44 lines
1.3 KiB
Coq
44 lines
1.3 KiB
Coq
(* Define the abstract syntax of the calculus
|
|
* by inductive definition of type-terms
|
|
* and expression-terms.
|
|
*)
|
|
|
|
From Coq Require Import Strings.String.
|
|
Module Terms.
|
|
|
|
(* types *)
|
|
Inductive ladder_type : Type :=
|
|
| type_unit : ladder_type
|
|
| type_id : string -> ladder_type
|
|
| type_var : string -> ladder_type
|
|
| type_num : nat -> ladder_type
|
|
| type_abs : string -> ladder_type -> ladder_type
|
|
| type_app : ladder_type -> ladder_type -> ladder_type
|
|
| type_fun : ladder_type -> ladder_type -> ladder_type
|
|
| type_rung : ladder_type -> ladder_type -> ladder_type
|
|
.
|
|
|
|
(* expressions *)
|
|
Inductive expr : Type :=
|
|
| expr_var : string -> expr
|
|
| expr_ty_abs : string -> expr -> expr
|
|
| expr_ty_app : expr -> ladder_type -> expr
|
|
| expr_tm_abs : string -> ladder_type -> expr -> expr
|
|
| expr_tm_app : expr -> expr -> expr
|
|
| expr_let : string -> ladder_type -> expr -> expr -> expr
|
|
| expr_ascend : ladder_type -> expr -> expr
|
|
| expr_descend : ladder_type -> expr -> expr
|
|
.
|
|
|
|
Coercion type_var : string >-> ladder_type.
|
|
Coercion expr_var : string >-> expr.
|
|
|
|
|
|
(*
|
|
Notation "( x )" := x (at level 70).
|
|
Notation "x ~ y" := (type_rung x y) (at level 69, left associativity).
|
|
Notation "< x y >" := (type_app x y) (at level 68, left associativity).
|
|
Notation "'$' x" := (type_id x) (at level 66).
|
|
*)
|
|
|
|
End Terms.
|