* http://cs.unibo.it/helm/.
*)
+(* $Id$ *)
+
(* TODO unify exceptions *)
-exception CicReductionInternalError;;
exception WrongUriToInductiveDefinition;;
exception Impossible of int;;
exception ReferenceToConstant;;
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 =
CicPp.ppobj (C.Variable ("DEBUG", None, t, [], [])) ^ "\n" ^ i
in
if !fdebug = 0 then
- prerr_endline (s ^ "\n" ^ List.fold_right debug_aux (t::env) "")
+ debug_print (lazy (s ^ "\n" ^ List.fold_right debug_aux (t::env) ""))
;;
module type Strategy =
type stack_term
type env_term
type ens_term
- val to_stack : Cic.term -> stack_term
- val to_stack_list : Cic.term list -> stack_term list
- val to_env : Cic.term -> env_term
- val to_ens : Cic.term -> ens_term
- val from_stack :
- unwind:
- (int -> env_term list -> ens_term Cic.explicit_named_substitution ->
- Cic.term -> Cic.term) ->
- stack_term -> Cic.term
- val from_stack_list :
- unwind:
- (int -> env_term list -> ens_term Cic.explicit_named_substitution ->
- Cic.term -> Cic.term) ->
+ type config = int * env_term list * ens_term Cic.explicit_named_substitution * Cic.term * stack_term list
+ val to_env : config -> env_term
+ val to_ens : config -> ens_term
+ val from_stack : stack_term -> config
+ val from_stack_list_for_unwind :
+ unwind: (config -> Cic.term) ->
stack_term list -> Cic.term list
- val from_env : env_term -> Cic.term
- val from_ens : ens_term -> Cic.term
+ val from_env : env_term -> config
+ val from_env_for_unwind :
+ unwind: (config -> Cic.term) ->
+ env_term -> Cic.term
+ val from_ens : ens_term -> config
+ val from_ens_for_unwind :
+ unwind: (config -> Cic.term) ->
+ ens_term -> Cic.term
val stack_to_env :
- reduce:
- (int * env_term list * ens_term Cic.explicit_named_substitution *
- Cic.term * stack_term list -> Cic.term) ->
- unwind:
- (int -> env_term list -> ens_term Cic.explicit_named_substitution ->
- Cic.term -> Cic.term) ->
+ reduce: (config -> config) ->
+ unwind: (config -> Cic.term) ->
stack_term -> env_term
val compute_to_env :
- reduce:
- (int * env_term list * ens_term Cic.explicit_named_substitution * Cic.term *
- stack_term list -> Cic.term) ->
- unwind:
- (int -> env_term list -> ens_term Cic.explicit_named_substitution ->
- Cic.term -> Cic.term) ->
+ reduce: (config -> config) ->
+ unwind: (config -> Cic.term) ->
int -> env_term list -> ens_term Cic.explicit_named_substitution ->
Cic.term -> env_term
val compute_to_stack :
- reduce:
- (int * env_term list * ens_term Cic.explicit_named_substitution * Cic.term *
- stack_term list -> Cic.term) ->
- unwind:
- (int -> env_term list -> ens_term Cic.explicit_named_substitution ->
- Cic.term -> Cic.term) ->
- int -> env_term list -> ens_term Cic.explicit_named_substitution ->
- Cic.term -> stack_term
+ reduce: (config -> config) ->
+ unwind: (config -> Cic.term) ->
+ config -> stack_term
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
+;;
+
+
module CallByNameStrategy =
struct
type stack_term = Cic.term
type env_term = Cic.term
type ens_term = Cic.term
- let to_stack v = v
- let to_stack_list l = l
+ 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
type stack_term = Cic.term
type env_term = Cic.term
type ens_term = Cic.term
- let to_stack v = v
- let to_stack_list l = l
+ 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,[])
type stack_term = Cic.term
type env_term = Cic.term
type ens_term = Cic.term
- let to_stack v = v
- let to_stack_list l = l
+ 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
type stack_term = Cic.term lazy_t
type env_term = Cic.term lazy_t
type ens_term = Cic.term lazy_t
- let to_stack v = lazy v
- let to_stack_list l = List.map to_stack l
+ 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,[]))
type stack_term = Cic.term lazy_t
type env_term = Cic.term lazy_t
type ens_term = Cic.term lazy_t
- let to_stack v = lazy v
- let to_stack_list l = List.map to_stack l
+ 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 (
type stack_term = Cic.term lazy_t
type env_term = Cic.term lazy_t
type ens_term = Cic.term lazy_t
- let to_stack v = lazy v
- let to_stack_list l = List.map to_stack l
+ 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)
type stack_term = reduce:bool -> Cic.term
type env_term = reduce:bool -> Cic.term
type ens_term = reduce:bool -> Cic.term
- let to_stack v =
- let value = lazy v in
- fun ~reduce -> Lazy.force value
- let to_stack_list l = List.map to_stack l
+ 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 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 =
module ClosuresOnStackByValueFromEnvOrEnsStrategy =
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
- let to_stack v = (0,[],[],v)
- let to_stack_list l = List.map to_stack l
- 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
+ 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 stack_to_env ~reduce ~unwind (k,e,ens,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)
+ 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
;;
int * Cic.term list * Cic.term Cic.explicit_named_substitution * Cic.term
type env_term = Cic.term
type ens_term = Cic.term
- let to_stack v = (0,[],[],v)
- let to_stack_list l = List.map to_stack l
+ 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
(* k is the length of the environment e *)
(* m is the current depth inside the term *)
- let unwind' m k e ens t =
+ let rec unwind' m k e ens t =
let module C = Cic in
let module S = CicSubstitution in
if k = 0 && ens = [] then
if n <= m then t else
let d =
try
- Some (RS.from_env (List.nth e (n-m-1)))
+ Some (RS.from_env_for_unwind ~unwind (List.nth e (n-m-1)))
with _ -> None
in
(match d with
)
| C.Var (uri,exp_named_subst) ->
(*
-prerr_endline ("%%%%%UWVAR " ^ String.concat " ; " (List.map (function (uri,t) -> UriManager.string_of_uri uri ^ " := " ^ CicPp.ppterm t) ens)) ;
+debug_print (lazy ("%%%%%UWVAR " ^ String.concat " ; " (List.map (function (uri,t) -> UriManager.string_of_uri uri ^ " := " ^ CicPp.ppterm t) ens))) ;
*)
if List.exists (function (uri',_) -> UriManager.eq uri' uri) ens then
- CicSubstitution.lift m (RS.from_ens (List.assq uri ens))
+ CicSubstitution.lift m (RS.from_ens_for_unwind ~unwind (List.assq uri ens))
else
let params =
- let o,_ =
- CicEnvironment.get_cooked_obj CicUniv.empty_ugraph uri
- in
+ let o,_ =
+ CicEnvironment.get_cooked_obj CicUniv.empty_ugraph uri
+ in
(match o with
C.Constant _ -> raise ReferenceToConstant
| C.Variable (_,_,_,params,_) -> params
| C.Appl l -> C.Appl (List.map (unwind_aux m) l)
| C.Const (uri,exp_named_subst) ->
let params =
- let o,_ =
- CicEnvironment.get_cooked_obj CicUniv.empty_ugraph uri
- in
+ let o,_ =
+ CicEnvironment.get_cooked_obj CicUniv.empty_ugraph uri
+ in
(match o with
C.Constant (_,_,_,params,_) -> params
| C.Variable _ -> raise ReferenceToVariable
C.Const (uri,exp_named_subst')
| C.MutInd (uri,i,exp_named_subst) ->
let params =
- let o,_ =
- CicEnvironment.get_cooked_obj CicUniv.empty_ugraph uri
- in
+ let o,_ =
+ CicEnvironment.get_cooked_obj CicUniv.empty_ugraph uri
+ in
(match o with
C.Constant _ -> raise ReferenceToConstant
| C.Variable _ -> raise ReferenceToVariable
C.MutInd (uri,i,exp_named_subst')
| C.MutConstruct (uri,i,j,exp_named_subst) ->
let params =
- let o,_ =
- CicEnvironment.get_cooked_obj CicUniv.empty_ugraph uri
- in
+ let o,_ =
+ CicEnvironment.get_cooked_obj CicUniv.empty_ugraph uri
+ in
(match o with
C.Constant _ -> raise ReferenceToConstant
| C.Variable _ -> raise ReferenceToVariable
&&
List.mem uri params
->
- (uri,CicSubstitution.lift m (RS.from_ens t)) ::
+ (uri,CicSubstitution.lift m (RS.from_ens_for_unwind ~unwind t)) ::
(filter_and_lift (uri::already_instantiated) tl)
| _::tl -> filter_and_lift already_instantiated tl
(*
| (uri,_)::tl ->
-prerr_endline ("---- SKIPPO " ^ UriManager.string_of_uri uri) ;
-if List.for_all (function (uri',_) -> not (UriManager.eq uri uri')) exp_named_subst' then prerr_endline "---- OK1" ;
-prerr_endline ("++++ uri " ^ UriManager.string_of_uri uri ^ " not in " ^ String.concat " ; " (List.map UriManager.string_of_uri params)) ;
-if List.mem uri params then prerr_endline "---- OK2" ;
+debug_print (lazy ("---- SKIPPO " ^ UriManager.string_of_uri uri)) ;
+if List.for_all (function (uri',_) -> not (UriManager.eq uri uri'))
+exp_named_subst' then debug_print (lazy "---- OK1") ;
+debug_print (lazy ("++++ uri " ^ UriManager.string_of_uri uri ^ " not in " ^ String.concat " ; " (List.map UriManager.string_of_uri params))) ;
+if List.mem uri params then debug_print (lazy "---- OK2") ;
filter_and_lift tl
*)
in
(filter_and_lift [] (List.rev ens))
in
unwind_aux m t
- ;;
+ and unwind (k,e,ens,t,s) =
+ let t' = unwind' 0 k e ens t in
+ if s = [] then t' else Cic.Appl (t'::(RS.from_stack_list_for_unwind ~unwind s))
+ ;;
+
+(*
let unwind =
- unwind' 0
+ let profiler_unwind = HExtlib.profile ~enable:profile "are_convertible.unwind" in
+ fun k e ens t ->
+ profiler_unwind.HExtlib.profile (unwind k e ens) t
;;
+*)
- let reduce ?(subst = []) context : config -> Cic.term =
+ let reduce ~delta ?(subst = []) context : config -> config =
let module C = Cic in
let module S = CicSubstitution in
let rec reduce =
function
- (k, e, _, (C.Rel n as t), s) ->
- let d =
+ (k, e, _, C.Rel n, s) as config ->
+ let config' =
try
Some (RS.from_env (List.nth e (n-1)))
with
- _ ->
+ Failure _ ->
try
begin
match List.nth context (n - 1 - k) with
None -> assert false
| Some (_,C.Decl _) -> None
- | Some (_,C.Def (x,_)) -> Some (S.lift (n - k) x)
+ | Some (_,C.Def (x,_)) -> Some (0,[],[],S.lift (n - k) x,[])
end
with
- _ -> None
+ Failure _ -> None
in
- (match d with
- Some t' -> reduce (0,[],[],t',s)
- | None ->
- if s = [] then
- C.Rel (n-k)
- else C.Appl (C.Rel (n-k)::(RS.from_stack_list ~unwind s))
- )
- | (k, e, ens, (C.Var (uri,exp_named_subst) as t), s) ->
+ (match config' with
+ Some (k',e',ens',t',s') -> reduce (k',e',ens',t',s'@s)
+ | None -> config)
+ | (k, e, ens, C.Var (uri,exp_named_subst), s) as config ->
if List.exists (function (uri',_) -> UriManager.eq uri' uri) ens then
- reduce (0, [], [], RS.from_ens (List.assq uri ens), s)
+ let (k',e',ens',t',s') = RS.from_ens (List.assq uri ens) in
+ reduce (k',e',ens',t',s'@s)
else
( let o,_ =
- CicEnvironment.get_cooked_obj CicUniv.empty_ugraph uri
- in
+ CicEnvironment.get_cooked_obj CicUniv.empty_ugraph uri
+ in
match o with
C.Constant _ -> raise ReferenceToConstant
| C.CurrentProof _ -> raise ReferenceToCurrentProof
| C.InductiveDefinition _ -> raise ReferenceToInductiveDefinition
- | C.Variable (_,None,_,_,_) ->
- let t' = unwind k e ens t in
- if s = [] then t' else
- C.Appl (t'::(RS.from_stack_list ~unwind s))
+ | C.Variable (_,None,_,_,_) -> config
| C.Variable (_,Some body,_,_,_) ->
let ens' = push_exp_named_subst k e ens exp_named_subst in
reduce (0, [], ens', body, s)
)
- | (k, e, ens, (C.Meta (n,l) as t), s) ->
+ | (k, e, ens, C.Meta (n,l), s) as config ->
(try
- let (_, term,_) = CicUtil.lookup_subst n subst in
+ let (_, term,_) = CicUtil.lookup_subst n subst in
reduce (k, e, ens,CicSubstitution.subst_meta l term,s)
- with CicUtil.Subst_not_found _ ->
- let t' = unwind k e ens t in
- if s = [] then t' else C.Appl (t'::(RS.from_stack_list ~unwind s)))
- | (k, e, _, (C.Sort _ as t), s) -> t (* s should be empty *)
- | (k, e, _, (C.Implicit _ as t), s) -> t (* s should be empty *)
- | (k, e, ens, (C.Cast (te,ty) as t), s) ->
- reduce (k, e, ens, te, s) (* s should be empty *)
- | (k, e, ens, (C.Prod _ as t), s) ->
- unwind k e ens t (* s should be empty *)
- | (k, e, ens, (C.Lambda (_,_,t) as t'), []) -> unwind k e ens t'
+ with CicUtil.Subst_not_found _ -> config)
+ | (_, _, _, C.Sort _, _)
+ | (_, _, _, C.Implicit _, _) as config -> config
+ | (k, e, ens, C.Cast (te,ty), s) ->
+ reduce (k, e, ens, te, s)
+ | (_, _, _, C.Prod _, _) as config -> config
+ | (_, _, _, C.Lambda _, []) as config -> config
| (k, e, ens, C.Lambda (_,_,t), p::s) ->
reduce (k+1, (RS.stack_to_env ~reduce ~unwind p)::e, ens, t,s)
- | (k, e, ens, (C.LetIn (_,m,t) as t'), s) ->
+ | (k, e, ens, C.LetIn (_,m,t), s) ->
let m' = RS.compute_to_env ~reduce ~unwind k e ens m in
reduce (k+1, m'::e, ens, t, s)
| (_, _, _, C.Appl [], _) -> assert false
| (k, e, ens, C.Appl (he::tl), s) ->
let tl' =
List.map
- (function t -> RS.compute_to_stack ~reduce ~unwind k e ens t) tl
+ (function t -> RS.compute_to_stack ~reduce ~unwind (k,e,ens,t,[])) tl
in
reduce (k, e, ens, he, (List.append tl') s)
- (* CSC: Old Dead Code
- | (k, e, ens, C.Appl ((C.Lambda _ as he)::tl), s)
- | (k, e, ens, C.Appl ((C.Const _ as he)::tl), s)
- | (k, e, ens, C.Appl ((C.MutCase _ as he)::tl), s)
- | (k, e, ens, C.Appl ((C.Fix _ as he)::tl), s) ->
- (* strict evaluation, but constants are NOT unfolded *)
- let red =
- function
- C.Const _ as t -> unwind k e ens t
- | t -> reduce (k,e,ens,t,[])
- in
- let tl' = List.map red tl in
- reduce (k, e, ens, he , List.append tl' s)
- | (k, e, ens, C.Appl l, s) ->
- C.Appl (List.append (List.map (unwind k e ens) l) s)
- *)
- | (k, e, ens, (C.Const (uri,exp_named_subst) as t), s) ->
+ | (_, _, _, C.Const _, _) as config when delta=false-> config
+ | (k, e, ens, C.Const (uri,exp_named_subst), s) as config ->
(let o,_ =
- CicEnvironment.get_cooked_obj CicUniv.empty_ugraph uri
- in
- match o with
+ CicEnvironment.get_cooked_obj CicUniv.empty_ugraph uri
+ in
+ match o with
C.Constant (_,Some body,_,_,_) ->
let ens' = push_exp_named_subst k e ens exp_named_subst in
(* constants are closed *)
reduce (0, [], ens', body, s)
- | C.Constant (_,None,_,_,_) ->
- let t' = unwind k e ens t in
- if s = [] then t' else C.Appl (t'::(RS.from_stack_list ~unwind s))
+ | C.Constant (_,None,_,_,_) -> config
| C.Variable _ -> raise ReferenceToVariable
| C.CurrentProof (_,_,body,_,_,_) ->
let ens' = push_exp_named_subst k e ens exp_named_subst in
reduce (0, [], ens', body, s)
| C.InductiveDefinition _ -> raise ReferenceToInductiveDefinition
)
- | (k, e, ens, (C.MutInd _ as t),s) ->
- let t' = unwind k e ens t in
- if s = [] then t' else C.Appl (t'::(RS.from_stack_list ~unwind s))
- | (k, e, ens, (C.MutConstruct _ as t),s) ->
- let t' = unwind k e ens t in
- if s = [] then t' else C.Appl (t'::(RS.from_stack_list ~unwind s))
- | (k, e, ens, (C.MutCase (mutind,i,_,term,pl) as t),s) ->
+ | (_, _, _, C.MutInd _, _)
+ | (_, _, _, C.MutConstruct _, _) as config -> config
+ | (k, e, ens, C.MutCase (mutind,i,outty,term,pl),s) as config ->
let decofix =
function
- C.CoFix (i,fl) as t ->
+ (k, e, ens, C.CoFix (i,fl), s) ->
let (_,_,body) = List.nth fl i in
let body' =
let counter = ref (List.length fl) in
fl
body
in
- (* the term is the result of a reduction; *)
- (* so it is already unwinded. *)
- reduce (0,[],[],body',[])
- | C.Appl (C.CoFix (i,fl) :: tl) ->
- let (_,_,body) = List.nth fl i in
- let body' =
- let counter = ref (List.length fl) in
- List.fold_right
- (fun _ -> decr counter ; S.subst (C.CoFix (!counter,fl)))
- fl
- body
- in
- (* the term is the result of a reduction; *)
- (* so it is already unwinded. *)
- reduce (0,[],[],body',RS.to_stack_list tl)
- | t -> t
+ reduce (k,e,ens,body',s)
+ | config -> config
in
(match decofix (reduce (k,e,ens,term,[])) with
- C.MutConstruct (_,_,j,_) ->
- reduce (k, e, ens, (List.nth pl (j-1)), s)
- | C.Appl (C.MutConstruct (_,_,j,_) :: tl) ->
+ (k', e', ens', C.MutConstruct (_,_,j,_), []) ->
+ reduce (k, e, ens, (List.nth pl (j-1)), [])
+ | (k', e', ens', C.MutConstruct (_,_,j,_), s') ->
let (arity, r) =
- let o,_ =
- CicEnvironment.get_cooked_obj CicUniv.empty_ugraph mutind
- in
- match o with
- C.InductiveDefinition (tl,ingredients,r,_) ->
- let (_,_,arity,_) = List.nth tl i in
- (arity,r)
+ let o,_ =
+ CicEnvironment.get_cooked_obj CicUniv.empty_ugraph mutind
+ in
+ match o with
+ C.InductiveDefinition (s,ingredients,r,_) ->
+ let (_,_,arity,_) = List.nth s i in
+ (arity,r)
| _ -> raise WrongUriToInductiveDefinition
in
let ts =
let rec eat_first =
function
(0,l) -> l
- | (n,he::tl) when n > 0 -> eat_first (n - 1, tl)
+ | (n,he::s) when n > 0 -> eat_first (n - 1, s)
| _ -> raise (Impossible 5)
in
- eat_first (num_to_eat,tl)
+ eat_first (num_to_eat,s')
in
- (* ts are already unwinded because they are a sublist of tl *)
- reduce (k, e, ens, (List.nth pl (j-1)), (RS.to_stack_list ts)@s)
- | C.Cast _ | C.Implicit _ ->
+ reduce (k, e, ens, (List.nth pl (j-1)), ts@s)
+ | (_, _, _, C.Cast _, _)
+ | (_, _, _, C.Implicit _, _) ->
raise (Impossible 2) (* we don't trust our whd ;-) *)
- | _ ->
- let t' = unwind k e ens t in
- if s = [] then t' else C.Appl (t'::(RS.from_stack_list ~unwind s))
- )
- | (k, e, ens, (C.Fix (i,fl) as t), s) ->
+ | config' ->
+ (*CSC: here I am unwinding the configuration and for sure I
+ will do it twice; to avoid this unwinding I should push the
+ "match [] with _" continuation on the stack;
+ another possibility is to just return the original configuration,
+ partially undoing the weak-head computation *)
+ (*this code is uncorrect since term' lives in e' <> e
+ let term' = unwind config' in
+ (k, e, ens, C.MutCase (mutind,i,outty,term',pl),s)
+ *)
+ config)
+ | (k, e, ens, C.Fix (i,fl), s) as config ->
let (_,recindex,_,body) = List.nth fl i in
let recparam =
try
- Some (RS.from_stack ~unwind (List.nth s recindex))
+ Some (RS.from_stack (List.nth s recindex))
with
_ -> None
in
(match recparam with
Some recparam ->
- (match reduce (0,[],[],recparam,[]) with
- (* match recparam with *)
- C.MutConstruct _
- | C.Appl ((C.MutConstruct _)::_) ->
- (* OLD
- let body' =
- let counter = ref (List.length fl) in
- List.fold_right
- (fun _ -> decr counter ; S.subst (C.Fix (!counter,fl)))
- fl
- body
- in
- reduce (k, e, ens, body', s) *)
- (* NEW *)
+ (match reduce recparam with
+ (_,_,_,C.MutConstruct _,_) as config ->
let leng = List.length fl in
- let fl' =
- let unwind_fl (name,recindex,typ,body) =
- (name,recindex,unwind k e ens typ,
- unwind' leng k e ens body)
+ let new_env =
+ let counter = ref 0 in
+ let rec build_env e =
+ if !counter = leng then e
+ else
+ (incr counter ;
+ build_env
+ ((RS.to_env (k,e,ens,C.Fix (!counter -1, fl),[]))::e))
in
- List.map unwind_fl fl
+ build_env e
in
- let new_env =
- let counter = ref 0 in
- let rec build_env e =
- if !counter = leng then e
- else
- (incr counter ;
- build_env ((RS.to_env (C.Fix (!counter -1, fl')))::e))
- in
- build_env e
- in
- reduce (k+leng, new_env, ens, body, s)
- | _ ->
- let t' = unwind k e ens t in
- if s = [] then t' else
- C.Appl (t'::(RS.from_stack_list ~unwind s))
- )
- | None ->
- let t' = unwind k e ens t in
- if s = [] then t' else
- C.Appl (t'::(RS.from_stack_list ~unwind s))
+ 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 in
+ let new_s =
+ replace recindex s (RS.compute_to_stack ~reduce ~unwind config)
+ in
+ reduce (k+leng, new_env, ens, body, new_s)
+ | _ -> config)
+ | None -> config
)
- | (k, e, ens, (C.CoFix (i,fl) as t),s) ->
- let t' = unwind k e ens t in
- if s = [] then t' else C.Appl (t'::(RS.from_stack_list ~unwind s))
+ | (_,_,_,C.CoFix _,_) as config -> config
and push_exp_named_subst k e ens =
function
[] -> ens
| (uri,t)::tl ->
- push_exp_named_subst k e ((uri,RS.to_ens (unwind k e ens t))::ens) tl
+ push_exp_named_subst k e ((uri,RS.to_ens (k,e,ens,t,[]))::ens) tl
in
- reduce
- ;;
- (*
- let rec whd context t =
- try
- reduce context (0, [], [], t, [])
- with Not_found ->
- prerr_endline (CicPp.ppterm t) ;
- raise Not_found
+ reduce
;;
- *)
- let rec whd ?(subst=[]) context t =
- reduce ~subst context (0, [], [], t, [])
+ let whd ?(delta=true) ?(subst=[]) context t =
+ unwind (reduce ~delta ~subst context (0, [], [], t, []))
;;
-
-(* DEBUGGING ONLY
-let whd context t =
- let res = whd context t in
- let rescsc = CicReductionNaif.whd context t in
- if not (CicReductionNaif.are_convertible context res rescsc) then
- begin
- prerr_endline ("PRIMA: " ^ CicPp.ppterm t) ;
- flush stderr ;
- prerr_endline ("DOPO: " ^ CicPp.ppterm res) ;
- flush stderr ;
- prerr_endline ("CSC: " ^ CicPp.ppterm rescsc) ;
- flush stderr ;
-CicReductionNaif.fdebug := 0 ;
-let _ = CicReductionNaif.are_convertible context res rescsc in
- assert false ;
- end
- else
- res
-;;
-*)
end
;;
-(*
-module R = Reduction CallByNameStrategy;;
-module R = Reduction CallByValueStrategy;;
-module R = Reduction CallByValueStrategyByNameOnConstants;;
-module R = Reduction LazyCallByValueStrategy;;
-module R = Reduction LazyCallByValueStrategyByNameOnConstants;;
-module R = Reduction LazyCallByNameStrategy;;
+(* 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;;
-module R = Reduction ClosuresOnStackByValueFromEnvOrEnsStrategy;;
+ OK 59.058s
+module R = Reduction ClosuresOnStackByValueFromEnvOrEnsStrategy;; OK 58.583s
module R = Reduction
- ClosuresOnStackByValueFromEnvOrEnsByNameOnConstantsStrategy;;
+ ClosuresOnStackByValueFromEnvOrEnsByNameOnConstantsStrategy;; OK 58.094s
+module R = Reduction(ClosuresOnStackByValueFromEnvOrEnsStrategy);; OK 58.127s
*)
-module R = Reduction(ClosuresOnStackByValueFromEnvOrEnsStrategy);;
+module R = Reduction(CallByValueByNameForUnwind);;
+(*module R = Reduction(ClosuresOnStackByValueFromEnvOrEnsStrategy);;*)
module U = UriManager;;
-let whd = R.whd;;
+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)
+let (===) x y =
+ Pervasives.compare x y = 0
(* t1, t2 must be well-typed *)
-let are_convertible ?(subst=[]) ?(metasenv=[]) =
+let are_convertible whd ?(subst=[]) ?(metasenv=[]) =
let rec aux test_equality_only context t1 t2 ugraph =
let aux2 test_equality_only t1 t2 ugraph =
with
Invalid_argument _ -> false,ugraph
)
- else
- false,ugraph
+ else
+ false,ugraph
| (C.Meta (n1,l1), C.Meta (n2,l2)) ->
- if n1 = n2 then
- let b2, ugraph1 =
- let l1 = CicUtil.clean_up_local_context subst metasenv n1 l1 in
- let l2 = CicUtil.clean_up_local_context subst metasenv n2 l2 in
- List.fold_left2
- (fun (b,ugraph) t1 t2 ->
- if b then
- match t1,t2 with
- None,_
- | _,None -> true,ugraph
- | Some t1',Some t2' ->
- aux test_equality_only context t1' t2' ugraph
- else
- false,ugraph
- ) (true,ugraph) l1 l2
- in
- if b2 then true,ugraph1 else false,ugraph
- else
- false,ugraph
+ if n1 = n2 then
+ let b2, ugraph1 =
+ let l1 = CicUtil.clean_up_local_context subst metasenv n1 l1 in
+ let l2 = CicUtil.clean_up_local_context subst metasenv n2 l2 in
+ List.fold_left2
+ (fun (b,ugraph) t1 t2 ->
+ if b then
+ match t1,t2 with
+ None,_
+ | _,None -> true,ugraph
+ | Some t1',Some t2' ->
+ aux test_equality_only context t1' t2' ugraph
+ else
+ false,ugraph
+ ) (true,ugraph) l1 l2
+ in
+ if b2 then true,ugraph1 else false,ugraph
+ else
+ false,ugraph
+ (* TASSI: CONSTRAINTS *)
+ | (C.Sort (C.Type t1), C.Sort (C.Type t2)) when test_equality_only ->
+ true,(CicUniv.add_eq t2 t1 ugraph)
+ (* TASSI: CONSTRAINTS *)
+ | (C.Sort (C.Type t1), C.Sort (C.Type t2)) ->
+ true,(CicUniv.add_ge t2 t1 ugraph)
+ (* TASSI: CONSTRAINTS *)
+ | (C.Sort s1, C.Sort (C.Type _)) -> (not test_equality_only),ugraph
(* TASSI: CONSTRAINTS *)
- | (C.Sort (C.Type t1), C.Sort (C.Type t2)) when test_equality_only ->
- true,(CicUniv.add_eq t2 t1 ugraph)
- (* TASSI: CONSTRAINTS *)
- | (C.Sort (C.Type t1), C.Sort (C.Type t2)) ->
- true,(CicUniv.add_ge t2 t1 ugraph)
- (* TASSI: CONSTRAINTS *)
- | (C.Sort s1, C.Sort (C.Type _)) -> (not test_equality_only),ugraph
- (* TASSI: CONSTRAINTS *)
| (C.Sort s1, C.Sort s2) -> (s1 = s2),ugraph
| (C.Prod (name1,s1,t1), C.Prod(_,s2,t2)) ->
- let b',ugraph' = aux true context s1 s2 ugraph in
- if b' then
+ let b',ugraph' = aux true context s1 s2 ugraph in
+ if b' then
aux test_equality_only ((Some (name1, (C.Decl s1)))::context)
- t1 t2 ugraph'
- else
- false,ugraph
+ t1 t2 ugraph'
+ else
+ false,ugraph
| (C.Lambda (name1,s1,t1), C.Lambda(_,s2,t2)) ->
let b',ugraph' = aux test_equality_only context s1 s2 ugraph in
if b' then
- aux test_equality_only ((Some (name1, (C.Decl s1)))::context)
- t1 t2 ugraph'
- else
- false,ugraph
+ aux test_equality_only ((Some (name1, (C.Decl s1)))::context)
+ t1 t2 ugraph'
+ else
+ false,ugraph
| (C.LetIn (name1,s1,t1), C.LetIn(_,s2,t2)) ->
let b',ugraph' = aux test_equality_only context s1 s2 ugraph in
- if b' then
+ if b' then
aux test_equality_only
((Some (name1, (C.Def (s1,None))))::context) t1 t2 ugraph'
- else
- false,ugraph
+ else
+ false,ugraph
| (C.Appl l1, C.Appl l2) ->
(try
List.fold_right2
(fun x y (b,ugraph) ->
- if b then
- aux test_equality_only context x y ugraph
- else
- false,ugraph) l1 l2 (true,ugraph)
+ if b then
+ aux test_equality_only context x y ugraph
+ else
+ false,ugraph) l1 l2 (true,ugraph)
with
Invalid_argument _ -> false,ugraph
)
| (C.Const (uri1,exp_named_subst1), C.Const (uri2,exp_named_subst2)) ->
let b' = U.eq uri1 uri2 in
- if b' then
+ if b' then
(try
List.fold_right2
(fun (uri1,x) (uri2,y) (b,ugraph) ->
- if b && U.eq uri1 uri2 then
- aux test_equality_only context x y ugraph
- else
- false,ugraph
+ if b && U.eq uri1 uri2 then
+ aux test_equality_only context x y ugraph
+ else
+ false,ugraph
) exp_named_subst1 exp_named_subst2 (true,ugraph)
with
Invalid_argument _ -> false,ugraph
)
- else
- false,ugraph
+ else
+ false,ugraph
| (C.MutInd (uri1,i1,exp_named_subst1),
C.MutInd (uri2,i2,exp_named_subst2)
) ->
let b' = U.eq uri1 uri2 && i1 = i2 in
- if b' then
+ if b' then
(try
List.fold_right2
(fun (uri1,x) (uri2,y) (b,ugraph) ->
if b && U.eq uri1 uri2 then
- aux test_equality_only context x y ugraph
- else
- false,ugraph
+ aux test_equality_only context x y ugraph
+ else
+ false,ugraph
) exp_named_subst1 exp_named_subst2 (true,ugraph)
with
Invalid_argument _ -> false,ugraph
)
- else
- false,ugraph
+ else
+ false,ugraph
| (C.MutConstruct (uri1,i1,j1,exp_named_subst1),
C.MutConstruct (uri2,i2,j2,exp_named_subst2)
) ->
let b' = U.eq uri1 uri2 && i1 = i2 && j1 = j2 in
- if b' then
+ if b' then
(try
List.fold_right2
(fun (uri1,x) (uri2,y) (b,ugraph) ->
- if b && U.eq uri1 uri2 then
- aux test_equality_only context x y ugraph
- else
- false,ugraph
+ if b && U.eq uri1 uri2 then
+ aux test_equality_only context x y ugraph
+ else
+ false,ugraph
) exp_named_subst1 exp_named_subst2 (true,ugraph)
with
Invalid_argument _ -> false,ugraph
)
- else
- false,ugraph
+ else
+ false,ugraph
| (C.MutCase (uri1,i1,outtype1,term1,pl1),
C.MutCase (uri2,i2,outtype2,term2,pl2)) ->
let b' = U.eq uri1 uri2 && i1 = i2 in
- if b' then
+ if b' then
let b'',ugraph''=aux test_equality_only context
- outtype1 outtype2 ugraph in
- if b'' then
- let b''',ugraph'''= aux test_equality_only context
- term1 term2 ugraph'' in
- List.fold_right2
- (fun x y (b,ugraph) ->
- if b then
- aux test_equality_only context x y ugraph
- else
- false,ugraph)
- pl1 pl2 (true,ugraph''')
- else
- false,ugraph
- else
- false,ugraph
+ outtype1 outtype2 ugraph in
+ if b'' then
+ let b''',ugraph'''= aux test_equality_only context
+ term1 term2 ugraph'' in
+ List.fold_right2
+ (fun x y (b,ugraph) ->
+ if b then
+ aux test_equality_only context x y ugraph
+ else
+ false,ugraph)
+ pl1 pl2 (b''',ugraph''')
+ else
+ false,ugraph
+ else
+ false,ugraph
| (C.Fix (i1,fl1), C.Fix (i2,fl2)) ->
let tys =
List.map (function (n,_,ty,_) -> Some (C.Name n,(C.Decl ty))) fl1
List.fold_right2
(fun (_,recindex1,ty1,bo1) (_,recindex2,ty2,bo2) (b,ugraph) ->
if b && recindex1 = recindex2 then
- let b',ugraph' = aux test_equality_only context ty1 ty2
- ugraph in
- if b' then
- aux test_equality_only (tys@context) bo1 bo2 ugraph'
- else
- false,ugraph
- else
- false,ugraph)
- fl1 fl2 (true,ugraph)
- else
- false,ugraph
+ let b',ugraph' = aux test_equality_only context ty1 ty2
+ ugraph in
+ if b' then
+ aux test_equality_only (tys@context) bo1 bo2 ugraph'
+ else
+ false,ugraph
+ else
+ false,ugraph)
+ fl1 fl2 (true,ugraph)
+ else
+ false,ugraph
| (C.CoFix (i1,fl1), C.CoFix (i2,fl2)) ->
let tys =
List.map (function (n,ty,_) -> Some (C.Name n,(C.Decl ty))) fl1
if i1 = i2 then
List.fold_right2
(fun (_,ty1,bo1) (_,ty2,bo2) (b,ugraph) ->
- if b then
- let b',ugraph' = aux test_equality_only context ty1 ty2
- ugraph in
- if b' then
- aux test_equality_only (tys@context) bo1 bo2 ugraph'
- else
- false,ugraph
- else
- false,ugraph)
- fl1 fl2 (true,ugraph)
- else
- false,ugraph
+ if b then
+ let b',ugraph' = aux test_equality_only context ty1 ty2
+ ugraph in
+ if b' then
+ aux test_equality_only (tys@context) bo1 bo2 ugraph'
+ else
+ false,ugraph
+ else
+ false,ugraph)
+ fl1 fl2 (true,ugraph)
+ else
+ false,ugraph
| (C.Cast _, _) | (_, C.Cast _)
- | (C.Implicit _, _) | (_, C.Implicit _) ->
- assert false
+ | (C.Implicit _, _) | (_, C.Implicit _) -> assert false
| (_,_) -> false,ugraph
end
in
- begin
- debug t1 [t2] "PREWHD";
- (*
- (match t1 with
- Cic.Meta _ ->
- prerr_endline (CicPp.ppterm t1);
- prerr_endline (CicPp.ppterm (whd ~subst context t1));
- prerr_endline (CicPp.ppterm t2);
- prerr_endline (CicPp.ppterm (whd ~subst context t2))
- | _ -> ()); *)
- let t1' = whd ~subst context t1 in
- let t2' = whd ~subst context t2 in
- debug t1' [t2'] "POSTWHD";
- aux2 test_equality_only t1' t2' ugraph
- end
+ debug t1 [t2] "PREWHD";
+ let t1' = whd ?delta:(Some true) ?subst:(Some subst) context t1 in
+ let t2' = whd ?delta:(Some true) ?subst:(Some subst) context t2 in
+ debug t1' [t2'] "POSTWHD";
+ aux2 test_equality_only t1' t2' ugraph
in
aux false (*c t1 t2 ugraph *)
;;
+(* DEBUGGING ONLY
+let whd ?(delta=true) ?(subst=[]) context t =
+ let res = whd ~delta ~subst context t in
+ let rescsc = CicReductionNaif.whd ~delta ~subst context t in
+ if not (fst (are_convertible CicReductionNaif.whd ~subst context res rescsc CicUniv.empty_ugraph)) then
+ begin
+ debug_print (lazy ("PRIMA: " ^ CicPp.ppterm t)) ;
+ flush stderr ;
+ debug_print (lazy ("DOPO: " ^ CicPp.ppterm res)) ;
+ flush stderr ;
+ debug_print (lazy ("CSC: " ^ CicPp.ppterm rescsc)) ;
+ flush stderr ;
+fdebug := 0 ;
+let _ = are_convertible CicReductionNaif.whd ~subst context res rescsc CicUniv.empty_ugraph in
+ assert false ;
+ end
+ else
+ res
+;;
+*)
+
+let are_convertible = are_convertible whd
+
+let whd = R.whd
+
+(*
+let profiler_other_whd = HExtlib.profile ~enable:profile "~are_convertible.whd"
+let whd ?(delta=true) ?(subst=[]) context t =
+ let foo () =
+ whd ~delta ~subst context t
+ in
+ profiler_other_whd.HExtlib.profile foo ()
+*)
+
+let rec normalize ?(delta=true) ?(subst=[]) ctx term =
+ let module C = Cic in
+ let t = whd ~delta ~subst ctx term in
+ let aux = normalize ~delta ~subst in
+ let decl name t = Some (name, C.Decl t) in
+ match t with
+ | C.Rel n -> t
+ | C.Var (uri,exp_named_subst) ->
+ C.Var (uri, List.map (fun (n,t) -> n,aux ctx t) exp_named_subst)
+ | C.Meta (i,l) ->
+ C.Meta (i,List.map (function Some t -> Some (aux ctx t) | None -> None) l)
+ | C.Sort _ -> t
+ | C.Implicit _ -> t
+ | C.Cast (te,ty) -> C.Cast (aux ctx te, aux ctx ty)
+ | C.Prod (n,s,t) ->
+ let s' = aux ctx s in
+ C.Prod (n, s', aux ((decl n s')::ctx) t)
+ | C.Lambda (n,s,t) ->
+ let s' = aux ctx s in
+ C.Lambda (n, s', aux ((decl n s')::ctx) t)
+ | C.LetIn (n,s,t) ->
+ (* the term is already in weak head normal form *)
+ assert false
+ | C.Appl (h::l) -> C.Appl (h::(List.map (aux ctx) l))
+ | C.Appl [] -> assert false
+ | C.Const (uri,exp_named_subst) ->
+ C.Const (uri, List.map (fun (n,t) -> n,aux ctx t) exp_named_subst)
+ | C.MutInd (uri,typeno,exp_named_subst) ->
+ C.MutInd (uri,typeno, List.map (fun (n,t) -> n,aux ctx t) exp_named_subst)
+ | C.MutConstruct (uri,typeno,consno,exp_named_subst) ->
+ C.MutConstruct (uri, typeno, consno,
+ List.map (fun (n,t) -> n,aux ctx t) exp_named_subst)
+ | C.MutCase (sp,i,outt,t,pl) ->
+ C.MutCase (sp,i, aux ctx outt, aux ctx t, List.map (aux ctx) pl)
+(*CSC: to be completed, I suppose *)
+ | C.Fix _ -> t
+ | C.CoFix _ -> t
+
+let normalize ?delta ?subst ctx term =
+(* prerr_endline ("NORMALIZE:" ^ CicPp.ppterm term); *)
+ let t = normalize ?delta ?subst ctx term in
+(* prerr_endline ("NORMALIZED:" ^ CicPp.ppterm t); *)
+ t
+
+
+(* performs an head beta/cast reduction *)
+let rec head_beta_reduce =
+ function
+ (Cic.Appl (Cic.Lambda (_,_,t)::he'::tl')) ->
+ let he'' = CicSubstitution.subst he' t in
+ if tl' = [] then
+ he''
+ else
+ let he''' =
+ match he'' with
+ Cic.Appl l -> Cic.Appl (l@tl')
+ | _ -> Cic.Appl (he''::tl')
+ in
+ head_beta_reduce he'''
+ | Cic.Cast (te,_) -> head_beta_reduce te
+ | t -> t