Mizzlr

function numerify(churchNumeral) {
	return churchNumeral(function (x) {
		return x + 1;
	})(0); // f is a function that increments the value by 1; z=0
}

// example
numerify(ZERO) // returns 0
var ONE = SUCC(ZERO)
numerify(ONE) // returns 1

Mizzlr

var ZERO = function (f) {
	return function(z) {
		return z;
	};
};

var SUCC = function (n) {
	return function (f) {
		return function (z) {
			return f(n(f)(z));

Mizzlr

# The above functions in python
NULL = lambda x: x
TRUE = lambda onTrue: lambda onFalse: onTrue
FALSE = lambda onTrue: lambda onFalse: onFalse
IF = lambda test: lambda onTrue: lambda onFalse: test(onTrue)(onFalse)
AND = lambda bool1: lambda bool2: bool1(bool2)(bool1)
OR = lambda bool1: lambda bool2: bool1(bool1)(bool2)
NOT = lambda booly: booly(FALSE)(TRUE)

# Very readable and terse indeed!

Mizzlr

var AND = function(bool1){
    return function(bool2){
        bool1(bool2)(bool1);
    };
};
// consider what happens for all combination of bool1 and bool2
// bool1(bool2)(bool1) = AND(bool1)(bool2)
// TRUE(FALSE)(TRUE) = FALSE ; TRUE returns the first argument
// TRUE(TRUE)(TRUE) = TRUE
// FALSE(TRUE)(FALSE) = FALSE ; FALSE returns the second argument

Mizzlr

function boolify (churchBoolean) {
	return churchBoolean (function (_) { return true; })
		( function (_) { return false; });
// function had to have one input argument
// because that is what is expected by TRUE or FALSE

// example
boolify(TRUE) // returns true
boolify(FALSE) // return false

Mizzlr

var IF = function (test) {
	return function (onTrue) {
		return function (onFalse) {
			return test(onTrue)(onFalse);
		};
	};
};

// example use
IF(TRUE)(trueBlock)(falseBlock);

Mizzlr

// onTrue and onFalse are also some function
var TRUE = function (onTrue) {
	return function (onFalse) {
		return onTrue(VOID);
	};
};

var FALSE = function (onTrue) {
	return function (onFalse) {
		return onFalse(VOID);

Mizzlr

function curry(f) {
	return function (x) {
		return function (y) {
			return f(x,y);
		};
	};
};

function uncurry(f) {
	return function (x,y) {

Mizzlr

var f1 = function(a,b){
    // do something with a and b
    return a + b;
};
var f2 = function(a){
    // can do something with a here
    return function(b){
        // can do something with a and b here
        return a + b;
    };

Mizzlr

var NULL = function(x) { return x;}