Monads and Adjunctions for Global Exceptions

Monads and Adjunctions for Global Exceptions (2006)

by Paul Blain Levy

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Datum	Value	Source
TITLE	Monads and Adjunctions for Global Exceptions	user correction
AUTHOR NAME	Paul Blain Levy	user correction
AUTHOR AFFIL	School of Computer Science; University of Birmingham	user correction
AUTHOR ADDR	Birmingham B15 2TT, U.K.	user correction
ABSTRACT	In this paper, we look at two categorical accounts of computational effects (strong monad as a model of the monadic metalanguage, adjunction as a model of call-by-push-value with stacks), and we adapt them to incorporate global exceptions. In each case, we extend the calculus with a construct, due to Benton and Kennedy, that fuses exception handling with sequencing. This immediately gives us an equational theory, simply by adapting the equations for sequencing. We study the categorical semantics of the two equational theories. In the case of the monadic metalanguage, we see that a monad supporting exceptions is a coalgebra for a certain comonad. We further show, using Beck’s theorem, that, on a category with equalizers, the monad constructor for exceptions gives all such monads. In the case of call-by-push-value (CBPV) with stacks, we generalize the notion of CBPV adjunction so that a stack awaiting a value can deal both with a value being returned, and with an exception being raised. We see how to obtain a model of exceptions from a CBPV adjunction, and vice versa by restricting to those stacks that are homomorphic with respect to exception raising.	SVM HeaderParse 0.2
YEAR	2006	user correction
CITATIONS	22 found	ParsCit 1.0