Boolean restriction categories and taut monads

Authors:
Ernie Manes
Affiliations:
Department of Mathematics and Statistics, University of Massachusetts Amherst, Massachusetts
Venue:
Theoretical Computer Science
Year:
2006

Citing 11
Cited 2

Partial morphisms in categories of effective objects

Information and Computation - Semantics of Data Types
Categories of partial maps

Information and Computation
Partiality, cartesian closedness, and toposes

Information and Computation
Notions of computation and monads

Information and Computation
Predicate transformer semantics

Predicate transformer semantics
Monads and algebras in the semantics of partial data types

Theoretical Computer Science
Automata, Languages, and Machines

Automata, Languages, and Machines
A Discipline of Programming

A Discipline of Programming
Restriction categories I: categories of partial maps

Theoretical Computer Science
Taut Monads and T0-spaces

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Implementing collection classes with monads

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Taut Monads, Dynamic Logic and Determinism

Electronic Notes in Theoretical Computer Science (ENTCS)
Boolean and classical restriction categories

Mathematical Structures in Computer Science

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Abstract

A Boolean category is a restriction category if and only if it has one exception and all morphisms are deterministic. In the category of sets, taut monads are precisely the Boolean ones. It follows that collection monad types in Haskell inherit an assertion calculus based on dynamic logic.