Most often, in a categorical semantics for a programming language, the substitution of terms is expressed by composition and finite products. However this does not deal with the order of evaluation of arguments, which may have major consequences when there are side-effects. In this paper Cartesian effect categories are introduced for solving this issue, and they are compared with strong monads,...

Models of iterated computation, such as (completely) iterative monads, often depend on a notion of guardedness, which guarantees unique solvability of recursive equations and requires roughly that recursive calls happen only under certain guarding operations. On the other hand, many models of iteration do admit unguarded iteration. Solutions are then no longer unique, and in general not even de...

C -algebras form rather general and rich mathematical structures that can be studied with different morphisms (preserving multiplication, or not), and with different properties (commutative, or not). These various options can be used to incorporate various styles of computation (set-theoretic, probabilistic, quantum) inside categories of C -algebras. At first, this paper concentrates on the com...

The notion of monads originates from the category theory. It became popular in the programming languages community after Moggi proposed a way to use monads to structure denotational semantics. Wadler and others showed how this can be eeectively used as a methodology for building interpreters. Monads are capable of capturing individual language features in a modular way. This paper evaluates two...

We introduce a description of the algebras for a monad in terms of extension systems, similar to the one for monads given in [Manes, 1976]. We rewrite distributive laws for monads and wreaths in terms of this description, avoiding the iteration of the functors involved. We give a profunctorial explanation of why Manes’ description of monads in terms of extension systems works.

In this paper we construct extensions of Set-monads – and, more generally, of lax Rel-monads – into lax monads of the bicategory Mat(V) of generalized V-matrices, whenever V is a well-behaved lattice equipped with a tensor product. We add some guiding examples.

Monads are used for various applications in computer science, and well-known is e.g. the interpretation of morphisms in the Kleisli category of the term monad as variable substitutions assigning variables to terms. An application building upon this observation is the equivalence between most general unifiers and co-equalizers in this category [13]. In this paper we will use monads with addition...

Monads are commonplace in computer science, and can be composed using Beck's distributive laws. Unfortunately, finding laws extremely difficult error-prone. The literature contains some general principles for constructing However, until now there have been no such techniques establishing when law exists. We present three families of theorems showing between two monads. first widely generalizes ...