Reversible combinatory logic

The λ-calculus is destructive: its main computational mechanism – beta reduction – destroys the redex and makes it thus impossible to replay the computational steps. Combinatory logic is a variant of the λ-calculus which maintains irreversibility. Recently, reversible computational models have been studied mainly in the context of quantum computation, as (without measurements) quantum physics is inherently reversible. However, reversibility also changes fundamentally the semantical framework in which classical computation has to be investigated. We describe an implementation of classical combinatory logic into a reversible calculus for which we present an algebraic model based on a generalisation of the notion of group.