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Monad compositions II: Kleisli strength

Published online by Cambridge University Press:  01 June 2008

ERNIE MANES  and
PHILIP MULRY
ERNIE MANES
Affiliation:
Department of Mathematics and Statistics, University of Massachusetts at Amherst, U.S.A.
PHILIP MULRY
Affiliation:
Department of Computer Science, Colgate University, Hamilton, New York, 13346, U.S.A. Email: pmulry@mail.colgate.edu
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Abstract

In this paper we introduce the concept of Kleisli strength for monads in an arbitrary symmetric monoidal category. This generalises the notion of commutative monad and gives us new examples, even in the cartesian-closed category of sets. We exploit the presence of Kleisli strength to derive methods for generating distributive laws. We also introduce linear equations to extend the results to certain quotient monads. Mechanisms are described for finding strengths that produce a large collection of new distributive laws, and consequently monad compositions, including the composition of monadic data types such as lists, trees, exceptions and state.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 18 , Issue 3 , June 2008 , pp. 613 - 643
Copyright
Copyright © Cambridge University Press 2008

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