A few improvements

Here we'll do what we can by slight modifications of the CPS transformer and code generator.

"prog" nodes

We'll start with a simple one, the cps_prog — the idea is that when the first expression has no side effects, we need not repeat it in the output. The following helper function will decide if an AST node can or cannot have side effects. It's not perfect; the golden rule here is to err on the safe side. If we're not sure, then it does have side effects.

For example, it's not easy to tell if "assign" or "call" nodes have no side effects. Assignment is a side effect by definition, but it can be discarded if that variable is never used again, or just immediately assigned again. A function call on the other hand might have no side effects if the called function is “pure”, but there is no easy way to attest this. Since we can't easily be sure, we assume they do have side effects.

function has_side_effects(exp) {
    switch (exp.type) {
      case "call":
      case "assign":
        return true;

      case "num":
      case "str":
      case "bool":
      case "var":
      case "lambda":
        return false;

      case "binary":
        return has_side_effects(exp.left)
            || has_side_effects(exp.right);

      case "if":
        return has_side_effects(exp.cond)
            || has_side_effects(exp.then)
            || (exp.else && has_side_effects(exp.else));

      case "let":
        for (var i = 0; i < exp.vars.length; ++i) {
            var v = exp.vars[i];
            if (v.def && has_side_effects(v.def))
                return true;
        return has_side_effects(exp.body);

      case "prog":
        for (var i = 0; i < exp.prog.length; ++i)
            if (has_side_effects(exp.prog[i]))
                return true;
        return false;
    return true;

I hope this function is clear without further comments. Having it, our cps_prog becomes this:

function cps_prog(exp, k) {
    return (function loop(body){
        if (body.length == 0) return k(FALSE);
        if (body.length == 1) return cps(body[0], k);
        if (!has_side_effects(body[0]))
            return loop(body.slice(1));
        return cps(body[0], function(first){
            if (has_side_effects(first)) return {
                type: "prog",
                prog: [ first, loop(body.slice(1)) ]
            return loop(body.slice(1));

So, the first two cases are the same: if the list is empty then we must return false, and if there's a single expression we must compile it because we want its result. But if there are at least two expressions, then we check: can we determine at compile time that the first one has no side effects? If so, then we drop it—we don't even compile it—just loop over the rest. And if it does have a side effect, we still check if its result has a side effect in the continuation (because it might be just a plain variable) and only include it if so.

"if" nodes

The previous cps_if passed the k on compiling both branches, resulting in massive code growth for consecutive if-s. The (quite expensive) fix is to wrap the rest of the program in a continuation, and we'll transform the "if" node into an IIFE which receives that continuation as an argument. The body of this IIFE will just call the continuation with the result of the if expression.

Here's a sample λ-to-λ transformation to show what we're after:

a = if foo then 1 else 2;
(λ (ifcont){
  if foo then ifcont(1) else ifcont(2);
})(λ (ifret){
  a = ifret;

This does add some overhead, but at least the growth is linear, not exponential (i.e. you don't see print(a) twice in the output).

Here's the new cps_if:

function cps_if(exp, k) {
    return cps(exp.cond, function(cond){
        var cvar = gensym("I");
        var cast = make_continuation(k);
        k = function(ifresult) {
            return {
                type: "call",
                func: { type: "var", value: cvar },
                args: [ ifresult ]
        return {
            type: "call",
            func: {
                type: "lambda",
                vars: [ cvar ],
                body: {
                    type: "if",
                    cond: cond,
                    then: cps(exp.then, k),
                    else: cps(exp.else || FALSE, k)
            args: [ cast ]

We have to invent a name for the continuation (cvar). After compiling the rest of the program into the cast continuation we turn k into a function which returns a "call" node for invoking the cast (which will be available in the value of cvar) with the argument which will contain the result of the if expression. That is the k that we now pass to both branches.

Adding stack guards and dropping returns

For this we need a small change in the code generator. The new js_lambda becomes:

function js_lambda(exp) {
    var code = "(function ";
    var CC = exp.name || "β_CC";
    code += make_var(CC);
    code += "(" + exp.vars.map(make_var).join(", ") + ")";
    code += "{ GUARD(arguments, " + CC + "); " + js(exp.body) + " })";
    return code;

If the function we compile is unnamed, we name it "β_CC", so we can pass it to GUARD. I have reversed GUARD's arguments, because they will add quite a lot to the output (see, we got rid of return-s, but must place these guards instead) — and by providing a longer constant string of characters we enable better compression of the output code after gzip.

After these “improvements”, the output for the fib function looks “turrible”:

fib = λ(n) {
  if n < 2 then n
    fib(n - 1) +
    fib(n - 2);

Let's try to run it:

By my measurements, it appears to be about 6 times faster than the straight evaluator and 30 times faster than the CPS evaluator. It's also roughly 30 times slower than the hand-coded JS. The thing which slows it down, besides the overhead introduced by the CPS transformation, is guarding the stack. Unfortunately, there is no way around this. If I drop the GUARD calls from the JS generator, the example above aborts with stack overflow.

Another bloat is added by the way we handle if-s. It's totally not necessary in the example above, since the if expression is the last thing in the function (its continuation just calls fib's continuation).

In the next section we'll write an optimizer that will further improve the quality of the output code.

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