delta:0 ~subst context recparam with
+           | (_,_,NCic.Const (NReference.Ref (_,_,NReference.Con _)), _) as c ->
+               let new_s =
+                 replace recindex s (RS.compute_to_stack ~reduce:aux ~unwind c)
+               in
+               let _,_,_,_,body = List.nth fixes fixno in
+               aux (0, [], body, new_s)
+           | _ -> config)
+     | (_, _, NCic.Const _, _) as config -> config
+     | (k, e, NCic.Match (_,_,term,pl),s) as config ->
+        let decofix = function
+          | (_,_,NCic.Const(NReference.Ref(_,_,NReference.CoFix c)as refer),s)->
+             let cofixes,_,_ = NCicEnvironment.get_checked_cofixes refer in
+             let _,_,_,_,body = List.nth cofixes c in
+             reduce ~delta:0 ~subst context (0,[],body,s)
+          | config -> config
+        in
+        (match decofix (reduce ~delta:0 ~subst context (k,e,term,[])) with
+        | (_, _, NCic.Const (NReference.Ref (_,_,NReference.Con (_,j))),[]) ->
+            aux (k, e, List.nth pl (j-1), s)
+        | (_, _, NCic.Const 
+             (NReference.Ref (_,_,NReference.Con (_,j)) as refer), s') ->
+          let leftno = NCicEnvironment.get_indty_leftno refer in
+          let _,params = HExtlib.split_nth leftno s' in
+          aux (k, e, List.nth pl (j-1), params@s)
+        | _ -> config)
+   in
+    aux
+  ;;
+
+  let whd ?(delta=0) ?(subst=[]) context t = 
+   unwind (reduce ~delta ~subst context (0, [], t, []))
+  ;;
+
+ end
+;;
+
+
+(* {{{ ROTTO = rompe l'unificazione poiche' riduce gli argomenti di un'applicazione
+           senza ridurre la testa
+module R = Reduction CallByNameStrategy;; OK 56.368s
+module R = Reduction CallByValueStrategy;; ROTTO
+module R = Reduction CallByValueStrategyByNameOnConstants;; ROTTO
+module R = Reduction LazyCallByValueStrategy;; ROTTO
+module R = Reduction LazyCallByValueStrategyByNameOnConstants;; ROTTO
+module R = Reduction LazyCallByNameStrategy;; OK 0m56.398s
+module R = Reduction
+ LazyCallByValueByNameOnConstantsWhenFromStack_ByNameStrategyWhenFromEnvOrEns;;
+ OK 59.058s
+module R = Reduction ClosuresOnStackByValueFromEnvOrEnsStrategy;; OK 58.583s
+module R = Reduction
+ ClosuresOnStackByValueFromEnvOrEnsByNameOnConstantsStrategy;; OK 58.094s
+module R = Reduction(ClosuresOnStackByValueFromEnvOrEnsStrategy);; OK 58.127s
+module R = Reduction(CallByValueByNameForUnwind);; 
+module R = Reduction(CallByNameStrategy);;
+module R = Reduction(ClosuresOnStackByValueFromEnvOrEnsStrategy);;}}} *)
+module RS = CallByValueByNameForUnwind';;
+
+module R = Reduction(RS);;
+module U = UriManager;;
+
+let whd = R.whd
+
+(*
+let whd =
+ let profiler_whd = HExtlib.profile ~enable:profile "are_convertible.whd" in
+  fun ?(delta=true) ?(subst=[]) context t ->
+   profiler_whd.HExtlib.profile (whd ~delta ~subst context) t
+*)
+
+(* mimic ocaml (<< 3.08) "=" behaviour. Tests physical equality first then
+ * fallbacks to structural equality *)
+let (===) x y = Pervasives.compare x y = 0 ;;
+
+module C = NCic
+
+(* t1, t2 must be well-typed *)
+let are_convertible whd ?(subst=[]) ?(metasenv=[])  =
+ let rec aux test_equality_only context t1 t2 =
+   let rec aux2 test_equality_only t1 t2 =
+     if t1 === t2 then
+       true
+     else
+       match (t1,t2) with
+       | (C.Sort (C.Type a), C.Sort (C.Type b)) -> a <= b
+       | (C.Sort s1,C.Sort (C.Type _)) -> (not test_equality_only)
+       | (C.Sort s1, C.Sort s2) -> s1 = s2
+
+       | (C.Prod (name1,s1,t1), C.Prod(_,s2,t2)) ->
+           aux true context s1 s2 &&
+           aux test_equality_only ((name1, C.Decl s1)::context) t1 t2
+       | (C.Lambda (name1,s1,t1), C.Lambda(_,s2,t2)) ->
+          aux true context s1 s2 && 
+          aux true ((name1, C.Decl s1)::context) t1 t2
+       | (C.LetIn (name1,ty1,s1,t1), C.LetIn(_,ty2,s2,t2)) ->
+          aux test_equality_only context ty1 ty2 &&
+          aux test_equality_only context s1 s2 &&
+          aux test_equality_only ((name1, C.Def (s1,ty1))::context) t1 t2
+
+       | (C.Meta (n1,(s1, C.Irl i1)), C.Meta (n2,(s2, C.Irl i2))) 
+          when n1 = n2 && s1 = s2 -> true
+       | (C.Meta (n1,(s1, l1)), C.Meta (n2,(s2, l2))) when n1 = n2 -> 
+          let l1 = NCicUtils.expand_local_context l1 in
+          let l2 = NCicUtils.expand_local_context l2 in
+          (try List.for_all2 
+            (fun t1 t2 -> aux test_equality_only context 
+              (NCicSubstitution.lift s1 t1) 
+              (NCicSubstitution.lift s2 t2))  
+            l1 l2
+          with Invalid_argument _ -> false)
+
+       | C.Meta (n1,l1), _ ->
+          (try 
+             let _,_,term,_ = NCicUtils.lookup_subst n1 subst in
+             let term = NCicSubstitution.subst_meta l1 term in
+              aux test_equality_only context term t2
+           with NCicUtils.Subst_not_found _ -> false)
+       | _, C.Meta (n2,l2) ->
+          (try 
+             let _,_,term,_ = NCicUtils.lookup_subst n2 subst in
+             let term = NCicSubstitution.subst_meta l2 term in
+              aux test_equality_only context t1 term
+           with NCicUtils.Subst_not_found _ -> false)
+
+       | (C.Appl l1, C.Appl l2) ->
+          (try List.for_all2 (aux test_equality_only context) l1 l2
+           with Invalid_argument _ -> false)
+
+       | (C.Match (ref1,outtype1,term1,pl1),
+          C.Match (ref2,outtype2,term2,pl2)) -> 
+           NReference.eq ref1 ref2 &&
+           aux test_equality_only context outtype1 outtype2 &&
+           aux test_equality_only context term1 term2 &&
+           (try List.for_all2 (aux test_equality_only context) pl1 pl2
+            with Invalid_argument _ -> false)
+
+       | (C.Implicit _, _) | (_, C.Implicit _) -> assert false
+       | (_,_) -> false
+  in
+   if aux2 test_equality_only t1 t2 then 
+     true
+   else
+     let rec convert_machines = function
+      | [] -> true
+      | ((k1,env1,h1,s1),(k2,env2,h2,s2))::tl ->
+          aux2 test_equality_only
+           (R.unwind (k1,env1,h1,[])) (R.unwind (k2,env2,h2,[])) &&
+          let problems =
+           let red_stack =
+             List.map
+               (fun si-> R.reduce ~delta:0 ~subst context(RS.from_stack si))
+           in
+           try Some (List.combine (red_stack s1) (red_stack s2) @ tl)
+           with Invalid_argument _ -> None
+          in
+          match problems with
+           | None -> false
+           | Some problems -> convert_machines problems
+     in
+      convert_machines 
+       [R.reduce ~delta:0 ~subst context (0,[],t1,[]),
+        R.reduce ~delta:0 ~subst context (0,[],t2,[])]
+ in
+  aux false 
+;;
+
+let are_convertible = are_convertible whd
+
+let rec head_beta_reduce ?(delta=max_int) ?(upto=(-1)) t l =
+ match upto, t, l with
+  | 0, C.Appl l1, _ -> C.Appl (l1 @ l)
+  | 0, t, [] -> t
+  | 0, t, _ -> C.Appl (t::l)
+  | _, C.Appl (hd::tl), _ -> head_beta_reduce ~delta ~upto hd (tl @ l)
+  | _, C.Lambda(_,_,bo), arg::tl ->
+     let bo = NCicSubstitution.subst arg bo in
+     head_beta_reduce ~delta ~upto:(upto - 1) bo tl
+  | _, C.Const (NReference.Ref (height, _, NReference.Def) as re), _ 
+    when delta <= height ->
+      let _, _, bo, _, _, _ = NCicEnvironment.get_checked_def re in
+      head_beta_reduce ~upto ~delta bo l
+  | _, t, [] -> t
+  | _, t, _ -> C.Appl (t::l)
+;;
+
+let head_beta_reduce ?delta ?upto t = head_beta_reduce ?delta ?upto t [];;
+
+(* vim:set foldmethod=marker: *)