Compiling with Continuations

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CPS also has the benefit of having very orthogonal features, which means a reduction in compiler complexity.

The paper we are commenting on is a good example. Of course, CPS has some disadvantages as well. It does fix an explicit evaluation order early in the compiler, which may not be desirable or may complicate some low-level optimizations in the code generator.

Continuation-passing style

As far as control and data flow analysis is concerned, there are results in either direction, although in pure quantity the results seem to favour CPS. This problem may be fixed with Gamma-CFA type analyses that merge fewer contexts unnecessarily. There may also be variations on analyses that improve precision for ANF, but most new analyses seem to be developed for CPS anyways. Olin Shivers was pointing out to me the other day that when you perform a CPS transformation, you can distinguish "CPS-lambdas", which take a single intermediate result, from "user-lambdas", which take some number of arguments in addition to a continuation and return a computation.

Now you have a representation of control that looks like a closure, but it doesn't have to be implemented exactly like a closure. Of course, you can reuse some or all of the runtime system's implementation of closures for representing continuations, but you can also use a different data structure say, an algebraic datatype representing evaluation contexts ; furthermore you can use the stack if the language's operations on evaluation contexts make it possible and reasonable to do so. Compiling with Continuation Passing Style

Frankly, you can use any of the implementation strategies of continuations you like; CPS just happens to be a syntactic representation that highlights the similarity between continuations and closures. Also note that exactly this two-level partitioning is used explicitly in this work , currently being discussed in another thread. I love cross-thread synchronicity, particularly when it's about CPS triumphalism! Create new account Request new password. Compiling with Continuations, Continued , Andrew Kennedy. By neelk at Comment viewing options Flat list - collapsed Flat list - expanded Threaded list - collapsed Threaded list - expanded Date - newest first Date - oldest first 10 comments per page 30 comments per page 50 comments per page 70 comments per page 90 comments per page comments per page comments per page Select your preferred way to display the comments and click "Save settings" to activate your changes.

In this section we will write a function that calculates hypotenuse using Pythagorean theorem. Traditional pyth function looks like this:. To transform traditional function to CPS one we need to change its signature.


Function will get another argument of function type and its return type depends on that function:. First we calculate square of a in pyth' function and pass lambda function as a continuation which will accept a square of a as a first argument. And so on until we reach the result of our calculations. To get the result of this function we can pass id function as a final argument which returns the value that was passed to it unchanged: This module provides Cont type, which implements Monad and some other useful functions.

The following snippet shows pyth' function using Cont type:. This function has the only argument of a function type; that function argument accepts the function too, which discards all computations going after its call.

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For example let's break the execution of pyth function if at least one of its arguments is negative returning zero:. Programming with continuations can also be useful when a caller does not want to wait until the callee completes. For example, in user-interface UI programming, a routine can set up dialog box fields and pass these, along with a continuation function, to the UI framework. This call returns right away, allowing the application code to continue while the user interacts with the dialog box.

Compiling with Continuations

Once the user presses the "OK" button, the framework calls the continuation function with the updated fields. Although this style of coding uses continuations, it is not full CPS. A similar idea can be used when the function must run in a different thread or on a different processor. The framework can execute the called function in a worker thread, then call the continuation function in the original thread with the worker's results.

This is in Java using the Swing UI framework:.

Compiling with Continuation Passing Style

Using Java 8 lambda notation above code shortens to final keyword might be skipped:. Every call in CPS is a tail call , and the continuation is explicitly passed. Using CPS without tail call optimization TCO will cause not only the constructed continuation to potentially grow during recursion, but also the call stack. This is usually undesirable, but has been used in interesting ways—see the Chicken Scheme compiler.

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  • As CPS and TCO eliminate the concept of an implicit function return, their combined use can eliminate the need for a run-time stack. Several compilers and interpreters for functional programming languages use this ability in novel ways. Continuation passing style can be used to implement continuations and control flow operators in a functional language that does not feature first-class continuations but does have first-class functions and tail-call optimization.

    Continuation-passing style

    Anyway, here's how Matt Might proposes to do it:. In short, the function is called with the expression, accompanied by a continuation or a function which produces a call when you give it a valid cps parameter. The functions lift and retrieve are used to control what kind of construct is built.

    This way, the code never needs to create superfluous continuations that'd have to be pruned out of the code. To make the compiling easy, the CPS must not contain cycles. It can be made sure by binding loop bodies into variables, so the body doesn't introduce a cycle. If you've been doing some booking during the CPS pass, you already have the shadow set and you don't need to compute it yourself. Next one needs to compute variables that must be fetched from the upscope. It happens by roughly following rules:.

    Now you have everything you need to construct the equivalent set of C -functions.