On a High-Level Approach to Implementing Exact Real Arithmetic in the Functional Logic Programming Language Curry

Abstract

While many functions on the real numbers are not exactly computable, the theory of exact real arithmetic investigates the computation of such functions with respect to any given precision. In this paper, we present an approach to implementing exact real arithmetic based on Type-2 Theory of Effectivity in the functional logic language Curry. It is demonstrated how the specific features of Curry can be used to obtain a high-level realisation that is close to the underlying theoretical concepts. The new Curry data type Real and its corresponding functions can easily be used in other function definitions.