Church encoding of True, False and Or

boolean-churchEncoding.ts

type TRUE = <A>(a: A) => <B>(b: B) => A;
type FALSE = <A>(a: A) => <B>(b: B) => B;
type OR = <A extends TRUE | FALSE>(a: A) => <B extends TRUE | FALSE>(b: B) => TRUE | FALSE;

// (λx.λy.x)
const TRUE: TRUE = a => b => a;
console.log(TRUE(1)(0));

// (λx.λy.y)
const FALSE: FALSE = a => b => b;
console.log(FALSE(1)(0));

// (λx.λy.x TRUE y)
const OR = a => b => a(TRUE)(b);
console.log(OR(TRUE)(FALSE)(1)(0));