Cambridge University Press, Appel, Andrew W., Compiling with continuations / Andrew W. Appel. p. 25 cm. Includes bibliographical references. Then, during CPS transformation, continuations desugar into functions. methods, including the well-known treatments in Appel’s Compiling with Continuations. This book shows how continuation-passing style is used as an intermediate representation to perform optimizations and program transformations. Continuations.
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All calls become tail calls, so in effect, there is no stack. My post on implementing exceptions. In the function-application transform, the values of both the function and the argument have to be converted into CPS. It is the transformation that newcomers often discover for themselves. Knowing how to convert code into CPS, either by hand or algorithmically, is a powerful weapon in the programmer’s arsenal. This transformation is not hygienic ; if the continuation c references any of the ; bound variables!
The transformation for letrec is not hygienic, because the transformation can introduce the letrec ‘d bindings into the scope of the continuation that gets passed to the transformer. The lambda calculus makes a nice platform for studying the architecture of a program transformation. For example, the following: There are some advantages [and disadvantages] to stackless compilation. Scaling to real language features The lambda calculus makes a nice platform for studying the architecture of a program transformation.
During compilation, high-level control constructs ranging from coroutines and exceptions to while loops and break statements steadily desugar into a mixture of two constructs: The naive transformation The naive transformation likely dates to Plotkin’s earliest work.
The goal of this article is to introduce CPS transforms in small, individually digestible pieces before stitching them back together as a unified whole.
Compiling with Continuations
In the higher-order transform, the function T: In this transformation, we have two functions, M and T: T ‘ g a ‘halt produces: The transform converts each with Tand then catches their results in newly-created continuations. My post on A-Normalization. If the transform receives a real function expecting the atomic version of a the supplied expression, then the transform can continuxtions whether it is necessary to bind it to a variable.
To start, split the grammar: If you’re new to continuation-passing style, I recommend my earlier post on continuation-passing style by example. To generate a fresh variable bound to a user value, the transform will use genusymand for a fresh variables bound to a continuation, the transform will use genksym:.
This simple shift in perspective is economical: Because continuations are used in a last-allocated, first-invoked fashion, we can implement them as a stack.
The transformation of function application is the main culprit: The M function only has to watch for lambda terms. Yet, if the transform tags wirh, call forms and lambdas as being user or continuationthe stack is recoverable.
Code is available in Racket ; techniques applicable to any language. This is two steps forward, and one step back: Fortunately, the hybrid CPS transform readily adapts to features like basic values, conditionals, side effects, sequencing and explicit recursion.
To generate a fresh variable bound to a user value, the transform will use genusymand for a fresh variables bound to a continuation, the transform will use genksym: More resources Andrew Kennedy points out that CPS is more advantageous as an intermediate form with respect to optimization than had been previously thought.
The transform T expr cont will transform expr into a CPS value, and then construct a call site that applies the term cont to that value:. For the fourth transform, it will become partitioned CPS, and for compilingg final transform, it will be a more realistic intermediate language with side effects, conditionals, basic values and explict recursion. Ultimately, however, that transformation must run on real code. The expression T expr cont might be read “the transformation of expr into continuation-passing style, such that cont will be invoked on its result.
If you’re using this in practice, alphatize the program first, or modify letrec to bind the continuation to a variable outside the scope of the letrec. For the first three transforms, the input language is the lambda calculus: Continuation-passing style If you’re new to continuation-passing style, I recommend my earlier post on continuation-passing style by example.
How to compile with continuations
Examples Even while this transformation is simple, its results are poor. Both of those lambda wtih are continuations. Consider an expanded input language: We can even use the stack pointer register.
In terms of unreasonable effectiveness, the transformation to continuation-passing style CPS ranks with the Y combinator. Appel’s Compiling with Continuations and Queinnec’s Lisp in Small Pieces are invaluable resources for the continuuations compiler cimpiling. How to compile with continuations [ article index ]  [ mattmight ] [ rss ].
Danvy, Millikin and Nielsen have been able to connect some of these methods, including the well-known treatments in Appel’s Compiling with Continuations and Queinnec’s Lisp in Small Pieces.