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coq: remove delta_step definition

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Michael Sippel 2024-09-04 12:46:37 +02:00
parent 1bd55cd8c3
commit d1742c51d5
Signed by: senvas
GPG key ID: F96CF119C34B64A6
1 changed files with 4 additions and 26 deletions
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30
coq/smallstep.v
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@ -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),