Computability
Exact real computer arithmetic with continued fractions
LFP '88 Proceedings of the 1988 ACM conference on LISP and functional programming
Exact real arithmetic formulating real numbers as functions
Research topics in functional programming
Complexity theory of real functions
Complexity theory of real functions
Semantics of programming languages: structures and techniques
Semantics of programming languages: structures and techniques
Dynamical systems, measures, and fractals via domain theory
Information and Computation
Selected papers of the workshop on Topology and completion in semantics
Handbook of logic in computer science (vol. 3)
Power domains and iterated function systems
Information and Computation
PCF extended with real numbers
Theoretical Computer Science - Special issue on real numbers and computers
Exact real arithmetic: a case study in higher order programming
LFP '86 Proceedings of the 1986 ACM conference on LISP and functional programming
Domain Theory in Stochastic Processes
LICS '95 Proceedings of the 10th Annual IEEE Symposium on Logic in Computer Science
On the Non-sequential Nature of Domain Models of Real-number Computation
Electronic Notes in Theoretical Computer Science (ENTCS)
Constructive analysis, types and exact real numbers
Mathematical Structures in Computer Science
Electronic Notes in Theoretical Computer Science (ENTCS)
| Hi-index | 0.01 |
Real PCF is an extension of the programming language PCF with a data type for real numbers. Although a Real PCF definable real number cannot be computed in finitely many steps, it is possible to compute an arbitrarily small rational interval containing the real number in a sufficiently large number of steps. Based on a domain-theoretic approach to integration, we show how to define integration in Real PCF. We propose two approaches to integration in Real PCF. One consists in adding integration as primitive. The other consists in adding a primitive for maximization of functions and then recursively defining integration from maximization. In both cases we have an adequacy theorem for the corresponding extension of Real PCF. Moreover, based on previous work on Real PCF definability, we show that Real PCF extended with the maximization operator is universal, which implies that it is also fully abstract.