…It's in words that the magic
is—Abracadabra, Open Sesame, and the rest—but the magic
words in one story aren't magical in the next. The real magic is to
understand which words work, and when, and for what; the trick is to learn
…And those words are made from the letters of our
alphabet: a couple-dozen squiggles we can draw with the pen. This is
the key! And the treasure, too, if we can only get our hands on it!
It's as if—as if the key to the treasure is
In our study of program design, we have seen that expert programmers
control the complexity of their designs with the same general
techniques used by designers of all complex systems. They combine
primitive elements to form compound objects, they abstract compound
objects to form higher-level building blocks, and they preserve
modularity by adopting appropriate large-scale views of system
structure. In illustrating these techniques, we have used
as a language for describing processes and for constructing computational
data objects and processes to model complex phenomena in the real world.
However, as we confront increasingly complex problems, we will find that
or indeed any fixed programming language, is not sufficient for our needs.
We must constantly turn to new languages in order to express our ideas more
effectively. Establishing new languages is a powerful strategy for
controlling complexity in engineering design; we can often enhance our
ability to deal with a complex problem by adopting a new language that
enables us to describe (and hence to think about) the problem in a different
way, using primitives, means of combination, and means of abstraction that
are particularly well suited to the problem at hand.
Programming is endowed with a multitude of languages. There are
physical languages, such as the
machine languages for particular
computers. These languages are concerned with the representation of
data and control in terms of individual bits of storage and primitive
machine instructions. The machine-language programmer is concerned
with using the given hardware to erect systems and utilities for the
efficient implementation of resource-limited computations. High-level
languages, erected on a machine-language substrate, hide concerns
about the representation of data as collections of bits and the
representation of programs as sequences of primitive instructions.
These languages have means of combination and abstraction, such as
that are appropriate to the larger-scale organization of systems.
new languages—plays an important role in all branches of engineering
design. It is particularly important to computer programming, because
in programming not only can we formulate new languages but we can also
implement these languages by constructing evaluators. An
evaluator (or interpreter) for a programming language is a
that, when applied to
a statement or expression
of the language, performs the actions required to evaluate that
It is no exaggeration to regard this as the most fundamental idea in
The evaluator, which determines the meaning of
expressions in a programming language, is just another program.
To appreciate this point is to change our images of ourselves as
programmers. We come to see ourselves as designers of languages,
rather than only users of languages designed by others.
In fact, we can regard almost any program as the evaluator for some
language. For instance, the polynomial manipulation system of
[2.5.3] embodies the rules of
polynomial arithmetic and implements them in terms of operations on
list-structured data. If we augment this system with
to read and print polynomial expressions, we have the core of a
special-purpose language for dealing with problems in symbolic mathematics.
The digital-logic simulator of
section [3.3.4] and the constraint
propagator of section [3.3.5] are legitimate
languages in their own right, each with its own primitives, means of
combination, and means of abstraction. Seen from this perspective, the
technology for coping with large-scale computer systems merges with the
technology for building new computer languages, and
computer science itself becomes no more (and no less) than the discipline
of constructing appropriate descriptive languages.
We now embark on a tour of the technology by which languages are
established in terms of other languages. In this chapter we shall use
as a base, implementing evaluators as
Lisp is particularly well suited to this task, because of its ability
to represent and manipulate symbolic expressions.
We will take the first step in understanding how languages are implemented
by building an evaluator for
The language implemented by our evaluator will be a subset of
the Scheme dialect of Lisp that we use in this
Although the evaluator described in this chapter is written for a
dialect of Lisp,
it contains the essential structure of an evaluator for any
designed for writing programs for a sequential machine. (In fact, most
language processors contain, deep within them, a little
The evaluator has been simplified for the purposes of illustration and
discussion, and some features have been left out that would be
important to include in a production-quality
system. Nevertheless, this simple evaluator is adequate to execute most of
the programs in this book.
An important advantage of making the evaluator accessible as a
program is that we can implement alternative evaluation rules by describing
these as modifications to the evaluator program. One place where we can use
this power to good effect is to gain extra control over the ways in which
computational models embody the notion of time, which was so central to the
discussion in chapter
. There, we mitigated some of the complexities
of state and assignment by using streams to decouple the representation of
time in the world from time in the computer. Our stream programs, however,
were sometimes cumbersome, because they were constrained by the
applicative-order evaluation of
In section [4.2], we'll change
the underlying language to provide for a more elegant approach, by modifying
the evaluator to provide for normal-order evaluation.
[4.3] implements a
more ambitious linguistic change, whereby statements and expressions
have many values, rather than just a single value. In this language of
nondeterministic computing, it is natural to express processes that
generate all possible values for statements and expressions and then search
for those values that satisfy certain constraints. In terms of models of
computation and time, this is like having time branch into a set of
possible futures and then searching for appropriate time
lines. With our nondeterministic evaluator, keeping track of multiple values
and performing searches are handled automatically by the underlying
mechanism of the language.
[4.4] we implement a
logic-programming language in which knowledge is expressed in terms
of relations, rather than in terms of computations with inputs and outputs.
Even though this makes the language drastically different from
or indeed from any conventional language, we will see that
the logic-programming evaluator shares the essential structure of the