Proving Non-Deterministic Computations in Agda

We investigate proving properties of Curry programs using Agda. First, we address the functional correctness of Curry functions that, apart from some syntactic and semantic differences, are in the intersection of the two languages. Second, we use Agda to model non-deterministic functions with two distinct and competitive approaches incorporating the non-determinism. The first approach eliminates non-determinism by considering the set of all non-deterministic values produced by an application. The second approach encodes every non-deterministic choice that the application could perform. We consider our initial experiment a success. Although proving properties of programs is a notoriously difficult task, the functional logic paradigm does not seem to add any significant layer of difficulty or complexity to the task

Adding plural arguments to Curry programs

Functional logic languages combine lazy (demand-driven) evaluation strategies from functional programming with non-deterministic computations from logic programming. To provide a strategy-independent semantics, most languages are based on the call-time choice semantics where parameters are passed as values. From an implementation point of view, the call-time choice semantics fits well with sharing performed by lazy languages. On the other hand, there are also situations where it is intended to pass non-deterministic arguments as sets of values in order to exploit the power of non-deterministic programming. This alternative parameter passing model is known under the name "plural" arguments. In this paper, we show how both mechanisms can be integrated in a single language. In particular, we present a novel technique to implement plural arguments in a call-time choice language so that existing implementations of contemporary functional logic languages can be easily re-used to implement plural parameter passing

Implementing a Functional Logic Programming Language via the Fair Scheme

This document presents a new compiler for the Functional Logic programming language Curry based on a novel pull-tabbing evaluation strategy called the Fair Scheme. A simple version of the Fair Scheme is proven sound, complete, and optimal. An elaborated version is also developed, which supports narrowing computations and other features of Curry, such as constraint programming, equational constraints, and set functions. The Fair Scheme is used to develop a new Curry system called Sprite, a high-quality, performant implementation whose aims are to promote practical uses of Curry and to serve as a laboratory for further research. An important aspect of Sprite is its integration with the popular imperative language Python. This combination allows one to write hybrid programs in which the programmer may move between declarative and non-declarative styles with relative ease. Benchmarking data show Sprite to be more complete than other Curry systems and competitive in terms of execution time, particularly for non-deterministic programs