Refunctionalization at Work

Danvy, Olivier

doi:10.1007/11783596_2

Cited by 13 publications

(23 citation statements)

References 12 publications

(15 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The programmatic transformation of formal semantics dates to work by Reynolds [15]. More recent work by Danvy et al has shown that formal semantics are highly amenable to program transformations and that it is possible to automatically convert denotational semantics into operational semantics and vice versa [2,3,1,[6][7][8]. These techniques, combined with ours, should permit the mechanizable construction of static analyzers for a wider variety of formal semantics paradigms.…”

Section: Related Workmentioning

confidence: 99%

Abstract Interpreters for Free

Might

2010

Static Analysis

View full text Add to dashboard Cite

Abstract. In small-step abstract interpretations, the concrete and abstract semantics bear an uncanny resemblance. In this work, we present an analysis-design methodology that both explains and exploits that resemblance. Specifically, we present a two-step method to convert a smallstep concrete semantics into a family of sound, computable abstract interpretations. The first step re-factors the concrete state-space to eliminate recursive structure; this refactoring of the state-space simultaneously determines a store-passing-style transformation on the underlying concrete semantics. The second step uses inference rules to generate an abstract state-space and a Galois connection simultaneously. The Galois connection allows the calculation of the "optimal" abstract interpretation. The two-step process is unambiguous, but nondeterministic: at each step, analysis designers face choices. Some of these choices ultimately influence properties such as flow-, field-and context-sensitivity. Thus, under the method, we can give the emergence of these properties a graphtheoretic characterization. To illustrate the method, we systematically abstract the continuation-passing style lambda calculus to arrive at two distinct families of analyses. The first is the well-known k-CFA family of analyses. The second consists of novel "environment-centric" abstract interpretations, none of which appear in the literature on static analysis of higher-order programs.

show abstract

Section: Related Workmentioning

confidence: 99%

Abstract Interpreters for Free

Might

2010

Static Analysis

View full text Add to dashboard Cite

show abstract

“…This disentangled specification, as it were, is in defunctionalized form [32,39,86]: 1 the control stack and the dump are defunctionalized data types, and run c and run d are the corresponding apply functions.…”

Section: Run : S * E * C * D -> Valuementioning

confidence: 99%

“…In ML, the tagged environments are grouped into data types, and auxiliary apply functions dispatch on the tags. The left inverse of defunctionalization is 'refunctionalization' [32,39]. 2 The term 'CPS' is due to Steele [93].…”

Section: Run : S * E * C * D -> Valuementioning

confidence: 99%

“…We assume a basic familiarity with Standard ML and with reasoning about pure ML programs as well as an elementary understanding of defunctionalization [32,39,86] and its left inverse, refunctionalization; of the CPS transformation [33,36,50,76,86,93] and its left inverse, the direct-style transformation; and of delimited continuations [13,33,41,48,63]. From Section 2.4, we use pure ML with delimitedcontrol operators as a meta-language.…”

Section: Prerequisites and Domain Of Discoursementioning

confidence: 99%

See 1 more Smart Citation

A Rational Deconstruction of Landin's J Operator

Danvy¹,

Millikin²

2006

BRICS

Self Cite

View full text Add to dashboard Cite

Landin's J operator was the first control operator for functional languages. It was specified with an extension of the SECD machine, which was the first abstract machine for functional languages. We present a family of compositional evaluation functions corresponding to this extension of the SECD machine, using a series of elementary transformations (transformation into continuation-passing style (CPS) and defunctionalization, chiefly) and their left inverses (transformation into direct style and refunctionalization). To this end, we modernize the SECD machine into a bisimilar one that operates in lock step with the original one but that (1) does not use a data stack and (2) uses the caller-save rather than the callee-save convention for environments. We then characterize the J operator in terms of CPS and in terms of delimited-control operators in the CPS hierarchy. As a byproduct, we also present a reduction semantics for applicative expressions with the J operator, based on Curien's original calculus of explicit substitutions. This reduction semantics mechanically corresponds to the modernized version of the SECD machine and to the best of our knowledge, it provides the first syntactic theory of applicative expressions with the J operator.The present work is concluded by a motivated wish to see Landin's name added to the list of co-discoverers of continuations. Methodologically, however, it mainly illustrates the value of Reynolds's defunctionalization and of refunctionalization as well as the expressive power of the CPS hierarchy (a) to account for the first control operator and the first abstract machine for functional languages and (b) to connect them to their successors.(A preliminary version appears in the proceedings of IFL 2005 [38].)

show abstract

“…The overarching goal of this work is to replace the required ingenuity by a mechanical derivation. A key idea towards this goal has been proposed by Rendel et al [31], namely to relate the data and codata worlds by refunctionalization [16] and defunctionalization [17,32].…”

Section: Introductionmentioning

confidence: 99%

Dualizing Generalized Algebraic Data Types by Matrix Transposition

Ostermann

Jabs

2018

Programming Languages and Systems

View full text Add to dashboard Cite

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.

show abstract

Refunctionalization at Work

Cited by 13 publications

References 12 publications

Abstract Interpreters for Free

Abstract Interpreters for Free

A Rational Deconstruction of Landin's J Operator

Dualizing Generalized Algebraic Data Types by Matrix Transposition

Contact Info

Product

Resources

About