Compiling a Functional Logic Language: The Fair Scheme

Abstract

Abstract. We present a compilation scheme for a functional logic programming language. The input program to our compiler is a constructor-based graph rewriting system in a non-confluent, but well-behaved class. This input is an intermediate representation of a functional logic program in a language such as Curry or T OY. The output program from our compiler consists of three procedures that make recursive calls and execute both rewrite and pull-tab steps. This output is an intermediate representation that is easy to encode in any number of programming languages. Our design evolves the Basic Scheme of Antoy and Peters by removing the "left bias" that prevents obtaining results of some computations-a behavior related to the order of evaluation, which is counter to declarative programming. The benefits of this evolution are not only the strong completeness of computations, but also the provability of non-trivial properties of these computations. We rigorously describe the compiler design and prove some of its properties. To state and prove these properties, we introduce novel definitions of "need" and "failure." For non-confluent constructor-based rewriting systems these concepts are more appropriate than the classic definition of need of Huet and Levy.

A New Functional-Logic Compiler for Curry: Sprite

“…The Fair Scheme implements this according to a strategy guided by the definitional trees encoded in ICurry. Case distinction as exemplified in (7) assumes that an expression being matched is not rooted by a function symbol. Thus, when a node needed to complete a match is labeled by a function symbol, the expression rooted by that node is evaluated until it is labeled by a non-function symbol.…”

“…Operationally, pattern-matching amounts to evaluating nested case expressions similar to the one shown in (7). Sprite implements this through a mechanism we call tagged dispatch.…”

“…In so doing, Sprite guarantees that no expression is ignored forever, hence no potential result is lost. A proof of correctness of compiled programs is provided in [7] for the abstract formulation of the compiler, the Fair Scheme. In this domain, correctness is the property that an executable program produces all and only the values intended by the corresponding source program.…”

“…The fingerprint is used to detect and remove inconsistent computations from the work queue. It is possible to syntactically pre-compute pull-tab steps: that is, a case statement such as the one in (7) could implement pull-tabbing by defining an appropriate righthand side rule for the choice branch. In fact, a major competing implementation of Curry does exactly that [8].…”

“…Sprite aims to be the first operationally complete Curry compiler, meaning it should produce all values of a source program (within time and space constraints). Our compiler is based on a compilation strategy named the Fair Scheme [7] that sets out rules for compiling a functional-logic program (in the form of a graph rewriting system) into abstract deterministic procedures that easily map to the instructions of a low-level programming language. Section 2 introduces Sprite at a high level, and describes the transformations it performs.…”