A generic account of continuation-passing styles

Hatcliff, John; Danvy, Olivier

doi:10.1145/174675.178053

Cited by 111 publications

(115 citation statements)

References 29 publications

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“…Its corresponding reduction theory is considered in [7] and [16] and includes rules for the 3 monadic laws. Our monadic λ-calculus λ M brings into play two more permutation rules.…”

Section: Monadic Lambda-calculusmentioning

confidence: 99%

“…Hence, this is an alternative syntactic proof of strong normalization of λJ mse . While the translation in the following section works on the types in usual CBN fashion [7], a more complicated type translation in Section 4.2 even yields strict simulation within λ M without the rule π λ,λ .…”

Section: Translations Of λJ Mse Into Monadic λ-Calculusmentioning

confidence: 99%

“…Our monadic translation when restricted to λ-calculus essentially captures the usual CBN monadic translation [7], call it ( ) • . This translation for variables and λ-abstraction behaves as our translation, and for applications does (tu) • := bind(t • , f.f u • ).…”

Section: Corollarymentioning

confidence: 99%

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Monadic Translation of Intuitionistic Sequent Calculus

Santo

Matthes²,

Pinto

2009

Lecture Notes in Computer Science

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Abstract. This paper proposes and analyses a monadic translation of an intuitionistic sequent calculus. The source of the translation is a typed λ-calculus previously introduced by the authors, corresponding to the intuitionistic fragment of the call-by-name variant of λµμ of Curien and Herbelin, and the target is a variant of Moggi's monadic meta-language, where the rewrite relation includes extra permutation rules that may be seen as variations of the "associativity" of bind (the Kleisli extension operation of the monad). The main result is that the monadic translation simulates reduction strictly, so that strong normalisation (which is enjoyed at the target, as we show) can be lifted from the target to the source. A variant translation, obtained by adding an extra monad application in the translation of types, still enjoys strict simulation, while requiring one fewer extra permutation rule from the target. Finally we instantiate, for the cases of the identity monad and the continuations monad, the meta-language into the simply-typed λ-calculus. By this means, we give a generic account of translations of sequent calculus into natural deduction, which encompasses the traditional mapping studied by Zucker and Pottinger, and CPS translations of intuitionistic sequent calculus.

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“…Its corresponding reduction theory is considered in [7] and [16] and includes rules for the 3 monadic laws. Our monadic λ-calculus λ M brings into play two more permutation rules.…”

Section: Monadic Lambda-calculusmentioning

confidence: 99%

Section: Translations Of λJ Mse Into Monadic λ-Calculusmentioning

confidence: 99%

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Monadic Translation of Intuitionistic Sequent Calculus

Santo

Matthes²,

Pinto

2009

Lecture Notes in Computer Science

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“…This contains the call-by-value embedding [16] of the simply-typed lambda-calculus into the computational metalanguage; with the attention on functions of type A → T B embodying call-by-value semantics.…”

Section: The Computational Metalanguagementioning

confidence: 99%

Reducibility and ⊤ ⊤-Lifting for Computation Types

Lindley

Stark

2005

Lecture Notes in Computer Science

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Abstract. We propose -lifting as a technique for extending operational predicates to Moggi's monadic computation types, independent of the choice of monad. We demonstrate the method with an application to Girard-Tait reducibility, using this to prove strong normalisation for the computational metalanguage λ ml . The particular challenge with reducibility is to apply this semantic notion at computation types when the exact meaning of "computation" (stateful, side-effecting, nondeterministic, etc.) is left unspecified. Our solution is to define reducibility for continuations and use that to support the jump from value types to computation types. The method appears robust: we apply it to show strong normalisation for the computational metalanguage extended with sums, and with exceptions. Based on these results, as well as previous work with local state, we suggest that this "leap-frog" approach offers a general method for raising concepts defined at value types up to observable properties of computations.

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“…Monadic normal forms offer the main advantages of CPS (i.e., all intermediate results are named and their computation is sequentialized), 1 and they have been used in compilers for functional languages [7,6,21,22,23,38,40,46]. Therefore, a one-pass transformation into monadic normal form with short-cut boolean evaluation could well be of practical use (i.e., outside academia).…”

Section: O Danvymentioning

confidence: 99%