Factorisation systems for logical relations and monadic lifting in type-and-effect system semantics

04/10/2018

∙

by   Ohad Kammar, et al.

∙

0

∙

share

Type-and-effect systems incorporate information about the computational effects, e.g., state mutation, probabilistic choice, or I/O, a program phrase may invoke alongside its return value. A semantics for type-and-effect systems involves a parameterised family of monads whose size is exponential in the number of effects. We derive such refined semantics from a single monad over a category, a choice of algebraic operations for this monad, and a suitable factorisation system over this category. We relate the derived semantics to the original semantics using fibrations for logical relations. Our proof uses a folklore technique for lifting monads with operations.