Results 1 
2 of
2
Applications of the KleeneKreisel Density Theorem to Theoretical Computer Science
, 2006
"... The KleeneKreisel density theorem is one of the tools used to investigate the denotational semantics of programs involving higher types. We give a brief introduction to the classical density theorem, then show how this may be generalized to set theoretical models for algorithms accepting real numbe ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
The KleeneKreisel density theorem is one of the tools used to investigate the denotational semantics of programs involving higher types. We give a brief introduction to the classical density theorem, then show how this may be generalized to set theoretical models for algorithms accepting real numbers as inputs and finally survey some recent applications of this generalization. 1
A Extensional HigherOrder Logic Programming
"... We propose a purely extensional semantics for higherorder logic programming. In this semantics program predicates denote sets of ordered tuples, and two predicates are equal iff they are equal as sets. Moreover, every program has a unique minimum Herbrand model which is the greatest lower bound of ..."
Abstract
 Add to MetaCart
We propose a purely extensional semantics for higherorder logic programming. In this semantics program predicates denote sets of ordered tuples, and two predicates are equal iff they are equal as sets. Moreover, every program has a unique minimum Herbrand model which is the greatest lower bound of all Herbrand models of the program and the least fixedpoint of an immediate consequence operator. We also propose an SLDresolution proof system which is proven sound and complete with respect to the minimum Herbrand model semantics. In other words, we provide a purely extensional theoretical framework for higherorder logic programming which generalizes the familiar theory of classical (firstorder) logic programming.