A Hierarchy of Semantics for Non-deterministic Term Rewriting Systems

13 years 5 months ago

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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...

Juan Rodríguez-Hortalá

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