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

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.