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 …

We initiate a formal theory of graded monads whose purpose is to adapt and to extend the
formal theory of monads developed by Street in the early 1970's. We establish in particular …

We address the task of deriving fixpoint equations from modal logics characterizing
behavioural equivalences and metrics (summarized under the term conformances). We rely …

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 …

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 …

We use modal logic as a framework for coalgebraic trace semantics, and show the flexibility
of the approach with concrete examples such as the language semantics of weighted …

Graded linear exponential comonads are an extension of linear exponential comonads wih
grading, and provide a categorical semantics of resource-sensitive exponential modality in …