Handbook of logic in computer science (vol. 3)
PCF extended with real numbers
Theoretical Computer Science - Special issue on real numbers and computers
Induction and recursion on the partial real line with applications to Real PCF
Theoretical Computer Science - Special issue on real numbers and computers
Information and Computation - Special issue: LICS 1996—Part 1
Exact real number computations relative to hereditarily total functionals
Theoretical Computer Science
Lazy Functional Algorithms for Exact Real Functionals
MFCS '98 Proceedings of the 23rd International Symposium on Mathematical Foundations of Computer Science
The realizability approach to computable analysis and topology
The realizability approach to computable analysis and topology
Topological and limit-space subcategories of countably-based equilogical spaces
Mathematical Structures in Computer Science
Theoretical Computer Science - Mathematical foundations of programming semantics
Affine functions and series with co-inductive real numbers
Mathematical Structures in Computer Science
Constructive analysis, types and exact real numbers
Mathematical Structures in Computer Science
The sequential topology on is not regular
Mathematical Structures in Computer Science
A Nonstandard Characterisation of the Type-structure of Continuous Functionals Over the Reals
Electronic Notes in Theoretical Computer Science (ENTCS)
Electronic Notes in Theoretical Computer Science (ENTCS)
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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 fact to an analogous comparison of type hierarchies over the external and internal real numbers in Dana Scott's category of equilogical spaces. We do not know whether similar coincidences hold at third-order types. However, we relate this question to a purely topological conjecture about the Kleene-Kreisel continuous functionals over the natural numbers. Finally, although it is known that, in the extensional approach, parallel primitives are necessary for programming total first-order functions, we demonstrate that, in the intensional approach, such primitives are not needed for second-order types and below.