Happy new year's, hackfolk!

A few weeks ago I wrote about the upcoming Guile 2.2 release, and specifically about its new register virtual machine. Today I'd like to burn some electrons on another new part in Guile 2.2, its intermediate language.

To recap, we switched from a stack machine to a register machine because, among other reasons, register machines can consume and produce named intermediate results in fewer instructions than stack machines, and that makes things faster.

To take full advantage of this new capability, it is appropriate to switch at the same time from the direct-style intermediate language (IL) that we had to an IL that names all intermediate values. This lets us effectively reason about each subexpression that goes into a computation, for example in common subexpression elimination.

As far as intermediate languages go, basically there are two choices these days: something SSA-based, or something CPS-based. I wrote an article on SSA, ANF and CPS a few years ago; if you aren't familiar with these or are feeling a little rusty, I suggest you go and take a look.

In Guile I chose a continuation-passing style language. I still don't know if I made the right choice. I'll go ahead and describe Guile's IL and then follow up with some reflections. The description below is abbreviated from a more complete version in Guile's manual.

guile's cps language

Guile's CPS language is composed of terms , expressions , and continuations . It was heavily inspired by Andrew Kennedy's Compiling with Continuations, Continued paper.

A term can either evaluate an expression and pass the resulting values to some continuation, or it can declare local continuations and contain a sub-term in the scope of those continuations.

$continue k src exp Evaluate the expression exp and pass the resulting values (if any) to the continuation labelled k . $letk conts body Bind conts in the scope of the sub-term body . The continuations are mutually recursive.

Additionally, the early stages of CPS allow for a set of mutually recursive functions to be declared as a term via a $letrec term. A later pass will attempt to transform the functions declared in a $letrec into local continuations. Any remaining functions are later lowered to $fun expressions. More on "contification" later.

Here is an inventory of the kinds of expressions in Guile's CPS language. Recall that all expressions are wrapped in a $continue term which specifies their continuation.

$void Continue with the unspecified value. $const val Continue with the constant value val . $prim name Continue with the procedure that implements the primitive operation named by name . $fun src meta free body Continue with a procedure. body is the $kentry $cont of the procedure entry. free is a list of free variables accessed by the procedure. Early CPS uses an empty list for free ; only after closure conversion is it correctly populated. $call proc args Call proc with the arguments args , and pass all values to the continuation. proc and the elements of the args list should all be variable names. The continuation identified by the term's k should be a $kreceive or a $ktail instance. $primcall name args Perform the primitive operation identified by name , a well-known symbol, passing it the arguments args , and pass all resulting values to the continuation. $values args Pass the values named by the list args to the continuation. $prompt escape? tag handler Push a prompt on the stack identified by the variable name tag and continue with zero values. If the body aborts to this prompt, control will proceed at the continuation labelled handler , which should be a $kreceive continuation. Prompts are later popped by pop-prompt primcalls.

The remaining element of the CPS language in Guile is the continuation. In CPS, all continuations have unique labels. Since this aspect is common to all continuation types, all continuations are contained in a $cont instance:

$cont k cont Declare a continuation labelled k . All references to the continuation will use this label.

The most common kind of continuation binds some number of values, and then evaluates a sub-term. $kargs is this kind of simple lambda .

$kargs names syms body Bind the incoming values to the variables syms , with original names names , and then evaluate the sub-term body .

Variables (e.g., the syms of a $kargs ) should be globally unique. To bind the result of an expression a variable and then use that variable, you would continue from the expression to a $kargs that declares one variable. The bound value would then be available for use within the body of the $kargs .

$kif kt kf Receive one value. If it is a true value, branch to the continuation labelled kt , passing no values; otherwise, branch to kf .

Non-tail function calls should continue to a $kreceive continuation in order to adapt the returned values to their uses in the calling function, if any.

$kreceive arity k Receive values from a function return. Parse them according to arity , and then proceed with the parsed values to the $kargs continuation labelled k .

$arity is a helper data structure used by $kreceive and also by $kclause , described below.

$arity req opt rest kw allow-other-keys? A data type declaring an arity. See Guile's manual for details.

Additionally, there are three specific kinds of continuations that can only be declared at function entries.

$kentry self tail clauses Declare a function entry. self is a variable bound to the procedure being called, and which may be used for self-references. tail declares the $cont wrapping the $ktail for this function, corresponding to the function's tail continuation. clauses is a list of $kclause $cont instances.

$ktail A tail continuation.

$kclause arity cont A clause of a function with a given arity. Applications of a function with a compatible set of actual arguments will continue to cont , a $kargs $cont instance representing the clause body.

reflections

Before starting Guile's compiler rewrite, I had no real-world experience with CPS-based systems. I had worked with a few SSA-based systems, and a few more direct-style systems. I had most experience with the previous direct-style system that Guile had, but never had to seriously design another kind of IL, so basically I was ignorant. It shows, I think; but time will tell if it came out OK anyway. At this point I am cautiously optimistic.

As far as fitness for purpose goes, the CPS IL works in the sense that it is part of a self-hosting compiler. I'll say no more on that point other than to mention that it has explicit support for a number of Guile semantic features: multiple-value returns; optional, rest, and keyword arguments; cheap delimited continuations; Guile-native constant literals.

Why not ANF instead? If you recall from my SSA and CPS article, I mentioned that ANF is basically CPS with fewer labels. It tries to eliminate "administrative" continuations, whereas Guile's CPS labels everything. There is no short-hand let form.

ANF proponents tout its parsimony as a strength, but I do not understand this argument. I like having labels for everything. In CPS, I have as many labels as there are expressions, plus a few for continuations that don't contain terms. I use them directly in the bytecode compiler; the compiler never has to generate a fresh label, as they are part of the CPS itself.

More importantly, labelling every control-flow point allows me to reason precisely about control flow. For example, if a function is always called with the same continuation, it can be incorporated in the flow graph of the calling function. This is called "contification". It is not the same thing as inlining, as it works for sets of recursive functions as well, and never increases code size. This is a crucial transformation for a Scheme compiler to make, as it turns function calls into goto s, and self-function calls into loop back-edges.

Guile's previous compiler did a weak form of contification, but because we didn't have names for all control points it was gnarly and I was afraid to make it any better. Now its contifier is optimal. See Fluet and Weeks' Contification using Dominators and Kennedy's CWCC, for more on contification.

One more point in favor of labelling all continuations. Many tranformations can be best cast as a two-phase process, in which you first compute a set of transformations to perform, and then you apply them. Dead-code elimination works this way; first you find the least fixed-point of live expressions, and then you residualize only those expressions. Without names, how are you going to refer to an expression in the first phase? The ubiquitous, thorough labelling that CPS provides does not have this problem.

So I am happy with CPS, relative to ANF. But what about SSA? In my previous article, I asked SSA proponents to imagine returning a block from a block. Of course it doesn't make any sense; SSA is a first-order language. But modern CPS is also first-order, is the thing! Modern CPS distinguishes "continuations" syntactically from functions, which is exactly the same as SSA's distinction between basic blocks and functions. CPS and SSA really are the same on this level.

The fundamental CPS versus SSA difference is, as Stephen Weeks noted a decade ago, one of data structures: do you group your expressions into basic blocks stored in a vector (SSA), or do you nest them into a scope tree (CPS)? It's not clear that I made the correct choice.

In practice with Guile's CPS you end up building graphs on the side that describe some aspect of your term. For example you can build a reverse-post-ordered control flow analysis that linearizes your continuations, and assigns them numbers. Then you can compute a bitvector for each continuation representing each one's reachable continuations. Then you can use this reachability analysis to determine the extent of a prompt's body, for example.

But this analysis is all on the side and not really facilitated by the structure of CPS itself; the CPS facilities that it uses are the globally unique continuation and value names of the CPS, and the control-flow links. Once the transformation is made, all of the analysis is thrown away.

Although this seems wasteful, the SSA approach of values having "implicit" names by their positions in a vector (instead of explicit ephemeral name-to-index mappings) is terrifying to me. Any graph transformation could renumber things, or leave holes, or cause vectors to expand... dunno. Perhaps I am too shy of the mutation foot-gun. I find comfort in CPS's minimalism.

One surprise I have found is that I haven't needed to do any dominator-based analysis in any of the paltry CPS optimizations I have made so far. I expect to do so once I start optimizing loops; here we see the cultural difference with SSA I guess, loops being the dominant object of study there. On the other hand I have had to solve flow equations on a few occasions, which was somewhat surprising, though enjoyable.

The optimizations I have currently implemented for CPS are fairly basic. Contification was tricky. One thing I did recently was to make all non-tail $call nodes require $kreceive continuations; if, as in the common case, extra values were unused, that was reflected in an unused rest argument. This required a number of optimizations to clean up and remove the extra rest arguments for other kinds of source expressions: dead-code elimination, the typical beta/eta reduction, and some code generation changes. It was worth it though, and now with the optimization passes things are faster than they were before.

Well, I find that I am rambling now. I know this is a lot of detail, but I hope that it helps some future compiler hacker understand more about intermediate language tradeoffs. I have been happy with CPS, but I'll report back if anything changes :) And if you are actually hacking on Guile, check the in-progress manual for all the specifics.

Happy hacking to all, and to all a good hack!