Monads provide a greatly useful capability to pure languages in simulating side-effects, but implementations such as the Monad Transformer Library [1] in Haskell prohibit reuse of those side-effects such as threading through two different states without some explicit workaround. Monad Factory provides a straightforward solution for opening the non-proper morphisms by indexing monads at both the...

Monads provide a way of structuring functional programs. Most real applications require a combination of primitive monads. Here we describe how some monads may be combined with others to yield a combined monad.

This paper is a contribution to the search for efficient and high-level mathematical tools specify reason about (abstract) programming languages or calculi. Generalising reduction monads of Ahrens et al., we introduce transition monads, thus covering new applications such as lambda-bar-mu-calculus, pi-calculus, Positive GSOS specifications, differential lambda-calculus, big-step, simply-typed, ...

Markov categories are a recent categorical approach to the mathematical foundations of probability and statistics. Here, this is advanced by stating proving equivalent conditions for second-order stochastic dominance, widely used way comparing distributions their spread. Furthermore, we lay foundation theory statistical experiments within classical Blackwell-Sherman-Stein Theorem. Our version n...