Kleisli simulation is a categorical notion introduced by Hasuo to verify finite trace inclusion. They allow us to give definitions of forward and backward simulation for various types of systems. A generic categorical theory behind Kleisli simulation has been developed and it guarantees the soundness of those simulations wrt. finite trace semantics. Moreover, those simulations can be aided by f...

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 theories, which is just their unrestrained combination. Tensors of theories arise in several context...

Leibniz's concept of monads had great importance for the development idealistic conception. Through Kant and his "Physical Monadology" she infiltrated into modern German philosophy. However, not only idealists referred to monads. Especially, that many scientific disciplines, which emanated from philosophy, related scope notions, example: psychology or sociology. its creators have often theory. ...

We give a logical reconstruction of all-solution predicates in terms of list comprehensions in Prolog's and we describe a variety of logic programming constructs in terms of monads and monad morphisms. Novel monad structures are described for lazy function lists, clause unfoldings and a monad morphism based embedding of Prolog in Prolog is given.

Strong monads are important for several applications, in particular, the denotational semantics of effectful languages, where strength is needed to sequence computations that have free variables. Strength non-trivial: it can be difficult determine whether a monad has any at all, and strong multiple ways. We therefore review some most known facts about prove new ones. In we present number equiva...

A systematic treatment of weak bisimulation and observational congruence on presheaf models is presented. The theory is developed with respect to a “hiding” functor from a category of paths to observable paths. Via a view of processes as bundles , we are able to account for weak morphisms (roughly only required to preserve observable paths) and to derive a saturation monad (on the category of p...