2018
DOI: 10.1007/978-3-030-02508-3_9
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Layer by Layer – Combining Monads

Abstract: We develop a modular method to build algebraic structures. Our approach is categorical: we describe the layers of our construct as monads, and combine them using distributive laws. Finding such laws is known to be difficult and our method identifies precise sufficient conditions for two monads to distribute. We either (i) concretely build a distributive law which then provides a monad structure to the composition of layers, or (ii) pinpoint the algebraic obstacles to the existence of a distributive law and sug… Show more

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Cited by 15 publications
(25 citation statements)
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“…Therefore T 2 has no projection axioms; all its equations are linear or dup. As explained in [4], the relevance of T is sufficient to preserve T 2 , hence there exists a distributive law DT ⇒ T D. Indeed, the failure to preserve one presentation of D does not mean that no distributive law can be found.…”
Section: Preserving Equationsmentioning
confidence: 99%
See 2 more Smart Citations
“…Therefore T 2 has no projection axioms; all its equations are linear or dup. As explained in [4], the relevance of T is sufficient to preserve T 2 , hence there exists a distributive law DT ⇒ T D. Indeed, the failure to preserve one presentation of D does not mean that no distributive law can be found.…”
Section: Preserving Equationsmentioning
confidence: 99%
“…Part of this question has been studied in the literature: in [15], Manes and Mulry show that for a monad to preserve linear equations, it suffices to have a symmetric monoidal structure. This argument is further developed in [4], where the authors give sufficient conditions on T for preserving the types of equations outlined by Gautam. In particular, it was shown that so-called relevant monads preserve dup equations, and affine monads preserve drop equations.…”
Section: Introductionmentioning
confidence: 99%
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“…A first series of laws describes how to go back and forth between the underlying monad m and its extension m • Ref m via a retraction pair of natural transformations. The underlying general category theoretic schema seems rather orthogonal to more classical existing techniques for combining monads [10,2]. Such a notion of a monad extension is probably worth being studied more in the depth.…”
Section: Related Work and Conclusionmentioning
confidence: 99%
“…As an example, we define (monadic) streams of values as inductively nested monad actions and we show that promises of such streams can simply be defined as streams of promises, that is, inductively nested monad promises. An associated artefact has been implemented in Haskell and available on the net 2 . It has been successfully applied to realtime synchronous processing and asynchronous control of audio streams [5] therefore illustrating the application scope of the proposed model.…”
Section: Introductionmentioning
confidence: 99%