Topology via logic
A semantics for complex objects and approximate answers
Journal of Computer and System Sciences
Handbook of theoretical computer science (vol. B)
Exact real arithmetic formulating real numbers as functions
Research topics in functional programming
Theoretical Computer Science
ESOP '90 Selected papers from the symposium on 3rd European symposium on programming
Handbook of logic in computer science (vol. 1)
Handbook of logic in computer science (vol. 3)
Recursive characterization of computable real-valued functions and relations
Theoretical Computer Science - Special issue on real numbers and computers
PCF extended with real numbers
Theoretical Computer Science - Special issue on real numbers and computers
Lazy computation with exact real numbers
ICFP '98 Proceedings of the third ACM SIGPLAN international conference on Functional programming
Induction and recursion on the partial real line with applications to Real PCF
Theoretical Computer Science - Special issue on real numbers and computers
An abstract data type for real numbers
Theoretical Computer Science
Computable analysis: an introduction
Computable analysis: an introduction
Exact real number computations relative to hereditarily total functionals
Theoretical Computer Science
Power Domains and Predicate Transformers: A Topological View
Proceedings of the 10th Colloquium on Automata, Languages and Programming
Semantics of Exact Real Arithmetic
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
On the non-sequential nature of the interval-domain model of real-number computation
Mathematical Structures in Computer Science
Sequentiality and Piecewise-affinity in Segments of Real-PCF
Electronic Notes in Theoretical Computer Science (ENTCS)
Sequential Real Number Computation and Recursive Relations
Electronic Notes in Theoretical Computer Science (ENTCS)
First-Order Universality for Real Programs
CiE '09 Proceedings of the 5th Conference on Computability in Europe: Mathematical Theory and Computational Practice
A denotational semantics for total correctness of sequential exact real programs
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
From coinductive proofs to exact real arithmetic
CSL'09/EACSL'09 Proceedings of the 23rd CSL international conference and 18th EACSL Annual conference on Computer science logic
CiE'10 Proceedings of the Programs, proofs, process and 6th international conference on Computability in Europe
Semantical proofs of correctness for programs performing non-deterministic tests on real numbers
Mathematical Structures in Computer Science
Minlog: a tool for program extraction supporting algebras and coalgebras
CALCO'11 Proceedings of the 4th international conference on Algebra and coalgebra in computer science
Hi-index | 5.23 |
We study a programming language with a built-in ground type for real numbers. In order for the language to be sufficiently expressive but still sequential, we consider a construction proposed by Boehm and Cartwright. The non-deterministic nature of the construction suggests the use of powerdomains in order to obtain a denotational semantics for the language. We show that the construction cannot be modelled by the Plotkin or Smyth powerdomains, but that the Hoare powerdomain gives a computationally adequate semantics. As is well known, Hoare semantics can be used in order to establish partial correctness only. Since computations on the reals are infinite, one cannot decompose total correctness into the conjunction of partial correctness and termination as is traditionally done. We instead introduce a suitable operational notion of strong convergence and show that total correctness can be proved by establishing partial correctness (using denotational methods) and strong convergence (using operational methods). We illustrate the technique with a representative example.