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