CPS transformation of beta-redexes

Danvy, Olivier; Nielsen, Lasse R.

doi:10.1016/j.ipl.2005.02.002

Cited by 10 publications

(2 citation statements)

References 21 publications

(24 reference statements)

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“…A beautiful operational theory has developed since Plotkin's pioneering work [22]. Call-by-value and call-by-name have been shown to be dual to each other [2], and continuation-based translations allowing to simulate one style with the other have been designed and analyzed very carefully [4,5]. Now, suppose to endow the λ-calculus with nondeterministic sums.…”

Section: Some Motivating Observationsmentioning

confidence: 99%

Probabilistic operational semantics for the lambda calculus

Lago

Zorzi²

2012

RAIRO-Theor. Inf. Appl.

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Probabilistic operational semantics for a nondeterministic extension of pure λ-calculus is studied. In this semantics, a term evaluates to a (finite or infinite) distribution of values. Small-step and big-step semantics, inductively and coinductively defined, are given. Moreover, small-step and big-step semantics are shown to produce identical outcomes, both in call-by-value and in call-by-name. Plotkin's CPS translation is extended to accommodate the choice operator and shown correct with respect to the operational semantics. Finally, the expressive power of the obtained system is studied: the calculus is shown to be sound and complete with respect to computable probability distributions.

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Section: Some Motivating Observationsmentioning

confidence: 99%

Probabilistic operational semantics for the lambda calculus

Lago

Zorzi²

2012

RAIRO-Theor. Inf. Appl.

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“…We additionally showed a novel rewrite logic approach to context reduction, together with its equivalence to a more efficient and flexible continuation-based definition. What distinguishes our equivalence result from efforts on efficient implementations of context reduction semantics by CPS transformations to higher-order continuations, e.g., [SF92,DN01,DN05], is that our continuations are first-order and our language definitions are theories in a logic, with algebraic denotational semantics and complete deduction, not implementations; yet, they can be executed by current rewrite engines at performance comparable with interpreter implementations. There is much related work on defining programming languages in various computational logical frameworks.…”

Section: Conclusion and Additional Related Workmentioning

confidence: 99%

A rewriting logic approach to operational semantics

Şerbănuţă¹,

Roşu²,

Meseguer³

2009

Information and Computation

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We show how one can use rewriting logic to faithfully capture (not implement) various operational semantic frameworks as rewrite logic theories, namely big-step and small-step semantics, reduction semantics using evaluation contexts, and continuation-based semantics. There is a one-to-one correspondence between an original operational semantics and its associated rewrite logic theory, both notationally and computationally. Once an operational semantics is defined as a rewrite logic theory, one can use standard, off-the-shelf context-insensitive rewrite engines to "execute" programs directly within their semantics; in other words, one gets interpreters for free for the defined languages, directly from their semantic definitions. Experiments show that the resulting correct-by-definition interpreters are also reasonably efficient.

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Mechanized Verification of CPS Transformations

Dargaye

Leroy

Logic for Programming, Artificial Intelligence, and Reasoning

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Abstract. Transformation to continuation-passing style (CPS) is often performed by optimizing compilers for functional programming languages. As part of the development and proof of correctness of a compiler for the mini-ML functional language, we have mechanically verified the correctness of two CPS transformations for a call-by-value λ-calculus with n-ary functions, recursive functions, data types and pattern-matching. The transformations generalize Plotkin's original call-by-value transformation and Danvy and Nielsen's optimized transformation, respectively. We used the Coq proof assistant to formalize the transformations and conduct and check the proofs. Originalities of this work include the use of big-step operational semantics to avoid difficulties with administrative redexes, and of two-sorted de Bruijn indices to avoid difficulties with α-conversion.

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CPS transformation of beta-redexes

Cited by 10 publications

References 21 publications

Probabilistic operational semantics for the lambda calculus

Probabilistic operational semantics for the lambda calculus

A rewriting logic approach to operational semantics

Mechanized Verification of CPS Transformations

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