My aim is to show that the heavenly machine is not a kind of divine, live being, but a kind of clockwork (and he who believes that a clock has soul attributes the maker's glory to the work), insofar as nearly all the manifold motions are caused by a most simple and material force, just as all motions of the clock are caused by a single weight.Johannes Kepler letter to Herwart von Hohenburg, 1605
We began this book by studying processes and by describing processes in terms of procedures functions written in Lisp. JavaScript. To explain the meanings of these procedures, functions, we used a succession of models of evaluation: the substitution model of chapter 1, the environment model of chapter 3, and the metacircular evaluator of chapter 4. Our examination of the metacircular evaluator, in particular, dispelled much of the mystery of how Lisp-like languages are interpreted. JavaScript-like languages are interpreted. But even the metacircular evaluator leaves important questions unanswered, because it fails to elucidate the mechanisms of control in a Lisp JavaScript system. For instance, the evaluator does not explain how the evaluation of a subexpression manages to return a value to the expression that uses this value, nor does the evaluator explain how some recursive procedures generate iterative processes (that is, are evaluated using constant space) whereas other recursive procedures generate recursive processes. These questions remain unanswered because the metacircular evaluator is itself a Lisp program and hence inherits the control structure of the underlying Lisp system. In order to provide a more complete description of the control structure of the Lisp evaluator, we must work at a more primitive level than Lisp itself. Also, the evaluator does not explain how some recursive functions can generate iterative processes (that is, be evaluated using constant space) whereas other recursive functions will generate recursive processes.[1] This chapter addresses both of these issues.
In this chapter we
We
will describe processes in terms of the step-by-step
operation of a traditional computer. Such a computer, or
register machine, sequentially executes
instructions that
manipulate the contents of a fixed set of storage elements called
registers. A typical register-machine instruction applies a
primitive operation to the contents of some registers and assigns the
result to another register. Our descriptions of processes executed by
register machines will look very much like machine-language
programs for traditional computers. However, instead of focusing on
the machine language of any particular computer, we will examine
several
Lisp
JavaScript
procedures
functions
and design a specific register machine to
execute each
procedure.
function.
Thus, we will approach our task from the
perspective of a hardware architect rather than that of a
machine-language computer programmer. In designing register machines,
we will develop mechanisms for implementing important programming
constructs such as recursion. We will also present a language for
describing designs for register machines. In
section 5.2 we will
implement a
Lisp
JavaScript
program that uses these descriptions to simulate the machines we design.
Most of the primitive operations of our register machines are very simple. For example, an operation might add the numbers fetched from two registers, producing a result to be stored into a third register. Such an operation can be performed by easily described hardware. In order to deal with list structure, however, we will also use the memory operations car, head, cdr, tail, and cons, pair, which require an elaborate storage-allocation mechanism. In section 5.3 we study their implementation in terms of more elementary operations.
In section 5.4, after we have accumulated experience formulating simple procedures functions as register machines, we will design a machine that carries out the algorithm described by the metacircular evaluator of section 4.1. This will fill in the gap in our understanding of how Scheme expressions JavaScript programs are interpreted, by providing an explicit model for the mechanisms of control in the evaluator. In section 5.5 we will study a simple compiler that translates Scheme JavaScript programs into sequences of instructions that can be executed directly with the registers and operations of the evaluator register machine.