Proving Productivity in Infinite Data Structures

Zantema, Hans; Raffelsieper, Matthias

doi:10.4230/lipics.rta.2010.401

Cited by 3 publications

(26 citation statements)

References 11 publications

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“…The above definition coincides with the definition of proper specifications given in [14] for orthogonal proper specifications. 1 We will illustrate the restrictions in the above definition later in Section 4.…”

Section: Specificationsmentioning

confidence: 69%

“…This has been studied mostly in the setting of streams, the simplest infinite objects. However, as already observed in [14], productivity is also of interest for other infinite structures, for example infinite trees, or mixtures of finite and infinite structures. A prominent example of the latter are lists in the programming language Haskell [10], which can be finite (by ending with a sentinel "[]") or which can go on forever.…”

Section: Introductionmentioning

confidence: 82%

“…We still have to impose some restrictions on specifications to make our approach work. These restrictions are given below in the definition of proper specifications, which are similar to those of [14].…”

Section: Specificationsmentioning

confidence: 99%

“…Existing approaches for automatically checking productivity, e.g., [2,3,14], are restricted to orthogonal systems. The main reason for this restriction is that it disallows non-determinism.…”

Section: Introductionmentioning

confidence: 99%

“…This paper presents an extension of the techniques in [14] to analyze productivity of specifications that may contain non-determinism. As in that work, the main technique to prove productivity is by analyzing termination of a corresponding context-sensitive term rewrite system [7].…”

Section: Introductionmentioning

confidence: 99%

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Productivity of Non-Orthogonal Term Rewrite Systems

Raffelsieper

2012

Electron. Proc. Theor. Comput. Sci.

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Productivity is the property that finite prefixes of an infinite constructor term can be computed using a given term rewrite system. Hitherto, productivity has only been considered for orthogonal systems, where non-determinism is not allowed. This paper presents techniques to also prove productivity of non-orthogonal term rewrite systems. For such systems, it is desired that one does not have to guess the reduction steps to perform, instead any outermost-fair reduction should compute an infinite constructor term in the limit. As a main result, it is shown that for possibly non-orthogonal term rewrite systems this kind of productivity can be concluded from context-sensitive termination. This result can be applied to prove stabilization of digital circuits, as will be illustrated by means of an example.

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Section: Specificationsmentioning

confidence: 69%

Section: Introductionmentioning

confidence: 82%

Section: Specificationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Productivity of Non-Orthogonal Term Rewrite Systems

Raffelsieper

2012

Electron. Proc. Theor. Comput. Sci.

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Termination of canonical context-sensitive rewriting and productivity of rewrite systems

Lucas

2015

Electron. Proc. Theor. Comput. Sci.

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Termination of programs, i.e., the absence of infinite computations, ensures the existence of normal forms for all initial expressions, thus providing an essential ingredient for the definition of a normalization semantics for functional programs. In lazy functional languages, though, infinite data structures are often delivered as the outcome of computations. For instance, the list of all prime numbers can be returned as a neverending stream of numerical expressions or data structures. If such streams are allowed, requiring termination is hopeless. In this setting, the notion of productivity can be used to provide an account of computations with infinite data structures, as it "captures the idea of computability, of progress of infinite-list programs" (B.A. Sijtsma, On the Productivity of Recursive List Definitions, ACM Transactions on Programming Languages and Systems 11(4): [633][634][635][636][637][638][639][640][641][642][643][644][645][646][647][648][649] 1989). However, in the realm of Term Rewriting Systems, which can be seen as (first-order, untyped, unconditional) functional programs, termination of Context-Sensitive Rewriting (CSR) has been showed equivalent to productivity of rewrite systems through appropriate transformations. In this way, tools for proving termination of CSR can be used to prove productivity. In term rewriting, CSR is the restriction of rewriting that arises when reductions are allowed on selected arguments of function symbols only. In this paper we show that well-known results about the computational power of CSR are useful to better understand the existing connections between productivity of rewrite systems and termination of CSR, and also to obtain more powerful techniques to prove productivity of rewrite systems.

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Proving Equality of Streams Automatically

Zantema¹,

Endrullis

2011

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Proving Productivity in Infinite Data Structures

Cited by 3 publications

References 11 publications

Productivity of Non-Orthogonal Term Rewrite Systems

Productivity of Non-Orthogonal Term Rewrite Systems

Termination of canonical context-sensitive rewriting and productivity of rewrite systems

Proving Equality of Streams Automatically

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