Cons-free Programming with Immutable Functions

TL;DR

This paper explores the potential of non-determinism in purely functional, higher-order programming languages to characterize complexity classes like NP and NEXP, using cons-free programs with immutable functions.

Contribution

It introduces an initial approach to characterize complexity hierarchies using cons-free, immutable higher-order functions in purely functional programming.

Findings

Proposes a method to represent complexity classes with functional programs.

Highlights the use of cons-free programs with immutable functions for complexity analysis.

Work remains incomplete, indicating ongoing research in this area.

Abstract

We investigate the power of non-determinism in purely functional programming languages with higher-order types. Specifically, we set out to characterise the hierarchy NP $\subseteq$ NEXP $\subseteq$ NEXP$^{(2)}$ $\subseteq \cdots \subseteq$ NEXP$^{(k)}$ $\subseteq \cdots$ solely in terms of higher-typed, purely functional programs. Although the work is incomplete, we present an initial approach using cons-free programs with immutable functions.