Related papers: A Diagrammatic Calculus for Algebraic Effects

An abstract mathematical framework is presented in this paper as a unification of several deformed or generalized algebra proposed recently in the context of generalized statistical theories intended to treat certain complex thermodynamic…

Effect handlers are a powerful abstraction for defining, customising, and composing computational effects. Statically ensuring that all effect operations are handled requires some form of effect system, but using a traditional effect system…

We introduce the calculus of neo-Peircean relations, a string diagrammatic extension of the calculus of binary relations that has the same expressivity as first order logic and comes with a complete axiomatisation. The axioms are obtained…

This paper presents the Functional Machine Calculus (FMC) as a simple model of higher-order computation with "reader/writer" effects: higher-order mutable store, input/output, and probabilistic and non-deterministic computation. The FMC…

This talk describes how a combination of symbolic computation techniques with first-order theorem proving can be used for solving some challenges of automating program analysis, in particular for generating and proving properties about the…

We introduce sound and complete labelled sequent calculi for the basic normal non-distributive modal logic L and some of its axiomatic extensions, where the labels are atomic formulas of the first order language of enriched formal contexts,…

This paper shows how to derive nested calculi from labelled calculi for propositional intuitionistic logic and first-order intuitionistic logic with constant domains, thus connecting the general results for labelled calculi with the more…

Being inspired by phasor analysis in linear circuit theory, and its algebraic counterpart - the AC-(operational)-calculus for sinusoids developed by W. Marten and W. Mathis - we define a complex structure on several spaces of real-valued…

There are versions of "calculus" in many settings, with various mixtures of algebra and analysis. In these informal notes we consider a few examples that suggest a lot of interesting questions.

The do-calculus is a well-known deductive system for deriving connections between interventional and observed distributions, and has been proven complete for a number of important identifiability problems in causal inference. Nevertheless,…

Determining identifiability of causal effects from observational data under latent confounding is a central challenge in causal inference. For linear structural causal models, identifiability of causal effects is decidable through symbolic…

In this paper, we first summarize the existing algorithms for computing all the generalized asymptotes of a plane algebraic curve implicitly or parametrically defined. From these previous results, we derive a method that allows to easily…

We explain how to compute in the algebraic closure of a valued field. These computations heavily rely on the \NPAz. They are made in the same spirit as the dynamic algebraic closure of a field. They give a concrete content to the theorem…

Algebraic lambda-calculi have been studied in various ways, but their semantics remain mostly untouched. In this paper we propose a semantic analysis of a general simply-typed lambda-calculus endowed with a structure of vector space. We…

These course notes are about computing modular forms and some of their arithmetic properties. Their aim is to explain and prove the modular symbols algorithm in as elementary and as explicit terms as possible, and to enable the devoted…

This note is about using computational effects for scalability. With this method, the specification gets more and more complex while its semantics gets more and more correct. We show, from two fundamental examples, that it is possible to…

Algebraic effect handlers are becoming an increasingly popular way of structuring effectful computations, and their performance is often a concern. One of the proposed approaches towards efficient compilation is tracking effect information…

Our goal is to define an algebraic language for reasoning about non-deterministic computations. Towards this goal, we introduce an algebra of string-to-string transductions. Specifically, it is an algebra of partial functions on words over…

We present a system for the investigation of computational properties of categorial grammar parsing based on a labelled analytic tableaux theorem prover. This proof method allows us to take a modular approach, in which the basic grammar can…

Recently, we have proposed a new diffusive representation for fractional derivatives and, based on this representation, suggested an algorithm for their numerical computation. From the construction of the algorithm, it is immediately…