Semantics of a sequential language 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...

A Denotational Semantics for Total Correctness of Sequential Exact Real Programs

We provide a denotational model for a functional programming language for exact real number computation. A well known difficulty in real number computation is that the tests x = y and x ≤ y are undecidable and hence cannot be used to control the execution flow of programs. One solution, proposed by Boehm and Cartwright, is to use a non-deterministic test. For any two rational numbers p < q and ...

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

Semantics of Exact Real Arithmetic

In this paper, we incorporate a representation of the non-negative extended real numbers based on the composition of linear fractional transformations with non-negative integer coeecients into the Programming Language for Computable Functions (PCF) with products. We present two models for the extended language and show that they are computationally adequate with respect to the operational seman...