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69
A FormulaeasTypes Notion of Control
 In Conference Record of the Seventeenth Annual ACM Symposium on Principles of Programming Languages
, 1990
"... The programming language Scheme contains the control construct call/cc that allows access to the current continuation (the current control context). This, in effect, provides Scheme with firstclass labels and jumps. We show that the wellknown formulaeastypes correspondence, which relates a constr ..."
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Cited by 252 (0 self)
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The programming language Scheme contains the control construct call/cc that allows access to the current continuation (the current control context). This, in effect, provides Scheme with firstclass labels and jumps. We show that the wellknown formulaeastypes correspondence, which relates a constructive proof of a formula ff to a program of type ff, can be extended to a typed Idealized Scheme. What is surprising about this correspondence is that it relates classical proofs to typed programs. The existence of computationally interesting "classical programs"  programs of type ff, where ff holds classically, but not constructively  is illustrated by the definition of conjunctive, disjunctive, and existential types using standard classical definitions. We also prove that all evaluations of typed terms in Idealized Scheme are finite.
A Generic Account of ContinuationPassing Styles
 Proceedings of the Twentyfirst Annual ACM Symposium on Principles of Programming Languages
, 1994
"... We unify previous work on the continuationpassing style (CPS) transformations in a generic framework based on Moggi's computational metalanguage. This framework is used to obtain CPS transformations for a variety of evaluation strategies and to characterize the corresponding administrative re ..."
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Cited by 87 (34 self)
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We unify previous work on the continuationpassing style (CPS) transformations in a generic framework based on Moggi's computational metalanguage. This framework is used to obtain CPS transformations for a variety of evaluation strategies and to characterize the corresponding administrative reductions and inverse transformations. We establish generic formal connections between operational semantics and equational theories. Formal properties of transformations for specific evaluation orders follow as corollaries. Essentially, we factor transformations through Moggi's computational metalanguage. Mapping terms into the metalanguage captures computational properties (e.g., partiality, strictness) and evaluation order explicitly in both the term and the type structure of the metalanguage. The CPS transformation is then obtained by applying a generic transformation from terms and types in the metalanguage to CPS terms and types, based on a typed term representation of the continuation ...
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 app ..."
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Cited by 69 (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.
The πCalculus in Direct Style
, 1997
"... We introduce a calculus which is a direct extension of both the and the π calculi. We give a simple type system for it, that encompasses both Curry's type inference for the calculus, and Milner's sorting for the πcalculus as particular cases of typing. We observe that the various contin ..."
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Cited by 66 (2 self)
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We introduce a calculus which is a direct extension of both the and the π calculi. We give a simple type system for it, that encompasses both Curry's type inference for the calculus, and Milner's sorting for the πcalculus as particular cases of typing. We observe that the various continuation passing style transformations for terms, written in our calculus, actually correspond to encodings already given by Milner and others for evaluation strategies of terms into the πcalculus. Furthermore, the associated sortings correspond to wellknown double negation translations on types. Finally we provide an adequate cps transform from our calculus to the πcalculus. This shows that the latter may be regarded as an "assembly language", while our calculus seems to provide a better programming notation for higherorder concurrency.
Representing Layered Monads
 PROCEEDINGS OF THE TWENTYSIXTH ANNUAL ACM SYMPOSIUM ON PRINCIPLES OF PROGRAMMING LANGUAGES
, 1999
"... There has already been considerable research on constructing modular, monadbased specications of computational effects (state, exceptions, nondeterminism, etc.) in programming languages. We present a simple framework in this tradition, based on a Churchstyle effecttyping system for an MLlike lan ..."
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Cited by 56 (2 self)
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There has already been considerable research on constructing modular, monadbased specications of computational effects (state, exceptions, nondeterminism, etc.) in programming languages. We present a simple framework in this tradition, based on a Churchstyle effecttyping system for an MLlike language. The semantics of this language is formally dened by a series of monadic translations, each one expanding away a layer of effects. Such a layered specication is easy to reason about, but its direct implementation (whether by parameterized interpretation or by actual translation) is often prohibitively inefficient. By exploiting deeper semantic properties of monads, however, it is also possible to derive a vastly more efficient implementation: we show that each layer of eects can be uniformly simulated by continuationpassing, and further that multiple such layers can themselves be simulated by a standard semantics for call/cc and mutable state. Thus, even multieffect programs can be execu...
Polymorphic type assignment and CPS conversion
 LISP and Symbolic Computation
, 1993
"... Meyer and Wand established that the type of a term in the simply typedcalculus may be related in a straightforward manner to the type of its callbyvalue CPS transform. This typing property maybe extended to Schemelike continuationpassing primitives, from which the soundness of these extensions ..."
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Cited by 37 (10 self)
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Meyer and Wand established that the type of a term in the simply typedcalculus may be related in a straightforward manner to the type of its callbyvalue CPS transform. This typing property maybe extended to Schemelike continuationpassing primitives, from which the soundness of these extensions follows. We study the extension of these results to the DamasMilner polymorphic type assignment system under both the callbyvalue and callbyname interpretations. We obtain CPS transforms for the callbyvalue interpretation, provided that the polymorphic let is restricted to values, and for the callbyname interpretation with no restrictions. We prove that there is no callbyvalue CPS transform for the full DamasMilner language that validates the MeyerWand typing property and is equivalent to the standard callbyvalue transform up toconversion. 1
Relational interpretations of recursive types in an operational setting
 Information and Computation
, 1997
"... Submitted for publication to Information and Computation. A summary of this paper appeared in TACS '97. ..."
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Cited by 35 (3 self)
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Submitted for publication to Information and Computation. A summary of this paper appeared in TACS '97.
Extensible Denotational Language Specifications
 SYMPOSIUM ON THEORETICAL ASPECTS OF COMPUTER SOFTWARE, NUMBER 789 IN LNCS
, 1994
"... Traditional denotational semantics assigns radically different meanings to one and the same phrase depending on the rest of the programming language. If the language is purely functional, the denotation of a numeral is a function from environments to integers. But, in a functional language with impe ..."
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Cited by 34 (5 self)
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Traditional denotational semantics assigns radically different meanings to one and the same phrase depending on the rest of the programming language. If the language is purely functional, the denotation of a numeral is a function from environments to integers. But, in a functional language with imperative control operators, a numeral denotes a function from environments and continuations to integers. This paper introduces a new format for denotational language specifications, extended direct semantics, that accommodates orthogonal extensions of a language without changing the denotations of existing phrases. An extended direct semantics always maps a numeral to the same denotation: the injection of the corresponding number into the domain of values. In general, the denotation of a phrase in a functional language is always a projection of the denotation of the same phrase in the semantics of an extended languageno matter what the extension is. Based on extended direct semantics, i...
Continuations and the Nature of Quantification
 NATURAL LANGUAGE SEMANTICS
, 2002
"... This paper proposes that the meanings of some natural language expressions should be thought of as functions on their own continuations. Continuations are a wellestablished technique in the theory of programming language semantics; in brief, a continuation is the entire default future of a computat ..."
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Cited by 30 (3 self)
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This paper proposes that the meanings of some natural language expressions should be thought of as functions on their own continuations. Continuations are a wellestablished technique in the theory of programming language semantics; in brief, a continuation is the entire default future of a computation. I show how a continuationbased grammar can unify several aspects of natural language quantification in a new way: merely stating the truth conditions for quantificational expressions in terms of continuations automatically accounts for scope displacement and scope ambiguity. To prove this claim, I exhibit a simple finite contextfree grammar with a strictly compositional semantics in which quantificational NPs are interpreted insitu but take semantic scope over larger constituents. There is no Quantifier Raising (nor any use of a level of Logical Form distinct from overt syntax), no Cooper Storage (or other similar mechanisms used in many recent HPSG, Categorial, or Typelogical treatments), and no need for typeshifting (as in Hendriks' Flexible Types account). Continuations also provide a natural account of generalized coordination that does not require either typeshifting or typepolymorphism. Compositionality issues are discussed in some detail.