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Trees and Dags An Introduction

Summary: Chapter 5
Trees and Dags
An Introduction
to Separation Logic
#2007 John C. Reynolds
February 28, 2007
In this chapter, we consider various representations of abstract tree­like
data. In general, such data are elements of (possibly many­sorted) initial or
free algebras without laws. To illustrate the use of separation logic, however,
it is simplest to limit our discussion to a particular form of abstract data.
For this purpose, as discussed in Section 1.7, we will use ``S­expressions'',
which were the form of data used in early LISP [43]. The set S­exps of
S­expressions is the least set such that
# # S­exps i# # # Atoms
or # = (# 0 · # 1 ) where # 0 , # 1 # S­exps.
Here atoms are values that are not addresses, while (# 0 · # 1 ) is the LISP nota­
tion for an ordered pair. (Mathematically, S­expressions are the initial lawless
algebra with an infinite number of constants and one binary operation.)
5.1 Trees


Source: Andrews, Peter B. - Department of Mathematical Sciences, Carnegie Mellon University


Collections: Mathematics