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Representing control: a study of the CPS transformation
, 1992
"... This paper investigates the transformation of v terms into continuationpassing style (CPS). We show that by appropriate jexpansion of Fischer and Plotkin's twopass equational specification of the CPS transform, we can obtain a static and contextfree separation of the result terms into "esse ..."
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Cited by 81 (7 self)
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This paper investigates the transformation of v terms into continuationpassing style (CPS). We show that by appropriate jexpansion of Fischer and Plotkin's twopass equational specification of the CPS transform, we can obtain a static and contextfree 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 onepass 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. Further we show how CPSbased control operators similar to but more general than 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 t...
A syntax for linear logic
 Presented at Conference on Mathematical Foundations of Programming Language Semantics
, 1993
"... Abstract. This tutorial paper provides an introduction to intuitionistic logic and linear logic, and shows how they correspond to type systems for functional languages via the notion of ‘Propositions as Types’. The presentation of linear logic is simplified by basing it on the Logic of Unity. An app ..."
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Cited by 72 (5 self)
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Abstract. This tutorial paper provides an introduction to intuitionistic logic and linear logic, and shows how they correspond to type systems for functional languages via the notion of ‘Propositions as Types’. The presentation of linear logic is simplified by basing it on the Logic of Unity. An application to the array update problem is briefly discussed. 1
Explicit Polymorphism and CPS Conversion
 IN TWENTIETH ACM SYMPOSIUM ON PRINCIPLES OF PROGRAMMING LANGUAGES
, 1992
"... We study the typing properties of CPS conversion for an extension of F ! with control operators. Two classes of evaluation strategies are considered, each with callbyname and callbyvalue variants. Under the "standard" strategies, constructor abstractions are values, and constructor applications ..."
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Cited by 68 (9 self)
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We study the typing properties of CPS conversion for an extension of F ! with control operators. Two classes of evaluation strategies are considered, each with callbyname and callbyvalue variants. Under the "standard" strategies, constructor abstractions are values, and constructor applications can lead to nontrivial control effects. In contrast, the "MLlike" strategies evaluate beneath constructor abstractions, reflecting the usual interpretation of programs in languages based on implicit polymorphism. Three continuation passing style sublanguages are considered, one on which the standard strategies coincide, one on which the MLlike strategies coincide, and one on which all the strategies coincide. Compositional, typepreserving CPS transformation algorithms are given for the standard strategies, resulting in terms on which all evaluation strategies coincide. This has as a corollary the soundness and termination of welltyped programs under the standard evaluation strategies. A similar result is obtained for the MLlike callbyname strategy. In contrast, such results are obtained for the callby value MLlike strategy only for a restricted sublanguage in which constructor abstractions are limited to values.
Secure Information Flow via Linear Continuations
 Higher Order and Symbolic Computation
, 2002
"... Securitytyped languages enforce secrecy or integrity policies by typechecking. This paper investigates continuationpassing style (CPS) as a means of proving that such languages enforce noninterference and as a rst step towards understanding their compilation. We present a lowlevel, secure calcu ..."
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Cited by 34 (6 self)
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Securitytyped languages enforce secrecy or integrity policies by typechecking. This paper investigates continuationpassing style (CPS) as a means of proving that such languages enforce noninterference and as a rst step towards understanding their compilation. We present a lowlevel, secure calculus with higherorder, imperative features and linear continuations.
Secure Information Flow and CPS
 In Proc. of the 10th European Symposium on Programming, volume 2028 of Lecture Notes in Computer Science
, 2001
"... Securitytyped languages enforce secrecy or integrity policies by type checking. This paper investigates continuationpassing style as a means of proving that such languages enforce noninterference and as a first step towards understanding their compilation. We present a lowlevel, secure calcul ..."
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Cited by 32 (10 self)
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Securitytyped languages enforce secrecy or integrity policies by type checking. This paper investigates continuationpassing style as a means of proving that such languages enforce noninterference and as a first step towards understanding their compilation. We present a lowlevel, secure calculus with higherorder, imperative features. Our type system makes novel use of ordered linear continuations.
There's No Substitute for Linear Logic
, 1991
"... Surprisingly, there is not a good fit between a syntax for linear logic in the style of Abramsky, and a semantics in the style of Seely. Notably, the Substitution Lemma is valid if and only if !A and !!A are isomorphic in a canonical way. An alternative syntax is proposed, that has striking parallel ..."
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Cited by 24 (1 self)
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Surprisingly, there is not a good fit between a syntax for linear logic in the style of Abramsky, and a semantics in the style of Seely. Notably, the Substitution Lemma is valid if and only if !A and !!A are isomorphic in a canonical way. An alternative syntax is proposed, that has striking parallels to Moggi's language for monads. In the old syntax, some terms look like the identity that should not, and vice versa; the new syntax eliminates this awkwardness. 1 Introduction This paper has two purposes: to show that linear logic has no substitute, and to propose one. The first part presents a standard syntax and semantics for linear logic, and notes some resulting difficulties. The linear logic is that of Girard [Gir87]. The syntax is based on lambda terms, following in the footsteps of Abramsky [Abr90]: the four rules associated with the `of course' type, Weakening, Contraction, Dereliction, and Promotion, are each represented by a separate term form. The semantics is based on categor...
On Exceptions versus Continuations in the Presence of State
 Programming Languages and Systems, 9th European Symposium on Programming, ESOP 2000,, number 1782 in LNCS
, 2000
"... . We compare the expressive power of exceptions and continuations when added to a language with local state in the setting of operational semantics. Continuations are shown to be more expressive than exceptions because they can cause a function call to return more than once, whereas exceptions only ..."
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Cited by 14 (3 self)
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. We compare the expressive power of exceptions and continuations when added to a language with local state in the setting of operational semantics. Continuations are shown to be more expressive than exceptions because they can cause a function call to return more than once, whereas exceptions only allow discarding part of the calling context. 1 Introduction Exceptions are part of nearly all modern programming languages, including mainstream ones like Java and C++. Continuations are present only in Scheme and the New Jersey dialect of ML, yet are much more intensely studied by theoreticians and logicians. The relationship between exceptions and continuations is not as widely understood as one would hope, partly because continuations, though in some sense canonical, are more powerful than would at rst appear, and because the control aspect of exceptions can be obscured by intricacies of typing and syntax. We have recently shown that exceptions and continuations, when added to a purely...
A typed foundation for directional logic programming
 In Proc. Workshop on Extensions to Logic Programming
, 1992
"... Abstract. A long standing problem in logic programming is how to impose directionality on programs in a safe fashion. The benefits of directionality include freedom from explicit sequential control, the ability to reason about algorithmic properties of programs (such as termination, complexity and d ..."
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Cited by 12 (1 self)
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Abstract. A long standing problem in logic programming is how to impose directionality on programs in a safe fashion. The benefits of directionality include freedom from explicit sequential control, the ability to reason about algorithmic properties of programs (such as termination, complexity and deadlockfreedom) and controlling concurrency. By using Girard’s linear logic, we are able to devise a type system that combines types and modes into a unified framework, and enables one to express directionality declaratively. The rich power of the type system allows outputs to be embedded in inputs and vice versa. Type checking guarantees that values have unique producers, but multiple consumers are still possible. From a theoretical point of view, this work provides a “logic programming interpretation ” of (the proofs of) linear logic, adding to the concurrency and functional programming interpretations that are already known. It also brings logic programming into the broader world of typed languages and typesaspropositions paradigm, enriching it with static scoping and higherorder features.
Three Steps for the CPS Transformation
, 1991
"... Transforming a #term into continuationpassing style (CPS) might seem mystical at first, but in fact it can be characterized by three separate aspects: . The values of all intermediate applications are given a name. . The evaluation of these applications is sequentialized based on a traversal o ..."
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Cited by 12 (4 self)
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Transforming a #term into continuationpassing style (CPS) might seem mystical at first, but in fact it can be characterized by three separate aspects: . The values of all intermediate applications are given a name. . The evaluation of these applications is sequentialized based on a traversal of their syntax tree. This traversal mimics the reduction strategy. . The resulting term is equipped with a continuation  a #abstraction whose application to intermediate values yields the final result of the whole evaluation. The first point is fulfilled using the uniform naming mechanism of #abstraction (Church encoding), which explains why continuations are represented as functions. The second point justifies why CPS terms are evaluationorder independent  their evaluation order is determined by the syntax tree traversal of the CPS transformation. The third point captures the essence of the CPS transformation. We have staged Fischer and Plotkin's original CPS transformer accordin...
Classical linear logic of implications
 In Proc. Computer Science Logic (CSL'02), Springer Lecture Notes in Comp. Sci. 2471
, 2002
"... Abstract. We give a simple term calculus for the multiplicative exponential fragment of Classical Linear Logic, by extending Barber and Plotkin’s system for the intuitionistic case. The calculus has the nonlinear andlinear implications as the basic constructs, andthis design choice allows a technica ..."
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Cited by 10 (4 self)
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Abstract. We give a simple term calculus for the multiplicative exponential fragment of Classical Linear Logic, by extending Barber and Plotkin’s system for the intuitionistic case. The calculus has the nonlinear andlinear implications as the basic constructs, andthis design choice allows a technically managable axiomatization without commuting conversions. Despite this simplicity, the calculus is shown to be sound andcomplete for categorytheoretic models given by ∗autonomous categories with linear exponential comonads. 1