Related papers: Partiality, Revisited: The Partiality Monad as a Q…

Monads play an important role in both the syntax and semantics of modern functional programming languages. The problem of combining them has been of profound interest at least since the 90s, and different approaches have been employed to…

Probability theory can be studied synthetically as the computational effect embodied by a commutative monad. In the recently proposed Markov categories, one works with an abstraction of the Kleisli category and then defines deterministic…

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…

This paper studies the problem of testing whether a system of linear equality and inequality constraints admits a solution when the coefficients of that system may have to be estimated. We show that a wide range of inferential questions in…

It is commonly agreed that the success of future proof assistants will rely on their ability to incorporate computations within deduction in order to mimic the mathematician when replacing the proof of a proposition P by the proof of an…

The apportionment problem constitutes a fundamental problem in democratic societies: How to distribute a fixed number of seats among a set of states in proportion to the states' populations? This--seemingly simple--task has led to a rich…

Partial orders are used extensively for modeling and analyzing concurrent computations. In this paper, we define two properties of partially ordered sets: width-extensibility and interleaving-consistency, and show that a partial order can…

In combinatorics, the probabilistic method is a very powerful tool to prove the existence of combinatorial objects with interesting and useful properties. Explicit constructions of objects with such properties are often very difficult, or…

The algebraic expression $3 + 2 + 6$ can be evaluated to $11$, but it can also be partially evaluated to $5 + 6$. In categorical algebra, such partial evaluations can be defined in terms of the $1$-skeleton of the bar construction for…

Many vision-related tasks benefit from reasoning over multiple modalities to leverage complementary views of data in an attempt to learn robust embedding spaces. Most deep learning-based methods rely on a late fusion technique whereby…

We examine the convergence properties of sequences of nonnegative real numbers that satisfy a particular class of recursive inequalities, from the perspective of proof theory and computability theory. We first establish a number of results…

We introduce the abstract notions of "monadic operational semantics", a small-step semantics where computational effects are modularly modeled by a monad, and "type-and-effect system", including "effect types" whose interpretation lifts…

Real numbers in constructive mathematics have always seemed to require compromises of one form or another. Classical proofs of Cauchy completeness require countable choice, Bishop's setoid construction introduces persistent bookkeeping…

We make use of a higher version of the Yoneda embedding to construct, from a given quasicategory, a tribe, as a subcategory of a well-behaved simplicial model category, that presents the same $(\infty,1)$-category as the former…

We present a straightforward embedding of quantified multimodal logic in simple type theory and prove its soundness and completeness. Modal operators are replaced by quantification over a type of possible worlds. We present simple…

First-order temporal logics are notorious for their bad computational behaviour. It is known that even the two-variable monadic fragment is highly undecidable over various linear timelines, and over branching time even one-variable…

We study concrete sheaf models for a call-by-value higher-order language with recursion. Our family of sheaf models is a generalization of many examples from the literature, such as models for probabilistic and differentiable programming,…

Continuous first-order logic is used to apply model-theoretic analysis to analytic structures (e.g. Hilbert spaces, Banach spaces, probability spaces, etc.). Classical computable model theory is used to examine the algorithmic structure of…

The set $M$ of $d\times d$ Hermitian matrices (observables) is studied as a partially ordered set with the L\"{o}wner partial order. Upper and lower sets in it, define the concept of cumulativeness (used mainly with scalar quantities) in…

Graded monads refine traditional monads using effect annotations in order to describe quantitatively the computational effects that a program can generate. They have been successfully applied to a variety of formal systems for reasoning…