Logic for Programming, Artificial Intelligence, and Reasoning

In functional languages such as OBJ*, CafeOBJ, and Maude, symbols are given strategy annotations which specify (the order in) which subterms are evaluated. Syntactically, they are given either as lists of natural numbers or as lists of integers associated to function symbols whose (absolute) values refer to the arguments of the corresponding symbol. A positive index enables the evaluation of an argument whereas a negative index means “evaluate on-demand”. While strategy annotations containing only natural numbers have been implemented and received some recent investigation endeavor (regarding, e.g., termination and completeness), fully general annotations (also called on-demand strategy annotations), which have been proposed to support laziness in OBJ-like languages, are disappointingly under-explored to date. In this paper, we first point out a number of problems of current proposals for handling on-demand strategy annotations. Then, we propose a solution to these problems which is based on a suitable extension of the E-evaluation strategy of OBJ-like languages (that only considers annotations given as natural numbers) to on-demand strategy annotations. Our strategy incorporates a better treatment of demandness and also exhibits good computational properties; in particular, we show how to use it for computing (head-)normal forms. We also introduce a transformation for proving termination of the new evaluation strategy by using standard techniques.

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