A computation in the continuation monad returns a final result given a continuation, ie. it is a function with type (X → R) → R. If we instead return the intermediate result at X then our computation is called a selection function. Selection functions appear in diverse areas of mathematics and computer science (especially game theory, proof theory and topology) but the existing literature does ...

Coalgebras in a Kleisli category yield a generic definition of trace semantics for various types of labelled transition systems. In this paper we apply this generic theory to generative probabilistic transition systems, short PTS, with arbitrary (possibly uncountable) state spaces. We consider the sub-probability monad and the probability monad (Giry monad) on the category of measurable spaces ...

We introduce basic concepts from object-oriented programming into dependent type theory based on the idea of modelling objects as interactive programs. We consider methods, interfaces, and the interaction between a fixed number of objects, including self-referential method calls. We introduce a monad like syntax for developing objects in dependent type theory.

We study the canonical weak distributive law $\delta$ of powerset monad over semimodule for a certain class semirings containing, in particular, positive semifields. For this subclass we characterise as convex closure free set. Using abstract theory laws, compose and monads via $\delta$, obtaining subsets semimodule.

Proof-by-reflection is a well-established technique that employs decision procedures to reduce the size of proof-terms. Currently, decision procedures can be written either in Type Theory—in a purely functional way that also ensures termination— or in an effectful programming language, where they are used as oracles for the certified checker. The first option offers strong correctness guarantee...

We give geometric characterisations of patch and Lawson topologies in the context of predicative point-free topology using the constructive notion of located subset. We present the patch topology of a stably locally compact formal topology by a geometric theory whose models are the points of the given topology that are located, and the Lawson topology of a continuous lattice by a geometric theo...

Monads are used in functional programming as a means of modeling and encapsulating computational effects at an appropriate level of abstraction. In previous work, we have introduced monad-based dynamic logic and have used it for the specification and verification of various monadic functional-imperative algorithms over different monads. The semantics of this logic was originally defined over pa...