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