Related papers: Complete Elgot Monads and Coalgebraic Resumptions
We consider a bag (multiset) monad on the category of standard Borel spaces, and show that it gives a free measurable commutative monoid. Firstly, we show that a recent measurability result for probabilistic database queries (Grohe and…
The original purpose of component-based development was to provide techniques to master complex software, through composition, reuse and parametrisation. However, such systems are rapidly moving towards a level in which software becomes…
Separate programming models for data transformation (declarative) and computation (procedural) impact programmer ergonomics, code reusability and database efficiency. To eliminate the necessity for two models or paradigms, we propose a…
This paper studies the design of programming languages with handlers of higher-order effectful operations -- effectful operations that may take in computations as arguments or return computations as output. We present and analyse a core…
In this work, we study 'reduction monads', which are essentially the same as monads relative to the free functor from sets into multigraphs. Reduction monads account for two aspects of the lambda calculus: on the one hand, in the monadic…
We propose an abstract framework for modeling state-based systems with internal behavior as e.g. given by silent or $\epsilon$-transitions. Our approach employs monads with a parametrized fixpoint operator $\dagger$ to give a semantics to…
Large scale real number computation is an essential ingredient in several modern mathematical proofs. Because such lengthy computations cannot be verified by hand, some mathematicians want to use software proof assistants to verify the…
We provide a novel transcription of monotone operator theory to the non-Euclidean finite-dimensional spaces $\ell_1$ and $\ell_{\infty}$. We first establish properties of mappings which are monotone with respect to the non-Euclidean norms…
In this paper, we introduce and investigate monadic NM-algebras: a variety of NM-algebras equipped with universal quantifiers. Also, we obtain some conditions under which monadic NM-algebras become monadic Boolean algebras. Besides, we show…
In various subjects including mathematics, one can hope to use mathematical thinking well when the right kinds of algebraic structure to consider can be discovered or spotted. Therefore, it would help to understand kinds of algebraic…
Finitary monads on $\mathsf{Pos}$ are characterized as the precisely the free-algebra monads of varieties of algebras. These are classes of ordered algebras specified by inequations in context. Analagously, finitary enriched monads on…
Game comonads provide a categorical syntax-free approach to finite model theory, and their Eilenberg-Moore coalgebras typically encode important combinatorial parameters of structures. In this paper, we develop a framework whereby the…
Coalgebras provide a uniform framework to study dynamical systems, including several types of automata. In this paper, we make use of the coalgebraic view on systems to investigate, in a uniform way, under which conditions calculi that are…
This paper studies fundamental questions concerning category-theoretic models of induction and recursion. We are concerned with the relationship between well-founded and recursive coalgebras for an endofunctor. For monomorphism preserving…
Motivated by recent work on weak distributive laws and their applications to coalgebraic semantics, we investigate the algebraic nature of semialgebras for a monad. These are algebras for the underlying functor of the monad subject to the…
We propose a new formalism for specifying and reasoning about problems that involve heterogeneous "pieces of information" -- large collections of data, decision procedures of any kind and complexity and connections between them. The essence…
Multiple data types naturally co-occur when describing real-world phenomena and learning from them is a long-standing goal in machine learning research. However, existing self-supervised generative models approximating an ELBO are not able…
Accounts of semantic phenomena often involve extending types of meanings and revising composition rules at the same time. The concept of monads allows many such accounts -- for intensionality, variable binding, quantification and focus --…
We develop universal algebra over an enriched category $\mathcal K$ and relate it to finitary enriched monads over $\mathcal K$. Using it, we deduce recent results about ordered universal algebra where inequations are used instead of…
The belief construction is a fundamental technique for transforming partially observable systems to fully observable ones while preserving the relevant semantics. It plays a central role in the analysis of partially observable systems, in…