Rewriting and narrowing for constructor systems with call-time choice semantics

López-Fraguas, Francisco Javier; Martin-Martin, Enrique; Rodríguez-Hortalá, Juan; Sánchez-Hernández, Jaime

doi:10.1017/s1471068412000373

Cited by 5 publications

(14 citation statements)

References 51 publications

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“…This is a long-standing and active area of research whose difficulties originate from the combination of laziness, non-determinism and sharing [41].…”

Section: Related Workmentioning

confidence: 99%

Compiling a Functional Logic Language: The Fair Scheme

Antoy

Jost

2014

Logic-Based Program Synthesis and Transformation

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Abstract. We present a compilation scheme for a functional logic programming language. The input program to our compiler is a constructor-based graph rewriting system in a non-confluent, but well-behaved class. This input is an intermediate representation of a functional logic program in a language such as Curry or T OY. The output program from our compiler consists of three procedures that make recursive calls and execute both rewrite and pull-tab steps. This output is an intermediate representation that is easy to encode in any number of programming languages. Our design evolves the Basic Scheme of Antoy and Peters by removing the "left bias" that prevents obtaining results of some computations-a behavior related to the order of evaluation, which is counter to declarative programming. The benefits of this evolution are not only the strong completeness of computations, but also the provability of non-trivial properties of these computations. We rigorously describe the compiler design and prove some of its properties. To state and prove these properties, we introduce novel definitions of "need" and "failure." For non-confluent constructor-based rewriting systems these concepts are more appropriate than the classic definition of need of Huet and Levy.

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“…This is a long-standing and active area of research whose difficulties originate from the combination of laziness, non-determinism and sharing [41].…”

Section: Related Workmentioning

confidence: 99%

Compiling a Functional Logic Language: The Fair Scheme

Antoy

Jost

2014

Logic-Based Program Synthesis and Transformation

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“…But classical narrowing, like classical rewriting, is not correct for call-time choice. In [18] we proposed a notion of narrowing adequate to FO letrewriting, and now we extend it to HO. As happens in [7,4], HOlet-narrowing may bind variables to HO-patterns.…”

Section: Definition 1 (Hypersemantics)mentioning

confidence: 99%

“…Finally, (Contxt) is a contextual rule where, as in [18], it is crucial to protect bound variables from narrowing (condition (i)) and to avoid variable capture (condition (ii), automatically fulfilled if mgu's are used in (Narr) and (VAct), and fresh shallow patterns -i.e., of the form h X 1 . .…”

Section: Definition 1 (Hypersemantics)mentioning

confidence: 99%

“…The first three points have been conceived as an extension to HO of our previous work on the FO case [19,18]. However, adapting it has not been routine; on the contrary, some results have been indeed a technical challenge.…”

Section: Definition 1 (Hypersemantics)mentioning

confidence: 99%

“…In [19] we proposed let-rewriting, a notion of rewriting with local bindings adequate to FO CRWL semantics, and at the same time simpler and more abstract than other reduction notions based on term graph rewriting [24,6] or natural operational semantics [1]. Let-rewriting was generalized to let-narrowing in [18].…”

Section: Introductionmentioning

confidence: 99%

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Rewriting and Call-Time Choice: The HO Case

López-Fraguas¹,

Rodríguez-Hortalá²,

Sánchez-Hernández³

Functional and Logic Programming

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Abstract. It is known that the behavior of non-deterministic functions with call-time choice semantics, present in current functional logic languages, is not well described by ordinary approaches to reduction like ordinary term rewriting systems or λ-calculus. The presence of HO features makes things more difficult, since reasoning principles that are essential in a standard (i.e., deterministic) functional setting, like extensionality, become wrong. In this paper we propose HOlet-rewriting, a notion of rewriting with local bindings that turns out to be adequate for programs with HO non-deterministic functions, as it is shown by strong equivalence results with respect to HOCRWL, a previously existing semantic framework for such programs. In addition, we give a sound and complete notion of HOlet-narrowing, we show by a case study the usefulness of the achieved combination of semantic and reduction notions, and finally we prove within our framework that a standard approach to the implementation of HO features, namely translation to FO, is still valid for HO nondeterministic functions.

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Singular and plural functions for functional logic programming

Riesco¹,

Rodríguez-Hortalá²

2012

Theory and Practice of Logic Programming

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Modern functional logic programming (FLP) languages use non-terminating and nonconfluent constructor systems (CS's) as programs in order to define non-strict non-deterministic functions. Two semantic alternatives have been usually considered for parameter passing with this kind of functions: call-time choice and run-time choice. While the former is the standard choice of modern FLP languages, the latter lacks some basic propertiesmainly compositionality-that have prevented its use in practical FLP systems. Traditionally it has been considered that call-time choice induces a singular denotational semantics, while run-time choice induces a plural semantics. We have discovered that this latter identification is wrong when pattern matching is involved, and thus in this paper we propose two novel compositional plural semantics for CS's that are different from run-time choice.We investigate the basic properties of our plural semantics-compositionality, polarity, monotonicity for substitutions, and a restricted form of the bubbling property for constructor systems-and the relation between them and to previous proposals, concluding that these semantics form a hierarchy in the sense of set inclusion of the set of values computed by them. Besides, we have identified a class of programs characterized by a simple syntactic criterion for which the proposed plural semantics behave the same, and a program transformation that can be used to simulate one of the proposed plural semantics by term rewriting. At the practical level, we study how to use the new expressive capabilities of these semantics for improving the declarative flavour of programs. As call-time choice is the standard semantics for FLP, it still remains the best option for many common programming patterns. Therefore we propose a language which combines call-time choice and our plural semantics, that we have implemented in the Maude system. The resulting interpreter is then employed to develop and test several significant examples showing the capabilities of the combined semantics.

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Rewriting and narrowing for constructor systems with call-time choice semantics

Cited by 5 publications

References 51 publications

Compiling a Functional Logic Language: The Fair Scheme

Compiling a Functional Logic Language: The Fair Scheme

Rewriting and Call-Time Choice: The HO Case

Singular and plural functions for functional logic programming

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