Inductive term: Type :=
| Var: nat -> term
| Abs: term -> term
| App: term -> term -> term.

Notation "'λ' body" := (Abs body) (at level 60, right associativity).
Notation "'❨' t1 t2 '❩'" := (App t1 t2) (at level 50).
Notation "'`' varidx " := (Var varidx) (at level 40).

Check λ`0.
Check λ❨`0 `0❩.
Check ❨λ❨`0 `0❩ λ❨`0 `0❩❩.

Require Import List.
Search In.