Related papers: Handling Algebraic Effects
We propose the first framework for defining relational program logics for arbitrary monadic effects. The framework is embedded within a relational dependent type theory and is highly expressive. At the semantic level, we provide an…
In this paper, we propose an abstract definition of dependent type theories as essentially algebraic theories. One of the main advantages of this definition is its composability: simple theories can be combined into more complex ones, and…
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…
Asynchronous effects of Ahman and Pretnar complement the conventional synchronous treatment of algebraic effects with asynchrony based on decoupling the execution of algebraic operation calls into signalling that an operation's…
Motivated by the sharp contrast between classical and quantum physics as probability theories, in these lecture notes I introduce the basic notions of operator algebras that are relevant for the algebraic approach to quantum physics.…
In previous work, we proposed a logic-based framework in which computation is the execution of actions in an attempt to make reactive rules of the form if antecedent then consequent true in a canonical model of a logic program determined by…
We consider the problem of modularizing control flow in a generic abstract interpretation framework. A generic abstract interpretation framework is not truly flexible if it does not allow interpreting with different path- and…
Studies of issues related to computability and computational complexity involve the use of a model of computation. Pivotal to such a model are the computational processes considered. Processes of this kind can be described using an…
Certain operator algebras A on a Hilbert space have the property that every densely defined linear transformation commuting with A is closable. Such algebras are said to have the closability property. They are important in the study of the…
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…
This survey provides an elementary introduction to operads and to their applications in homotopical algebra. The aim is to explain how the notion of an operad was prompted by the necessity to have an algebraic object which encodes higher…
Unlike computation or the numerical analysis of differential equations, simulation does not have a well established conceptual and mathematical foundation. Simulation is an arguable unique union of modeling and computation. However,…
We show that the classical mechanics of an algebraic model are implied by its quantizations. An algebraic model is defined, and the corresponding classical and quantum realizations are given in terms of a spectrum generating algebra.…
What is Sequence Algebra? This is a question that any teacher or student of mathematics or computer science can engage with. Sequences are in Calculus, Combinatorics, Statistics and Computation. They are foundational, a step up from number…
In distributed classification, each learner observes its environment and deduces a classifier. As a learner has only a local view of its environment, classifiers can be exchanged among the learners and integrated, or merged, to improve…
Maxwell equation in geometric algebra formalism with equally weighted basic solutions is subjected to continuously acting Clifford translation. The received states, operators acting on observables, are analyzed with different values of the…
This paper presents an algebraic theory of instruction sequences with instructions for Turing tapes as basic instructions, the behaviours produced by the instruction sequences concerned under execution, and the interaction between such…
Biological systems exhibit processes on a wide range of time and length scales. This work demonstrates that models, wherein the interaction between system constituents is captured by algebraic operations, inherently allow for successive…
The delay monad provides a way to introduce general recursion in type theory. To write programs that use a wide range of computational effects directly in type theory, we need to combine the delay monad with the monads of these effects.…
The present text surveys some relevant situations and results where basic Module Theory interacts with computational aspects of operator algebras. We tried to keep a balance between constructive and algebraic aspects.