Real Number Computability and Domain Theory

Real Number Computability and Domain Theory

We present the different constructive definitions of real number that can be found in the literature. Using domain theory we analyse the notion of computability that is substantiated by these definitions and we give a definition of computability for real numbers and for functions acting on them. This definition of computability turns out to be equivalent to other definitions given in the litera...

Formalisation of Computability of Operators and Real-Valued Functionals via Domain Theory

A Domain-Theoretic Approach to Computability on the Real Line

In recent years, there has been a considerable amount of work on using continuous domains in real analysis. Most notably are the development of the generalized Riemann integral with applications in fractal geometry, several extensions of the programming language PCF with a real number data type, and a framework and an implementation of a package for exact real number arithmetic. Based on recurs...

Computability Theory

Computability Theory

formalisms of computability