We've gained a good understanding of assignment as a tool in modeling,
as well as an appreciation of the complex problems that assignment
raises. It is time to ask whether we could have gone about things in a
different way, so as to avoid some of these problems. In this
section, we explore an alternative approach to modeling state, based
on data structures called streams. As we shall see, streams can
mitigate some of the complexity of modeling state.
Let's step back and review where this complexity comes from. In an
attempt to model real-world phenomena, we made some apparently
reasonable decisions: We modeled real-world objects with local state
by computational objects with local variables. We identified time
variation in the real world with time variation in the computer. We
implemented the time variation of the states of the model objects in
the computer with assignments to the local variables of the model
Is there another approach? Can we avoid identifying time in the
computer with time in the modeled world? Must we make the model
change with time in order to model phenomena in a changing world?
Think about the issue in terms of mathematical functions. We can
describe the time-varying behavior of a quantity $x$ as a function of
If we concentrate on $x$ instant by instant, we think of
it as a changing quantity. Yet if we concentrate on the entire
time history of values, we do not emphasize change—the function
itself does not change.
If time is measured in discrete steps, then we can model a time function as
a (possibly infinite) sequence. In this section, we will see how to
model change in terms of sequences that represent the time histories
of the systems being modeled. To accomplish this, we introduce new
data structures called streams. From an abstract point of view,
a stream is simply a sequence. However, we will find that the
straightforward implementation of streams as lists (as in
[2.2.1]) doesn't fully reveal
the power of stream processing. As an alternative, we introduce the
delayed evaluation, which enables us to represent
very large (even infinite) sequences as streams.
Stream processing lets us model systems that have state without ever
using assignment or mutable data. This has important implications,
both theoretical and practical, because we can build models that avoid
the drawbacks inherent in introducing assignment. On the other hand,
the stream framework raises difficulties of its own, and the question
of which modeling technique leads to more modular and more easily
maintained systems remains open.