A walk in the semantic park

Danvy, Olivier; Johannsen, Jacob; Zerny, Ian

doi:10.1145/1929501.1929503

Cited by 17 publications

(23 citation statements)

References 13 publications

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“…For instance, Olivier Danvy and associates [16,17] have used defunctionalization, refunctionalization, and some other transformations such as CPS-transformation to inter-derive "semantic artifacts" such as big-step semantics, small-step semantics, and abstract machines ("The inter-derivations illustrated here witness a striking unity of computation, be this for reduction semantics, abstract machines, and normalization function: they all truly define the same elephant." -Danvy et al [15]). …”

Section: Applicationsmentioning

confidence: 99%

Dualizing Generalized Algebraic Data Types by Matrix Transposition

Ostermann

Jabs

2018

Programming Languages and Systems

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Abstract. We characterize the relation between generalized algebraic datatypes (GADTs) with pattern matching on their constructors one hand, and generalized algebraic co-datatypes (GAcoDTs) with copattern matching on their destructors on the other hand: GADTs can be converted mechanically to GAcoDTs by refunctionalization, GAcoDTs can be converted mechanically to GADTs by defunctionalization, and both defunctionalization and refunctionalization correspond to a transposition of the matrix in which the equations for each constructor/destructor pair of the (co-)datatype are organized. We have defined a calculus, GADT T , which unifies GADTs and GAcoDTs in such a way that GADTs and GAcoDTs are merely different ways to partition the program.We have formalized the type system and operational semantics of GADT T in the Coq proof assistant and have mechanically verified the following results: (1) The type system of GADT T is sound, (2) defunctionalization and refunctionalization can translate GADTs to GAcoDTs and back, (3) both transformations are type-and semantics-preserving and are inverses of each other, (4) (co-)datatypes can be represented by matrices in such a way the aforementioned transformations correspond to matrix transposition, (5) GADTs are extensible in an exactly dual way to GAcoDTs; we thereby clarify folklore knowledge about the "expression problem".We believe that the identification of this relationship can guide future language design of "dual features" for data and codata.

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Section: Applicationsmentioning

confidence: 99%

Dualizing Generalized Algebraic Data Types by Matrix Transposition

Ostermann

Jabs

2018

Programming Languages and Systems

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“…We obtain a natural semantics (a big-step normaliser) that is the starting point of the functional correspondence [1,7,11] (the derivation of an abstract machine from a natural semantics).…”

Section: From Denotational Semantics To 2cps-normalisermentioning

confidence: 99%

“…We then derive the reduction semantics form the search functions, by CPS transformation, simplification, and defunctionalisation. This standard practice [2,7,8,10,11] is not essential to establish a syntactic correspondence, but it reveals better the correspondence between reduction contexts and defunctionalised continuations. Moreover, the transformation step clarifies two important points and justifies the accompanying design decisions.…”

Section: Implementing the Reduction Semanticsmentioning

confidence: 99%

“…The syntactic correspondence [6,7,9] consists of refocusing, inlining of contraction function, lightweight-fusion by fix point promotion [19], and compression of corridor transitions. These steps are standard and hence merely outlined in the paper, except for the specific details concerning our layered semantics.…”

Section: The Syntactic Correspondencementioning

confidence: 99%

“…• We extend λ · → to λρ · → , the simply-typed lambda calculus of closures with explicit casts (Section 8) whose implementable reduction semantics is the starting point of the syntactic correspondence [6,7,9] on the left-hand-side of Figure 1. We state the theorems generalising the conjectures in [20] (Section 8.1), and prove them via program transformation by linking the two sides of the diagram at the 2CPS-normaliser (Section 10, etc).…”

Section: Introductionmentioning

confidence: 99%

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Deriving interpretations of the gradually-typed lambda calculus

García-Pérez

Nogueira

Sergey

2014

Proceedings of the ACM SIGPLAN 2014 Workshop on Partial Evaluation and Program Manipulation

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Siek and Garcia (2012) have explored the dynamic semantics of the gradually-typed lambda calculus by means of definitional interpreters and abstract machines. The correspondence between the calculus's mathematically described small-step reduction semantics and the implemented big-step definitional interpreters was left as a conjecture. We prove and generalise Siek and Garcia's conjectures using program transformation. We establish the correspondence between the definitional interpreters and the reduction semantics of a closure-converted gradually-typed lambda calculus that unifies and amends various versions of the calculus. We use a layered approach and two-level continuation-passing style so that the correspondence is parametric on the subsidiary coercion calculus. We have implemented the whole derivation for the eager errordetection policy and the downcast blame-tracking strategy. The correspondence can be established for other choices of error-detection policies and blame-tracking strategies, by plugging in the appropriate artefacts for the particular subsidiary coercion calculus.

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One Step at a Time

Vesely

Fisher

2019

Programming Languages and Systems

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Big-step and small-step are two popular flavors of operational semantics. Big-step is often seen as a more natural transcription of informal descriptions, as well as being more convenient for some applications such as interpreter generation or optimization verification. Smallstep allows reasoning about non-terminating computations, concurrency and interactions. It is also generally preferred for reasoning about type systems. Instead of having to manually specify equivalent semantics in both styles for different applications, it would be useful to choose one and derive the other in a systematic or, preferably, automatic way.Transformations of small-step semantics into big-step have been investigated in various forms by Danvy and others. However, it appears that a corresponding transformation from big-step to small-step semantics has not had the same attention. We present a fully automated transformation that maps big-step evaluators written in direct style to their small-step counterparts. Many of the steps in the transformation, which include CPS-conversion, defunctionalisation, and various continuation manipulations, mirror those used by Danvy and his co-authors. For many standard languages, including those with either call-by-value or call-by-need and those with state, the transformation produces small-step semantics that are close in style to handwritten ones. We evaluate the applicability and correctness of the approach on 20 languages with a range of features.

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A walk in the semantic park

Cited by 17 publications

References 13 publications

Dualizing Generalized Algebraic Data Types by Matrix Transposition

Dualizing Generalized Algebraic Data Types by Matrix Transposition

Deriving interpretations of the gradually-typed lambda calculus

One Step at a Time

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