[Functional Programming] Church Encodings: Numberals

const log = console.log;

// zero :: &fa.a
const zero = f => x => x; // zero is F
// once :: &fa.fa
const once = f => x => f(x); // once it I
// twice :: &fa.f(fa)
const twice = f => x => f(f(x));
// thrice :: &fa.f(f(fa))
const thrice = f => x => f(f(f(x)));

const T = true;
const F = false;
const I = x => x;
const not = x => !x;

log(zero(not)(T)) // true, because only return second arguement
log(once(not)(T)) // false
log(twice(not)(F)) // false
log(thrice(not)(T)) // false

log('****')

/** SUCCSOR 
SUCC N1 = N2
SUCC N2 = N3
SUCC(SUCC N1) = N3

SUCC &fa.fa = &fa.f(fa)
SUCC N2, then n is 2, do f n times, then add one f more
*/
const succ = n => f => x => f(n(f)(x));
// conver chunch number to JS number.
// jsnum :: take a chunch number, call (x => x + 1) n times, and start from 0.
const jsnum = n => n(x => x + 1)(0);
log(succ(zero)(not)(T)) // false
log(jsnum(succ(zero))) // 1
log(jsnum(succ(succ(zero)))) // 2

const n0 = zero;
const n1 = once;
const n2 = twice;
const n3 = thrice;
const n4 = succ(thrice);

log(jsnum(succ(n2))) // 3