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A Recipe for State-and-Effect Triangles

Bart Jacobs.

In the semantics of programming languages one can view programs as state transformers, or as predicate transformers. Recently the author has introduced state-and-effect triangles which capture this situation categorically, involving an adjunction between state- and predicate-transformers. The&nbsp;[&hellip;]

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Hyper Normalisation and Conditioning for Discrete Probability Distributions

Bart Jacobs.

Normalisation in probability theory turns a subdistribution into a proper distribution. It is a partial operation, since it is undefined for the zero subdistribution. This partiality makes it hard to reason equationally about normalisation. A novel description of normalisation is given as a&nbsp;[&hellip;]

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Relating Apartness and Bisimulation

Herman Geuvers ; Bart Jacobs.

A bisimulation for a coalgebra of a functor on the category of sets can be described via a coalgebra in the category of relations, of a lifted functor. A final coalgebra then gives rise to the coinduction principle, which states that two bisimilar elements are equal. For polynomial functors, this&nbsp;[&hellip;]

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