Superstructural Reversible Logic

In some substructural logics, the memory used by proofs is treated as a first-class multiplicative resource, but the choices made by those proofs are not. Since we can convert between space and time complexity, these “resource conscious” logics are therefore not actually guaranteed to preserve memory—for example, linear logic allows the erasure and duplication of natural numbers with time complexity proportional to their size. In order to fully account for space-time tradeoffs, we augment contexts to track all information, not just multiplicative resources. This creates a reversible, fully resource-preserving logic which allows us to examine the hidden information effects in linear logic and study reversible computation from a proof-theoretic perspective.