Abstract
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.
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Notes
- 1.
The proof can be found at https://github.com/KoenP/LocalAsGlobal.
- 2.
Gibbons and Hinze [4] were mistaken in their claim that the type \( s \rightarrow [( a , s )]\) constitutes a model of their backtrackable state laws; it is not a model because its
does not commute with itself. One could consider a relaxed semantics that admits \( s \rightarrow [( a , s )]\), but that is not the focus of this paper.
does not commute with itself. One could consider a relaxed semantics that admits References
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Acknowledgements
We would like to thank Matija Pretnar, the members of IFIP WG 2.1, the participants of Shonan meeting 146 and the MPC reviewers for their insightful comments. We would also like to thank the Flemish Fund for Scientific Research (FWO) for their financial support.
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Pauwels, K., Schrijvers, T., Mu, SC. (2019). Handling Local State with Global State. In: Hutton, G. (eds) Mathematics of Program Construction. MPC 2019. Lecture Notes in Computer Science(), vol 11825. Springer, Cham. https://doi.org/10.1007/978-3-030-33636-3_2
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DOI: https://doi.org/10.1007/978-3-030-33636-3_2
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