Related papers: A Category-Theoretic Framework for Dependent Effec…
Monads are extensively used nowadays to abstractly model a wide range of computational effects such as nondeterminism, statefulness, and exceptions. It turns out that equipping a monad with a (uniform) iteration operator satisfying a set of…
We give an account of the basic combinatorial structure underlying the notion of type dependency. We do so by considering the category of all dependent sequent calculi, and exhibiting it as the category of algebras for a monad on a presheaf…
Behavioural metrics provide a quantitative refinement of classical two-valued behavioural equivalences on systems with quantitative data, such as metric or probabilistic transition systems. In analogy to the linear-time/branching-time…
Two novel descriptions of weak {\omega}-categories have been recently proposed, using type-theoretic ideas. The first one is the dependent type theory CaTT whose models are {\omega}-categories. The second is a recursive description of a…
Dijkstra monads enable a dependent type theory to be enhanced with support for specifying and verifying effectful code via weakest preconditions. Together with their closely related counterparts, Hoare monads, they provide the basis on…
We study the algebraic effects and handlers as a way to support decision-making abstractions in functional programs, whereas a user can ask a learning algorithm to resolve choices without implementing the underlying selection mechanism, and…
In dependently typed programming, proofs of basic, structural properties can be embedded implicitly into programs and do not need to be written explicitly. Besides saving the effort of writing separate proofs, a most distinguishing and…
We define a notion of grading of a monoid T in a monoidal category C, relative to a class of morphisms M (which provide a notion of M-subobject). We show that, under reasonable conditions (including that M forms a factorization system),…
Programming benefits from a clear separation between pure, mathematical computation and impure, effectful interaction with the world. Existing approaches to enforce this separation include monads, type-and-effect systems, and capability…
Based on Gandy's principles for models of computation we give category-theoretic axioms describing locally deterministic updates to finite objects. Rather than fixing a particular category of states, we describe what properties such a…
Multi-modal word semantics aims to enhance embeddings with perceptual input, assuming that human meaning representation is grounded in sensory experience. Most research focuses on evaluation involving direct visual input, however, visual…
This paper presents preliminary work on a general system for integrating dependent types into substructural type systems such as linear logic and linear type theory. Prior work on this front has generally managed to deliver type systems…
In this paper, we revisit Moggi's celebrated calculus of computational effects from the perspective of logic of monoidal action (actegory). Our development takes the following steps. Firstly, we perform proof-theoretic reconstruction of…
Several relational program logics have been introduced for integrating reasoning about relational properties of programs and measurement of quantitative difference between computational effects. Towards a general framework for such logics,…
We formulate a framework for describing behaviour of effectful higher-order recursive programs. Examples of effects are implemented using effect operations, and include: execution cost, nondeterminism, global store and interaction with a…
Premonoidal categories and Freyd categories provide an encompassing framework for the semantics of call-by-value programming languages. Premonoidal categories are a weakening of monoidal categories in which the interchange law for the…
Refinement calculus is a powerful and expressive tool for reasoning about sequential programs in a compositional manner. In this paper we present an extension of refinement calculus for reactive systems. Refinement calculus is based on…
Hybrid computation combines discrete and continuous dynamics in the form of an entangled mixture inherently present both in various natural phenomena, and in applications ranging from control theory to microbiology. The emergent behaviours…
A type theory is presented that combines (intuitionistic) linear types with type dependency, thus properly generalising both intuitionistic dependent type theory and full linear logic. A syntax and complete categorical semantics are…
Two very basic constructions involving experimental procedures are the formation of coarse-grained versions of experiments, and the formation of branching sequential experiments. The latter allow for the conditioning of states on the…