Rewriting and Call-Time Choice: The HO Case

Abstract

Abstract. It is known that the behavior of non-deterministic functions with call-time choice semantics, present in current functional logic languages, is not well described by ordinary approaches to reduction like ordinary term rewriting systems or λ-calculus. The presence of HO features makes things more difficult, since reasoning principles that are essential in a standard (i.e., deterministic) functional setting, like extensionality, become wrong. In this paper we propose HOlet-rewriting, a notion of rewriting with local bindings that turns out to be adequate for programs with HO non-deterministic functions, as it is shown by strong equivalence results with respect to HOCRWL, a previously existing semantic framework for such programs. In addition, we give a sound and complete notion of HOlet-narrowing, we show by a case study the usefulness of the achieved combination of semantic and reduction notions, and finally we prove within our framework that a standard approach to the implementation of HO features, namely translation to FO, is still valid for HO nondeterministic functions.

Safe typing of functional logic programs with opaque patterns and local bindings

“…This somehow non-typical behavior does not emerge by the allowance of HO patterns itself; as it is known [9], it stems from the mere combination of HO-functions, lazy evaluation and call-time choice semantics for non-determinism, a cocktail which is present in current FLP systems, whether or not they support HOpatterns. However, HO patterns can be a source of problems from the point of view of the types.…”

“…In Section 3 we expose the type system and prove its soundness wrt. let-rewriting, an operational reduction semantics for FL programs presented in [9]. Section 4 contains a type inference relation, which lets us find the most general type of expressions.…”

Liberal Typing for Functional Logic Programs

“…The operational semantics of our programs is based on let-rewriting (López-Fraguas et al, 2008), a high level notion of reduction step devised to express call-time choice through the use of let-bindings that represent subexpression sharing. For this paper, we have extended let-rewriting with two rules for managing failure of pattern matching ( Figure 2), playing a role similar to the rules for pattern matching failure in GADTs (Cheney and Hinze, 2003;Peyton Jones et al, 2006).…”

“…(Antoy and Tolmach, 1999;López-Fraguas et al, 2008). In short, this translation introduces a new function symbol @ (to be read as 'apply'), and then adds calls to @ in some points in the program and appropriate rules for evaluating it.…”

“…HO patterns correspond to an intensional view of functions, i.e., different descriptions of the same 'extensional' function can be distinguished by the semantics. This is not an exoticism: it is known (López-Fraguas et al, 2008) that extensionality is not a valid principle within the combination of HO, non-determinism and call-time choice. It is also known that HO-patterns cause some bad interferences with types: (González-Moreno et al, 2001) and considered that problem, and this paper makes also some contributions in this sense.…”