Abstract not found

We consider the natural combinations of algebraic computational effects such as side-effects, exceptions, interactive input/output, and nondeterminism with continuations. Continuations are not an algebraic effect, but previously developed combinations of algebraic effects given by sum and tensor extend, with effort, to include commonly used combinations of the various algebraic effects with continuations. Continuations also give rise to a third sort of combination, that given by applying the continuations monad transformer to an algebraic effect. We investigate the extent to which sum and tensor extend from algebraic effects to arbitrary monads, and the extent to which Felleisen et al.’s C operator extends from continuations to its combination with algebraic effects. To do all this, we use Dubuc’s characterisation of strong monads in terms of enriched large Lawvere theories.

The question of how to combine monads arises naturally in many areas with much recent interest focusing on the coproduct of two monads. In general, the coproduct of arbitrary monads does not always exist. Although a rather general construction was given by

We present a locally finitely presentable category with a finitely presentable regular generator G and a finitely presentable object A, such that is not a coequalizer of morphisms whose domains and codomains are finite coproducts of objects in G, thereby settling a problem by Gabriel and Ulmer. We also show that in - orthogonality classes in Alg S (category of S-sorted -algebras) for a -ary signature , -presentable objects have a presentation by less than generators and relations and use this to exhibit an example of a reflective subcategory of a locally finitely presentable category which is closed under directed colimits, but not a @ 0 - orthogonality class, disproving a characterization of -orthogonality classes in the book by Ad'amek and Rosick'y.

A fundamental question, in modelling computational effects, is how to give a unified semantic account of modularity, i.e., a mathematical theory that supports the various combinations one naturally makes of computational effects such as exceptions, side-effects, interactive input/output, nondeterminism, and, particularly

A fundamental question, in modelling computational effects, is how to give a unified semantic account of modularity, i.e., a mathematical theory that supports the various combinations one naturally makes of computational effects such as exceptions, side-effects, interactive input/output, nondeterminism, and, particularly for this workshop, continuations [2, 3, 5]. We have begun to give such an account over recent years for all of these effects other than continuations [8], describing the sum and the tensor, or commutative combination, of effects, starting from Eugenio Moggi's proposal to use monads to give semantics for each individual effect [15]. That has yielded the most commonly used combinations of the various effects. Here, we extend our account to include continuations. We consider three distinct ways in which continuations combine with the other effects: sum, tensor, and by applying the continuations monad transformer C(-); we analyse each of these in the following three Detections. We did not...

theorem for algebras over nominal sets. We isolate a ‘uniform ’ fragment of our equational logic, which corresponds to the nominal logics present in the literature. We give semantically invariant translations of theories for nominal algebra and NEL into ‘uniform ’ theories and systematically prove HSP theorems for models of these theories. 1.

Abstract. Given a diagram of Π-algebras (graded groups equipped with an action of the primary homotopy operations), we ask whether it can be realized as the homotopy groups of a diagram of spaces. The answer given here is in the form of an obstruction theory, of somewhat wider application, formulated in terms of generalized Π-algebras. This extends a program begun in [DKS1, BDG] to study the realization of a single Π-algebra. In particular, we explicitly analyze the simple case of a single map, and provide a detailed example, illustrating the connections to higher homotopy operations. A recurring problem in algebraic topology is the rectification of homotopy-commutative diagrams: given a diagram F: D → ho T ∗ (i.e., a functor from a small category to the homotopy category of topological spaces), we ask whether F lifts to ˆ F: D → T∗, and if so, in how many ways.