mpri-funcprog-project/coq/CPSSpecialCases.v

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Require Import MyTactics.
Require Import LambdaCalculusSyntax.
Require Import LambdaCalculusValues.
Require Import CPSDefinition.
Require Import CPSContextSubstitution.
Require Import CPSKubstitution.
(* The translation of an application whose left-hand side is a value. *)
Lemma cps_app_value:
forall v1 t2 c,
is_value v1 ->
cps (App v1 t2) c =
cps t2 (M (App (App (lift 1 (cpsv v1)) (Var 0)) (lift 1 (reify c)))).
Proof.
intros. cps. simpl.
rewrite cps_kubstitution_0. asimpl.
reflexivity.
Qed.
(* The translation of a value-value application. *)
Lemma cps_app_value_value:
forall v1 v2 c,
is_value v1 ->
is_value v2 ->
cps (App v1 v2) c =
App (App (cpsv v1) (cpsv v2)) (reify c).
Proof.
intros.
rewrite cps_app_value by obvious.
rewrite cps_value by eauto. asimpl.
reflexivity.
Qed.
(* The translation of a [Let] construct whose left-hand side is a value. *)
Lemma cps_let_value:
forall v1 t2 c,
is_value v1 ->
cps (Let v1 t2) c =
Let (cpsv v1) (cps t2 (liftc 1 c)).
Proof.
intros. cps. simpl. f_equal.
eapply cps_kubstitution. (* [cps_substitution] could be used too *)
{ autosubst. }
{ rewrite substc_substc. autosubst. }
Qed.