Following the program of Moggi, the semantics of a simple non-deterministic functional language with recursion and failure is described by a monad. We show that this monad cannot be any of the known power domain constructions, because they do not handle non-termination properly. Instead, a novel construction is proposed and investigated. It embodies both non-determinism (choice and failure) and...

In [4] we proved that a commutative monad on a symmetric monoidal closed category carries the structure of a symmetric monoidal monad ([4], Theorem 3.2). We here prove the converse, so that, taken together, we have: there is a 1-1 correspondence between commutative monads and symmetric monoidal monads (Theorem 2.3 below). The main computational work needed consists in constructing an equivalenc...

Each datatype constructor comes equiped not only with a so-called map and fold (catamorphism), as is widely known, but, under some condition, also with a kind of map and fold that are related to an arbitrary given monad. This result follows from the preservation of initiality under lifting from the category of algebras in a given category to a certain other category of algebras in the Kleisli c...

We present an advanced modeling and verification toolbox for functional programs with state and exceptions. The toolbox integrates an extensible, monad-based, component model, a monad-based Hoare logic and weakest precondition calculus, and proof systems for temporal logic and bisimilarity. It is implemented in Isabelle/HOL using shallow embeddings and incorporates as much modeling and reasonin...

The delay datatype was introduced by Capretta [2] as a means to incorporate general recursion to Martin-Löf type theory and it is useful in this setting for modeling non-terminating behaviours. This datatype is a (strong) monad and constitutes a constructive alternative to the maybe monad. For a given set X, each element of DX is a possibly infinite computation that returns a value of X, if it ...

It is known that factorisation systems in categories can be viewed as unitary pseudo algebras for the monad P = (–)2, in Cat. We show in this note that an analogous fact holds for proper (i.e., epimono) factorisation systems and a suitable quotient of the former monad, deriving from a construct introduced by P. Freyd for stable homotopy. Some similarities of P with the structure of the path end...