mirror of
https://github.com/CatalaLang/catala.git
synced 2024-09-20 00:41:05 +03:00
554 lines
18 KiB
Plaintext
554 lines
18 KiB
Plaintext
module Catala.Translation
|
|
|
|
module L = Catala.LambdaCalculus
|
|
module D = Catala.DefaultCalculus
|
|
|
|
(*** Translation definitions *)
|
|
|
|
|
|
(**** Helpers *)
|
|
|
|
let rec translate_ty (ty: D.ty) : Tot L.ty = match ty with
|
|
| D.TBool -> L.TBool
|
|
| D.TUnit -> L.TUnit
|
|
| D.TArrow t1 t2 -> L.TArrow (translate_ty t1) (translate_ty t2)
|
|
|
|
let translate_lit (l: D.lit) : Tot L.lit = match l with
|
|
| D.LTrue -> L.LTrue
|
|
| D.LFalse -> L.LFalse
|
|
| D.LUnit -> L.LUnit
|
|
| D.LEmptyError -> L.LError L.EmptyError
|
|
| D.LConflictError -> L.LError L.ConflictError
|
|
|
|
let process_exceptions_f (tau: L.ty) : Tot L.exp =
|
|
let a = 0 in
|
|
let e = 1 in
|
|
let e' = 2 in
|
|
let a' = 3 in
|
|
let e'' = 4 in
|
|
L.EAbs (L.Named a) (L.TOption tau) (L.EAbs (L.Named e) (L.TArrow L.TUnit tau) (
|
|
L.EApp (L.EAbs (L.Named e') (L.TOption tau) (
|
|
L.EMatchOption (L.EVar a) tau
|
|
(L.EVar e')
|
|
(L.EAbs (L.Named a') tau (
|
|
L.EMatchOption (L.EVar e') tau
|
|
(L.EVar a)
|
|
(L.EAbs (L.Named e'') tau (L.ELit (L.LError L.ConflictError)))
|
|
))
|
|
))
|
|
(L.ECatchEmptyError (L.ESome (L.EApp (L.EVar e) (L.ELit L.LUnit) L.TUnit)) L.ENone)
|
|
(L.TOption tau)
|
|
))
|
|
|
|
let typ_process_exceptions_f (tau: L.ty)
|
|
: Lemma (L.typing L.empty (process_exceptions_f tau)
|
|
(L.TArrow (L.TOption tau) (L.TArrow (L.TArrow L.TUnit tau) (L.TOption tau))))
|
|
=
|
|
assert_norm(L.typing L.empty (process_exceptions_f tau)
|
|
(L.TArrow (L.TOption tau) (L.TArrow (L.TArrow L.TUnit tau) (L.TOption tau))))
|
|
|
|
(**** Main translation *)
|
|
|
|
let build_default_translation
|
|
(exceptions: list L.exp)
|
|
(just: L.exp)
|
|
(cons: L.exp)
|
|
(tau: L.ty)
|
|
=
|
|
L.EMatchOption
|
|
(L.EFoldLeft
|
|
(process_exceptions_f tau)
|
|
L.ENone (L.TOption tau)
|
|
(L.EList exceptions) (L.TArrow L.TUnit tau))
|
|
tau
|
|
(L.EIf
|
|
just cons
|
|
(L.ELit (L.LError L.EmptyError)))
|
|
(L.EAbs (L.Named 0) tau (L.EVar 0))
|
|
|
|
let rec translate_exp (e: D.exp) : Tot L.exp = match e with
|
|
| D.EVar x -> L.EVar x
|
|
| D.EApp e1 e2 tau_arg ->
|
|
L.EApp (translate_exp e1) (translate_exp e2) (translate_ty tau_arg)
|
|
| D.EAbs x ty body -> L.EAbs (L.Named x) (translate_ty ty) (translate_exp body)
|
|
| D.ELit l -> L.ELit (translate_lit l)
|
|
| D.EIf e1 e2 e3 -> L.EIf
|
|
(translate_exp e1)
|
|
(translate_exp e2)
|
|
(translate_exp e3)
|
|
| D.EDefault exceptions just cons tau ->
|
|
build_default_translation
|
|
(translate_exp_list exceptions)
|
|
(translate_exp just)
|
|
(translate_exp cons)
|
|
(translate_ty tau)
|
|
and translate_exp_list (l: list D.exp) : Tot (list L.exp) =
|
|
match l with
|
|
| [] -> []
|
|
| hd::tl -> (L.EAbs L.Silent L.TUnit (translate_exp hd))::(translate_exp_list tl)
|
|
|
|
let translate_env (g: D.env) : Tot L.env =
|
|
FunctionalExtensionality.on_dom L.var_name
|
|
(fun v -> match g v with None -> None | Some t -> Some (translate_ty t))
|
|
|
|
(*** Typing preservation *)
|
|
|
|
(**** Helpers and lemmas *)
|
|
|
|
let extend_translate_commute (g: D.env) (x: D.var) (tau: D.ty)
|
|
: Lemma (L.extend (translate_env g) x (translate_ty tau) == translate_env (D.extend g x tau))
|
|
=
|
|
FunctionalExtensionality.extensionality L.var_name (fun _ -> option L.ty)
|
|
(L.extend (translate_env g) x (translate_ty tau))
|
|
(translate_env (D.extend g x tau))
|
|
|
|
let translate_empty_is_empty () : Lemma (translate_env D.empty == L.empty) =
|
|
FunctionalExtensionality.extensionality L.var_name (fun _ -> option L.ty)
|
|
(translate_env D.empty)
|
|
L.empty
|
|
|
|
(**** Typing preservation theorem *)
|
|
|
|
#push-options "--fuel 1 --ifuel 1 --z3rlimit 30"
|
|
let rec translation_preserves_typ (g: D.env) (e: D.exp) (tau: D.ty) : Lemma
|
|
(requires (D.typing g e tau))
|
|
(ensures (L.typing (translate_env g) (translate_exp e) (translate_ty tau)))
|
|
(decreases %[e; 1])
|
|
=
|
|
match e with
|
|
| D.EVar _ -> ()
|
|
| D.EApp e1 e2 tau_arg ->
|
|
translation_preserves_typ g e1 (D.TArrow tau_arg tau);
|
|
translation_preserves_typ g e2 tau_arg
|
|
| D.EAbs x tau_arg body -> begin
|
|
match tau with
|
|
| D.TArrow tau_in tau_out ->
|
|
if tau_in = tau_arg then begin
|
|
translation_preserves_typ (D.extend g x tau_in) body tau_out;
|
|
extend_translate_commute g x tau_in
|
|
end else ()
|
|
| _ -> ()
|
|
end
|
|
| D.ELit _ -> ()
|
|
| D.EIf e1 e2 e3 ->
|
|
translation_preserves_typ g e1 D.TBool;
|
|
translation_preserves_typ g e2 tau;
|
|
translation_preserves_typ g e3 tau
|
|
| D.EDefault exceptions just cons tau_out ->
|
|
if tau = tau_out then begin
|
|
let tau' = translate_ty tau in
|
|
translation_preserves_typ_exceptions g e exceptions tau;
|
|
typ_process_exceptions_f tau';
|
|
translation_preserves_typ g just D.TBool;
|
|
translation_preserves_typ g cons tau;
|
|
let result_exp = L.EMatchOption
|
|
(L.EFoldLeft
|
|
(process_exceptions_f tau')
|
|
L.ENone (L.TOption tau')
|
|
(L.EList (translate_exp_list exceptions)) (L.TArrow L.TUnit tau'))
|
|
tau'
|
|
(L.EIf
|
|
(translate_exp just)
|
|
(translate_exp cons)
|
|
(L.ELit (L.LError L.EmptyError)))
|
|
(L.EAbs (L.Named 0) tau' (L.EVar 0))
|
|
in
|
|
let open FStar.Tactics in
|
|
assert(L.typing (translate_env g) result_exp tau') by begin
|
|
compute ();
|
|
smt ()
|
|
end
|
|
end else ()
|
|
and translation_preserves_typ_exceptions
|
|
(g: D.env)
|
|
(e: D.exp)
|
|
(exceptions: list D.exp{exceptions << e})
|
|
(tau: D.ty)
|
|
: Lemma
|
|
(requires (D.typing_list g exceptions tau))
|
|
(ensures (L.typing_list
|
|
(translate_env g)
|
|
(translate_exp_list exceptions)
|
|
(L.TArrow L.TUnit (translate_ty tau))))
|
|
(decreases %[e; 0; exceptions])
|
|
=
|
|
match exceptions with
|
|
| [] -> ()
|
|
| hd::tl ->
|
|
translation_preserves_typ g hd tau;
|
|
translation_preserves_typ_exceptions g e tl tau;
|
|
let g' = translate_env g in
|
|
let hd' = translate_exp hd in
|
|
let tl' = translate_exp_list tl in
|
|
let tau' = translate_ty tau in
|
|
let thunked_tau' = L.TArrow L.TUnit tau' in
|
|
assert(L.typing_list g' tl' thunked_tau');
|
|
assert(L.typing g' hd' tau');
|
|
assert(L.typing g' (L.EAbs L.Silent L.TUnit hd') thunked_tau')
|
|
#pop-options
|
|
|
|
let translation_preserves_empty_typ (e: D.exp) (tau: D.ty) : Lemma
|
|
(requires (D.typing D.empty e tau))
|
|
(ensures (L.typing L.empty (translate_exp e) (translate_ty tau)))
|
|
=
|
|
translate_empty_is_empty ();
|
|
translation_preserves_typ D.empty e tau
|
|
|
|
(*** Translation correctness *)
|
|
|
|
(**** Helpers *)
|
|
|
|
let typed_l_exp (tau: L.ty) = e:L.exp{L.typing L.empty e tau}
|
|
|
|
let rec take_l_steps (tau: L.ty) (e: typed_l_exp tau) (fuel: nat)
|
|
: Tot (option (typed_l_exp tau))
|
|
(decreases fuel) =
|
|
if fuel = 0 then Some e else
|
|
match L.step e with
|
|
| None -> None
|
|
| Some e' ->
|
|
L.preservation e tau;
|
|
take_l_steps tau e' (fuel - 1)
|
|
|
|
let not_l_value (tau: L.ty) = e:L.exp{not (L.is_value e) /\ L.typing L.empty e tau}
|
|
|
|
let stepping_context (tau tau': L.ty) = typed_l_exp tau -> not_l_value tau'
|
|
|
|
let step_lift_commute_non_value
|
|
(tau tau': L.ty)
|
|
(f: stepping_context tau tau')
|
|
(n:nat)
|
|
(e: typed_l_exp tau{Some? (take_l_steps tau e n)})
|
|
: prop
|
|
=
|
|
take_l_steps tau' (f e) n == Some (f (Some?.v (take_l_steps tau e n)))
|
|
|
|
let is_stepping_agnostic_lift
|
|
(tau tau': L.ty)
|
|
(f:stepping_context tau tau')
|
|
(n: nat)
|
|
: prop
|
|
=
|
|
forall (e: typed_l_exp tau{Some? (take_l_steps tau e n)}). step_lift_commute_non_value tau tau' f n e
|
|
|
|
let stepping_agnostic_lift
|
|
(tau tau': L.ty)
|
|
(n: nat)
|
|
: Type
|
|
= f:(stepping_context tau tau'){is_stepping_agnostic_lift tau tau' f n}
|
|
|
|
let if_cond_lift'
|
|
(tau: L.ty)
|
|
(e2 e3: typed_l_exp tau)
|
|
: stepping_context L.TBool tau
|
|
=
|
|
fun e1 -> L.EIf e1 e2 e3
|
|
|
|
#push-options "--fuel 2 --ifuel 1"
|
|
let rec if_cond_lift_is_stepping_agnostic
|
|
(tau: L.ty)
|
|
(e2 e3: typed_l_exp tau)
|
|
(n: nat)
|
|
(e: typed_l_exp L.TBool{Some? (take_l_steps L.TBool e n)})
|
|
: Lemma
|
|
(requires (True))
|
|
(ensures (step_lift_commute_non_value L.TBool tau (if_cond_lift' tau e2 e3) n e))
|
|
(decreases n)
|
|
=
|
|
if n = 0 then () else begin
|
|
L.progress e L.TBool;
|
|
L.preservation e L.TBool;
|
|
let Some e' = L.step e in
|
|
if_cond_lift_is_stepping_agnostic tau e2 e3 (n-1) e'
|
|
end
|
|
#pop-options
|
|
|
|
let if_cond_lift
|
|
(tau: L.ty)
|
|
(e2 e3: typed_l_exp tau)
|
|
(n: nat)
|
|
: stepping_agnostic_lift L.TBool tau n
|
|
=
|
|
Classical.forall_intro (if_cond_lift_is_stepping_agnostic tau e2 e3 n);
|
|
if_cond_lift' tau e2 e3
|
|
|
|
let lift_multiple_l_steps
|
|
(tau tau': L.ty)
|
|
(e1: not_l_value tau)
|
|
(e2: typed_l_exp tau)
|
|
(n: nat)
|
|
(f : stepping_agnostic_lift tau tau' n)
|
|
: Lemma
|
|
(requires (take_l_steps tau e1 n == Some e2))
|
|
(ensures (take_l_steps tau' (f e1) n == Some (f e2)))
|
|
=
|
|
assert(step_lift_commute_non_value tau tau' f n e1)
|
|
|
|
#push-options "--fuel 9 --ifuel 0"
|
|
let process_exceptions_untouched_by_subst (x: L.var_name) (e: L.exp) (tau: L.ty) : Lemma
|
|
(L.subst x e (process_exceptions_f tau) == process_exceptions_f tau)
|
|
=
|
|
()
|
|
#pop-options
|
|
|
|
#push-options "--fuel 3 --ifuel 1 --z3rlimit 50"
|
|
let rec substitution_correctness (x: D.var) (e_x e: D.exp)
|
|
: Lemma (ensures (
|
|
translate_exp (D.subst x e_x e) == L.subst x (translate_exp e_x) (translate_exp e)))
|
|
(decreases %[e; 1])
|
|
=
|
|
match e with
|
|
| D.EVar y -> ()
|
|
| D.ELit _ -> ()
|
|
| D.EIf e1 e2 e3 ->
|
|
substitution_correctness x e_x e1;
|
|
substitution_correctness x e_x e2;
|
|
substitution_correctness x e_x e3
|
|
| D.EAbs _ _ body ->
|
|
substitution_correctness x e_x body
|
|
| D.EApp e1 e2 _ ->
|
|
substitution_correctness x e_x e1;
|
|
substitution_correctness x e_x e2
|
|
| D.EDefault exceptions just cons tau ->
|
|
substitution_correctness x e_x just;
|
|
substitution_correctness x e_x cons;
|
|
substitution_correctness_list x e_x e exceptions;
|
|
process_exceptions_untouched_by_subst x (translate_exp e_x) (translate_ty tau)
|
|
and substitution_correctness_list (x: D.var) (e_x: D.exp) (e: D.exp) (l: list D.exp{l << e})
|
|
: Lemma (ensures (
|
|
translate_exp_list (D.subst_list x e_x l) ==
|
|
L.subst_list x (translate_exp e_x) (translate_exp_list l)))
|
|
(decreases %[e; 0; l])
|
|
=
|
|
match l with
|
|
| [] -> ()
|
|
| hd::tl ->
|
|
substitution_correctness x e_x hd;
|
|
substitution_correctness_list x e_x e tl
|
|
#pop-options
|
|
|
|
(**** Main theorems *)
|
|
|
|
let translation_correctness_value (e: D.exp) : Lemma
|
|
((D.is_value e) <==> (L.is_value (translate_exp e)))
|
|
= ()
|
|
|
|
#push-options "--fuel 2 --ifuel 1 --z3rlimit 50"
|
|
let rec translation_correctness_step (de: D.exp) (dtau: D.ty) : Pure nat
|
|
(requires (Some? (D.step de) /\ D.typing D.empty de dtau))
|
|
(ensures (fun n ->
|
|
translation_preserves_empty_typ de dtau;
|
|
let de' = Some?.v (D.step de) in
|
|
D.preservation de dtau;
|
|
translation_preserves_empty_typ de' dtau;
|
|
take_l_steps (translate_ty dtau) (translate_exp de) n == Some (translate_exp de')
|
|
))
|
|
(decreases %[de; 2])
|
|
=
|
|
let le = translate_exp de in
|
|
translation_preserves_empty_typ de dtau;
|
|
let de' = Some?.v (D.step de) in
|
|
let ltau = translate_ty dtau in
|
|
match de with
|
|
| D.EVar _ -> 0
|
|
| D.ELit _ -> 0
|
|
| D.EAbs _ _ _ -> 0
|
|
| D.EIf de1 de2 de3 ->
|
|
let le1 = translate_exp de1 in
|
|
let le2 = translate_exp de2 in
|
|
let le3 = translate_exp de3 in
|
|
if not (D.is_value de1) then begin
|
|
let de1' = Some?.v (D.step de1) in
|
|
D.preservation de1 D.TBool;
|
|
translation_preserves_empty_typ de1 D.TBool;
|
|
translation_preserves_empty_typ de2 dtau;
|
|
translation_preserves_empty_typ de3 dtau;
|
|
translation_preserves_empty_typ de1' D.TBool;
|
|
let le1' : typed_l_exp L.TBool = translate_exp de1' in
|
|
let n_e1 = translation_correctness_step de1 D.TBool in
|
|
assert(take_l_steps L.TBool le1 n_e1 == Some le1');
|
|
lift_multiple_l_steps L.TBool ltau le1 le1' n_e1
|
|
(if_cond_lift ltau le2 le3 n_e1);
|
|
n_e1
|
|
end else 1
|
|
| _ -> admit()
|
|
|
|
let _ = ()
|
|
|
|
(*
|
|
| D.EApp e1 e2 tau_arg ->
|
|
admit();
|
|
let e1' = translate_exp e1 in
|
|
let e2' = translate_exp e2 in
|
|
let ltau_arg = translate_ty tau_arg in
|
|
if not (D.is_value e1) then begin
|
|
let stepped_e1 = Some?.v (D.step e1) in
|
|
let stepped_e1' = translate_exp stepped_e1 in
|
|
let n_e1 = translation_correctness_step e1 (D.TArrow tau_arg tau) in
|
|
lift_multiple_l_steps
|
|
e1' stepped_e1'
|
|
(L.TArrow ltau_arg ltau) ltau
|
|
n_e1 (fun e1' -> L.EApp e1' e2' (translate_ty tau_arg));
|
|
n_e1
|
|
end else begin match e1 with
|
|
| D.ELit D.LConflictError -> 0
|
|
| D.ELit D.LEmptyError -> 0
|
|
| _ ->
|
|
if not (D.is_value e2) then begin
|
|
let stepped_e2 = Some?.v (D.step e2) in
|
|
let stepped_e2' = translate_exp stepped_e2 in
|
|
let n_e2 = translation_correctness_step e2 tau_arg in
|
|
lift_multiple_l_steps
|
|
e2' stepped_e2'
|
|
ltau_arg ltau
|
|
n_e2 (fun e2' -> L.EApp e1' e2' (translate_ty tau_arg));
|
|
n_e2
|
|
end else begin
|
|
match e1, e2 with
|
|
| _, D.ELit D.LConflictError -> 0
|
|
| _, D.ELit D.LEmptyError -> 0
|
|
| D.EAbs x1 t1 body, e2 ->
|
|
substitution_correctness x1 e2 body;
|
|
0
|
|
end
|
|
end
|
|
| D.EDefault exceptions just cons tau' ->
|
|
admit();
|
|
if tau' <> tau then 0 else begin
|
|
match D.step_exceptions e exceptions just cons tau with
|
|
| Some e' ->
|
|
admit()//translation_correctness_exceptions_step e exceptions just cons tau
|
|
| None -> admit()
|
|
end
|
|
*)
|
|
let _ = ()
|
|
|
|
(*
|
|
and translation_correctness_exceptions_step
|
|
(e: D.exp)
|
|
(exceptions: list D.exp {exceptions << e})
|
|
(just: D.exp{just << e})
|
|
(cons: D.exp{cons << e})
|
|
(tau: D.ty)
|
|
: Pure nat
|
|
(requires (
|
|
D.typing_list D.empty exceptions tau /\
|
|
D.typing D.empty just D.TBool /\
|
|
D.typing D.empty cons tau /\
|
|
e == D.EDefault exceptions just cons tau /\ Some? (D.step e) /\
|
|
Some? (D.step_exceptions e exceptions just cons tau)
|
|
))
|
|
(ensures (fun n ->
|
|
assume(L.typing L.empty (translate_exp e) (translate_ty tau));
|
|
multiple_l_steps
|
|
(translate_exp e)
|
|
(translate_ty tau)
|
|
(translate_exp (Some?.v (D.step e)))
|
|
n))
|
|
(decreases %[e; 1])
|
|
=
|
|
if List.Tot.for_all (fun except -> D.is_value except) exceptions then
|
|
admit()
|
|
else translation_correctness_exceptions_left_to_right_step e exceptions just cons tau
|
|
|
|
and translation_correctness_exceptions_left_to_right_step
|
|
(e: D.exp)
|
|
(exceptions: list D.exp {exceptions << e})
|
|
(just: D.exp{just << e})
|
|
(cons: D.exp{cons << e})
|
|
(tau: D.ty)
|
|
: Pure nat
|
|
(requires (
|
|
D.typing_list D.empty exceptions tau /\
|
|
D.typing D.empty just D.TBool /\
|
|
D.typing D.empty cons tau /\
|
|
Some? (D.step_exceptions_left_to_right e exceptions just cons tau)
|
|
))
|
|
(ensures (fun n ->
|
|
assume(L.typing L.empty (build_default_translation
|
|
(translate_exp_list exceptions)
|
|
(translate_exp just)
|
|
(translate_exp cons)
|
|
(translate_ty tau)) (translate_ty tau));
|
|
multiple_l_steps
|
|
(build_default_translation
|
|
(translate_exp_list exceptions)
|
|
(translate_exp just)
|
|
(translate_exp cons)
|
|
(translate_ty tau))
|
|
(translate_ty tau)
|
|
(translate_exp
|
|
(Some?.v (D.step_exceptions_left_to_right e exceptions just cons tau))) n
|
|
))
|
|
(decreases %[e; 0; exceptions])
|
|
=
|
|
match exceptions with
|
|
| [] -> admit(); 0
|
|
| hd::tl ->
|
|
let ljust = translate_exp just in
|
|
let lcons = translate_exp cons in
|
|
let ltl = translate_exp_list tl in
|
|
let ltau = translate_ty tau in
|
|
let lhd = translate_exp hd in
|
|
if D.is_value hd then begin
|
|
match D.step_exceptions_left_to_right e tl just cons tau with
|
|
| Some (D.ELit D.LConflictError) -> admit()
|
|
| Some (D.EDefault tl' just' cons' tau') ->
|
|
assume(just = just' /\ cons = cons' /\ tau = tau');
|
|
admit()
|
|
(*let ltl' = translate_exp_list tl' in
|
|
let n_tl = translation_correctness_exceptions_left_to_right_step e tl just cons tau in
|
|
assert(multiple_l_steps
|
|
(build_default_translation ltl ljust lcons ltau)
|
|
(build_default_translation ltl' ljust lcons ltau) n_tl);
|
|
assume(multiple_l_steps
|
|
(build_default_translation (lhd::ltl) ljust lcons ltau)
|
|
(build_default_translation (lhd::ltl') ljust lcons ltau) n_tl);
|
|
assume((translate_exp
|
|
(Some?.v (D.step_exceptions_left_to_right e exceptions just cons tau)))
|
|
==
|
|
(build_default_translation
|
|
(lhd::ltl')
|
|
(translate_exp just)
|
|
(translate_exp cons)
|
|
(translate_ty tau)));
|
|
n_tl*)
|
|
end else begin
|
|
match D.step hd with
|
|
| Some (D.ELit D.LConflictError) -> admit()
|
|
| Some stepped_hd ->
|
|
let stepped_hd' = translate_exp stepped_hd in
|
|
let n_hd = translation_correctness_step hd tau in
|
|
let hd' = translate_exp hd in
|
|
let tl' = translate_exp_list tl in
|
|
admit()
|
|
end
|
|
*)
|
|
(*** Wrap-up theorem *)
|
|
|
|
let translation_correctness (de: D.exp) (dtau: D.ty)
|
|
: Lemma
|
|
(requires (D.typing D.empty de dtau))
|
|
(ensures (
|
|
let le = translate_exp de in
|
|
let ltau = translate_ty dtau in
|
|
L.typing L.empty le ltau /\ begin
|
|
if D.is_value de then L.is_value le else begin
|
|
D.progress de dtau;
|
|
D.preservation de dtau;
|
|
let de' = Some?.v (D.step de) in
|
|
translation_preserves_empty_typ de dtau;
|
|
translation_preserves_empty_typ de' dtau;
|
|
let le' : typed_l_exp ltau = translate_exp de' in
|
|
exists (n:nat). (take_l_steps ltau le n == Some le')
|
|
end
|
|
end
|
|
))
|
|
=
|
|
translation_preserves_empty_typ de dtau;
|
|
if D.is_value de then translation_correctness_value de else begin
|
|
D.progress de dtau;
|
|
let n = translation_correctness_step de dtau in
|
|
()
|
|
end
|