Related papers: Monads, partial evaluations, and rewriting
We show that some recent constructions in the literature, named `weak' generalizations, can be systematically treated by passing from 2-categories to categories enriched in the Cartesian monoidal category of Cauchy complete categories.
We observe that normalization by evaluation for simply-typed lambda-calculus with weak coproducts can be carried out in a weak bi-cartesian closed category of presheaves equipped with a monad that allows us to perform case distinction on…
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…
In this paper, we give precise mathematical form to the idea of a structure whose data and axioms are faithfully represented by a graphical calculus; some prominent examples are operads, polycategories, properads, and PROPs. Building on the…
The variant of calculation of functions of set and their application is offered. In particular: the new measure of system of sets generalizing classical concept of a measure is entered; the variation of set that has allowed to construct a…
Computational effects are commonly modelled by monads, but often a monad can be presented by an algebraic theory of operations and equations. This talk is about monads and algebraic theories for languages for inference, and their…
Selective rationalization has become a common mechanism to ensure that predictive models reveal how they use any available features. The selection may be soft or hard, and identifies a subset of input features relevant for prediction. The…
The non-empty finite subsets of a multiplicatively written monoid form a monoid under setwise multiplication. The same holds for finite subsets containing the identity element. Partly due to their unusual arithmetic properties, these…
Modal logic is a paradigm for several useful and applicable formal systems in computer science. It generally retains the low complexity of classical propositional logic, but notable exceptions exist in the domains of description, temporal,…
Regular languages -- the languages accepted by deterministic finite automata -- are known to be precisely the languages recognized by finite monoids. This characterization is the origin of algebraic language theory. In this paper, we…
We introduce a functorial construction which, from a monoid, produces a set-operad. We obtain new (symmetric or not) operads as suboperads or quotients of the operad obtained from the additive monoid. These involve various familiar…
Partial Combinatory Algebras (PCAs) provide a foundational model of the untyped $\lambda$-calculus and serve as the basis for many notions of computability, such as realizability theory. However, PCAs support a very limited notion of…
It came to the attention of myself and the coauthors of (S., Rozowski, Silva, Rot, 2022) that a number of process calculi can be obtained by algebraically presenting the branching structure of the transition systems they specify. Labelled…
Monadic decomposibility --- the ability to determine whether a formula in a given logical theory can be decomposed into a boolean combination of monadic formulas --- is a powerful tool for devising a decision procedure for a given logical…
Though modern neural networks have achieved impressive performance in both vision and language tasks, we know little about the functions that they implement. One possibility is that neural networks implicitly break down complex tasks into…
Emerging computational paradigms, such as probabilistic and hybrid programming, introduce new primitive operations that often need to be combined with classic programming constructs. However, it still remains a challenge to provide a…
Abstract. This article determines relations between two notions concerning monoids: factorability structure, introduced to simplify the bar complex; and quadratic normalisation, introduced to generalise quadratic rewriting systems and…
Generalized operads, also called generalized multicategories and $T$-monoids, are defined as monads within a Kleisli bicategory. With or without emphasizing their monoidal nature, generalized operads have been considered by numerous authors…
In this paper, we present an Agda formalization of a normalizer for simply-typed lambda terms. The normalizer consists of two coinductively defined functions in the delay monad: One is a standard evaluator of lambda terms to closures, the…
We introduce the $\mathcal{T}$-construction, an endofunctor on the category of generalized operads as a general mechanism by which various notions of plethystic substitution arise from more ordinary notions of substitution. In the special…