Related papers: A Diagrammatic Calculus for Algebraic Effects

In this note, we establish some new results on some special types of function algebras and also give new proofs to some existing ones

We extend the signal flow calculus---a compositional account of the classical signal flow graph model of computation---to encompass affine behaviour, and furnish it with a novel operational semantics. The increased expressive power allows…

Effectus theory is a new branch of categorical logic that aims to capture the essentials of quantum logic, with probabilistic and Boolean logic as special cases. Predicates in effectus theory are not subobjects having a Heyting algebra…

Inspired by some new advances on normal factor graphs (NFGs), we introduce NFGs as a simple and intuitive diagrammatic approach towards encoding some concepts from linear algebra. We illustrate with examples the workings of such an approach…

We set up a left ring of fractions over a certain ring of boundary problems for linear ordinary differential equations. The fraction ring acts naturally on a new module of generalized functions. The latter includes an isomorphic copy of the…

Obtaining a non-parametric expression for an interventional distribution is one of the most fundamental tasks in causal inference. Such an expression can be obtained for an identifiable causal effect by an algorithm or by manual application…

We provide an effect system CatEff based on a category-graded extension of algebraic theories that correspond to category-graded monads. CatEff has category-graded operations and handlers. Effects in CatEff are graded by morphisms of the…

We propose an approach to image processing related to algebraic operators acting in the space of images. In view of the interest in the applications in optics and computer science, mathematical aspects of the paper have been simplified as…

Incremental computation has recently been studied using the concepts of change structures and derivatives of programs, where the derivative of a function allows updating the output of the function based on a change to its input. We…

We show that, when the actions of a Mazurkiewicz trace are considered not merely as atomic (i.e., mere names) but transformations from a specified type of inputs to a specified type of outputs, we obtain a novel notion of presentation for…

We offer a simple graphical representation for proofs of intuitionistic logic, which is inspired by proof nets and interaction nets (two formalisms originating in linear logic). This graphical calculus of proofs inherits good features from…

This paper is concerned with graphical criteria that can be used to solve the problem of identifying casual effects from nonexperimental data in a causal Bayesian network structure, i.e., a directed acyclic graph that represents causal…

In this Master of Science Thesis I introduce geometric algebra both from the traditional geometric setting of vector spaces, and also from a more combinatorial view which simplifies common relations and operations. This view enables us to…

Influence diagrams are a directed graph representation for uncertainties as probabilities. The graph distinguishes between those variables which are under the control of a decision maker (decisions, shown as rectangles) and those which are…

This paper proposes a new category theoretic account of equationally axiomatizable classes of algebras. Our approach is well-suited for the treatment of algebras equipped with additional computationally relevant structure, such as ordered…

Quantum effects play an important role in quantum measurement theory. The set of all quantum effects can be organized into an algebraical structure called effect algebra. In this paper, we study various topologies on the Hilbert space…

Causal structure learning from observational data remains a non-trivial task due to various factors such as finite sampling, unobserved confounding factors, and measurement errors. Constraint-based and score-based methods tend to suffer…

Algebraic effects and handlers are a powerful abstraction to build non-local control-flow mechanisms such as resumable exceptions, lightweight threads, co-routines, generators, and asynchronous I/O. All of such features have very evolved…

We provide a Lawvere-style definition for partial theories, extending the classical notion of equational theory by allowing partially defined operations. As in the classical case, our definition is syntactic: we use an appropriate class of…

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…