In programming, some data acts as a resource (eg, file handles, channels) subject to usage
constraints. This poses a challenge to software correctness as most languages are agnostic …

Effects and coeffects are two general, complementary aspects of program behaviour. They
roughly correspond to computations which change the execution context (effects) versus …

Modern probabilistic programming languages aim to formalize and automate key aspects of
probabilistic modeling and inference. Many languages provide constructs for programmable …

Algorithms operating on real numbers are implemented as floating-point computations in
practice, but floating-point operations introduce roundoff errors that can degrade the …

We define and study a probability monad on the category of complete metric spaces and
short maps. It assigns to each space the space of Radon probability measures on it with …

When modelling side-effects using a monad, we need to equip the monad with effectful
operations. This can be done by noting that each algebra of the monad carries …

The framework of graded semantics uses graded monads to capture behavioural
equivalences of varying granularity, for example as found in the linear-time/branching-time …

Concurrent Kleene Algebra (CKA) extends basic Kleene algebra with a parallel composition
operator, which enables reasoning about concurrent programs. However, CKA …

Strong monads and premonoidal categories play a central role in clarifying the denotational
semantics of effectful programming languages. Unfortunately, this theory excludes many …

Markov categories, having tensors with copying and discarding, provide a setting for
categorical probability. This paper uses finite colimits and what we call uniform states in …