52 lines
1.3 KiB
Coq
52 lines
1.3 KiB
Coq
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From Coq Require Import Strings.String.
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Require Import terms.
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Require Import subst.
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Include Terms.
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Include Subst.
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Module Smallstep.
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Reserved Notation " s '-->α' t " (at level 40).
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Reserved Notation " s '-->β' t " (at level 40).
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Reserved Notation " s '-->δ' t " (at level 40).
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Inductive beta_step : expr -> expr -> Prop :=
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| E_AppLeft : forall e1 e1' e2,
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e1 -->β e1' ->
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(expr_tm_app e1 e2) -->β (expr_tm_app e1' e2)
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| E_AppRight : forall e1 e2 e2',
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e2 -->β e2' ->
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(expr_tm_app e1 e2) -->β (expr_tm_app e1 e2')
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| E_AppTmAbs : forall x τ e a,
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(expr_tm_app (expr_tm_abs x τ e) a) -->β (expr_subst x a e)
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| E_AppTyAbs : forall x e a,
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(expr_ty_app (expr_ty_abs x e) a) -->β (expr_specialize x a e)
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| E_AppLet : forall x t e a,
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(expr_let x t a e) -->β (expr_subst x a e)
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where "s '-->β' t" := (beta_step s t).
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(*
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Inductive multi {X : Type} (R : relation X) : relation X :=
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| multi_refl : forall (x : X), multi R x x
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| multi_step : forall (x y z : X),
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R x y ->
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multi R y z ->
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multi R x z.
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Notation " s -->β* t " := (multi beta_step s t) (at level 40).
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*)
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(*
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Inductive delta_expand : expr -> expr -> Prop :=
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| E_ImplicitCast
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(expr_tm_app e1 e2)
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*)
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End Smallstep.
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