Proceedings of the Workshop on Continuations

Journal of Functional Programming, 2002

This paper presents a new two-stage CPS algorithm. The first stage plants trivial partial continuations via a recursive-descent traversal and the second stage is a rewrite system that transforms all nontail calls into tail calls. The algorithm combines the metaphors of the Plotkin-style CPS transformation along with reduction in the λ-calculus.

1989

We present a new static analysis method for rst-class continuations that uses an e ect system to classify the control domain behavior of expressions in a typed polymorphic language. We introduce two new control effects, goto and comefrom, that describe the control ow properties of expressions. An expression that does not have a goto e ect is said to be continuation following because it will always call its passed return continuation. An expression that does not have a comefrom effect is said to be continuation discarding because it will never preserve its return continuation for later use. Unobservable control e ects can be masked by the e ect system. Control e ect soundness theorems guarantee that the e ects computed statically by the e ect system are a conservative approximation of the dynamic behavior of an expression. The e ect system that we describe performs certain kinds of control ow analysis that were not previously feasible. We discuss how this analysis can enable a variety of compiler optimizations, including parallel expression scheduling in the presence of complex control structures, and stack allocation of continuations. The e ect system we describe has been implemented as an extension to the FX-87 programming language.

Proceedings of the 1988 ACM conference on LISP and functional programming, 1988

Scheme and Smalltalk continuations may have unlimited extent. This means that a purely stack-based implementation of continuations, as suffices for most languages, is inadequate. Several implementation strategies have been described in the literature. Determining which is best requires knowledge of the kinds of programs that will commonly be run. Danvy, for example, has conjectured that continuation captures occur in clusters. That is, the same continuation, once captured, is likely to be captured again. As evidence, Danvy cited the use of continuations in a research setting. We report that Danvy's conjecture is somewhat true in the commercial setting of MacScheme+ToolsmithTM, which provides tools for developing Macintosh user interfaces in Scheme. These include an interrupt-driven event system and multitasking, both implemented by liberal use of continuations. We describe several implementation strategies for continuations and compare four of them using benchmarks. We conclude that the most popular strategy may have a slight edge when continuations are not used at all, but that other strategies perform better when continuations are used and Danvy's conjecture holds.

Proceedings of the 18th ACM SIGPLAN international conference on Functional programming - ICFP '13, 2013

Continuations are programming abstractions that allow for manipulating the "future" of a computation. Amongst their many applications, they enable implementing unstructured program flow through higher-order control operators such as callcc. In this paper we develop a Hoare-style logic for the verification of programs with higher-order control, in the presence of dynamic state. This is done by designing a dependent type theory with first class callcc and abort operators, where pre-and postconditions of programs are tracked through types. Our operators are algebraic in the sense of Plotkin and Power, and Jaskelioff, to reduce the annotation burden and enable verification by symbolic evaluation. We illustrate working with the logic by verifying a number of characteristic examples.

Categorial grammars in the tradition of Lambek are asymmetric: sequent statements are of the form Γ ⇒ A, where the succedent is a single formula A, the antecedent a structured configuration of formulas A 1 , . . . , A n . The absence of structural context in the succedent makes the analysis of a number of phenomena in natural language semantics problematic. A case in point is scope construal: the different possibilities to build an interpretation for sentences containing generalized quantifiers and related expressions. In this paper, we explore a symmetric version of categorial grammar, based on work by Grishin . In addition to the Lambek product, left and right division, we consider a dual family of type-forming operations: coproduct, left and right difference. Communication between the two families is established by means of structurepreserving distributivity principles. We call the resulting system LG. We present a Curry-Howard interpretation for LG(/, \, , ) derivations, based on Curien and Herbelin's λµ µ calculus [10]. We discuss continuation-passing-style (CPS) translations mapping LG derivations to proofs/terms of Intuitionistic Multiplicative Linear Logic -the categorial system LP which serves as the logic for natural language meaning assembly. We show how LG, thus interpreted, associates sentences with quantifier phrases with the appropriate range of meanings, thus overcoming the expressive limitations of asymmetric categorial grammars in this area.