type Int = "Int";
type Bool = "Bool";
type Atom = Int | Bool;
type SimpleType = Arrow | Atom;
type Arrow = {
  left:    SimpleType;
  right:   SimpleType;
};

type Identifier = string;

type Binding = {
  name:    Identifier;
  type?:   SimpleType;
};

type Abstraction = {
  binding: Binding;
  body:    ASTNode;
};

type ASTNode = Abstraction | Application | Identifier;

//

class Environment<T> {
  constructor(private readonly _captures: Map<Identifier, T>, private readonly _parent?: Environment) {}

  public add(identifier: Identifier, substitution: T): Environment<T> {
    const captures = new HashMap(); captures.put(identifier, substitution);
    return new Environment<>(captures, this);
  }

  public get(identifier: Identifier): T? {
    if (this._captures.has(identifier)) return this._captures.get(identifier);
    return this._parent?.get(identifier);
  }
}

//const tokenize
// const parse
// const check