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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My post on implementing exceptions. The transformation for letrec is cntinuations hygienic, because the transformation can introduce the letrec ‘d bindings into the scope of comoiling continuation that gets passed to the transformer.
Appel’s Compiling with Continuations and Queinnec’s Lisp in Small Pieces are invaluable resources for the functional compiler writer. It is the transformation that newcomers often discover for themselves. 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:.
Complex expressions may not terminate, and they may produce side effects. T ‘ g a ‘halt produces: The goal of this article is to introduce CPS transforms in small, individually digestible pieces before stitching them back together as a unified whole.
In the higher-order transform, the function T: 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:. 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.
To start, split the grammar: The transform now has three principal functions: Examples Even while this transformation is simple, its results are poor. This simple shift in perspective is economical: A hybrid transform Combining the naive and higher-order transforms provides the best of both worlds. The wrinkle in the previous transform was that it forced function application to bind its function and its arguments to variables, even if they were already atomic.
How to compile with continuations
Both of those lambda terms are continuations. 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.
My post on A-Normalization. Fortunately, the hybrid CPS transform readily adapts to features like basic values, conditionals, side effects, sequencing and explicit recursion. The M function only has to watch for lambda terms.
In the function-application transform, the values of both the function and the argument have to be converted into CPS. When a continuation gets invoked, deallocate its space by resetting the stack pointer to that continuation. The lambda calculus wifh a nice platform for studying the architecture of a program transformation.
More resources Andrew Kennedy points out that CPS is more advantageous as an intermediate form with respect to optimization than had been previously thought. Because continuations are used in a last-allocated, first-invoked fashion, we can implement them as a stack.
How to compile with continuations
Continuation-passing style If you’re new to continuation-passing style, I recommend my earlier post on continuation-passing style by example. Code is available in Racket ; techniques applicable to any language.
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.
The transform converts each with Tand then catches their results in newly-created continuations. When a continuation gets allocated, bump the stack pointer. Atomic expressions always produce a value and never cause side effects. Knowing how to convert witg into CPS, either by hand or algorithmically, is a powerful weapon in the programmer’s arsenal.
Yet, if the transform tags variables, call forms and lambdas as being user or continuationthe stack is recoverable. All calls become tail calls, so in effect, there is no stack. For the first three transforms, the input language is the lambda calculus: For the fourth transform, it will become partitioned CPS, and for the final transform, it will be a more realistic intermediate language with side effects, conditionals, basic values and explict recursion.
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: In terms of unreasonable effectiveness, the transformation to continuation-passing style CPS ranks with the Y combinator.
We can even use the stack pointer register.
Compiling with Continuations
Conrinuations transformation is not hygienic ; if the continuation c references any of the ; bound variables! If the transform receives a real function expecting the atomic version of a the supplied expression, then the transform can check whether it is necessary to bind it to a variable.
Consider an expanded input language: The transformation of function application is the main culprit: There are some advantages [and disadvantages] to stackless compilation. For example, the following: Ultimately, however, that transformation must run on real code. This is two steps forward, and one step back: How to compile with continuations [ article index ]  [ mattmight ] [ rss ].
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 continuaations letrec.
In this transformation, we have two functions, M and T: Scaling to real language features The lambda calculus makes a nice platform for studying the architecture of a program transformation.