CPS Transforms in JavaScript and Scheme

js_direct.js

// Example 1
function pyth(x, y) {
    return Math.sqrt (x*x + y*y);
}

// Example 2
function factorial(n) {
    if (n === 0) {
        return 1;
    }
    return n * factorial (n - 1);
}

// Example 3
function factorial(n) {
    return f_aux (n, 1);
}
function f_aux(n, a) {
    if (n === 0) {
        return a;
    }
    return f_aux (n - 1, n * a);
}

js_transformed.js

// Example 1
function pyth(x, y, callback) {
    mul (x, x, function(a) {
        mul (y, y, function(b) {
            add (a, b, function(c) {
                sqrt (c, callback);
            })
        });
    });
}

// Example 2
function factorial(n, callback) {
    eq (n, 0, function(a) {
        if (a) {
            callback (1);
        } else {
            sub (n, 1, function(b) {
                factorial (b, function(c) {
                    mul (n, c, callback);
                });
            });
        }
    });
}

// Example 3
function factorial(n, callback) {
    f_aux (n, 1, callback);
}
function f_aux(n, m, callback) {
    eq (n, 0, function(a) {
        if (a) {
            callback (m);
        } else {
            sub (n, 1, function(b) {
                mul (n, m, function(c) {
                    f_aux (b, c, callback);
                });
            });
        }
    });
}

// Shared
function eq(a, b, callback) {
    callback (a === b);
}
function mul(a, b, callback) {
    callback (a * b);
}
function add(a, b, callback) {
    callback (a + b);
}
function sub(a, b, callback) {
    callback (a - b);
}
function sqrt(n, callback) {
    callback (Math.sqrt (n));
}

scheme_direct.scm

; Example 1
(define (pyth x y)
 (sqrt (+ (* x x) (* y y))))

; Example 2
(define (factorial n)
 (if (= n 0)
     1     ; NOT tail-recursive
     (* n (factorial (- n 1))))

; Example 3
(define (factorial n)
 (f-aux n 1))
(define (f-aux n a)
 (if (= n 0)
     a        ; tail-recursive
     (f-aux (- n 1) (* n a))))

scheme_transformed.scm

; Example 1
(define (pyth& x y k)
 (*& x x (lambda (x2)
          (*& y y (lambda (y2)
                   (+& x2 y2 (lambda (x2py2)
                              (sqrt& x2py2 k))))))))

; Example 2
(define (factorial& n k)
 (=& n 0 (lambda (b)
          (if b                    ; growing continuation
              (k 1)                ; in the recursive call
              (-& n 1 (lambda (nm1)
                       (factorial& nm1 (lambda (f)
                                        (*& n f k)))))))))

; Example 3
(define (factorial& n k) (f-aux& n 1 k))
(define (f-aux& n a k)
 (=& n 0 (lambda (b)
          (if b                    ; same continuation
              (k a)                ; in the recursive call
              (-& n 1 (lambda (nm1) 
                       (*& n a (lambda (nta)
                                (f-aux& nm1 nta k)))))))))