A Lightweight Combination of Semantics for Non-deterministic Functions

arXiv:0903.2205v1 [cs.PL] 12 Mar 2009 A Lightweight Combination of Semantics for Non-deterministic Functions ⋆ Francisco Javier L´opez-Fraguas, Juan Rodr´ıguez-Hortal´a, and Jaime S´anchez-Hern´andez Departamento de Sistemas Inform´aticos y Computaci´on Universidad Complutense de Madrid, Spain fraguas@sip.ucm.es, jrodrigu@fdi.ucm.es, jaime@sip.ucm.es Abstract. The use of non-deterministic functions is a distinctive feature of modern functional logic languages. The semantics commonly adopted is call-time choice, a notion that at the operational level is related to the sharing mechanism of lazy evaluation in functional languages. However, there are situations where run-time choice, closer to ordinary rewriting, is more appropriate. In this paper we propose an extension of existing call- time choice based languages, to provide support for run-time choice in localized parts of a program. The extension is remarkably simple at three relevant levels: syntax, formal operational calculi and implementation, which is based on the system Toy. 1 Introduction Non-strict non-deterministic functions are a distinctive feature of modern func- tional logic languages (see [5] for a recent survey). It is known that the introduc- tion of non-determinism in a functional setting gives rise to a variety of semantic decisions (see e.g. [12]). For term-rewriting based specifications, Hussmann [7] established a major distinction between call-time choice and run-time choice. Call-time choice is closely related to call-by-value and, in the case of strict se- mantics, it is easily implemented by innermost rewriting. In the case of non-strict semantics, things are more complicated, since the call-by-value view of call-time choice must include partial values. Operationally, this needs something simi- lar to the sharing mechanism followed, for efficiency reasons, in (deterministic) functional languages under lazy evaluation. In contrast, run-time choice does not share, corresponds rather to call-by-name, and is realized by ordinary rewriting. For deterministic programs, run-time and call-time are able to produce the same set of values, but in general the set of values reachable by run-time choice is larger than that of call-time choice. Non-deterministic functions with non-strict and call-time choice semantics were introduced in the functional logic setting with the CRWL framework [4], ⋆This work has been partially supported by the Spanish projects MERIT-FORMS- UCM (TIN2005-09207-C03-03), FAST-STAMP (TIN2008-06622-C03-01/TIN) and Promesas-CAM (S-0505/TIC/0407) . A Lightweight Combination of Semantics for Non-deterministic Functions 53 in which programs are possibly non-confluent and non-terminating constructor- based term rewriting systems (CTRS). Since then, they are common part of daily programming in systems like Curry [6] or Toy [11]. Run-time choice has been rarely [1] considered as a valuable global alternative to call-time choice. However, there might be parts in a program or individual functions for which run-time choice could be a better option, and therefore it would be convenient to have both possibilities (run-time/call-time) at programmer’s disposal. The following example illustrates the interest of combining both semantics. Example 1. Modeling grammar rules for string generation can be directly done by CTRS like the following (non-confluent and non-terminating) one, in which we assume that texts (terminals) are represented as strings (lists of characters), that can be concatenated with ++ (defined in a standard way): letter →”a” .... letter →”z” word →” ” word →letter++word Disregarding syntax, this CTRS is a valid program in functional logic systems like Curry or Toy. The program acts as a non-deterministic generator of the texts in the language defined by the grammar. Each individual reduction leads to a string in the language. The generation of palindromes (of even length, for simplicity) could be done by the rewrite rules: palindrome →palAux(word) palAux(X) →X ++ reverse(X) where reverse is defined in any standard way. It is important to remark that the definition of palindrome/palAux works fine only if call-time choice is adopted for non-determinism, meaning operationally that in the (partial) reduction palindrome →palAux(word) →word ++ reverse(word) the two occurrences of word created by the rule of palAux must be shared. If run-time choice (i.e., ordinary rewriting) were used, the two occurrences of word could follow independent ways, and therefore palindrome could be reduced, for instance, to ”oops”, which is not a palindrome. Two useful operators to structure grammar specifications are the alternative ‘|’ and Kleene’s ‘∗’ for repetitions: X | Y →X X | Y →Y star X →” ” star X →X++star(X) With them letter and word could be redefined as follows: letter →”a” | ”b” | ... | ”z” word →star(letter) The annoying fact is that this does not work! At least not under call-time choice, which implies that this is an uncorrect definition of sta

…(Full text truncated)…

This content is AI-processed based on ArXiv data.