Handling Local State with Global State

摘要

Equational reasoning is one of the most important tools of functional programming. To facilitate its application to monadic programs, Gibbons and Hinze have proposed a simple axiomatic approach using laws that characterise the computational effects without exposing their implementation details. At the same time Plotkin and Pretnar have proposed algebraic effects and handlers, a mechanism of layered abstractions by which effects can be implemented in terms of other effects. This paper performs a case study that connects these two strands of research. We consider two ways in which the nondeterminism and state effects can interact: the high-level semantics where every nondeterministic branch has a local copy of the state, and the low-level semantics where a single sequentially threaded state is global to all branches. We give a monadic account of the folklore technique of handling local state in terms of global state, provide a novel axiomatic characterisation of global state and prove that the handler satisfies Gibbons and Hinze's local state axioms by means of a novel combination of free monads and contextual equivalence. We also provide a model for global state that is necessarily non-monadic.