In#nite trees form a free completely iterative theory over any given signature—this fact, proved by Elgot, Bloom and Tindell, turns out to be a special case of a much more general categorical result exhibited in the present paper. We prove that whenever an endofunctor H of a category has #nal coalgebras for all functors H ( ) + X , then those coalgebras, TX , form a monad. This monad is complet...

A Proof of the uniqueness of monad sets 4 A.

This paper proposes and analyses a monadic translation of an intuitionistic sequent calculus. The source of the translation is a typed λ-calculus previously introduced by the authors, corresponding to the intuitionistic fragment of the call-by-name variant of λμμ̃ of Curien and Herbelin, and the target is a variant of Moggi’s monadic meta-language, where the rewrite relation includes extra permu...

Enrichment of ordinary monads over Cat or Gpd is fundamental to Max Kelly’s unified theory of coherence for categories with structure. So here, we investigate existence and unicity of enrichments of ordinary func­ tors, natural transformations, and hence also monads, over Cat and Gpd. We show that every ordinary natural transformation between 2-functors whose domain 2-category has either tensor...

A monad for concurrent programming that is suitable for being built into Haskell is presented. The monad consists of only four primitives with a very simple semantics. A number of examples demonstrate that monads encapsulating other, more sophisticated communication paradigms known from concurrent functional languages such as Concurrent ML, Facile, and Erlang can be naturally and systematically...

Effectuses have recently been introduced as categorical models for quantum computation, with probabilistic and Boolean (classical) computation as special cases. These ‘probabilistic’ models are called commutative effectuses. All known examples of such commutative effectuses are Kleisli categories of a monad. This paper answers the open question what properties a monad should satisfy so that its...

We develop an equational definition of exception monads that characterizes Moggi’s exception monad transformer. This axiomatization is then used to define an extension of previously described monadindependent computational logics by abnormal termination. Instantiating this generic formalism with the Java monad used in the LOOP project yields in particular the known Hoare calculi with abnormal t...

In this paper, I show that general recursive definitions can be represented in the free monad which supports the ‘effect’ of making a recursive call, without saying how these calls should be executed. Diverse semantics can be given within a total framework by suitable monad morphisms. The Bove-Capretta construction of the domain of a general recursive function can be presented datatype-generica...

The monadic style of language speciication has the advantages of modularity and extensibility: it is simple to add or change features in an interpreter to reeect modiications in the source language. It has proven dif-cult to extend the method to compilation. We demonstrate that by introducing machine-like stores (code and data) into the monadic semantics and then partially evaluating the result...