Logical Full Abstraction and PCF
John R. Longley, Gordon D. Plotkin · ERA · 2000
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 restrictions on logical complexity and on the level of types.