Representing Control: a Study of the CPS Transformation

Abstract

This paper investigates the transformation of λν-terms into continuation-passing style (CPS). We show that by appropriate η-expansion of Fisher and Plotkin's two-pass equational specification of the CPS transform, we can obtain a static and context-free separation of the result terms into “essential” and “administrative” constructs. Interpreting the former as syntax builders and the latter as directly executable code, We obtain a simple and efficient one-pass transformation algorithm, easily extended to conditional expressions, recursive definitions, and similar constructs. This new transformation algorithm leads to a simpler proof of Plotkin's simulation and indifference results.We go on to show how CPS-based control operators similar to, more general then, Scheme's call/cc can be naturally accommodated by the new transformation algorithm. To demonstrate the expressive power of these operators, we use them to present an equivalent but even more concise formulation of the efficient CPS transformation algorithm. Finally, we relate the fundamental ideas underlying this derivation to similar concepts from other work on program manipulation; we derive a one-pass CPS transformation of λn-terms; and we outline some promising areas for future research.

A New Method for Dependent Parsing

“…f [4][5][6] are defined in the same way as f [1][2][3] , so the parsing engine ends up using the 4-box to bind p 2 , and the 5,6-box to calculate the predicate (p 2 − p 1 = x). If this evaluates to true, the engine uses the 5,6 box to calculate the final value, (), of the successful parse; otherwise, this run of the parse fails.…”

“…C[ [·]] is written in the style of a continuation-passing transform, and we use contexts K as the continuation argument of the transform. By using contexts, rather than target language expressions, as arguments to the transform, we obtain a one-pass algorithm whose result does not have administrative redexes [3].…”

Towards Compatible and Interderivable Semantic Specifications for the Scheme Programming Language, Part I: Denotational Semantics, Natural Semantics, and Abstract Machines

“…Background: It is the author's thesis 2 that functional representations of small-step operational semantics (i.e., structured operational semantics), reduction semantics (i.e., small-step operational semantics with an explicit representation of the reduction context), small-step abstract machines, big-step abstract machines, big-step operational semantics (i.e., natural semantics), and denotational semantics are inter-derivable using elementary program transformations such as CPS transformation [18,44,47,51], defunctionalization [21,47], fixed-point fusion [19,43], and refocusing [22].…”

“…2008 Workshop on Scheme and Functional Programming tent [28]. It is endowed with a variety of specifications: a CPS transformation [18], a CPS interpreter [30,48], a denotational semantics [33], a computational monad [55], a big-step operational semantics [29], the CEK machine [26], calculi in the form of reduction semantics [25], and a number of implementation techniques [12,15,31]-not to mention its call-by-name variant in the archival version of Krivine's machine [34]. Question: How do we know that all the artifacts 1 in this semantic jungle define the same call/cc?…”

Enforcing Safety Properties Using Type Specialization

“…Figure 5 defines the translation. It follows the basic strategy of Danvy and Filinski's one-pass translation to continuationpassing style [7,6] x0(σ, x1, . .…”