Induction and recursion on the partial real line with applications to Real PCF (1997)
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| Venue: | Theoretical Computer Science |
| Citations: | 5 - 1 self |
BibTeX
@ARTICLE{Escardo97inductionand,
author = {Martín Hötzel Escardo and Thomas Streicher},
title = {Induction and recursion on the partial real line with applications to Real PCF},
journal = {Theoretical Computer Science},
year = {1997},
volume = {210},
pages = {157}
}
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Abstract
The partial real line is an extension of the Euclidean real line with partial real numbers, which has been used to model exact real number computation in the programming language Real PCF. We introduce induction principles and recursion schemes for the partial unit interval, which allow us to verify that Real PCF programs meet their specification. They resemble the so-called Peano axioms for natural numbers. The theory is based on a domain-equation-like presentation of the partial unit interval. The principles are applied to show that Real PCF is universal in the sense that all computable elements of its universe of discourse are definable. These elements include higher-order functions such as integration operators. Keywords: Induction, coinduction, exact real number computation, domain theory, Real PCF, universality. Introduction The partial real line is the domain of compact real intervals ordered by reverse inclusion [28,21]. The idea is that singleton intervals represent total rea...
