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DOI: 10.4230/LIPIcs.FSTTCS.2008.1764

A Hierarchy of Semantics for Non-deterministic Term Rewriting Systems

Authors: Juan Rodriguez-Hortala

Published in: LIPIcs, Volume 2, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (2008)

Abstract

Formalisms involving some degree of nondeterminism are frequent in computer science. In particular, various programming or specification languages are based on term rewriting systems where confluence is not required. In this paper we examine three concrete possible semantics for non-determinism that can be assigned to those programs. Two of them --call-time choice and run-time choice-- are quite well-known, while the third one --plural semantics-- is investigated for the first time in the context of term rewriting based programming languages. We investigate some basic intrinsic properties of the semantics and establish some relationships between them: we show that the three semantics form a hierarchy in the sense of set inclusion, and we prove that call-time choice and plural semantics enjoy a remarkable compositionality property that fails for run-time choice; finally, we show how to express plural semantics within run-time choice by means of a program transformation, for which we prove its adequacy.

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Juan Rodriguez-Hortala. A Hierarchy of Semantics for Non-deterministic Term Rewriting Systems. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 2, pp. 328-339, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{rodriguezhortala:LIPIcs.FSTTCS.2008.1764,
  author =	{Rodriguez-Hortala, Juan},
  title =	{{A Hierarchy of Semantics for Non-deterministic Term Rewriting Systems}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
  pages =	{328--339},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-08-8},
  ISSN =	{1868-8969},
  year =	{2008},
  volume =	{2},
  editor =	{Hariharan, Ramesh and Mukund, Madhavan and Vinay, V},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2008.1764},
  URN =		{urn:nbn:de:0030-drops-17643},
  doi =		{10.4230/LIPIcs.FSTTCS.2008.1764},
  annote =	{Keywords: Functional-logic programming, term rewriting systems, constructor-based rewriting logic, non-determinism, call-time choice semantics, run-time choice}
}

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A Hierarchy of Semantics for Non-deterministic Term Rewriting Systems

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