On Full Abstraction for PCF: I, II, and III

On Full Abstraction for Pcf : I , Ii And

Logical Full Abstraction and PCF

We introduce the concept of logical full abstraction, generalising the usual equational notion. We consider the language PCF and two extensions with “parallel” operations. The main result is that, for standard interpretations, logical full abstraction is equivalent to equational full abstraction together with universality; the proof involves constructing enumeration operators. We also consider ...

Full Abstraction and the Context Lemma 1

It is impossible to add a combinator to PCF to achieve full abstraction for models such asBerry's stable domains in a way analogous to the addition of the \parallel-or" combinatorthat achieves full abstraction for the familiar cpo model. In particular, we de ne a generalnotion of rewriting system of the kind used for evaluating simply typed -terms in Scott'sPCF. Any simply t...

SURVEY ON THE SENSITIVITY AND SPECIFICITY OF BETA ANGLE IN DIFFERENTIATING SKELETAL CLASS II AND III MALOCCLUSIONS FROM CLASS I

Background & Aims: A successful treatment in the field of medical sciences depends on an accurate diagnosis. In orthodontic diagnosis and treatment planning also analyzing the sagittal jaw base relationship is important. Various methods have been suggested for this. This study aimed to investigate the accuracy of beta angle in sagittal jaw base relationship diagnosis. Materials & Methods: In t...

Full abstraction for non-deterministic and probabilistic extensions of PCF I: The angelic cases

We examine several extensions and variants of Plotkin’s language PCF, including non-deterministic and probabilistic choice constructs. For each, we give an operational and a denotational semantics, and compare them. In each case, we show soundness and computational adequacy: the two semantics compute the same values at ground types. Beyond this, we establish full abstraction (the observational ...