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DataOblivious Stream Productivity
 Utrecht University
"... Abstract. We are concerned with demonstrating productivity of specifications of infinite streams of data, based on orthogonal rewrite rules. In general, this property is undecidable, but for restricted formats computable sufficient conditions can be obtained. The usual analysis, also adopted here, d ..."
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Cited by 14 (3 self)
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Abstract. We are concerned with demonstrating productivity of specifications of infinite streams of data, based on orthogonal rewrite rules. In general, this property is undecidable, but for restricted formats computable sufficient conditions can be obtained. The usual analysis, also adopted here, disregards the identity of data, thus leading to approaches that we call dataoblivious. We present a method that is provably optimal among all such dataoblivious approaches. This means that in order to improve on our algorithm one has to proceed in a dataaware fashion. 3 1
Productivity of Stream Definitions
, 2008
"... We give an algorithm for deciding productivity of a large and natural class of recursive stream definitions. A stream definition is called ‘productive’ if it can be evaluated continually in such a way that a uniquely determined stream in constructor normal form is obtained as the limit. Whereas prod ..."
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Cited by 13 (3 self)
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We give an algorithm for deciding productivity of a large and natural class of recursive stream definitions. A stream definition is called ‘productive’ if it can be evaluated continually in such a way that a uniquely determined stream in constructor normal form is obtained as the limit. Whereas productivity is undecidable for stream definitions in general, we show that it can be decided for ‘pure’ stream definitions. For every pure stream definition the process of its evaluation can be modelled by the dataflow of abstract stream elements, called ‘pebbles’, in a finite ‘pebbleflow net(work)’. And the production of a pebbleflow net associated with a pure stream definition, that is, the amount of pebbles the net is able to produce at its output port, can be calculated by reducing nets to trivial nets.
ABSTRACT MODELS OF TRANSFINITE REDUCTIONS
, 2010
"... We investigate transfinite reductions in abstract reduction systems. To this end, we study two abstract models for transfinite reductions: a metric model generalising the usual metric approach to infinitary term rewriting and a novel partial order model. For both models we distinguish between a we ..."
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Cited by 6 (6 self)
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We investigate transfinite reductions in abstract reduction systems. To this end, we study two abstract models for transfinite reductions: a metric model generalising the usual metric approach to infinitary term rewriting and a novel partial order model. For both models we distinguish between a weak and a strong variant of convergence as known from infinitary term rewriting. Furthermore, we introduce an axiomatic model of reductions that is general enough to cover all of these models of transfinite reductions as well as the ordinary model of finite reductions. It is shown that, in this unifying axiomatic model, many basic relations between termination and confluence properties known from finite reductions still hold. The introduced models are applied to term rewriting but also to term graph rewriting. We can show that for both term rewriting as well as for term graph rewriting the partial order model forms a conservative extension to the metric model.
Properties of Infinite Reduction Paths in Untyped λCalculus
"... this paper is to formalize the two ..."
UNIQUE NORMAL FORMS IN INFINITARY WEAKLY ORTHOGONAL TERM REWRITING
"... Abstract. We present some contributions to the theory of infinitary rewriting for weakly orthogonal term rewrite systems, in which critical pairs may occur provided they are trivial. We show that the infinitary unique normal form property (UN ∞ ) fails by a simple example of a weakly orthogonal TRS ..."
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Abstract. We present some contributions to the theory of infinitary rewriting for weakly orthogonal term rewrite systems, in which critical pairs may occur provided they are trivial. We show that the infinitary unique normal form property (UN ∞ ) fails by a simple example of a weakly orthogonal TRS with two collapsing rules. By translating this example, we show that UN ∞ also fails for the infinitary λβηcalculus. As positive results we obtain the following: Infinitary confluence, and hence UN ∞ , holds for weakly orthogonal TRSs that do not contain collapsing rules. To this end we refine the compression lemma. Furthermore, we consider the triangle and diamond properties for infinitary multisteps (complete developments) in weakly orthogonal TRSs, by refining an earlier clusteranalysis for the finite case. 1.