Algebraic theory of processes
Computational lambda-calculus and monads
Proceedings of the Fourth Annual Symposium on Logic in computer science
A probabilistic powerdomain of evaluations
Proceedings of the Fourth Annual Symposium on Logic in computer science
Category theory for computing science
Category theory for computing science
Notions of computation and monads
Information and Computation
Information and Computation
Nondeterminism and Probabilistic Choice: Obeying the Laws
CONCUR '00 Proceedings of the 11th International Conference on Concurrency Theory
Notions of Computation Determine Monads
FoSSaCS '02 Proceedings of the 5th International Conference on Foundations of Software Science and Computation Structures
Combining Computational Effects: commutativity & sum
TCS '02 Proceedings of the IFIP 17th World Computer Congress - TC1 Stream / 2nd IFIP International Conference on Theoretical Computer Science: Foundations of Information Technology in the Era of Networking and Mobile Computing
CAAP '94 Proceedings of the 19th International Colloquium on Trees in Algebra and Programming
Monads and Modular Term Rewriting
CTCS '97 Proceedings of the 7th International Conference on Category Theory and Computer Science
Combining effects: sum and tensor
Theoretical Computer Science - Clifford lectures and the mathematical foundations of programming semantics
Discrete Lawvere theories and computational effects
Theoretical Computer Science - Algebra and coalgebra in computer science
Probabilistic Completion of Nondeterministic Models
Electronic Notes in Theoretical Computer Science (ENTCS)
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We introduce the notion of discrete countable Lawvere V-theory and study constructions that may be made on it. The notion of discrete countable Lawvere V-theory extends that of ordinary countable Lawvere theory by allowing the homsets of an ordinary countable Lawvere theory to become homobjects of a well-behaved axiomatically defined category such as that of ω-cpo's. Every discrete countable Lawvere V-theory induces a V-enriched monad, equivalently a strong monad, on V. We show that discrete countable Lawvere V-theories allow us to model all the leading examples of computational effects other than continuations, and that they are closed under constructions of sum, tensor and distributive tensor, which are the fundamental ways in which one combines such effects. We also show that discrete countable Lawvere V-theories are closed under taking an image, allowing one to treat observation as a mathematical primitive in modelling effects.