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# The semantic marriage of monads and effects

Orchard, Dominic A., Petricek, Tomas, Mycroft, Alan (2014) The semantic marriage of monads and effects. CoRR, abs/14 . (Unpublished) (KAR id:57492)

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Official URL
http://arxiv.org/abs/1401.5391

## Abstract

Wadler and Thiemann unified type-and-effect systems with monadic semantics via a syntactic correspondence and soundness results with respect to an operational semantics. They conjecture that a general, “coherent” denotational semantics can be given to unify effect systems with a monadic-style semantics. We provide such a semantics based on the novel structure of an indexed monad, which we introduce. We redefine the semantics of Moggi’s computational ?-calculus in terms of (strong) indexed monads which gives a oneto-one correspondence between indices of the denotations and the effect annotations of traditional effect systems. Dually, this approach yields indexed comonads which gives a unified semantics and effect system to contextual notions of effect (called coeffects), which we have previously described

Item Type: Article Faculties > Sciences > School of ComputingFaculties > Sciences > School of Computing > Programming Languages and Systems Group Dominic Orchard 05 May 2017 13:40 UTC 29 May 2019 17:53 UTC https://kar.kent.ac.uk/id/eprint/57492 (The current URI for this page, for reference purposes) https://orcid.org/0000-0002-7058-7842
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