## Towards a Semantics of Emerald Expressed in Map Theory

Klaus Grue
PDF.

Preseented at the ECOOP'94 workshop on logical foundations of object
oriented programming, Bologna, Italy, 1994.

### Abstract

This paper presents a semantics for a subset of an object oriented, concurrent
and distributed language with Emerald as the chosen example. The concurrent and
distributed aspects posses particular problems, and the paper focuses on these
aspects. In particular the paper covers parallelism in which a created process
can continue to run after the creating process halts. The semantics is presented
in a continuation passing style in map theory.

Map theory is a foundation of mathematics with the same expressive power
(w.r.t.\ consistency) as set theory, but it builds upon $\lambda$-calculus and
functions instead of logic and sets. It allows unlimited recursion which,
combined with its expressive power, makes it ideal for expressing semantics of
programming languages.

The paper serves three purposes: First, it gives a semantics for a subset of
Emerald, which can be scaled up to cover all of Emerald. Second, it shows how
map theory can be used in definitions of semantics. Third, it shows how
distribution and parallelism can be modelled.

Klaus Grue, August 27, 1996