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Trees and Dags An Introduction

Summary: Chapter 5
Trees and Dags
An Introduction
to Separation Logic
c 2009 John C. Reynolds
February 12, 2009
In this chapter, we consider various representations of abstract tree-like
data. In general, such data are elements of (possibly many-sorted) 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 "S-expressions",
which were the form of data used in early LISP [99]. The set S-exps of
S-expressions is the least set such that
S-exps iff Atoms
or = (0 1) where 0, 1 S-exps.
Here atoms are values that are not addresses, while (0 1) is the LISP nota-
tion for an ordered pair. (Mathematically, S-expressions are the initial lawless
algebra with an infinite number of constants and one binary operation.)
5.1 Trees
We use the word "tree" to describe a representation of S-expressions by


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


Collections: Mathematics