PCF extended with real numbers
Theoretical Computer Science - Special issue on real numbers and computers
An abstract data type for real numbers
Theoretical Computer Science
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LFP '86 Proceedings of the 1986 ACM conference on LISP and functional programming
Domain representations of topological spaces
Theoretical Computer Science
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Computable analysis: an introduction
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Theoretical Computer Science
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Theoretical Computer Science
On the non-sequential nature of the interval-domain model of real-number computation
Mathematical Structures in Computer Science
Compact metric spaces as minimal-limit sets in domains of bottomed sequences
Mathematical Structures in Computer Science
Domain-theoretic Foundations of Functional Programming
Domain-theoretic Foundations of Functional Programming
Coinduction for Exact Real Number Computation
Theory of Computing Systems
Proofs and Computations
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A calculus XPCF of 1@?-sequences, which are infinite sequences of {0,1,@?} with at most one copy of bottom, is proposed and investigated. It has applications in real number computation in that the unit interval I is topologically embedded in the set @S"@?","1^@w of 1@?-sequences and a real function on I can be written as a program which inputs and outputs 1@?-sequences. In XPCF, one defines a function on @S"@?","1^@w only by specifying its behaviors for the cases that the first digit is 0 and 1. Then, its value for a sequence starting with a bottom is calculated by taking the meet of the values for the sequences obtained by filling the bottom with 0 and 1. The validity of the reduction rule of this calculus is justified by the adequacy theorem to a domain-theoretic semantics. Some example programs including addition and multiplication are shown. Expressive powers of XPCF and related languages are also investigated.