Summary: Axioms for Definability and Full Completeness
Samson Abramsky
May 7, 1999
1 Introduction
The term ``full abstraction'' was coined by Robin Milner in [Mil75]. In 1977 two seminal
papers on the programming language PCF, by Milner and Plotkin, appeared in Theoretical
Computer Science [Mil77, Plo77]. These papers initiated an extensive body of work centering
on the Full Abstraction problem for PCF (see [BCL86, Cur93, Ong95] for surveys).
The importance of full abstraction for the semantics of programming languages is that it
is one of the few quality filters we have. Specifically, it provides a clear criterion for assessing
how definitive a semantic analysis of some language is. It must be admitted that to date
the quest for fully abstract models has not yielded many obvious applications; but it has
generated much of the deepest work in semantics. Perhaps it is early days yet.
Recently, game semantics has been used to give the first syntax­independent constructions
of fully abstract models for a number of programming languages, including PCF [AJM96,
HO96, Nic94], richer functional languages [AM95, McC96b, McC96a, HY97], and languages
with non­functional features such as reference types and non­local control constructs [AM97c,
AM97b, AM97a, Lai97]. A noteworthy feature is that the key definability results for the
richer languages are proved by a reduction to definability for the functional fragment, using
a technique of factorization theorems. Thus the results originally obtained for PCF prove to

Source: Abramsky, Samson - Computing Laboratory, University of Oxford

Collections: Computer Technologies and Information Sciences