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Exploring the Boundaries of Monad Tensorability on Set

Nathan Bowler ; Sergey Goncharov ; Paul Blain Levy ; Lutz Schröder.

We study a composition operation on monads, equivalently presented as large equational theories. Specifically, we discuss the existence of tensors, which are combinations of theories that impose mutual commutation of the operations from the component theories. As such, they extend the sum of two&nbsp;[&hellip;]

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Efficient and Modular Coalgebraic Partition Refinement

Thorsten Wißmann ; Ulrich Dorsch ; Stefan Milius ; Lutz Schröder.

We present a generic partition refinement algorithm that quotients coalgebraic systems by behavioural equivalence, an important task in system analysis and verification. Coalgebraic generality allows us to cover not only classical relational systems but also, e.g. various forms of weighted systems&nbsp;[&hellip;]

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Model Theory and Proof Theory of Coalgebraic Predicate Logic

Tadeusz Litak ; Dirk Pattinson ; Katsuhiko Sano ; Lutz Schröder.

We propose a generalization of first-order logic originating in a neglected work by C.C. Chang: a natural and generic correspondence language for any types of structures which can be recast as Set-coalgebras. We discuss axiomatization and completeness results for several natural classes of such&nbsp;[&hellip;]

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Unguarded Recursion on Coinductive Resumptions

Sergey Goncharov ; Lutz Schröder ; Christoph Rauch ; Julian Jakob.

We study a model of side-effecting processes obtained by starting from a monad modelling base effects and adjoining free operations using a cofree coalgebra construction; one thus arrives at what one may think of as types of non-wellfounded side-effecting trees, generalizing the infinite resumption&nbsp;[&hellip;]

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