Exact real arithmetic formulating real numbers as functions
Research topics in functional programming
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
Computable analysis: an introduction
Computable analysis: an introduction
Domain-theoretic Foundations of Functional Programming
Domain-theoretic Foundations of Functional Programming
Semantics of a sequential language for exact real-number computation
Theoretical Computer Science
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We consider a functional language that performs non-deterministic tests on real numbers and define a denotational semantics for that language based on Smyth powerdomains. The semantics is only an approximate one because the denotation of a program for a real number may not be precise enough to tell which real number the program computes. However, for many first-order total functions f : n → , there exists a program for f whose denotation is precise enough to show that the program indeed computes the function f. In practice, it is not difficult to find programs like this that possess a faithful denotation. We provide a few examples of such programs and the corresponding proofs of correctness.