Synthesizing Set Functions

TL;DR

This paper presents a technique to synthesize set functions in Curry, enabling reasoning about non-deterministic computations and facilitating their implementation within Curry systems.

Contribution

It introduces a method to automatically generate set functions from Curry functions using standard constructs, enhancing reasoning and implementation of non-determinism.

Findings

Enables reasoning about set functions in Curry.

Provides an implementation approach for set functions.

Potential to influence non-determinism implementation strategies.

Abstract

Set functions are a feature of functional logic programming to encapsulate all results of a non-deterministic computation in a single data structure. Given a function $f$ of a functional logic program written in Curry, we describe a technique to synthesize the definition of the set function of $f$. The definition produced by our technique is based on standard Curry constructs. Our approach is interesting for three reasons. It allows reasoning about set functions, it offers an implementation of set functions which can be added to any Curry system, and it has the potential of changing our thinking about the implementation of non-determinism, a notoriously difficult problem.