Coinduction for Exact Real Number Computation

Comparing Functional Paradigms for Exact Real-Number Computation

We compare the definability of total functionals over the reals in two functional-programming approaches to exact real-number computation: the extensional approach, in which one has an abstract datatype of real numbers; and the intensional approach, in which one encodes real numbers using ordinary datatypes. We show that the type hierarchies coincide up to second-order types, and we relate this...

Certified Exact Transcendental Real Number Computation in Coq

Reasoning about real number expressions in a proof assistant is challenging. Several problems in theorem proving can be solved by using exact real number computation. I have implemented a library for reasoning and computing with complete metric spaces in the Coq proof assistant and used this library to build a constructive real number implementation including elementary real number functions an...

Exact real arithmetic for interval number systems

An interval number system is given by an initial interval cover of the extended real line and by a finite system of nonnegative Möbius transformations. Each sequence of transformations applied to an initial interval determines a sequence of nested intervals whose intersection contains a unique real number. We adapt in this setting exact real algorithms which compute arithmetical operations to a...

PCF extended with real numbers : a domain-theoretic approach to higher-order exact real number computation

We develop a theory of higher-order exact real number computation based on Scott domain theory. Our main object of investigation is a higher-order functional programming language, Real PCF, which is an extension of PCF with a data type for real numbers and constants for primitive real functions. Real PCF has both operational and denotational semantics, related by a computational adequacy proper...

A GMP-FC++ Implementation of a Calculator for Exact Real Number Computation Based on LRT