From d1742c51d50a3ae78cc068f0eb36dbe47ddb92c6 Mon Sep 17 00:00:00 2001
From: Michael Sippel <micha@fragmental.art>
Date: Wed, 4 Sep 2024 12:46:37 +0200
Subject: [PATCH] coq: remove delta_step definition
---
coq/smallstep.v | 30 ++++--------------------------
1 file changed, 4 insertions(+), 26 deletions(-)
diff --git a/coq/smallstep.v b/coq/smallstep.v
index 63f1cc1..2a88c99 100644
--- a/coq/smallstep.v
+++ b/coq/smallstep.v
@@ -65,38 +65,16 @@ Inductive beta_step : expr_term -> expr_term -> Prop :=
(expr_ty_app (expr_ty_abs x e) a) -->β (expr_specialize x a e)
| E_AppLam : forall x τ e a,
- (expr_tm_app (expr_tm_abs x τ e) a) -->β (expr_subst x a e)
+ (expr_app (expr_abs x τ e) a) -->β (expr_subst x a e)
+
+ | E_AppMorph : forall x τ e a,
+ (expr_app (expr_morph x τ e) a) -->β (expr_subst x a e)
| E_AppLet : forall x t e a,
(expr_let x t a e) -->β (expr_subst x a e)
where "s '-->β' t" := (beta_step s t).
-
-
-Inductive delta_step : expr_term -> expr_term -> Prop :=
-
- | E_ImplicitCast : forall (Γ:context) (f:expr_term) (h:string) (a:expr_term) (τ:type_term) (s:type_term) (p:type_term),
-
- (context_contains Γ h (type_morph p s)) ->
- Γ |- f \is (type_fun s τ) ->
- Γ |- a \is p ->
- (expr_tm_app f a) -->δ (expr_tm_app f (expr_tm_app (expr_var h) a))
-
-where "s '-->δ' t" := (delta_step s t).
-
-
-Inductive eval_step : expr_term -> expr_term -> Prop :=
- | E_Beta : forall s t,
- (s -->β t) ->
- (s -->eval t)
-
- | E_Delta : forall s t,
- (s -->δ t) ->
- (s -->eval t)
-
-where "s '-->eval' t" := (eval_step s t).
-
Inductive multi {X : Type} (R : X -> X -> Prop) : X -> X -> Prop :=
| Multi_Refl : forall (x : X), multi R x x
| Multi_Step : forall (x y z : X),