Lightweight fusion by fixed point promotion

Ohori, Atsushi; Sasano, Isao

doi:10.1145/1190215.1190241

Cited by 19 publications

(29 citation statements)

References 18 publications

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“…From small-step to big-step abstract machine: The small-step abstract machine is transformed into a big-step abstract machine using Ohori and Sasano's lightweight fusion [18,37].…”

Section: A1 the Syntactic Correspondencementioning

confidence: 99%

A synthetic operational account of call-by-need evaluation

Danvy

Zerny

2013

Proceedings of the 15th Symposium on Principles and Practice of Declarative Programming

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We present the first operational account of call by need that connects syntactic theory and implementation practice. Syntactic theory: the storeless operational semantics using syntax rewriting to account for demand-driven computation and for caching intermediate results. Implementational practice: the store-based operational technique using memo-thunks to implement demand-driven computation and to cache intermediate results for subsequent sharing. The implementational practice was initiated by Landin and Wadsworth and is prevalent today to implement lazy programming languages such as Haskell. The syntactic theory was initiated by Ariola, Felleisen, Maraist, Odersky and Wadler and is prevalent today to reason equationally about lazy programs, on par with Barendregt et al.'s term graphs. Nobody knows, however, how the theory of call by need compares to the practice of call by need: all that is known is that the theory of call by need agrees with the theory of call by name, and that the practice of call by need optimizes the practice of call by name.Our operational account takes the form of three new calculi for lazy evaluation of lambda-terms and our synthesis takes the form of three lock-step equivalences. The first calculus is a hereditarily compressed variant of Ariola et al.'s call-by-need lambdacalculus and makes "neededness" syntactically explicit. The second calculus distinguishes between strict bindings (which are induced by demand-driven computation) and non-strict bindings (which are used for caching intermediate results). The third calculus uses memo-thunks and an algebraic store. The first calculus syntactically corresponds to a storeless abstract machine, the second to an abstract machine with local stores, and the third to a lazy Krivine machine, i.e., a traditional store-based abstract machine implementing lazy evaluation. The machines are intensionally compatible with extensional reasoning about lazy programs and they are lock-step equivalent. Each machine functionally corresponds to a natural semantics for call by need in the style of Launchbury, though for non-preprocessed λ-terms.Our results reveal a genuine and principled unity of computational theory and computational practice, one that readily applies to variations on the general theme of call by need.

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“…From small-step to big-step abstract machine: The small-step abstract machine is transformed into a big-step abstract machine using Ohori and Sasano's lightweight fusion [18,37].…”

Section: A1 the Syntactic Correspondencementioning

confidence: 99%

A synthetic operational account of call-by-need evaluation

Danvy

Zerny

2013

Proceedings of the 15th Symposium on Principles and Practice of Declarative Programming

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“…For example, context-sensitive reduction semantics for Curien's original calculus of closures [17] give rise to a variety of known and new abstract machines with environments and effects [11]. Recently [25], Kevin Millikin and the author have characterized the structural relation between smallstep abstract machines and big-step abstract machines using Atsushi Ohori and Isao Sasano's lightweight fusion by fixed-point promotion [50].…”

Section: Introductionmentioning

confidence: 99%

Defunctionalized interpreters for programming languages

Danvy

2008

Proceedings of the 13th ACM SIGPLAN International Conference on Functional Programming

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This document illustrates how functional implementations of formal semantics (structural operational semantics, reduction semantics, small-step and big-step abstract machines, natural semantics, and denotational semantics) can be transformed into each other. These transformations were foreshadowed by Reynolds in "Definitional Interpreters for Higher-Order Programming Languages" for functional implementations of denotational semantics, natural semantics, and big-step abstract machines using closure conversion, CPS transformation, and defunctionalization. Over the last few years, the author and his students have further observed that functional implementations of small-step and of big-step abstract machines are related using fusion by fixed-point promotion and that functional implementations of reduction semantics and of smallstep abstract machines are related using refocusing and transition compression. It furthermore appears that functional implementations of structural operational semantics and of reduction semantics are related as well, also using CPS transformation and defunctionalization. This further relation provides an element of answer to Felleisen's conjecture that any structural operational semantics can be expressed as a reduction semantics: for deterministic languages, a reduction semantics is a structural operational semantics in continuation style, where the reduction context is a defunctionalized continuation. As the defunctionalized counterpart of the continuation of a one-step reduction function, a reduction context represents the rest of the reduction, just as an evaluation context represents the rest of the evaluation since it is the defunctionalized counterpart of the continuation of an evaluation function.

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“…These two specifications are equivalent because the latter is a 'fused' version of the former, based on Ohori and Sasano's recent work on lightweight fusion [10]. Ohori and Sasano proved the full correctness of the derivation method we apply in the following section.…”

Section: Our Answermentioning

confidence: 91%

A Simple Application of Lightweight Fusion to Proving the Equivalence of Abstract Machines

Danvy¹,

Millikin²

2007

BRICS

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We show how Ohori and Sasano's recent lightweight fusion by fixed-point promotion provides a simple way to prove the equivalence of the two standard styles of specification of abstract machines: (1) as a transition function together with a 'driver loop' implementing the iteration of this transition function; and (2) as a function directly iterating upon a configuration until reaching a final state, if ever. The equivalence hinges on the fact that the latter style of specification is a fused version of the former one. The need for such a simple proof is motivated by our recent work on syntactic correspondences between reduction semantics and abstract machines, using refocusing. * IT-parken,

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Lightweight fusion by fixed point promotion

Cited by 19 publications

References 18 publications

A synthetic operational account of call-by-need evaluation

A synthetic operational account of call-by-need evaluation

Defunctionalized interpreters for programming languages

A Simple Application of Lightweight Fusion to Proving the Equivalence of Abstract Machines

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