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Distances between States and between Predicates

Bart Jacobs ; Abraham Westerbaan.

This paper gives a systematic account of various metrics on probability distributions (states) and on predicates. These metrics are described in a uniform manner using the validity relation between states and predicates. The standard adjunction between convex sets (of states) and effect modules (of&nbsp;[&hellip;]

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Bases as Coalgebras

Bart Jacobs.

The free algebra adjunction, between the category of algebras of a monad and the underlying category, induces a comonad on the category of algebras. The coalgebras of this comonad are the topic of study in this paper (following earlier work). It is illustrated how such coalgebras-on-algebras can be&nbsp;[&hellip;]

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Generic Trace Semantics via Coinduction

Ichiro Hasuo ; Bart Jacobs ; Ana Sokolova.

Trace semantics has been defined for various kinds of state-based systems, notably with different forms of branching such as non-determinism vs. probability. In this paper we claim to identify one underlying mathematical structure behind these "trace semantics," namely coinduction in a Kleisli&nbsp;[&hellip;]

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