Related papers: Handling Algebraic Effects
As dynamic and control systems become more complex, relying purely on numerical computations for systems analysis and design might become extremely expensive or totally infeasible. Computer algebra can act as an enabler for analysis and…
One of the fundamental results in computability is the existence of well-defined functions that cannot be computed. In this paper we study the effects of data representation on computability; we show that, while for each possible way of…
One can perform equational reasoning about computational effects with a purely functional programming language thanks to monads. Even though equational reasoning for effectful programs is desirable, it is not yet mainstream. This is partly…
Choreographic programming (CP) is a paradigm for programming distributed applications as single, unified programs, called choreographies, that are then compiled to node-local programs via endpoint projection (EPP). Recently, library-level…
Compositionality is a key property for dealing with complexity, which has been studied from many points of view in diverse fields. Particularly, the composition of individual computations (or programs) has been widely studied almost since…
An often used model for quantum theory is to associate to every physical system a C*-algebra. From a physical point of view it is unclear why operator algebras would form a good description of nature. In this paper, we find a set of…
By considering generalized logarithm and exponential functions used in nonextensive statistics, the four usual algebraic operators : addition, subtraction, product and division, are generalized. The properties of the generalized operators…
Many computer algebra systems have more than 1000 built-in functions, making expertise difficult. Using mock dialog boxes, this article describes a proposed interactive general-purpose wizard for organizing optional transformations and…
Effect algebras were introduced as an abstract algebraic model for Hilbert space effects representing quantum mechanical measurements. We study additional structures on an effect algebra $E$ that enable us to define spectrality and spectral…
In computer science, especially when dealing with quantum computing or other non-standard models of computation, basic notions in probability theory like "a predicate" vary wildly. There seems to be one constant: the only useful example of…
Convolution is a ubiquitous operation in mathematics and computing. The Kripke semantics for substructural and interval logics motivates its study for quantale-valued functions relative to ternary relations. The resulting notion of…
All operator algebras have (not necessarily irreducible) boundary representations. A unital operator algebra has enough such boundary representations to generate its C*-envelope.
Effect algebras form an algebraic formalization of the logic of quantum mechanics. For lattice effect algebras E we investigate a natural implication and prove that the implication reduct of E is term equivalent to E. Then we present a…
In this article, we only consider finite effect algebras. We define the concepts of classical and quantum effect algebras and show that an effect algebra $E$ is classical if and only if there exists an observable that measures every effect…
Combining local exceptions and first class continuations leads to programs with complex control flow, as well as the possibility of expressing powerful constructs such as resumable exceptions. We describe and compare games models for a…
Some effects are considered to be higher-level than others. High-level effects provide expressive and succinct abstraction of programming concepts, while low-level effects allow more fine-grained control over program execution and…
Dynamic evaluation is a paradigm in computer algebra which was introduced for computing with algebraic numbers. In linear algebra, for instance, dynamic evaluation can be used to apply programs which have been written for matrices with…
Statistics and Optimization are foundational to modern Machine Learning. Here, we propose an alternative foundation based on Abstract Algebra, with mathematics that facilitates the analysis of learning. In this approach, the goal of the…
Systems of cooperation and interaction are usually studied in the context of real or complex vector spaces. Additional insight, however, is gained when such systems are represented in vector spaces with multiplicative structures, i.e., in…
Effect handlers have been gathering momentum as a mechanism for modular programming with user-defined effects. Effect handlers allow for non-local control flow mechanisms such as generators, async/await, lightweight threads and coroutines…