The $\aleph$-Calculus: A declarative model of reversible programming

TL;DR

The paper introduces the $\u2115$-Calculus, a declarative, reversible computing model that is Turing complete and does not need history data, with an implemented interpreter demonstrating its practicality.

Contribution

It presents a novel reversible calculus that is declarative, Turing complete, and avoids history accumulation, advancing reversible programming models.

Findings

The $\u2115$-Calculus is reversible and Turing complete.

It has a local term-rewriting semantics.

An interpreter implementation was developed.

Abstract

A novel model of reversible computing, the $\aleph$-calculus, is introduced. It is declarative, reversible-Turing complete, and has a local term-rewriting semantics. Unlike previously demonstrated reversible term-rewriting systems, it does not require the accumulation of history data. Terms in the $\aleph$-calculus, in combination with the program definitions, encapsulate all program state. An interpreter was also written.