ALGEBRAIC INFORMATION EFFECTS

Abstract

From the informational perspective, programs that are usually considered as pure have effects, for example, the simply typed lambda calculus is considered as a pure language. However, β–reduction does not preserve information and embodies information effects. To capture the idea about pure programs in the informational sense, a new model of computation — reversible computation was proposed. This work focuses on type-theoretic approaches for reversible effect handling. The main idea of this work is inspired by compact closed categories. Compact closed categories are categories equipped with a dual object for every object. They are well-established as models of linear logic, concurrency, and quantum computing. This work gives computational interpretations of compact closed categories for conventional product and sum types, where a negative type represents a computational effect that “reverses execution flow” and a fractional type represents a computational effect that “allocates/deallocates space”.