POL.txt

% Programming a Program-Oriented-Language
% Charles H. Moore
% 2011
          
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\begin{center}
\LARGE\textsf{Preface}\par
\end{center}

This is an unpublished book I wrote long ago. Just after I'd written
the first versions of Forth. Perhaps it explains the motivation behind
Forth. There is some interest in it, and publishing is no longer
relevant since I can post it on my website.

I have a typescript that I recovered from Forth, Inc long ago. I had
typed it on my Smith-Corona portable, complete with overstrikes and
annotations. It is illegible enough to discourage a casual reader, so
I'm re-keying it in HTML.

This is useful, since I used to be a good typist and that skill has
deteriorated. My fingers can use the exercise and I'm curious if I can
reduce my error rate.

I'm making minimal changes to the text; just enough to fit HTML. The
language remains quaint, ungrammatical or unclear. Any remaining typos
are modern.

-- Chuck Moore 2011

written \~ June 1970

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# Introduction

I'm not sure why you're reading this book. It's taken me a while to
discover why I'm writing it. Let's examine the title: *Programming a
Problem-Oriented-Language*. The key word is programming. I've written
many programs over the years. I've tried to write *good* programs, and
I've observed the manner in which I write them rather critically. My
goal has been to decrease the effort required and increase the quality
produced.

In the course of these observations, I've found myself making the same
mistakes repeatedly. Mistakes that are obvious in retrospect, but
difficult to recognise in context. I thought that if I wrote a
prescription for programming, I could at least remind myself of
problems. And if the result is of value to me, it should be of value to
others; if what I say is new to you, you may learn something of value;
if I cover familiar ground, you at least get a new point of view.

I've also been distressed at the lack of concern from others about
problems I consider significant. It amounts to a general indifference to
quality; a casual attitude of confidence that one's programs are pretty
good, in any case as good as necessary. I'm convinced this confidence is
misplaced. Moreover this attitude is reinforced by the massive trend to
high-level languages and a placid acceptance of their inefficiencies:
What's the use of designing a really good algorithm if the compiler's
going to botch it up anyway?

So I've written a book about programming. I have no great taste for
debating over a one-way communication link and no real interest in
convincing you that I'm right in what I say. So you'll probably find
that I'm being brusk. I'm quite likely to state bluntly something you
may take issue with. Please do! My intention is to document an approach
I've found useful, and perhaps to stimulate critical interest in
programming. If you care enough to take issue, I'm delighted.

Back to the title. What about Problem-Oriented-Language? I didn't start
out to write about that; and I'm not sure that I'm qualified to do so.
But I discovered that in order to justify what I was doing and identify
the appropriate circumstances for doing it, the term became essential.

A problem-oriented-language is a language tailored to a particular
application. To avoid that uniquely clumsy term, I'll usually substitute
*application language* as synonymous. Very often such a language isn't
recognised for what it is. For instance, if your program reads a code in
column 80 to identify an input card, you are implementing an application
language. A very crude one, a very awkward one; mostly because you
hadn't given the matter any thought. Recognising the problem, I'm sure
you can design a better solution. This book will show you how.

## The Basic Principle

We have a large number of subjects to talk about. I'm going to throw
before you a lot of techniques that you may be able to use. This is
basically the result of the nature of a digital computer: a general
purpose tool for processing information.

A computer can do anything. I hope that your realize that, providing you
allow me to define "anything", I can prove this. I mean real,
incontrovertible, mathematical-type proof. A computer cannot do
everything. I can prove this, too. But most important, with only you and
I to program it, a computer can not even do very much. This is of the
nature of an empirical discovery.

So to offer guidance when the trade-offs become obscure, I am going to
define the Basic Principle:

> Keep it Simple

As the number of capabilities you add to a program increases, the
complexity of the program increases exponentially. The problem of
maintaining compatibility among these capabilities, to say nothing of
some sort of internal consistency in the program, can easily get out of
hand. You can avoid this if you apply the Basic Principle. You may be
acquainted with an operating system that ignored the Basic Principle.

It is very hard to apply. All the pressures, internal and external,
conspire to add features to your program. After all, it only takes a
half-dozen instructions; so why not? The only opposing pressure is the
Basic Principle, and if you ignore it, there is no opposing pressure.

In order to help you apply the Basic Principle, I'm going to tell you
how many instructions you should use in some routines. And how large a
program with certain capabilities should be. These numbers are largely
machine independent; basically they measure the complexity of the task.
They are based upon routines I have used in my programs, so I can
substantiate them. Let me warn you now that I'll be talking about
programs that will fit comfortably in 4K words of core.

The Basic Principle has a corollary:

> Do Not Speculate!

Do not put code in your program that *might* be used. Do not leave hooks
on which you can hang extensions. The things you might want to do are
infinite; that means that each one has 0 probability of realization. If
you need an extension later, you can code it later - and probably do a
better job than if you did it now. And if someone else adds the
extension, will they notice the hooks you left? Will you document that
aspect of your program?

The Basic Principle has another corollary:

> Do It Yourself!

Now we get down the the nitty-gritty. This is our first clash with the
establishment. The conventional approach, enforced to a greater or
lesser extent, is that you shall use a standard subroutine. I say that
you should write your own subroutines.

Before you can write your own subroutine, you have to know how. This
means, to be practical, that you have written it before; which makes it
difficult to get started. But give it a try. After writing the same
subroutine a dozen times on as many computers and languages, you'll be
pretty good at it. If you don't plan to be programming that long, you
won't be interested in this book.

What sort of subroutines do you write for yourself? I have acquired
respect for SQRT subroutines. They're tricky things; seem to attract a
lot of talent. You can use the library routine to good advantage. Input
subroutines now. They seem to have crawled out from under a rock. I
somehow can't agree that the last word was said 15 years ago when FORMAT
statements were invented.

As I will detail later, the input routine is the most important code in
your program. After all, no one sees your program; but everyone sees
your input. To abdicate to a system subroutine that hasn't the slightest
interest in your particular problem is foolish. The same can be said for
output subroutine and disk-access subroutine.

Moreover, the task is not that great as to deter you. Although it takes
hundreds of instructions to write a general purpose subroutine, you can
do what you need with tens of instructions. In fact, I would advise
against writing a subroutine longer that a hundred instructions.

So if you want to read double-precision, complex integers; don't rely on
the COBOL input subroutine, or wait till the manufacturer revises it.
It's a lot easier to write your own.

But suppose everyone wrote their own subroutines? Isn't that a step
backward; away from the millennium when our programs are machine
independent, when we all write in the same language, maybe even on the
same computer? Let me take a stand: I can't solve the problems of the
world. With luck, I can write a good program.

## Preview

I'm going to tell you how to write a program. It is a specific program;
that is, a program with a specific structure and capabilities. In
particular, it is a program that can be expanded from simple to complex
along a well defined path, to handle a wide range of problems, likewise
varying from simple to complex. One of the problems it considers is
exactly the problem of complexity. How can you control your program so
that it doesn't grow more complicated than your application warrants?

First I'll define "input", and mention some general rules of programming
that apply to all programs, whether they have input or not. Actually we
will be almost exclusively concerned with input, so I've not much to say
about programs lacking input.

By admitting input, a program acquires a control language by which a
user can guide the program through a maze of possibilities. Naturally,
this increases the flexibility of the program, it also requires a more
complex application to justify it. However it is possible to achieve a
considerable simplification of the program, by recognising that it needs
a control language as a tool of implementation.

The next step is a problem-oriented-language. By permitting the program
to dynamically modify its control language, we mark a qualitative change
in capability. We also change our attention from the program to the
language it implements. This is an important, and dangerous, diversion.
For it's easy to lose sight of the problem amidst the beauty of the
solution.

In a sense, our program has evolved into a meta-language, which
describes a language we apply to the application. But having mentioned
meta-language, I want to explain why I won't use the term again. You see
things get pretty complicated, particularly on a philosophic level. To
precisely describe our situation requires not 2 levels of language -
language and meta-language - but a least 4 levels. To distinguish
between these levels requires subtle arguments that promote not clarity
but confusion. Moreover, the various levels can often be interchanged in
practice, which reduces the philosophic arguments to hair-splitting.

A problem-oriented-language can express any problem I've encountered.
And remember, we're not concerned with the language, but with the
program that makes the language work. By modifying the language we can
apply the same program to many applications. However there are a class
of extensions to the language that constitute another qualitative
change. They don't increase the capacity of the program, but the
increase the capability of the language. That is, they make the language
more expressive. We will consider some such extensions in Chapter 8. I
gathered them together chiefly because they share the common property
that I don't quite comprehend their potential. For example, I think the
language applies the concepts of English.

Finally, I want to describe a process whereby you can implement this
program in machine language. That is, a bootstrap technique whereby a
basic program can modify and expand itself.

I hope you find the ideas I describe of value to you. In particular, I
hope that you will agree that the program I describe has a certain
inevitability; that it must do certain things, it must do them in a
certain order, and that a certain set of conventions yield an optimal
solution.

I've gone to some lengths to simplify. I hope that you don't find too
many violations of the Basic Principle, for it's much easier to
elaborate upon a program than it is to strip it to basics. You should
feel free to build upon my basic routines, provided that you recognise
that you are adding a convenience. If you confuse what is expedient with
what is necessary, I guarantee your program will never stop growing.

You will notice a lack of flow-charts. I've never liked them, for they
seem to include a useless amount of information - either too little or
too much. Besides they imply a greater rigidity in program structure
than usually exists. I will be quite specific about what I think you
should do and how you should do it. But I will use words, and not
diagrams. I doubt that you would give a diagram the attention it
deserved, anyway. Or that I would in preparing it.

# Programs without input

The simplest possible program is one that has no input. That is a
somewhat foolish statement, but if you'll give me a chance to explain we
can establish some useful definitions.

First consider the word "input". I want to use it in a specific sense:

> Input is information that controls a program.

In particular, I do not consider as input:

  * Moving data between media within the computer. For instance,
    * copying tape onto disk, or disk into core.

  * Reading data into the computer. This is really a transfer between media:
    * from card to core.

However, data very often has input mixed with it - information that
identifies or disposes of the data. For example, a code in col. 80 might
identify a card. It is input, the rest of the card probably data.

Many programs have input of a kind I shall disregard: operating systems
use control cards to specify which files to assign, which subroutines to
collect, etc. Such information is definitely input to the operating
system. Although it may affect the operation of your program, ignore it
because it is not under your control - unless your program is the
operating system itself.

In order to sharpen your recognition of input, let me describe a program
that has input. Consider a program that fits a smooth curve through
measured data points. It needs a lot of information in order to run: the
number of data points, the spacing between points, the number of
iterations to perform, perhaps even which function to fit. This
information might be built into the program; if it is not, it must be
supplied as input. The measured data itself, the object of the entire
program, is not input; but must be accompanied by input in order to to
intelligible.

A program that has no input may be extremely complex. Lacking input
simply means the program knows what to do without being told. That built
into the code is all the information needed to run. If you are willing
to re-compile the program, you can even modify it without input.

But I'll be viewing programs from the input side. I'll be ranking
programs according to the complexity of their input and I plan to
demonstrate that a modest increase in the complexity of input can
provide a substantial decrease in the complexity of the program. From
this point of view, a program with no input is simple.

Since I'm going to be talking about input, a program without input
leaves me nothing to talk about. But I want to make some points about
programs in general, so I'll make them here. For one thing, we will be
climbing a tree. When we reach the higher branches we'll have enough
trouble keeping our balance without worrying about the roots.

## Choosing a language

We shall be less interested in computer language than most programmers.
For 3 reasons: First, we will eventually define our own
application-oriented language. How we implement that language is of
lesser concern. Second, you probably aren't in a position to pick a
language. Your installation probably has reduced your choice to nil.
Third, we won't be talking about problems at the language level.

This last comment deserves elaboration. I assume that you are already a
competent programmer. I'm not interested in teaching you how a computer
works, or how a language conceals the computer. I want to talk about
problems common to all programs in a machine-independent and
language-independent manner. I will leave to you the details of
implementation. I am not going to write a program, I am going to show
you how to write a program.

I hope that you are a good enough programmer to think in computerese.
That is, as someone discusses their application, you interpret it in
terms of computer operations: a loop here, a calculation there, a
decision . . . The details are largely irrelevant, the gross structure
of the program is of concern.

As you put more thought into the problem, you begin to relate it to your
particular machine: this data comes off tape, that loop is stopped by .
. ., this is really a 3-way branch. you modify the problem as required
by your particular hardware configuration.

Finally, you must translate your program into a particular language. You
encounter a new class of problem: your FORTRAN won't run that loop
backwards, COBOL doesn't have a 3-way branch, you couldn't access the
data that way. . . Current languages put more constraints on this last
coding process than they should.

I'll have a bit more to say about languages, but mostly we'll stay at
the most abstract level - talking computerese. We won't be talking in
meta-language exclusively. I may tell you to load an index-register or
to jump on negative and you'll have to translate that into the
equivalent for your computer and language.

Now let's look at the major failing of higher-level languages. In
attempting to achieve machine-independence and to be applicable to a
wide range of applications, they only give you access to a fraction of
the capabilities of your computer. If you compare the number of loop
control instructions on your computer to the number of loop constructs
in your language, you'll see what I mean.

Let me indulge in a 1-sentence characterization of 3 popular languages
to illustrate their restricted capabilities:

 * FORTRAN is great at evaluating complicated algebraic expressions.
 * COBOL is great a processing packed decimal data.
 * ALGOL is great a providing loops and conditional statements.

Each language can be very efficient at its sort of job. But if you want
conditional loops involving complicated decimal expressions you have a
problem.

We are going to be concerned with efficiency. We are going to do some
things that if we don't do efficiently, we can't do at all. Most of
these things will not fit in the framework of a higher-level language.
Some will; others will demand controlled use of the hardware that a
compiler doesn't permit. For example, upon entering a FORTRAN subroutine
it may save the registers it uses. If you didn't need to save them
you've wasted time and space. An ALGOL subroutine may expect registers
available that you have reserved; then you have to save them. It may
well cost you more effort to interface with the compiler than it saves
you in return.

Moreover, none of these languages are very good at moving things around.
Most statements are data transfers - count them in your latest program.
There is a profound philosophical truth concealed in how much we can
accomplish by moving numbers around. If we can move several things with
one instruction, or put the same register several places - we can't
afford not to.

You will have to code in assembler! Not the whole program, if you
insist, but the important parts that we'll be concentrating on. You
might be able to do some of these in FORTRAN, but it simply isn't worth
the effort. I'll show you where higher-level subroutines can go, and I
think you'll agree there is good reason to restrict them to that
function.

I recognise the drawbacks of assembler and chafe at them as much as
anyone. I don't like to punch and debug 10 times as many cards either.
But I will in order to get the performance I need. By the way, I will
use the word "compiler" to include assembler; we will *compile* an
assembly language program.

Later I'll show you how to write a program in a forgotten language:
machine language. By that I mean sitting at the console and entering
absolute, binary instructions with the switches. Depending on the
hardware and software available, and the nature of your application, it
may just be the best language of all.

## Choosing a computer

Of course I don't expect that you're in a position to choose a computer.
Nor am I going to discuss hardware at all. But I do have a mental image
of the kind of computer, and explaining it may help you understand some
of my comments.

Most applications can be programmed very nicely on a small computer: say
4K of 16-bit words with a typical instruction set, floating-point
hardware if needed. If, that is, the computer is augmented with random
access secondary memory, which I will call disk. The capacity of disk is
unimportant, even a small disk providing plenty for our purposes, and is
determined by the application. However, it is important to be able to
copy the disk onto another disk, or tape, for back-up. Thus I envisage a
small computer with 2 secondary memories, and of course a keyboard or
card-reader and printer or scope for input and output.

Instead of running applications in serial on a small computer, you can
run them in parallel on a large one. I see no advantage, for the amount
of core and disk you can afford to use for a single application is about
that available on a small computer. You don't gain speed, you suffer
from a complex operating system, and you have a enormous capital
investment. But the configuration I have in mind remains the same: 4K of
core, secondary memory and input/output device.

## Arrangement and formatting

Now I'm going to tell you how to write a program. Independent of
language or computer. Things you ought to be doing already, but probably
aren't because on one ever told you to. Little things. But if you don't
do them you won't have a good program; and we're going to write a good
program.

Remember the Basic Principle! If you didn't read the Introduction, do it
now.

Declare all variables. Even in FORTRAN when you don't have to. Everyone
likes to know what parameters you are using, presumably need to use;
likes to count them, to see if they could use fewer; is annoyed if you
slip one in without mentioning it.

Define everything you can before you reference it. Even in FORTRAN when
you don't have to. Why not? You don't like to read a program backwards
either. 'Everything you can' means everything except forward jumps. You
better not have many forward jumps.

Make variables as GLOBAL as possible. Why not? You can save some space
and clarify your requirements. For instance, how many Is, Js and Ks do
you need? In most cases a single copy in COMMON would suffice (you have
to declare them, remember, and may as well put them in COMMON); you can
redefine it locally if you must; and it is of interest that you must.

Indent! High-level languages, even modern assemblers, fail to insist
that you start in column x. But you do! The unbelievable appeal of a
straight left margin! Paper is 2-dimensional. Use it! If you indent all
statements inside a loop, it's obvious at a glance the extent of the
loop. If you indent conditionally executed statements you'll find that
nested conditions sort themselves out - automatically. If you indent
little statements you wish you didn't have to include (I = I) you'll
find they intrude less as you glance through the listing. Always indent
the same amount, 3 spaces/level is good. Be consistently and be accurate.
Sloppy indenting is obvious.

## Mnemonics

You will find as you read, that I have strong opinions on some subjects
and no opinion of others. Actually I have strong opinions on all, but
sometimes I can't make up my mind which to express. Fortunately it
leaves you some decisions to make for yourself.

Use words with mnemonic value. Unfortunately what is mnemonic to you may
not be mnemonic to me; and I'm the one who judges. Also unfortunately,
mnemonic words tend to be long, which conflicts with:

Use short words. You don't want to type long words, and I don't want to
read them. In COBOL this means avoid dashes and avoid qualification,
though both can be useful upon occasion.

So let me suggest a compromise: abbreviate in some consistent fashion
and stick to your own rules. I can probably figure out the rules you're
using. You might even mention them in a comment.

Use words with the correct grammatical connotations: nouns for
variables, verbs for subroutines, adjectives for . . . Do *not* use
clever words (GO TO HELL). Their cuteness wears off very fast and their
mnemonic value is too subjective. Besides they offer an unwanted insight
into your personality.

Use comments sparingly! (I bet that's welcome.) Remember that program
you looked through - the one with all the comments? How helpful were all
those comments? How soon did you quit reading them? Programs are
self-documenting, even assembler programs, with a modicum of help from
mnemonics. It does no good to say:

    LA B . Load A with B

In fact it does positive bad: if I see comments like that I'll quit
reading them - and miss the helpful ones.

What comments should say is *what* the program is doing. I have to
figure out *how* it's doing it from the instructions anyway. A comment
like this is welcome:

> COMMENT SEARCH FOR DAMAGED SHIPMENTS

Mnemonics apply to variables and labels (You can even get mnemonic value
in FORTRAN statement numbers). Where possible you should apply them to
registers also. You may do well to assign several names to the same
entity, to indicate its current use. However, don't waste effort naming
things that don't need names. If you need a counter, use I, J, K; to
assign a big name (EXC-CNTR) to an insignificant variable is no help.

## Routines and subroutines

There are two words I need to establish precise definitions for: A
*subroutine* is a set of instructions that return from whence they came.
A *routine* is a set of instructions that return to some standard place.

To put it another way, you *jump* to a routine, you *call* a subroutine.
The difference is retained in higher-level languages: GO TO versus CALL
or ENTER.

So what? Subroutines suffer from nesting. If you call a subroutine from
within a subroutine you must somehow save the original return address.
I'm sure you can rattle-off a dozen hardware/software ways of doing
this. They're all expensive.

If you jump somewhere, not intending to come back, you can save trouble,
time and space. But only if you really never come back. To simulate a
subroutine call is worse than ever.

Higher-level languages conceal this by nesting automatically. The best
solution is to nest if you must, but only when you must, and never to
save the same address more than once. That is, upon entering a
subroutine, save the return address if you intend to call other
subroutines. When you're finally ready to return, then un-nest.

Obvious? Perhaps. But it's usually done wrong! Sometimes the problem
only arises with recursive subroutine calls; depending on hardware. It
always arises with re-entrant programming.

So we can get in and out of routines and subroutines. How do we pass
parameters? Again, there are as many answers as computers, languages and
programmers. We shall standardize: you pass what you can in registers;
the rest via a push-down stack.

It is extremely important for routines to be able to communicate
*efficiently*. I hope you are aware of the cost of a FORTRAN subroutine
call. I consider it a basic flaw in the language. We will be moving
among so many subroutines that failing to minimize overhead could easily
halve our running speed.

You must also consider the value of a subroutine. It isolates a logical
function and it eliminates repeated instructions. The first is
acceptable only at minimal cost. The second only if space is saved: a
1-instruction subroutine is ridiculous; a 2-instruction must be called
from 3 places to break even. Be careful!

Finally, it is important to use registers efficiently. Assign registers
for specific purposes and use them consistently. Re-assign registers if
you must to avoid conflicts. Do not move data from one register to
another; see that it is where it belongs in the first place.

When I say register, I'm obviously thinking assembler. However, you will
have to simulate the function of registers with subscripts, etc. in
other languages, and the same considerations apply.

# Programs with input

A program without input is a program with a single task. A program with
input may have many tasks, which it will perform as directed by its
input. Thus I consider input to be control information, and the control
information to define a control language.

We shall have a problem in this chapter, for we are discussing a loop.
Each element of the loop depends on its predecessor and successor, and
we have nowhere to start. I have done the best I could, but am obliged
to refer to things before I define them. Especially in the next section
where I try to justify some of the details we'll encounter immediately
after.

This chapter is full of details, more than I anticipated when I started
it. Although I'm surprised there's so much to say, I think it's all of
value. I only caution you not to get lost in the details; the structure,
the concept of the program are what is important.

To set the stage, let me briefly outline how our program must operate.
You are sitting at a keyboard typing input. You type a string of
characters that the computer breaks into words. It finds each word in a
dictionary, and executes the code indicated by the dictionary entry,
perhaps using parameters also supplied by the entry. The process of
reading words, identifying them and executing code for them is certainly
not unusual. I am simply trying to systematize the process, to extract
the inevitable functions and see that they are efficiently performed.

## Nouns and verbs

I've mentioned the dictionary and we'll soon examine the details
required to implement it. But first I'd like to talk a bit about
individual entries to try and give you a feel for what we're doing.

We're going to read words from your input, find them in the dictionary,
and execute their code. A particular kind of word is a literal, a word
that identifies itself:

    1 17 -3 .5

We won't find such words in the dictionary, but we can identify them by
their appearance. Such words act as if they were in the dictionary, and
the code executed for them places them on a push-down stack.

Other words act upon arguments found on this stack, for example:

    `+` -- add the last 2 numbers placed on the stack, leave the sum there.
    `,` -- type the number on top of the stack, and remove it from the stack.

If we type a phrase such as:

    1 17 + ,

We are saying: put 1 onto the stack, 17 onto the stack, add them, and
type their sum. Each word performs its specific, limited function;
independently of any other word. Yet the combination of words achieves
something useful. In fact if we type:

    4837 758 + -338 + 23 + 4457 + -8354 + ,

we can even do something non-trivial: each number is added to the sum of
its predecessors, and the result typed.

This is basically the value of our program. It lets us combine simple
operations in a flexible way to accomplish a task.

Let's look more closely at the words we used above. They fall into 2
distinct classes; English even provides names for them:

  * Nouns place arguments onto the stack.
  * Verbs operate upon arguments on the stack.

All words cause code to be executed. However in the case of nouns, the
code does very little: simply place a number on the stack. Verbs are
considerably more varied in their effects. They may do as little as add
2 arguments, or as much as type out a result - which requires a great
deal of code.

In effect, nouns place arguments onto the stack in anticipation of verbs
that will act upon them. The word anticipation is a good one. In order
to keep our verbs simple, we promise that their arguments are available.
We could define a verb that reads the next word and uses it as an
argument; but in general we don't. It is not the business of a verb to
provide its own arguments; we use nouns to provide arguments before we
execute the verb. In fact, this substantially simplifies our program.

We can extend the characterization of entries a little further. Verbs
have different numbers of arguments:

  *  Unary verbs modify the number on the stack.
  *  Binary verbs combine 2 arguments to leave a single result.

Arithmetic operations are binary, arithmetic functions are usually
unary. However, there are more verbs than we can usefully categorize.
For example, the verb "," that types the stack is not unary, since it
removes the number from the stack. Although it does have a single
argument.

Another way of distinguishing verbs is:

  * Destructive verb removes its arguments from the stack.
  * Non-destructive verb leaves its arguments on the stack.

Unary and binary verbs, as well as the type verb ",", are destructive.
The verb DUP, which I define to duplicate the top of the stack, is
non-destructive. In general verbs are destructive. In fact, I
deliberately define verbs to be destructive in order to simplify the
task of remembering which are and which aren't. I recommend that you do
the same.

Literals are nouns. We can define other words as nouns; words that use
their parameter field to place numbers onto the stack:

  * Constants place the contents of their parameter field onto the stack.
  * Variables place the address of their parameter field onto the stack.

For example, if PI is a constant, it places 3.14 onto the stack. Thus:

    1. PI 2. \* / ,

reads: place 1. onto the stack, place 3.14 onto the stack, place 2. onto
the stack, multiply (2. and PI), divide (1. by 2PI), and type. Constants
are particularly useful when you're using code numbers. It lets you give
names to numbers that might otherwise be hard to remember.

However the most important nouns by far are literals and variables. A
variable gives a name to a location and not to a value, as elementary
programming texts laboriously explain. However, what higher-level
languages conceal is that variables may be used in 2 distinct ways:

  * To name a location from which a value is to be taken.
  * To name a location into which a value is to be stored.

A constant automatically performs the first; and inherently prevents the
second (you can't store a value into a constant, for you don't know
where the constant came from). Rather than try to distinguish function
by context, as compilers do, we shall define 2 verbs that act upon
variables:

  * `@` replace the address on the stack with its contents.
  * `=` Store into the address on the stack, the value just beneath it on the stack.

Thus if I type, where X is a variable,

    X @ ,

I mean: place the address of X onto the stack, fetch its value, and
type. And if I type,

    X @ Y @ + ,

I mean: fetch the value of X, the value of Y, add, and type. On the
other hand,

    X @ Y =

will: fetch the address of X, then its value, fetch the address of Y,
and store the value of X into Y. But if I type

    X Y =

I'm saying: fetch the address of X, the address of Y, and store the
address of X into Y. Maybe this is that I mean to do, it's not
unreasonable.

I don't want to belabor the point, for we're getting ahead of ourselves.
But variables require special verbs, one of which (@) is not ordinarily
explicit. Incidentally, I originally used the word VALUE for @. But the
verb is used so often it deserves a single character name, and I thought
@ (at) had some mnemonic value, besides being otherwise useless.

I urge you to adopt the verb @. Although you can conceal it in various
ways - we'll discuss one later - it adds needless complication. Such a
useful verb oughtn't be invisible. Besides it lets you store addresses
in variables - indirect addressing

    X Y = Y @ @ ,

reads: store the address of X in Y; place the address of Y on the stack,
fetch its value (the address of X) fetch *its* value (the contents of
X), and type.

I hope I've given you some idea of how you can put arguments onto the
stack and act on them with verbs. Although I define constants and
variables, unary and binary verbs, I hope it's clear that these are only
examples. You must define the nouns and verbs and perhaps other kinds of
words that are useful for your application. In fact, I think that is
what programming is all about. If you have available a program such as I
will now describe, once you decide what entries an application requires,
you'll find it absolutely trivial to code those entries, and thus
complete your problem.

## Control loop

Our program has a structure that is easy to miss: it is a single loop.
However, it is a loop that is diffuse - scattered among all the code in
the program. Very few instructions are gathered together to form an
identifiable loop, so the loop warrants some explanation.

We are going to read a word from the input string, look up that word in
the dictionary, and jump to the routine it specifies. Each routine will
return to the top of the loop to read another word. We will be
discussing many routines and it will be helpful to have a term to
identify "return to the top of the loop to read another word". I will
use the word RETURN; you should provide a standard macro or label in
your program for the same purpose.

Actually, you accomplish 2 purposes: you mark the end of a routine. And
you identify the preceding code as being a routine, as distinct from a
subroutine. Thus, I use the word RETURN with a totally different meaning
from the FORTRAN RETURN statement. I shall speak of EXITing from a
subroutine.

Included in your control loop should be a check that the parameter stack
has not exceeded its limits. This is best done after RETURNing from a
routine, and only needs to be done for routines that use the stack. Thus
there are 2 possible RETURN points (actually 3).

The control loop must be efficient. If you count the instructions it
contains, you measure the overhead associated with your program. You
will be executing some very small routines, and it's embarrassing to
find overhead dominating machine use. In particular you don't need to
check other than the parameter stack.

One more routine belongs in this section: an error routine. Whenever an
error is detected, a routine should jump to ERROR which will type the
offending word and an error message. It will then reset all stacks and
the input pointer and RETURN normally.

The problem of how to treat error messages is an important one. We are
in a position to do a good job: to avoid setting and testing flags; to
avoid cascading back through subroutine calls. By clearing the return
stack we eliminate any pending subroutine returns. By not returning with
an error flag, we avoid having the subroutine have to worry about
errors. This simplifies the code, but we must have a standard method of
handling problems.

The image of a person at a keyboard in invaluable for this purpose. No
matter what problem arises, we needn't worry about what to do. Pass the
buck; ask the user. For example, he types a word not in the dictionary.
What to do? Ask him: type the word and an error message, in this case
"?". He tries to add 2 numbers and there's only 1 on the stack: type the
word and "STACK!". He tries to access a field beyond the limit of his
memory: type the word and "LIMIT!".

Of course you want to be careful not to pose the user problems he can't
solve. Faced with a message "MEMORY PARITY" what can he do about it? But
he's certainly in a better position than your program to take corrective
action to most problems. And of course it's up to you to decide what
situations are problems.

By the way. Since you don't check the stack until after you executed a
routine, it will exceed stack limits before you know it. Thus stack
overflow and underflow should be non-fatal. A good solution is to let
the parameter stack overflow into the return stack, and underflow into
the message buffer. The return stack should never underflow.

## Word subroutine

I've described the control loop that will run our program. The first
thing it does is to read a word; so the first thing we shall discuss is
how to read a word.

What is a word? Not a computer word, as I'm sure you realise, although
we shall have to use the word "word" in that sense. A word is a string
of characters bounded by spaces. It is extracted from a larger string of
characters by the routine we are discussing.

Let me contrast this definition with more conventional input routines.
FORTRAN formatted input, for example, doesn't speak of words but of
fields. The meaning of a number is determined by the field it resides
in; that is, by its position on a card. Since we are not using cards,
the notion of position becomes clumsy and we replace it with order: The
order of the words we read is significant, though their position is not.
We lose, however, the ability to leave a field empty, since we cannot
recognise an empty word. All our data must be explicit, which is
probably a good idea but a slow one to learn. Decide now that you will
not specify input conventions that have optional parameters.

Very well, let's write the WORD subroutine. It uses the input pointer to
point at the current position in the source text, the output pointer to
point at the current position in memory where we will move the word. We
must move it; partly to align it on a computer-word boundary and partly
because we may want to modify it.

Fetch input characters and discard them so long as they're spaces.
Thereafter deposit them until you find another space. Deposit this space
and as many others as needed to fill out the last computer-word. If you
have a character-oriented machine you may be amused at my insistence on
word-alignment. Mainly I'm anticipating the search subroutine when we'll
want to compare as large a piece of the word as possible. If a word
holds 6 characters (or even 2) it's much more efficient to compare them
in parallel than serially, even if you have the hardware.

You may want to set an upper limit on word length. Such a limit should
include the largest number you will be using. Then the question arises
as to what to do with a longer word. You might simply discard the excess
characters, providing you don't plan to dissect the word (Chapter 8).
Better, perhaps, that you force a space into the word at the limit. That
is, break the word into 2 words. Presumably something's wrong and you
will eventually discover it in attempting to process the fragments.
However this limit should be large enough - 10 to 20 characters - so
that it does not constitute a real restriction on your input. It should
also be 1 character less than a multiple of your computer-word length,
so that you can always include the terminal space in the aligned word.

Words are bounded by spaces. You can probably find objections to such a
simple definition. For instance, arithmetic expressions often do not
have spaces between words. We shall discuss this in Chapter 9. Let me
just say that we need to embed periods, dashes, and other characters in
words in order not to unreasonably restrict our potential vocabulary.
We'd like these to be words:

    1,000 1.E-6 I.B.M. B&O 4'3" $4.95

### Message I/O

The WORD subroutine presumably examines input characters. Where does it
get these characters?

Although it's possible to read cards, I'm going to assume that you have
a keyboard to type input. Now there are 2 kinds of keyboards, buffered
and unbuffered. A buffered keyboard stores the message until you type an
end-of-message character. An unbuffered keyboard sends each character as
you type it. Your hardware, in turn, may buffer input for you or not.

In any case we may want to examine each character more than once, so we
want buffered input. Even if you can process characters as they arrive,
don't. Store them into a message buffer.

Set aside a 1-line message buffer. Its size is the maximum size of a
message, either input or output, so if you plan to use a 132 position
printer make it large enough.

If you simulate buffering, you should implement a backspace character
and a cancel message character. For you will make a lot of typing
errors. If your hardware buffers, but does not provide these
capabilities, you should do so. This probably means a prescan of the
input; any other technique gets too complicated, and probably costs more
in the end.

Mark the end of an input message with an end-of-message word. This is a
word bounded by spaces like any other. It may or may not coincide with
the end-of-message character that you typed, depending on your hardware
and character set as to whether the required spaces can be provided.
This word permits ready detection of the last word in a message. It will
have a specific definition and perform a valuable task.

In addition to a keyboard, you must have some sort of output device: a
printer or scope. Again it may be buffered or unbuffered. Unlike input,
we have no reason not to use unbuffered output. However if you have
several output devices, odds are one is buffered. If so, treat them all
as buffered, simulating the buffering where needed.

We will use the same message buffer for both input and output. My
motivation is to save space, or rather to increase the utilization of
space. My reasoning is that input and output are mutually exclusive.
There are exceptions, but we don't usually read input and prepare output
simultaneously. At least we never have to.

However, we do need a switch (1 bit) that states whether the message
buffer still contains input. The first time (or perhaps every time) we
type output, we must reset this switch. We'll use it later.

We need a receive subroutine that will exit when we have a complete
input message. Likewise a transmit subroutine that will exit after
sending an output message. It should await an acknowledgement if the
hardware provides one. Don't try to overlap transmission of one message
with preparation of the next. Transmission is so slow and preparation so
fast that no noticeable increase in speed is available. And it
complicates the program considerably.

### Moving characters

I will speak of fetching and depositing characters several times, mostly
concerned with input and output. For example, the WORD subroutine moves
characters from the message buffer to a word buffer. A simple task
conceptually, but a difficult one to implement. We would have exactly
the same problem moving arrays from place to place. But in fact we
needn't move arrays and we must move characters.

Let us define 2 entities: an input pointer and an output pointer. For
the moment you can think of them as index registers, although we will
have to generalize later. Let's also write 2 subroutines, although your
hardware may permit them to be instructions: FETCH will load the
character identified by the input pointer into a register, and advance
the input pointer; DEPOSIT will store that register at the position
identified by the output pointer, and advance the output pointer.

Depending on your computer, FETCH and DEPOSIT can be veery simple, or
extremely complex. If they require more than 1 instruction, they should
be subroutines, for we'll use them often. By combining them, we can
perform a move. However, it's important to be able to examine the
character before depositing it. A hardware move instruction is of little
value.

The input and output pointers use index registers. However, those
registers should only be used during a move. They should be loaded prior
to a move and saved after it, for they will be used for a number of
purposes, and it becomes impractical to store anything there
permanently.

## Decimal conversion

After isolating and aligning a word from the input string, your control
loop searches the dictionary for it. If it isn't in the dictionary, it
might be a number. A number is a special kind of word that doesn't need
a dictionary entry; by examining the word itself we can decide what to
do with it. The code executed for a number will place the binary
representation of the number onto the stack.

We will discuss the stack in the next section. First let's define a
number more precisely.

### Numbers

It is very hard to state exactly what is a number and what is not. You
will have to write a NUMBER subroutine to convert numbers to binary, and
this subroutine is the definition of a number. If it can convert a word
to binary, that word is a number; otherwise not.

It is foolish to examine a word to see if it is a number, and then to
convert the number to binary. Examination and conversion can be combined
into one process very easily.

There is one kind of word that invariably is a number: a string of
digits possible prefixed with a minus. Such numbers are usually
converted to binary integers. For example:

    1 4096 -3 7777 0 00100 10000000 6AF2 -B

are some decimal, octal and hex numbers. The number does not specify its
base, and a word that may be a hexadecimal number, may not be a decimal
number.

So already base has complicated numbers. And beyond simple integers are
endless other kinds of numbers: fixed-point fractions, floating-point
fractions double-precision integers, complex fractions, etc. And such
numbers can have many different formats as words: decimal point, implied
decimal point, exponents, suffixes. Indeed, the same word may represent
different numbers depending on its context.

One of your major tasks will be to decide what kinds of numbers you need
for your application, how you will format them, and how you will convert
them. Each kind of number must be uniquely identifiable by the NUMBER
subroutine, and for each you must provide an output conversion routine.

I suggest the following guidelines: always define integers and negative
integers; do not permit a prefixed plus sign, it is useless on a number
and useful as a word; if you have floating-point hardware, distinguish
floating-point fractions by a decimal point; if you lack floating-point
hardware, use the decimal point to identify fixed-point fractions; don't
simulate floating-point; don't permit exponents on fractions. These
rules permit a simple NUMBER subroutine which I will outline.

Your application may need special number formats:

  * `45'6` for `45 ft. 6 in.`, an integer
  *  `1,000,000` an integer
  * `$45.69` an integer

It is not hard to include such numbers in NUMBER, but you cannot include
all possible formats. Some are incompatible:

  * `3'9` for `3 ft. 9 in.`
  * `12'30` for `12 min. 30 sec.` of arc
  * `12'30` for `12 min. 30 sec.` of time
  *  `4'6` for `4 shillings 6 pence`

Basic Principle!

Fixed-point numbers are rarely used. I am convinced of their value and
would like to show you. With floating-point hardware, they offer only
the advantage of greater significance, which is probably not worth much.
However, without floating-point hardware they offer most of the
capabilities of floating-point numbers, without the very great cost of
floating-point software. The exception is a wide range of exponents.

I am convinced that exponents are badly misused on computers. Most
applications use real numbers that can be used on a desk-calculator -
say between 10^6^ and 10^-6^. Such numbers can be equally well
represented in fixed-point format. Floating-point is not needed,
although if hardware is available it might as well be used. There are
cases, especially in physics, when large exponents occur - 10^43^ or
10^-13^. But this usually indicates that the proper units have not been
chosen, or maybe even that logarithms should be used.

Of course compilers do not implement fixed-point, so people don't use
it. We are in a position to implement it, and to take advantage of the
speed possible with fixed-point (integer) instructions. What does a
fixed-point number look like? Choose the number of decimal places you
want to use. You may change this from time-to-time, but shouldn't mix
numbers with different precision. Have your NUMBER subroutine align all
numbers (with decimal points) as if you had typed exactly that number of
decimal places. Thereafter treat that number like an integer. That is,
if you choose 3 decimal places:

  *  1. is considered 1.000 and treated as 1000
  *  3.14 is 3.140 and 3140
  *  2.71828 is 2.718 and 2718
  * -.5 is -.500 and -500

I wouldn't bother rounding unless your application demanded it, or your
hardware made it easy.

You can add and subtract such numbers without concern; their decimal
points are aligned. After multiplying 2 numbers, you must divide by 1000
to re-align the decimal points. Hardware usually facilitates this; the
result of a multiply is a double-precision product in the proper
position for a dividend. Before dividing 2 numbers, you must multiply
the dividend by 1000 to maintain precision and align the decimal points.
Again this is easy.

So providing your words are large enough to store the number of decimal
places you need, fixed-point arithmetic is easy. If you have the
hardware, double-precision numbers and operations let you deal with
larger numbers. Just as easily. And much easier than simulating
floating-point operations. You may have to write your own square-root
and trig-function subroutines, but there are approximations available
that make this not-difficult. And they'll be much faster than the
equivalent simulated floating-point subroutines.

Aligning decimal points is easy to visualize, and avoids truncation
problems. However you may prefer to align binary points. That is,
instead of 3 decimal places, keep 10 binary places to the right of the
point. The multiplication and division by 1000 can then be replaced by
binary shifts - the equivalent for binary - which are much faster. You
must balance the gain in speed against the problem of alignment during
conversion (input and output) and truncation during multiplication and
division being more subtle. And possibly the difficulty of explaining
your arithmetic.

### Input conversion

Now let's discuss the NUMBER subroutine in detail. First, why is it a
subroutine? If you examine the program I've outlined so far, and even
the program as augmented by the end of the book, you'll find NUMBER is
called only once - in the control loop. By my own rules NUMBER should
thus be in-line code. However, I can't bring myself to put it in line;
the logic in NuMBER is so complex that I want to isolate it away from
the control loop, to emphasize its logical function - one purpose of a
subroutine - and to reduce confusion in the control loop itself; also
I'm never confident that I won't want to call NUMBER from some other
routine, in fact I have. But I think that such violations of programming
standards should be explicitly recognised.

The key to a good NUMBER subroutine is another subroutine that it calls.
This subroutine has 2 entry points: SIGNED tests the next character for
minus, sets a switch, zeros number-so-far and falls into NATURAL.
NATURAL fetches characters, tests that they're digits, multiplies the
number-so-far by 10 and adds the digit. It repeats until it finds a
non-digit.

With this routine, NUMBER can work as follows: set the input pointer to
the start of the aligned word, call SIGNED. If the stopping character is
a decimal point, clear counter, call NATURAL to get the fraction, and
use counter to choose a power-of-ten to convert to a floating or
fixed-point fraction. In any case, apply SIGNED's switch to make
number-so-far negative. Exit.

The routine that calls NUMBER can test the stopping character:

  *  If it is a space, the conversion was successful.
  * Otherwise, the word was not a number.

For example, the following are numbers:

    0 3.14 -17 -.5

The following are not:

    0- 3.14. +17 -.5Z X 6.-3 1.E3

In each case NUMBER will stop on a non-space. The number-so-far will be
correctly converted up to that point (possibly 0) but it is of no value.

SIGNED/NATURAL is a valid subroutine since it is called twice. Moreover,
if you define other number formats, you'll find it useful. For example,
the format `ft'in`

> After calling SIGNED, if the stopping character is a ' multiply
> number-so-far by 12 and call NATURAL. Then proceed as usual, testing
> for decimal point.

If you want to verify that "in" are less than 12, you'll want to modify
this slightly.

In NATURAL the number-so-far is multiplied by 10. Don't use a literal
10, but rather define a field (BASE) and store a 10 there as
multiplier. Then you can change BASE to 8 (or 16) and handle octal
numbers. You can even change it to 2 to use binary numbers. NATURAL
should test for digits by comparing them with BASE, thus prohibiting 9
in an octal number. Hexadecimal input numbers cause an additional
problem because the digits A-Z do not follow 9 in standard character
sets. It is thus harder to recognise digits; but this problem is
isolated in a single place (NATURAL) and is easy to code:

>     An origin must usually be subtracted from a digit to get its binary
>    value. If BASE is 16, a different origin is subtracted from A-F.

NUMBER should be efficient, at least in recognising words that are not
numbers. Not so much because you will use so many numbers, but because
you will examine many words that aren't numbers. We will discuss this
further in Chapter 8. It is also important that you examine the aligned
copy of a word. There are several reasons: to avoid trouble with the
input pointer, to guarantee a terminal space. However this creates a
problem: the largest number you will use must fit in the aligned word;
this may require a longer word than you would otherwise use. A number
longer than word-size will have its right-most digits discarded. This
will probably not destroy its numeric appearance so that no error will
be detected; but the conversion will be incorrect. This problem is not
serious, just be aware of it.

### Output conversion

Numeric output is harder than numeric input because there is an extra
step involved. During input, you multiply the number by 10 and add each
digit. You can work from left to right. During output, you divide by 10,
save the remainder for the digit, and repeat with the quotient until it
becomes 0. You get the digits from right to left, but you want to type
them from left to right.

Thus you need somewhere to store the digits temporarily. A good place is
the far end of the message buffer. The space is unused since you
presumably have enough space for the number. Of course, you can use the
stack. If you place a space at the right end of your temporary storage,
and then deposit the digits from right to left, you can use the TYPE~B~
subroutine to finally type the number.

You'll probably want to handle both negative numbers and fractions.
Remember the number is negative and work with its absolute value. After
you're finished, prefix a minus. Fractions require 2 conversion loops:
one to convert the fraction, counting the number of digits and
depositing a decimal point; another to convert the integer, stopping
when the quotient becomes 0. You don't want to test the quotient in the
fraction.

If you take the care, and spend a couple of instructions, you can
improve the appearance of your numbers by:

  * Not typing a decimal point if the number has no decimal places.
  * Not typing a leading zero to the left of the decimal point.

You will probably have several dictionary entries specifying different
output formats. For example, each kind of number: integer, float,
complex will need its own output routine. However the actual conversion
should be done by a single subroutine with parameters to distinguish
special cases. That is, a single subroutine inverse to the NUMBER
subroutine. The similarities among different numbers are much greater
than their differences.

If you use decimal fixed-point fractions, you already have a field D
that specifies the number of decimal places. The same field is used to
control decimal placement on output. Ordinarily decimal places on input
and output will be the same. Even with floating-point numbers you need
that field, since you're rarely interested in full precision output.

If you want to produce reports - carefully formatted columns of numbers
- you will need to right-justify numbers. That is, to line up decimal
points. For this you need another parameter F, the width of the field in
which the number is to be right-justified. It's easy to use: after
converting the number right-left, compute the number of spaces you need
and call SPACE. Then call TYPE~B~. In determining spaces, remember that
TYPE~B~ always types a space *after* the number. Thus you will always
have at least a single space between numbers. If the number won't fit in
the field you specify, you'll still have that one space, and the full
number will be typed - fouling up the report format - but showing you
the bad number.

Let me acknowledge that if you are going to right-justify numbers you
can place the digits directly into position from right to left, for you
know where the rightmost digit must go. But then you must space-fill the
message buffer before starting output, and you can't type unbuffered
output immediately. However, my main objection is that you can't compose
free-format output. For example, place a number in a sentence without
extra leading spaces. And very often unformatted output is adequate,
saving you having to specify field sizes you don't care about.

Depending on your formatting requirements, there are other dictionary
entries you might want: A SPACE entry, to space the number of positions
on the stack. It can even space backwards - by changing the output
pointer - if the stack is negative. This is useful if you want to
suppress that space provided by TYPE~B~. A tab entry might calculate the
amount to space in order to reach a specific position on the stack.

## Stacks

We will be using several push-down stacks and I want to make sure you
can implement them. A push-down stack operates in a last-in first-out
fashion. It is composed of an array and a pointer. The pointer
identifies the last word placed in the array. To place a word onto the
stack you must advance the pointer, and store the word (in that order).
To take a word off the stack you must fetch the word and drop the
pointer (in that order). There is no actual pushing-down involved,
though the effect is the same.

A stack pointer is an excellent use for an index register, if you have
enough. Indirect addressing is also a possibility, especially if you
have an add-to-memory instruction.

### Return stack

This stack stores return information. One use is to store the return
address for subroutines, when subroutine calls use an index register.
The last-in first-out nature of a stack is exactly the behavior required
for nested subroutine calls. We will later encounter several other kinds
of return information that can be stored in the same stack. It is
important not to attempt to combine the return stack and the parameter
stack. They are not synchronized. 8 words is probably enough space for
the return stack.

### Parameter stack

This stack is the one I intend when I say simply stack. Numbers,
constants, variables are all placed on this stack, as will be discussed
later. This stack is used to pass parameters among routines. Each
routine can find its arguments there, regardless of how many other
parameters are present, or how long ago they were placed there. You
should not implement a parameter stack less than 16 words long.

A valuable refinement to the parameter stack is to set aside a register
to hold the word on top of the stack. Several rules must be religiously
observed if this is not to cause trouble:

  * You must never use this register for any other purpose.
  * You must keep this register full; no flag to indicate that it's
    empty.

If you cannot fulfill these conditions, you're better off with the stack
entirely in core.

We need some terminology:

  * You *place* a word *onto* then stack, thereby increasing its size.
  * You *drop* a word *from* the stack, thereby decreasing its size.
  * The word on top of the stack is called the *top* word.
  * The word immediately below the top of the stack is called the
    *lower* word.

You may need to control the parameter stack from the input. These words
(dictionary entries) are extremely useful, and illustrate the
terminology above:

  * `DROP` drop the top word from the stack.
  * `DUP` place the top word onto the stack, thereby duplicating it.
  * `SWAP` exchange the top and lower words.
  * `OVER` place the lower word onto the stack; move it over the top word.

## Dictionary

Every program with input must have a dictionary. Many programs without
input have dictionaries. However these are often not recognised as such.
A common 'casual' dictionary is a series of `IF ... ELSE IF ... ELSE
IF ...` statements, or their equivalent. Indeed this is a reasonable
implementation if the dictionary is small (8 entries) and
non-expandable.

It is important to acknowledge the function and existence of a
dictionary, to concentrate it in a single place and to standardize the
format of entries. A common characteristic of bad programs is that the
equivalent of a dictionary is scattered all over the program at great
cost in space, time and apparent complexity.

The most important property of an entry is one that is usually
overlooked. Each entry should identify a routine that is to be executed.
Very often many entries execute the same routine. Perhaps there are few
routines to choose among. This tends to conceal the importance of
specifying what is to be done for each entry. By placing the address of
a routine in each entry, an optimal and standard procedure for getting
to that code can be designed.

Significantly, the IF . . . ELSE IF construction has the characteristic
of associating a routine with each entry.

### Entry format

There are 2 distinct ways to organize dictionary entries. The choice may
depend upon hardware characteristics, but I recommend the second. A
dominant feature of entries is that they have variable length. A part of
the entry may be the code to be executed, or parameters or an area of
storage, all of which may have arbitrary length.

One possibility is to split an entry into two portions, one of fixed
size, one of variable size. This permits scanning fixed size entries to
identify a word and often there are hardware instructions to speed this
search. A part of the fixed entry can be a link to a variable area; of
course you choose the fixed size so as to make the link in the nature of
an overflow - an exception.

However, since input is relatively small volume (even as augmented in
definitions), to minimize the time required to search the dictionary
does not lead to a global optimum. You can gain greater flexibility, a
simpler allocation of core, and ultimately greater speed by chaining the
variable-sized entries together directly. This is the organization I
shall discuss.

An entry has 4 fields: the word being defined, the code to be executed,
a link to the next entry and parameters. Each of these warrants
discussion.

The format of a word must be decided in conjunction with the word input
routine. It should have a fixed size which may be smaller than that
defined by NEXT, but must be a multiple of hardware word size. However,
more sophisticated applications use the dictionary words to construct
output messages. Then it is important not to truncate words, in which
case the word field must have variable length. To mark the size of this
field the terminal space should be used rather than a character count.
To handle a variable word field within a variable entry, the word should
extend in one direction (backwards) and the parameter in the other
(forwards). Fixed or variable word size requires application of the
Basic Principle.

The code field should contain the address of a routine rather than an
index to a table or other abbreviation. Program efficiency depends
strongly on how long it takes to get to the code once a entry is
identified, as discussed in 3.9. However, the small size of your program
may permit this address to fit in less space than the hardware address
field.

The link field may likewise be smaller than hardware-specified. It
should contain the absolute location of the next entry rather than its
distance from the current entry.

The parameter field will typically contain 4 kinds of information:

  * A number, constant or variable, of variable size. The nature of the
    number is determined by the code it executes.  
  * Space in which numbers will be stored - an array. The size of the
    array may be a parameter, or may be implicit in the code executed.
  *  A definition: an array of dictionary entries representing
    virtual-computer instructions; see 3.9.
  * Machine instructions: code compiled by your program which is itself
    executed for this entry. Such data must probably be aligned on word
    boundary, the other need not.

### Search strategies

One basic principle applies to dictionary search: it must be backwards -
from latest to oldest entries. You have perhaps noticed that the
dictionary is *not* arranged in any order (ie. alphabetical) other than
that in which entries are made. This permits the same word to be
re-defined, and the latest meaning to be obtained. There is no trade-off
valuable enough to compromise this property.

To identify a word, place it (or its first portion) in a register and
compare for equality with each entry (or its first portion). An
algebraic comparison is adequate. Concern is sometimes expressed that
treating words as floating-point numbers may permit a false equality.
This has 0 probability and you can always change the word - ignore it.

A full-word compare (rather than a character-by-character) should be
used for speed. A match is usually found on the first portion, and
extensions may be treated with less efficiency (though still full-word
compares).

Fixed-length entries may be scanned with a simple loop. Linked entries
require an equally simple loop, but usually a slower one. However the
speed of a linked search can be increased without limit: Rather than
link each entry to its physical predecessor, link it to a predecessor in
one of a number of chains. Scramble the word to determine which chain it
belongs in, both when you enter it and when you search for it. Thus,
only a fraction of the total dictionary need be searched to find the
word or assure its absence.

The number of chains should be a power of 2: 8 will provide a useful
increase in speed. The scramble technique may be very simple: add the
first few characters together and use the low-order bits. In order to
maintain a linked dictionary, the next available location and the
location of the last entry must be kept. A multiply-chained dictionary
requires the location of the last entry for each chain: a small price in
space for a large gain in time.

However, search time is not a important consideration, and I advise
against multiple chains unless the dictionary is very large (hundreds of
entries).

### Initialization

The dictionary is built into your program and is presumably initialized
by your compiler. This is certainly true if you have fixed-size entries.
Variable-sized entries must be linked together, however, and this can be
beyond the ability of your compiler, especially if you have multiple
chains.

In such a case, it is a simple matter to write a loop that scans the
dictionary and establishes the links. It should scan the core occupied
by the dictionary and recognise an entry by some unique flag (7's in the
link field). It can the pick up the word, scramble it and add it to the
appropriate chain.

This is purely temporary code. Although it may call permanent
subroutines to scramble and link, the initialization code will have no
further use. Thus it should be placed where it can be overlaid as the
program proceeds. The message buffer, if large enough, or the disk
buffer are possibilities.

Other things may need initializing, particularly any registers that are
assigned specific tasks. All such duties should be concentrated in this
one place.

## Control language, example

Applications tend to be complicated before they become interesting. But
here's a fairly common problem that shows off a control language to
advantage. Implementation would be tricky, execution would be
inefficient; but the program would be simple, and its application
flexible.

The problem is to examine a sequential file, select certain records,
sort them, and list them - in many different ways. Suppose these
variables define the fields in the record:

    NAME AGE SALARY DEPT JOB SENIORITY

Let's define these verbs:

    LIST SORT EQUAL GREATER LESS

Each acts upon the temporary file produced by the previous, in
accordance with the following examples:

List in alphabetical order all employees in dept 6:

    6 DEPT EQUAL NAME SORT LIST

First we choose records with dept = 6 and copy them into a temporary
file. Then we sort that file by name. Then we list it.

List twice, by seniority, all employees holding job 17 in dept 3:

    17 JOB EQUAL 3 DEPT EQUAL SENIORITY SORT LIST LIST

List, by age, all employees whose salary is greater than $10,000; and
identify those whose seniority is less than 3:

    10000 SALARY GREATER AGE SORT LIST 3 SENIORITY LESS LIST

Several comments seem indicated. We can apply a logical "and" by using
several select verbs in sequence; we cannot use a logical "or". We can
sort on several fields, if our sorting technique does not unnecessarily
re-arrange records. We need 2 more verbs:

    REWIND END

to start over with the original file, and to quit.

Actually many other capabilities could be provided, including the
ability to locate specific records and modify them. But rather than
design a particular application, I just want to show how nouns and verbs
combine to provide great flexibility with a simple program. Notice how
even such a simple example uses all our facilities: the word subroutine,
the number subroutine, the dictionary, the stack. We're not speculating,
we are providing essential code.



# Programs that grow

So far our dictionary has been static. It contains all the entries you
need - placed there when the program was compiled. This need not be. We
can define entries that will cause additional entries to be made and
deleted. Let me point out why this might be desirable.

You have a program that controls an application. Based upon the words
you type, it will do as you direct. In Chapter 3 we provided the ability
to type out results. Not the sort of results that are the inevitable
result of the application, but variables that you'd maybe like to see.
More a conversational sort of output, since it is controlled directly by
input.

There are 2 problems with this situation. Firsts, to add an entry to
your dictionary you must re-compile the program. Clearly, you won't be
adding many entries - but maybe you won't have to. Second, all your
entries must be present at the same time. This creates, not so much a
volume problem, as a complexity problem. If your application is complex,
it becomes increasingly difficult to make all aspects compatible. For
instance, to find distinct names for all fields. Third, if you find an
error in an entry you must recompile the program. You have no ability to
correct an entry - though of course you could define entries to provide
that ability.

If you can create dictionary entries you can accomplish 2 things: You
can apply your program to different aspects of your application -
without conflicts and reducing complexity. You can create a dictionary
entry differently, and thus correct an error. In fact, the purpose of
your program undergoes a gradual but important change. You started with
a program that controlled an application. You now have a program that
provides the capability to control an application. In effect, you have
moved up a level from language to meta-language. This is an extremely
important step. It may not be productive. It leads you from talking *to*
your application to talking *about* your application.

Another way of viewing the transition is the entries in your dictionary.
At first they were words that executed pieces of code that constituted
your application program. A purely control function. Now they tend to
become words that let you construct your application program. They
constitute a problem-oriented-language. The distinction need not be
abrupt but it is irreversible. You change from an application to a
system programmer - your system being your application.

I hesitate to say whether this is good or bad. By now you surely know -
it depends on the application. I suspect any application of sufficient
complexity, and surely any application of any generality, must develop a
specialized language. Not a control language, but a descriptive
language.

Some examples: A simulator does not want a control language. It is
important to be able to describe with great facility the system being
simulated. A linear-programming problem needs a language that can
describe the problem. A compiler actually provides a descriptive
language for use with the programs it compiles. A compiler-compiler
describes compilers. What is a compile-compiler that can execute the
compiler it describes and in turn execute the program it compiled? That
is the question!

Let me now assume that you have a problem that qualifies for a
descriptive language. What dictionary entries do you need?

## Adding dictionary entries

Let us now assume that you want to expand your dictionary; that you have
a sufficiently complex application to justify a specialized language.
How do you make a dictionary entry?

Recall the control loop: it reads a word and searches the dictionary. If
you want to define a word, you must not let the control loop see it.
Instead you must define an entry that will read the next word and use it
before RETURNing to the control loop. In effect, it renders the
following word invisible. It must call the word subroutine, which is why
it is a subroutine rather than a routine. Let us call such an entry a
*defining* entry, its purpose is to define the next word.

In principle we only need one defining entry, but we must supply as a
parameter the address of the code to be executed for the entry it
defines. Remember that 4 fields are required for each entry: the word,
its code address, a link, and (optionally) parameters. The word we
obtain from the word subroutine; the link we construct; the parameters
we take from the stack. We could also take the address from the stack,
but it's more convenient to have a separate defining word for each kind
of entry to be constructed. That is, to have a separate defining entry
for each address we need, that provides the address from its parameter
field.

I'm afraid this is confusing. We have one entry that supplies the
address field of a new entry from its own parameter field. Let's take an
example; suppose we want to define a constant:

    0 CONSTANT ZERO

0 is placed on the stack; the code for the word CONSTANT reads the next
word, ZERO, and constructs a dictionary entry for it: it establishes the
link to a previous entry, stores 0 from the stack into the parameter
field, and from its own parameter field stores the address of the code
ZERO will execute. This is, presumably, the address of code that will
place the contents of the parameter field onto the stack.

Thus for each kind of entry we will be making, we need a defining entry
to supply the code address and do the work. Since all defining entries
have much in common, you should write an ENTRY subroutine they can call.
It should have as parameter the code address, and construct all of the
new entry except the parameter field, which is specialized by the
defining entry.

Other defining entries might be:

  * `0 INTEGER I` -- an integer-size parameter field is initialized to 0; its address will be placed on the stack.
  * `1. REAL X` -- a floating-point parameter field is initialized to 1.
  * `8 ARRAY TEMP` -- an 8 word parameter field is cleared to 0; the
    address of its 1st word will be placed on the stack.

I must emphasize the word "might". Different applications will require
different defining entries; even the same word might act differently for
different applications. But you are in a position to define any kind of
noun you need, and then create as many instances of that noun as you
like. It is a futile exercise to attempt to establish a universal set of
nouns. Compiler languages have repeatedly stumbled by not providing
enough, and no matter how many they provide, someone will want one more.

For example, you might define the following noun:

    `0 8 INDEX J` -- J is defined to be an index, that varies from 0 to 8.
    When executed, it adds its value to the top of the stack.

If you then define appropriate verbs to advance, test and reset J, you
can have a powerful indexing facility. Or define:

    3 VECTOR X 3 VECTOR Y 9 VECTOR Z

and define arithmetic verbs to implement vector arithmetic:

    X Z = Z Y + add X and Y, store in Z.
    X Y Z \*C multiply X and Y (outer product), store in Z.

Anything you need for your application you can define. But you can never
define everything. Basic Principle!


## Deleting entries

So far we've only discussed defining nouns. Actually you'll be using
more verbs than nouns, but they require much longer explanations. Here
is one kind of verb.

If you can add entries to your dictionary, eventually you're going to
want to get rid of them. You'll need to delete entries in order to
re-enter them correctly, or delete entries in order to make room for
another application. After all, your dictionary is finite; no matter how
large you make it, you will be aware of its upper limit. Parkinson's Law
may be rephrased: Dictionaries expand to fill the available space.

There is only one feasible way to delete entries. That is to delete all
entries after a certain point. If you were to delete specific entries,
you would leave holes in the dictionary, since it occupies contiguous
core. If you attempt to pack the dictionary to recover the holes, you
are faced with a wicked re-location problem, since we use absolute
addresses. To avoid absolute addresses is inefficient and unnecessary.

Deleting trailing entries is a completely satisfactory solution. I know
of no argument to prove this, except to say try it and see. You'll find
that, in practice, you add a bunch of entries; find a problem; delete
those entries; fix the problem; and reenter all the entries. Or you fill
your dictionary for one application; clear it; and re-fill with another
application. Or you might re-load the same application just to clear
some fields. In each case, you want to get rid of all the latest
entries.

One exception is when you use some entries to construct others. The
constructing entries are then no longer needed, and there is no way to
get rid of them. It happens; I may even give some examples later. But
all you lose is dictionary space, and I can't see a practical solution.

OK, how do you delete trailing entries? You want to mark a point in your
dictionary and reset evereything to that position. One thing is the
dictionary pointer that identifies the next available word in the
dictionary. That's easy. However you must reset the chain heads that
identify the previous entry for each of your search chains. It only
takes a small loop: follow each chain back, as you do when searching,
until you find a link that precedes your indicated point.

If you have fixed-size entries, you must reset the pointer to the
parameter area, but you don't have to follow links.

A convenient way to specify the point you want to delete from is to
place a special entry there. A verb that will delete itself and
evereything following it when you execute it. For example,

    REMEMBER HERE

is a defining entry. When you type HERE, it is forgotten; it both marks
a place in the dictionary and executes the deleting code. HERE doesn't
need a parameter field, unless you use fixed-length entries, whereupon
it must save the current value of the parameter pointer. This is our
first example of a verb-defining entry.


## Operations

**Recall that the stack is where arguments are found. There are some
words you may want to define to provide arithmetic capabilities. They
are of little value to a control language, but essential to add power to
it. I'll use logical constructs TRUE (1) and FALSE (0). And remember the
definition of top and lower from 3.6.**

Unary operators: change the number on top of the stack.

  *  MINUS changes sign of top.
  *  ABS sets sign positive.
  *  ZERO if top is zero, replace it with TRUE; otherwise place FALSE
    onto the stack.
  *  NONZERO if top is nonzero, place TRUE onto the stack; otherwise
    leave it alone (leave FALSE on the stack).

Binary operators: Remove top from the stack and replace lower by a
function of both.

  *  + add top to lower.
  *  \* multiply lower by top.
  *  - subtract top from lower.
  *  / divide lower by top, leave the quotient.
  *  MOD divide lower by top, leave the remainder.
  *  MAX if top is larger than lower, replace lower by top.
  *  MIN if top is smaller than lower, replace lower by top.
  *  \*\* raise lower to power of top.

These are only samples. Clearly you are free to define whatever words
you feel useful. Keep in mind that you must place the arguments on the
stack before you operate on them. Numbers are automatically placed on
the stack. Constants are too. Thus the following make sense:

    1 2 +
    PI 2. \*
    1 2 + 3 \* 7 MOD 4 MAX
    1 2 3 + \*

This notation permits arithmetic calculation in the same manner a desk
calculator. It is often called parenthesis-free representation or
perhaps right-handed Polish, but it is simply the way you work with
arguments on a stack. Conventional algebraic notation is much harder to
implement (8.2).

Other binary operations are the arithmetic relations: these leave a
truth value on the stack:

  *  `=` are they equal?
  *  `<` is top greater than lower?
  *  `\>` is top less than lower?
  *  `\>=` is top not greater than lower?
  *  `<=` is top not less than lower?

The logical operations include a unary and several binary:

  *  NOT if top is FALSE, replace with TRUE; otherwise replace with FALSE.
  *  OR logical or.
  *  AND logical and.
  *  IMP logical implication.
  *  XOR logical exclusive or.

Your stack must have a fixed word-length. However the operations
mentioned above might apply to several kinds of numbers: integers,
fixed-point fractions, floating-point fractions, double-precision
fractions, complex numbers, vectors of the above kinds. The truth values
are only 1 bit. Clearly, the stack must be able to hold the largest
number you expect to use. Less clear is how you should distinguish among
various kinds of numbers.

One way is to define separate operations for each kind of number:

  *  `+` integer and fixed-point add (they are the same).
  *  `+F` floating-point add.
  *  `+D` double-precision add.

Another is to make a stack entry long enough to contain a code
identifying the kind of number. This makes the code defining each
operation more elaborate and raises the problem of illegal arguments. I
recommend not checking arguments and defining separate operations, for
reasons of simplicity. Actually, you are working with one kind of number
at a time and the problem may never arise.

Do not bother with mixed-mode arithmetic. You never *need* it, and it's
not convenient often enough to be worth the great bother. With multiple
word numbers (complex, double-precision) you may put the address of the
number on the stack. However, this leads to 3-address operations with
the result generally replacing one of the arguments. And this, in turn,
leads to complications about constants.

In general, the number of things you *might* do with numbers increases
indefinitely. Many of these are mutually incompatible. Basic Principle!

## Definition entries

I must now describe an entry more complicated than any so far, though
not the most complicated that you'll see. It is also exceptional in that
it's not optional. For this ability is required for any effective
application language: to be able to define one word in terms of others.
To abbreviate, if you will. You recall that I characterised words as
being simple in themselves, but powerful in combination. Well here is a
way to combine words.

A definition consists of a defining entry ":" followed by a series of
words terminated by ";". The intention is that the word defined by ":"
has the meaning expressed by the words that follow. For example:

    : ABS DUP 0 LESS IF MINUS THEN ;

This is a definition of the word ABS. Its purpose is to take the
absolute value of the number on the stack. It does this by executing a
series of words that have the proper effect.

You may consider this a rather clumsy definition of ABS. Especially
since there is an instruction on your computer that does exactly that.
you're quite right, definitions tend to be clumsy. But they let us use
words that we hadn't the foresight to provide entries for. Given certain
basic words we can construct any entry we need. Definitions provide a
succinct distinction between a control language and an application
language: The control language must have all its capabilities built in;
the application language can construct those capabilities it needs.

To implement definitions is simple, yet awkwardly subtle. The parameter
field of a definition contains the addresses of the dictionary entries
that define it. You must somehow deposit these entries in the parameter
area, and later fetch them when you execute the definition. The
complementary processes of definition and execution are more involved
than for any other entry we've encountered.

Before I describe these processes in detail, let me try to clarify
exactly what a definition is. You recall that the code executed for a
word is a routine, and not a subroutine. And yet a series of words is
like a series of subroutine calls, for the control loop serves the
function of returning to a position where the next word can be found.
You might consider a definition to be just that: a series of subroutine
calls with the addresses of the subroutines constituting the definition.

Another viewpoint is concealed in an abbreviation I use: I speak of
"executing a word", when I really mean executing the code associated
with the word. Or even more precisely, executing the code whose address
is stored in the dictionary entry for the word. The abbreviation is not
only convenient, it suggests that a word is an instruction that can be
executed. And indeed, it is helpful to think of a word as an
instruction: an instruction for a computer that is being simulated by
our real computer. Let's call that imaginary computer the "virtual
computer". Thus when you type words you are presenting instructions to
the virtual computer. The control loop becomes the instruction fetch
circuitry of the virtual computer.

If we extend this analogy to definitions, a definition becomes a
subroutine for the virtual computer. And the process of defining a
definition is equivalent to compiling this subroutine. We'll return to
this analogy later.

You'll see that the virtual computer is a real help in understanding
definitions. In fact, it originally led me to apply compiler techniques
to definitions - techniques that otherwise wouldn't have occurred to me.
But although it may be helpful to programmers, it is only confusing to
non-programmers. So I prefer the name "definition" for this type of
entry, and the phrase "defining one word in terms of others" as its
explanation.

Definitions are extremely powerful. Why, is hard to explain, hard even
to comprehend. Their value is best appreciated by hindsight. You
complete a ludicrously simple implementation of an application, discover
that you used a dozen definitions and nested them 8 deep. The
definitions appear responsible for the simplicity.

But there are several properties that emphasize the value of definitions
over their equivalent, a series of subroutine calls. First, you needn't
be concerned about call sequence, about what registers are available and
what must be saved; simply type a word. Second, one definition can
execute another. That is, you can nest definitions, again without any
concern about saving return addresses or other register conflicts. You
can even use definitions recursively without concern. Third, you can
pass arguments among definitions effortlessly, in fact invisibly, since
they are on the stack. Again you have no concern for calling sequence or
storage conflicts. Plenty of temporary storage is available, too; again
on the stack.

Of course you have to pay for this convenience, though probably less
than you would with FORTRAN subroutine calls. The price is the control
loop. It's pure overhead. Executing the code for each entry of course
proceeds at computer speed; however obtaining the address of the next
code to execute takes some instructions, about 8. This is why I urge you
to optimize your control loop.

Notice that if the code executed for words is long compared to the
control loop, the cost is negligible. This is the principle of control
languages. As the code shrinks to control loop size, and smaller,
overhead rises to 50% and higher. This is the price of an application
language. Note, however, that 50% overhead is easily reached with
operating systems and compilers that support an application program.

I suggest that you compromise. Code the computation-limited portions of
your problem and use definitions for the rest. The use of definitions to
control, rather than perform, calculations is inexpensive. And the ease
of constructing them reduces the time and effort, and thus cost, of
implementation.

### Defining a definition

The defining entry ":" acts just like any other. It passes the address
EXECUTE to the ENTRY subroutine. I'll discuss that code in the next
section.

It then sets a switch STATE. The control loop must be changed to test
STATE: if it is 0, words are executed as I've already described; if it
is 1, words are compiled. Let me repeat: if you add definitions to your
program, you must modify the control loop so that it will either execute
or compile words. If you plan to include definitions from the start, you
should plan the control loop accordingly. Implement the switch so that
executing words is as fast a possible; you'll execute many more words
than you'll compile.

To compile a word is simple. After finding it in the dictionary, you
have the address of its dictionary entry. Deposit this address in the
parameter field. Notice 2 things: we already have a mechanism for
depositing words in the dictionary. ENTRY uses it as well as many
defining entries for parameters. The dictionary pointer DP identifies
the next available word in the dictionary. All you must do to compile a
word is to store its address at DP and advance DP. Also notice that we
deposit the address of the *entry* not the address of the code executed.
This is so we have access not only to the code but also to the parameter
field, and even the word itself should we need it.

All right, so much for compiling words. What about numbers? A number
presented to a compiler is called a literal. And literals are a problem
to any compiler. Fortunately we can define our virtual computer so that
it can handle literals in-line. You must again modify the control loop
to test STATE when a number is successfully converted.

Before showing how to compile a number, let me define pseudo-entries. A
pseudo-entry is a dictionary entry that is not in the dictionary. That
is, it has the format of an entry but it is not linked to other entries.
Thus it would never be found during a dictionary search. You see, we
occasionally need entries to permit the virtual computer to run
smoothly, but we don't want to slow the dictionary search by including
non-referenceable entries.

As you've probably guessed, in order to compile a literal you compile a
pseudo-entry. You then follow it by the number itself; that is, you
compile the number also. The result is a double-length virtual-computer
instruction. The code executed for the pseudo-entry must fetch the
number and place it onto the stack. Thus literals that are compiled have
the same effect, when executed, as if they were executed immediately.

Notice that if you have different-size literals, you'll need different
pseudo-entries for them And having brought up the subject, let me
discuss word length a moment. Word length for the virtual computer
should be about 12 bits. This is because each instruction is composed of
simply a dictionary address and 12 bits is enough to identify one of
perhaps 1000 entries. If your real computer word length is longer than
18 bits you should pack several virtual-computer instructions into one
word. This is possibly awkward, since you must modify DP to address
other than a real computer word. But you'll save a lot of space.

Incidentally, since literals require extra space when compiled, you might
define commonly used literals as words:

    1 CONSTANT 1

Recall that numbers may be words, since the dictionary is searched
before numeric conversion is attempted. And a word requires only a
single-length virtual-computer instruction. On the other hand, a
dictionary entry takes much more space than a compiled literal, so watch
the trade-off.

The code in the control loop that compiles words much watch for ";". It
is compiled as usual, but it also resets STATE to prevent further
compiling. It also performs another task, which requires a digression.

Notice that when we're compiling a definition we're searching the
dictionary for each word. If we reference the word we've just defined,
we'll find it. Thus we'll have made a recursive reference. If you want
recursive definitions, fine. However it's extremely convenient to
exchange recursion for re-definition. That is, to understand a reference
to itself inside a definition to refer to an earlier definition. For
example,

    : = SWAP = ;

Here I redefine the = verb to operate upon arguments in the opposite
order. I could use a different word for that purpose, but = has mnemonic
significance.

In any case, the capability is easy to provide. Let ":" bugger the
search so the latest entry cannot be found. And let ";" unbugger the
search and thereby activate the new definition. If you want recursive
definitions, you could provide a defining entry ":R" that did not
bugger, providing you make ";" work for both. I'll mention another
technique later.

### Executing a definition

I named the code executed for a definition EXECUTE. It must modify the
instruction-fetch circuitry of the virtual computer.

Recall the structure of the control loop: the routine NEXT~W~ provides
the address of a dictionary entry; the routine associated with this
entry is entered; it ultimately returns to NEXT~W~. The same procedure
is required in order to execute a definition, with the exception that
NEXT~W~ is replaced by NEXT~I~. Where NEXT~W~ read a word and found it
in the dictionary, NEXT~I~ simply fetches the next entry from the
parameter field of the definition.

Thus you need a variable that identifies the routine to be entered for
the next entry. One implementation is to define a field NEXT that
contains either the address of NEXT~W~ or NEXT~I~. If you jump indirect
to NEXT, you will enter the appropriate routine. One task of EXECUTE is
therefore to store the address of NEXT~I~ into NEXT, causing subsequent
entries to be obtained in a different way.

Of course NEXT~I~ must know where to find the next entry. Here the
virtual computer analogy is extended by the addition of an instruction
counter. If you define a field, preferably an index register, named IC
it can act exactly like an instruction counter on a real computer. It
identifies the next entry to be executed, and must be advanced during
execution.

You can now see the complete operation of NEXT~I~: fetch the entry
identified by IC, advance IC to the next entry, and return to the same
point NEXT~W~ does to execute the entry (or compile it, as the case may
be). If you use definitions at all, you'll use them extensively. So
NEXT~I~ should be optimized at the cost of NEXT~W~. In particular, the
code that executes (compiles) entries should be fallen into from NEXT~I~
and jumped to from NEXT~W~. This saves one instruction (a jump) in the
control loop using NEXT~I~. This can be 20% of the loop, apart from
actually executing the entry's code, for a substantial saving.

Now let's return to EXECUTE. Clearly, in addition to establishing
NEXT~I~ it must initialize IC. But first it must save IC. The process is
analogous to a virtual-computer subroutine call. The obvious place to
save IC is the return stack. Although it is used for other purposes,
none of these conflict with such use. If one definition is executed from
within another, it is clear the current IC must be saved. Otherwise the
current value of IC is undefined.

One more routine is involved in this process. The code executed for ";"
must return from the definition. This means simply that it must restore
IC from the return stack. However it must also restore the value of
NEXT, which was set to NEXT~I~ by EXECUTE. You might store the old value
of NEXT in the return stack and let ";" recover it. Simpler, perhaps, is
to let the undefined value of IC be zero, and act as a flag to restore
NEXT to NEXT~W~. For while executing definitions, NEXT will always
contain NEXT~I~. Only when returning from a definition that originated
within the source text must NEXT~W~ be reestablished. Since while
executing source text IC is irrelevant, it might as well by useful in
this limited way.

That's all there is to it. The combination of EXECUTE, NEXT~I~ and ";"
provide a powerful and efficient subroutine facility. Notice that the
code "executed" for a definition might actually be compiled, depending
on the field STATE, as discussed earlier. Notice also that the entries
executed by a definition might compile other entries. That is, one entry
might deposit numbers in the dictionary, using DP. Thus although the
fields IC and DP are similar in use, DP deposits entries and IC fetches
them, they may both be in use at the same time. If you're short of index
registers, don't try to combine them.


### Conditions

Let me review briefly the process of defining a definition: The word ":"
sets a switch that modifies the control loop; it will now compile words
instead of executing them. The word ";" is compiled, but also causes the
switch to be reset, ending the process of compilation. Following words
will now be executed as usual.

We can thus view ";" as being an exceptional word, for it is - in a
sense - executed during compilation, at which time it resets that
switch. Of course it is also executed during execution of the
definition, with a different effect: it resets IC.

There are other words like ";" that must be executed during compilation.
These words control the compilation. They perform code more complicated
that simply depositing an entry address. In particular, they are
required to provide forward and backward branching.

Rather than talk abstractly about a difficult and subtle point, I'll
give some examples of words that I've found useful. As always, you are
free to choose your own conventions, but they will probably resemble
mine in their basic effects.

Define the words IF, ELSE and THEN to permit the following conditional
statement format:

    boolean value IF true statement ELSE false statement THEN continue

The words have a certain mnemonic value, though they are permuted from
the familiar ALGOL format. Such a statement can only appear in a
definition, for IF, ELSE and THEN are instruction-generating words.

At definition time, the word IF is executed. It compiles a forward jump.
Now I must sidetrack the discussion and define jumps. A jump instruction
for the virtual computer is similar to a literal. An in-line literal is
a double-length instruction. The code executed for the pseudo-entry
comprising the first half, uses the second half as a parameter. Likewise
for jumps: a pseudo-entry uses an in-line parameter to change the
virtual-computer instruction-counter (IC). This parameter is the amount,
positive or negative, to be added to IC: positive for a forward jump,
negative for a backward jump. It is a relative jump address, and the
whole construction is used by some real computers.

Actually we need 2 jump pseudo-entries: a conditional jump and an
unconditional jump. The conditional jump jumps only if the stack is
non-zero, and it is a destructive operation (its argument is dropped).

All right, back to IF. At definition time it compiles the conditional
jump pseudo-entry, followed by a 0. For it doesn't know how far to jump.
And it places the location of the 0, the unknown address, onto the
stack. Remember that the stack is currently not in use, because we're
defining. Later it will be used by those words we're defining, but at the
moment we're free to use it to help in the process.

Now look at ELSE. At definition time it compiles an unconditional jump
pseudo-entry followed by 0. But then it stores the current value of DP,
the next available location, into the location on the stack. Thus it
provides the distance for the conditional jump generated by IF. Actually
it must subtract to get a relative address, but the principle is clear.
In turn it leaves the location of its address on the stack.

Finally we come to THEN. It fixes-up the address that ELSE left
dangling. That is, it subtracts the stack from DP and stores the result
indirectly in the stack; and destructively. Thus the combination of IF,
ELSE and THEN use the stack to construct forward jump virtual-computer
instructions. Since ELSE and THEN act identically in fixing-up the
missing address, ELSE can be omitted without any modification. Also
since the stack is used to store unfulfilled jumps, IF . . . THEN
statements may be nested. The only restriction is that all addresses are
determined; that is, that all locations are removed from the stack. This
will be the case if every IF has a matching THEN; ELSE is always
optional.

Of course there's nothing unusual about this technique. All compilers
generate forward jumps in this manner. What is somewhat unusual is
applying it to the compilation of instructions for a virtual-computer.
But it seems to be the best way.

Let's consider a related construction. Very often we are faced with
logical expressions that consist of a string of ANDs or a string of ORs.
The truth value of such expressions may be determined before the entire
expression is evaluated. You can save time by quitting once you know the
final result. For example, consider the statement:

    a b AND c AND IF . . . THEN

where a, b, c are boolean expressions; and the statement would read in
ALGOL

    *if* a *and* b *and* c *then* . . .

If a is false, we might as well quit, since the disjunction cannot
possibly be true. If you re-write the statement as:

    a IF b IF c IF . . . THEN THEN THEN

the effect is the same; if a, b and c are all true the conditional
statement is executed. Otherwise not. Each IF generates a forward jump
that is caught by its matching THEN. Note that you must still match IFs
with THENs. In fact this is one sort of nested IF . . . THEN statement.
It is an extremely efficient construction.

Now consider the corresponding statement with ORs:

    a b OR c OR IF . . . THEN

or in ALGOL

    *if* a *or* b *or* c *then*

If a is true you may as well quit, for the conjunction cannot be false.
If you re-write the statement as

    a -IF b -IF c IF HERE HERE . . . THEN

and if you define

    : HERE SWAP THEN ;
    : -IF NOT IF ;

the statement works as follows: if a is true, -IF will jump; if b is
true, -if will jump; if c is false, IF will jump. The first HERE will
catch b's jump (the SWAP gets c's address out of the way); the second
HERE catches a's jump; THEN catches c's jump. Thus a and b jump into the
condition, while c jumps over it.

This is a slightly clumsy statement, but I've found no simpler solution.
If you used them regularly, you'd doubtless acquire facility, and it
would seem quite natural. Just watch that you match all IFs. Moreover
the same technique could be applied to more complex logical expressions
- with even greater clumsiness.


### Loops

I'll continue with a couple more examples of words executed at
definition time. This time examples of backward jumps, used to construct
loops.

Consider the pair of words BEGIN and END, as used in a statement like:

    BEGIN . . . boolean END

BEGIN stores DP onto the stack, thus marking the beginning of a loop.
END generates a conditional backward jump to the location left by BEGIN.
That is, it deposits a conditional jump pseudo-entry, subtracts DP+1
from the stack, and deposits that relative address. If the boolean value
is false during execution, you stay in the loop. When it becomes true,
you exit.

BEGIN and END provide a loop terminated by a logical condition. Let's
define another loop. This one counts an index through a range to control
the looping:

    a b DO . . . CONTINUE

`a` and `b` represent arguments on the stack. DO acts just like BEGIN.
CONTINUE requires a new pseudo-entry that tests the top 2 words on the
stack for equality, and jumps if they are unequal. During compilation
CONTINUE deposits this pseudo-entry and then computes the jump distance
as did END. Thus CONTINUE uses another conditional jump: one that tests
the stack for equal, instead of for false. It is also a non-destructive
operation, so long as its arguments are unequal. When they become equal
and terminate the loop, it drops them.

Presumably, inside the DO . . . CONTINUE loop the arguments are modified
so as to terminate the loop. This can be done many ways. For example, to
run the loop from 1 to 10:

    10 0 DO 1 + . . . CONTINUE

The first argument is 10, the stopping value; the second is 0, which is
immediately incremented to 1, the index value. Within the loop this
index is available for use. the DUP operation will obtain a copy. Each
time through the loop the index will be incremented by 1. After the loop
is executed for index value 10, the CONTINUE operation will stop the
loop and drop the 2 arguments - now both 10.

Alternatively, the same loop could be written:

    11 1 DO . . . 1 + CONTINUE

Here the index is incremented at the end of the loop, instead of the
beginning. Upon reaching 11 and exceeding the limit of 10, the loop is
stopped.

Naturally loops can be counted backwards, or indeed many other methods
of modifying the index used. It will always terminate on equality. Of
course, such a flexible loop control runs the risk of never stopping at
all. If you increment the index incorrectly, it will happily run
forever. But used carefully, it's a convenient tool.

A refinement of DO . . . CONTINUE is not difficult. If the arguments are
equal to start with, DO can generate a conditional forward jump that
CONTINUE will fix-up. Thus you may do a loop *no* times. However, such
loops are the exception; but if you encounter one, you'll find the
conditional statement required to protect it most awkward.

### Implementation

I hope you now appreciate the need for words that are executed at define
time. I'm sure you're aware of the need for branches and loops. Perhaps
you'll notice that I did not mention labels; the branch generating words
I mentioned, and others you can invent, are perfectly capable of
handling jumps without labels. You saw in the definition of HERE how the
stack can be manipulated to permit overlapping jumps as well as nested
ones. However in a sense we have many labels, for every dictionary entry
effectively assigns a name to a piece of code.

Now to consider some problems I glossed over. Clearly you must be able
to recognize those words that are to be executed during definitions.
That is, IF, THEN, BEGIN, END, etc. must somehow override the normal
mechanism whereby the control loop would compile them. I mentioned a
switch that distinguished execution from compilation. Let's establish a
similar flag (1 bit) in each dictionary entry, with the values

    1: execute
    0: compile

applying both to switch and flag.

For a given entry, 'or' the switch and flag together; if either is 1,
execute the word, else compile it.

The above rule is correct, and even fairly efficient. Remember that we
want the control loop efficient! And it's adequate providing all words
that must be executed are built into your system dictionary.
Unfortunately, it's not adequate for the examples I gave above, which
probably means it's inadequate, since those were pretty simple examples.
But complication is part of the fun of programming. So pay attention and
I'll try to explain some problems I don't understand very well myself.

## Editor: I don't understand my concern about SWAP below. The word !
did not endure. Don't try to reconcile what I said. I can't.

Consider the definition of HERE I gave above:

    : HERE SWAP THEN ;

Here is one of those imperative words; it must be executed at definition
time. But it is defined as an ordinary definition - and would be
compiled. Even if we managed to execute HERE, the first word in its
definition is SWAP: a most ordinary word, and one that would certainly
be compiled, except that we intend it, too, to be executed. The next
word, THEN, offers no problem - or does it? If we can execute HERE we'll
also execute THEN, since it's imperative. However we have a problem at
the time we *define* HERE; we'll try to *execute* THEN, when we want to
*compile* it. That is, sometimes we want to compile imperative words;
and sometimes we want to execute ordinary words - even in a definition.

So, what to do? I bet you think I have a solution. Your faith is
touching, but I don't have a very good one. It suffers a small
restriction, but a nagging one: you may not execute a literal in a
definition. To phrase it positively: literals must be compiled inside
definitions. Let's see how it works.

Consider the switch STATE. It's normally 0; ":" makes it 1 to indicate
compilation. Let's define a new defining entry ":!" that acts exactly
like ":" with 2 exceptions:

  *  It sets the entry flag to 1; to mark an imperative word.
  *  It sets STATE to 2; to force all words to be compiled. Since the
    test in the control loop is to execute if STATE and flag are equal,
    nothing will execute.

";" is unchanged; its sets STATE to 0 for both sorts of definitions.
This solves all our problems except SWAP. How do we execute words that
ordinarily would be compiled?

Define a new entry "!". Let it execute the last entry compiled and
remove it from the compilation. Now we can re-write the definition of
HERE as

  *  :! HERE SWAP ! THEN ;

and it will work. I'll review the rules:

  *  All words are normally executed.
  *  Only words flagged imperative are executed in definitions.
  *  Any word can be made imperative by following it with an "!".
  *  A definition can be made imperative by using ":!" instead of ":" to
    define it.

Now the restriction I mentioned should be apparent. A literal cannot be
made imperative with a "!" because it's a double-length instruction -
and the "!" code has no way of knowing that. Oh well, we could set a
field to indicate the length of the last compiled instruction, but it's
not that great a problem. Besides, in that case successive !s wouldn't
work.

## Code entries

I've explained definitions and how they, in effect, compile instructions
for the virtual-computer. What about compiling code for your real
computer then? Of course you can. But you probably won't.

The Basic Principle intrudes. If you add code entries to your program,
you add enormous power and flexibility. Anything your computer can do,
any instructions it has, any tricks you can play with its hardware are
at you fingertips. This is fine, but you rarely need such power. And the
cost is appreciable. You'll need many entries (say 10) to provide a
useful compiler; plus all the instruction mnemonics. Moreover you'll
have to design an application language directed at the problem of
compiling code.

I don't want to down-grade the possibility or value of such efforts, but
you wrote your program in some language to start with. If you need
additional code it's much easier to re-compile your program and add what
you need. Only if you have an application that needs tailored code. or
can profit by providing different code to different users, or different
code at different times, can you satisfy the Basic Principle.

On the other hand, if you start with code entries, you can construct all
the other entries I've been talking about: arithmetic operators, noun
entries, definitions. In Chapter 9 I'll show how you can use code
entries in a really essential role; and achieve a significantly more
efficient and powerful program than by any other means. But except for
that I'm afraid they are marginal.

So how can you generate code? First you need a defining entry that
defines a code entry. The characteristic of a code entry is that it
executes code stored in its parameter field. Thus the address passed to
ENTRY by its defining entry (say CODE) must be the location into which
will be placed the first instruction. This is not DP, because the entry
itself takes space; but is simply DP plus a constant.

Second you need an entry to deposit a number at DP. We have used such a
routine several times, constructing variables and definitions, but we've
not had an entry for it. I suggest the word "," although that might
conflict with your output entries. All it does is move a number from the
stack to the parameter field. Instructions are numbers of course. You'll
construct them on the stack and then deposit them. Incidentally, this is a
useful entry - apart from compiling code. You'll find it useful for
initializing data arrays of all kinds.

Now you can appreciate the source of my earlier caution. You'll have to
provide a flock of entries that access code compiled into your program
that we've not needed to reference directly before. For example RETURN:
when you routine is finished, it must jump to the control loop, just as
you built-in entries do. However you don't know the location of the
control loop in core; and it moves as you change your program. So you
must have an entry to generate a RETURN instruction.

Likewise, if you plan to compile defining entries you must provide
entries that will generate subroutine calls to ENTRY. Other code might
want to access WORD or NUMBER or indeed any facility already available
in your program. Moreover you will have to define variable entries for
those fields you will use: D and F for output; perhaps STATE and BASE;
Basically, the problem is that you must make available outside your
program, all the labels available inside it already. You must use them
enough to justify the effort.

All right, you've done that much. Now you've got to decide how to
construct an instruction. They have several fields - instruction, index,
address - that you'll want to put onto the stack separately and combine
somehow. This is easy to do, but hard to design. You probably don't want
to copy your assembler, and probably couldn't follow its format
conveniently anyway. In fact you can do a good job of designing a
readable compiler language; but it will take some effort. Definitions
provide all the tools you need.

For example, you might write a definition that will "or" together an
instruction and address and deposit it. Or if your hardware's awkward,
you can provide a definition that converts absolute addresses to
relative, or supplies appropriate paging controls. Whatever you need, or
want can be readily defined. Done properly, such a compiler is a
substantial application in itself, and if you're going to do it at all,
plan to spend the necessary time and effort.

We discussed conditional statements and loops for the virtual computer.
Precisely the same techniques apply here, with due allowance for
hardware variations. In fact, I originally applied the stack-oriented
branch generation to code for my real computer. Such statements are
really the difference between an assembler and a compiler. Keep in mind
the Basic Principle.

One valuable use of a compiler is the permit the definition of new kinds
of nouns. That is, to construct new defining entries. As an example
consider using the primitive compiler to define instruction entries as
described just above. Or you might want to define entries that multiply
the top of the stack by a constant.

As usual when adding an ability, several distinct entries must cooperate
to provide it. In this case ENTER and ;CODE. Let me illustrate:

    : UNIT ENTER , ;CODE 1 V LDA , SP MPY , SP STA , NEXT ,
    2.54 UNIT IN
    4. IN

The first line defines the word UNIT. The next line uses this defining
entry to define the word IN (inches). The last line uses IN in a way
that puts 4 inches onto the stack, as centimeters. The 3 lines are
equivalent to

    : IN 2.54 \* ;

which is certainly simpler. But if you want to define many UNITs, a
special defining entry is much more convenient and efficient.

The first special word is ENTER. It calls the ENTRY subroutine used by
all your defining entries, but passes a 0 address as the location of the
code to be executed. Look at the definition of UNIT. The word ENTER is
imperative. It generates a double-length pseudo-instruction; a
pseudo-entry for the first half and a 0 constant for the second. At
execution time, the pseudo-entry will call ENTRY to construct a new
dictionary entry, passing the following constant as the address of code
to be executed. The word ;CODE is a combination of the words ";" and
CODE. It terminates the definition of UNIT and stores DP into the
address field established by ENTER. Thus the code that follows ;CODE is
the code that will be executed for all entries created by UNIT. ;CODE
knows where to store DP because ENTER is restricted to being the first
word in any definition that uses it; and ;CODE knows which definition it
is terminating.

The restriction on the position of ENTER is unimportant, it may as well
be first as anywhere else. In the case of UNIT, only a "," to deposit
the constant was needed. Other nouns might need more elaborate
processing to establish their parameter field.

You notice I gave an example of code following ;CODE. You see
instruction mnemonics and addresses deposited by ",". I don't want to
explain this compiler language, for it is not relevant for your
computer.

One more suggestion might prove helpful. You might define a new kind of
constant: an instruction. When executed, an instruction expects an
address on the stack, extracts a constant from its parameter field and
constructs and deposits a completed instruction. You'll probably have a
large number of instructions, and use a large number. This will save you
many deposit entries.

I'm sorry, but I think it's infeasible to attempt an example. If you
can't see how to construct your own code entries from what I've already
said, forget it. The application is extremely machine dependent - and
rightly so. Don't attempt to apply the same code to several computers;
definitions already do that for you. The purpose of code is to exploit
the properties of your particular computer.



# Programs with memory

You may perhaps grant the value of a program that grows, without being
willing to provide the volume of input required. Naturally it does
little good to have a hundred dictionary entries if you must type every
one. Obviously we need a place to save entries and obviously that place
is disk (or drum, or other random secondary memory).

What is not obvious is how to store entries. It ought to be a Second
Principle that you never save anything on disk without being able to
modify it, but this rule is universally ignored. To simply copy
dictionary entries violates another cardinal principle: never store core
address on disk. You could never modify your program without chasing
down all code addresses.

Fortunately there is a solution. Store on disk the text from which
dictionary entries are constructed. It is a simple matter to divert the
input routine from reading your message buffer to reading disk. This
chapter will show how.


## Organization of disk

There is only one way to organize disk. In the same way that core is
divided into a large number of words, disk must be divided into a large
number of blocks. In the same way that words are the smallest field that
can be fetched from core, blocks are the smallest field that can be
fetched from disk. A block contains 256 words.

A block contains 256 words because that is the size of a 1-byte address,
and because 256 4-byte words hold 1024 bytes which is the amount of text
that can be displayed on a typical scope.

However, here is another instance in which your application and hardware
must play a dominant role. Disks usually have a hardware block-size that
offers advantages. You must choose a multiple of that. Your application
may involve storing data on disk, and you must choose a block size
useful for data as well as text. I say no less than 512 characters nor
more than 1024. 128 word blocks have recently been mentioned; fine if
the words are 6 or 3 bytes (characters).


### Getting blocks

In trying to anticipate the organization of a random file, certain
principles are obvious. Cross-references between blocks will probably be
wanted. Such references are simple if they use absolute block addresses;
extremely clumsy otherwise. We may use absolute addresses if we promise
never to move a block. This means we can never pack disk. We agree
cheerfully because we didn't want to pack disk anyway.

This means that as the data in blocks becomes useless, space will become
available in block-sized holes. We must somehow re-use these holes.
Which means that we must allocate, and re-allocate, disk in block-sized
pieces.

All addresses start at 0, block addresses included (otherwise you find
yourself forever adding and subtracting 1). However we cannot use block 0
- for anything. You will find that most addressing errors involve block
0. If you look at block 0 from time to time you will find the most
amazing things there. You will find block 1 a useful place to store
things you need to remember from run to run. Like the address of the
first block available for re-use - none: 0. And the address of the last
block used - initially: 1.

You will want to copy disk (onto another disk, or tape) for protection.
You need only copy the number of blocks used, which is usually less than
half the disk capacity, or else you're pretty worried about space. If
you destroy block 1 (you will) you will have to re-load the entire disk
from your back-up. Never try to recover just block 1, you'll end up
horribly confused.

You may want to put your object program on this disk. Fine! It won't even
take many blocks. You may need to start it in block 0 in order to do an
initial load (bootstrap). OK, but be able to re-load the program (only)
from back-up because you will destroy block 0. Only if you destroy the
block (we'll call it block 1) containing available space information
must you re-load data (all data). Unless you destroy many blocks. Choose
the path of least confusion, not least effort. Re-loading disk will
confuse you, you'll forget what you've changed and be days discovering
it. Much better you spend hours re-typing text and re-entering data.

So when you need a block, you type a word (GET) which reads block 1,
places the block up for re-use on the stack, reads that block, places
the contents of its first word into block 1, and re-writes block 1. The
first word, of course, contains the address of the next block up for
re-use. If no block was available for re-use (initially the case), GET
increments the last block used, puts it on the stack and re-writes block
1. GET then clears your new block to 0 and re-writes it.

Several comments: Notice that GET places its result on the stack - the
logical place where it is available for further use. Notice that blocks
are re-used in preference to expanding the disk used. This makes sense
except for the problem of arm motion. Forget arm motion. You just have
to live with it. This is, after all, a random memory. Don't neglect
clearing the block to 0.


### Releasing blocks

To release a block, put it on the stack and say RELEASE. It will read
block 1, extract the next block for re-use, place the stack there and
write block 1; then read the released block and place the old next-block
in the first word. All we're doing, of course, in constructing the chain
of available blocks used by GET. Possibly the block you release is
linked to other blocks. You must release all those, too. A convenient
way is to use the first word as a link field. Then the available block
chain is the same as any other block chain. To concatenate chains you
place the first block in block 1, run down the chain to the last block
(0 in link) and place the old next-block in that link.

Don't be tempted to maintain a count of the available blocks. Its not
worth the trouble. If you must know, you can count the length of the
available chain.

If you have enough different kinds of blocks, it may be useful to store
a code identifying the block in the first word (or second). You can then
examine all blocks of a certain kind. Available blocks should have code
0.

How many blocks you can have is probably limited by the disk, however it
may be limited by the field you choose to store block addresses in. Be
careful! You can circumvent the first limit by modifying your read
subroutine to choose one of several disks. You must re-format all your
block addresses (cross-references on disk, remember) to expand the
second.


### Reading and writing disk

I'm sure you know how to read disk. However, do not choose a block size
that causes the slightest difficulty: like half a block between tracks.
If you check the GET routine, you'll see that you'll need 2 blocks in
core at once. This is a reasonable minimum, it makes it easy to move
things from one block to another. However, you'll have lots of core left
over and you might as well use it for buffering disk; especially if
access time is noticeable.

You'll want a table specifying which blocks are in core: your read
routine can check this table before reading.

But you should not write a block when you change it. Rather mark it 'to
be written' in the buffer table. When you come to re-use that buffer,
write the old block first. The principle is that you're likely to change
a block again if you change it once. If you minimize writes you can save
a lot of disk accesses. Of course, there is a trade-off - if you program
crashes, you may have updated blocks in core that aren't on disk. You
should be able to re-start your program and preserve the core buffers.

Of course, multiple core buffers imply an allocation problem. A simple
round-robin is as effective a scheme as any.

If you are going to scan data sequentially, you can save many accesses
by reading consecutive blocks at the same time. However it is likely
that random reads may be interspersed with these sequential ones. An
effective solution is to store the *last* block in the sequential area
and the number of blocks somewhere for your read subroutine. If the
block isn't in core, and is within the sequential range, it can read as
many consecutive blocks as there are consecutive buffers available.
Don't attempt more than this - ie, making more buffers available. The
net effect is that you will do the best you can with sequential blocks,
subject to interfering constraints.

You will inevitably spend a lot of effort reading-writing disk. But
remember the Basic Principle!


## Text on disk

You will store a lot of text on disk - hundreds of blocks - but this is
probably a small fraction of your disk. The rest is presumably data for
your application(s).

A block that contains text (I mean text to be read and executed by your
program) contains one long character string. If the first word contains
control information, it starts in the second word and extends until a
particular word marks the end (perhaps ;S). This end word is important
because it is inconvenient to have the input routine test for
end-of-block. You quickly learn not to leave that word out.

A block that contains text should have a special name, for you will be
using it often in conversation. I have called such blocks SHEETs - since
the text filled a sheet of paper - and SCREENs - since the text filled
the screen of a scope. Define the word READ to save the input address,
the block and character position of the next character to be scanned, on
the return stack; and reset the input pointer to the block on the stack
and the first character position. Define the word ;S to restore the
original input pointer. Very simply you can have your program read block
123:

    123 READ

However . . . there's always a however, isn't there. You must modify
your word routine to read the current block before scanning. This is
expensive but essential (of course no actual read is performed if the
block is in core), for the last word executed may have caused a block to
be read that overlaid the block the word was read from. This can
especially occur if one screen directs the reading of others (as they
will). No other solution to this problem has been satisfactory, so
swallow the code - which need not be great.

You will find that with text on disk, the original characterization of
'input' as low volume is strained. You will read many words and do many
dictionary searches. However, on a microsecond computer, you won't
notice it.


### Text editing

Never put anything on disk you can't modify! And we haven't discussed
how you get text on disk in the first place. Do not load it from cards!
You're misdirecting your effort toward card reading, and you had to
punch the cards anyway. Type it. The definitions required to edit the
text stored in blocks (SCREENs) is simple.

You must be able to handle character strings surrounded with quotes
(4.1). Given that, I shall exhibit a text editing screen. This is a
simple example of the value of definitions. You may notice it is the
first non-trivial example I've given. You should be motivated by now to
give it proper attention.

Naturally, you're going to have to type these definitions twice. Once to
put them into your dictionary; again, to use them to put them in a
screen (bootstrapping). In fact you'll probably type them many times,
but 2 is minimum.

I'm going to exhibit an annotated copy of the EDIT screen I used in a
particular program. It uses system entries whose value may not be clear.
They are borrowed from other aspects of the application.

    0 C1 42 \# :R RECORD

Here I am constructing a field description: RECORD is a 42 character
field starting in character 1 of word 0 of the current block
(understood). I'm using blocks that can hold 15 42-character lines; a
word has 6 characters, so that's 15 7-word lines.

    : LINE 1 - 7 \* RECORD + ;

Here I'm defining a verb that will convert a line number (1-15) to a
field address. It modifies the RECORD descriptor by changing the word
specification (low order bits). Thus line 1 starts in word 0; line 2 in
word 7; etc.

    : T CR LINE ,C ;

If I type 3 T - I want line 3 typed. T does a carriage return (CR),
executes LINE to compute the field address, and copies the (character)
field into the message buffer (,C).

    : R LINE =C ;

If I type " NEW TEXT" 6 R - I want line 6 to be replaced by the text in
quotes. The leading quote puts a string descriptor on the stack. R then
executes LINE, followed by =C to store the quote string in the field.
The block will automatically be re-written, since it was changed.

    : LIST 15 0 DO 1 +
    CR DUP LINE ,C DUP ,I CONTINUE ;

LIST will list the entire block: 15 42-character lines followed by line
numbers. It sets up a DO-CONTINUE loop with the stack varying from 1 -
15. Each time through the loop it: does a CR; copies the stack and
executes LINE; types the field (,C); copies the stack again and types it
as an integer (,I).

    : I 1 + DUP 15 DO 1 -
    DUP LINE DUP 7 + =C CONTINUE R ;

If I type " NEW TEXT" 6 I - I want the text inserted after line 6. "I"
must first shift lines 7 - 14 down one position (losing line 15) and
then replace line 7. It adds 1 to the line number, sets up a backwards
DO-CONTINUE loop starting at 14, constructs two field descriptors, LINE
and LINE+7, and shifts them (,C). When the loop if finished, it does an
R.

    : D 15 SWAP DO 1 +
    DUP LINE DUP 7 - =C CONTINUE " " 15 R ;

If I type 12 D - I want to delete line 12. D must move lines 13-15 up
one position and clear line 15: It sets up a DO-CONTINUE loop from
stack+1 to 15. Each iteration it: constructs fields LINE and LINE-7 and
shifts them (=C). Then it replaces line 15 with spaces.

That's it. With 10 lines of code I can define a text-editor. It's not
the most efficient possible, but it's fast enough and illustrates many
points: In dealing with small amounts of text, you needn't be clever;
let the machine do the work. The verb LINE is an extremely useful one;
such useful verbs are invariably an empirical discovery. The verbs ,C
and =C are the heart of the method; incidentally, they only work on fields
less than 64 characters. Notice how one definition wants to reference
another (R used by I and D; LINE used by all). Notice how I and D are
similar yet different. And notice how a few verbs eliminate a lot of
bookkeeping and let you concentrate on the problem and not the details.



# Programs with output

By now I'm sure you're aware that the heart of your program is its
control loop. It not only controls the operation, but also the
philosophy and organization of the program. Let me review its operation:
it reads a word, finds it in the dictionary and executes its code;
failing that it converts it to a binary number and places it onto the
stack; failing that it types an error message.

So far I've ignored that error message; not because it's unimportant or
trivial to implement, but because it's part of a difficult subject -
output. Logically I oughtn't have delayed discussing output this long,
for even a control language needs output. But as usual in this program
it is involved with other features that we've only just discussed. I'll
leave it to you to implement those features of the output capabilities
I'll present, that your application requires.

Most compilers, and therefore most programmers, regard output the
inverse of input. For example, FORTRAN uses the same FORMAT statements
for output as for input, thereby suggesting that the two processes are
very similar. But are they?

*You* compose input: you select words and combine them into fairly
complex phrases; your program spends considerable effort deciphering
this input and extracting its meaning. In reply it will not go through
any such elaborate procedure. You'll see that most of its output
consists of the word OK. You are talking to the computer, but it is
hardly talking to you; at best it's grunting.

I maintain that the two processes have nothing in common, that the
computer does not prepare output in a manner analogous to you preparing
input. In Chapter 8 I'll describe a way your program can compose complex
output messages. Although such a technique might provide a 2-way dialog,
it has even less similarity to interpreting input.


## Output routines

You will need 3 output subroutines; conceivably you could get by with 2.
One to type a number of spaces. One to type a number of characters from
a specified location (TYPE~N~). One to type characters until it
encounters a space (TYPE~B~) and including the space. This last depends
on your dictionary format, for it is used to type entry words. Of
course, these should use the fetch and deposit subroutines you use for
input.

Let us use the composition of an error message as an example. You have
just typed an input message, the carriage is positioned at the last
character. First you want a space. Then use TYPE~B~ to type the current
word. It caused the error and will tell you where it occurred. You don't
need this for an unbuffered device. Then use TYPE~B~ again to type a
word that describes the error. Avoid long error messages - you're the
one who will wait while they're typed. You can detect a number of
errors, so it's worth your while to devise a routine to generate them.

After finding an error, you of course quit doing whatever you were
doing. There is no point in trying to continue when you're standing by
ready to correct and start again. However it is convenient to reset
things that you'd probably have to reset anyway. In particular, set the
stacks empty. This is sometimes unfortunate since the parameter stack
might help you locate an error. But it usually is most convenient. Don't
try to reset the dictionary since you're not sure what you may want to
reset it to.


## Acknowledgement

I mentioned in Chapter 3 that you must write subroutines to send and
receive messages. Now I must expand on exactly how you should use these
subroutines.

Recall that input and output share the same message buffer. This now
causes trouble. However it considerably simplifies the more powerful
message routines of Chapter 7. On balance the single message buffer
seems optimal.

First let me call the subroutine that sends a message SEND. It sends a
single line and should add a carriage return to the line, as well as any
other control characters needed, and translate characters as required.
The routine that receives a message is QUERY. It is a routine, and not a
subroutine. QUERY calls SEND to send a message, and then awaits and
processes an input message. stripping control characters and translating
characters as required. It initializes the input pointer IP and jumps to
NEXT~W~. Notice that your program can send output via SEND wherever it
pleases. However it can only receive input in conjunction with output,
via QUERY. You have no provision for receiving successive messages
without intervening output. This is exactly the behavior you need, and
actually simplifies the coding of message I/O.

Now let me describe the use of QUERY. Each input message is terminated
with an end-of-message word, a non-printing character surrounded by
spaces. This word has a dictionary entry that types the word OK and
jumps to QUERY. Thus after interpreting each input message, your program
types a brief acknowledgement - OK, message received and understood -
and awaits further input.

Notice that if an input message generates output it destroys itself.
That is, the output is placed in the message buffer irrespective of the
input already there. Thus a word that generates output should be the
last word in a message, since succeeding words will not be seen. In
particular, the end-of-message word won't be seen and the reply OK won't
be typed. This is what you want: OK is only typed in lieu of any other
output.

OK should appear on the same line as the input message, separated from
the last word by a least one space. QUERY should not acknowledge receipt
of a message - as most time-sharing systems do - with a carriage-return.
The only acknowledgement is the OK at completion of interpretation.
Placing OK on the same line helps distinguish output from input and
compresses the conversation, especially valuable on a limited-size scope
face. A user must not type input until he receives output. It's only
important to enforce this rule with multi-user programs. For this see
Chapter 7.

In order to determine whether there is input in the message buffer,
establish a field EMPTY. QUERY should set empty false and each output
generating entry should set it true. Actually output generating verbs
have much in common with each other, and each should jump to a routine
that does the following:

  * Drop the stack. Each output verb must have an argument. Its last
    argument can be dropped at this point, and the stack pointer checked
    against its lower limit.
  * Set EMPTY true.
  * If NEXT contains NEXT~W~ and SCREEN is 0, jump to QUERY. Under these
    circumstances there is no further input available in the message
    buffer.
  * Jump to NEXT.

Notice that if entries are coming from a definition or from a screen, no
conflict can arise with the message buffer. Only if input is currently
being read from the message buffer is there a problem.

However there are 2 places where source of input is changed. This is in
the code for ";" and ";S". If ";" restores NEXT~W~ to NEXT, it must
guarantee that input is available. That is, jump to QUERY if EMPTY is
true and SCREEN is 0. Likewise, if ";S" restores SCREEN to 0, it should
jump to QUERY if EMPTY is true (NEXT is guaranted to be NEXT~W~.

The logic required is summarized in Fig 6.2 and is the price paid for
duplexing the message buffer. One final complication concerns EMPTY. If
true, it states that input has been destroyed; it does not indicate that
output is currently in the message buffer. Output may have been placed
there and already sent. If the message buffer is empty, type OK before
jumping to QUERY.


## Character strings

Everything isn't easy, and this particular feature is my nemesis.
Perhaps a measure of its value is the difficulty of its implementation.
A character string is an awkward entity. Mostly because there is nowhere
to put it. Numeric literals go on the stack in a most natural fashion.
Character strings won't fit, and that isn't what we want to do with them
anyway.

My solution is this. When you see a character string, leave it alone.
Put on the stack a descriptor giving the address of the first character
and the number of characters in the string. Skip over the string. That
is, advance the input pointer to its end. You can't do it in quite that
order, of course, because only by skipping can you discover the number
of characters.

What does a character string look like? Of all the ways you might
choose, one is completely natural:

    "ABCDEF . . . XYZ"

A character string is enclosed in quotes. It can contain any character
except a quote, specifically including spaces.

We get in trouble immediately! How do you recognize a character string?
By the leading quote, for course. But do you modify your word subroutine
to recognize that quote? If you do so you may never use a leading quote
for any other purpose. Much better that the quote is a word by itself,
treated like any other dictionary entry, for it can then be re-defined.
But words are terminated by spaces, and I still resist making quote an
exception. So let's type character strings:

    " ABCDEF . . . XYZ"

The extra space is annoying, but in Chapter 8 I will tell you how to
eliminate it without the objections I just raised. So a character string
is started with a quote-space and terminated by a quote.

Remember that we leave the character string alone, merely remembering
where it is. We are talking about character strings in the input buffer
(so far), and we had better use the string before we destroy it with
output or additional input. *When* it is destroyed depends on many
things, so the best rule is to use it immediately.

What can you do with a character string? I've only found 2 uses. They
are very similar, but part of the frustration of implementing them is to
take advantage of the similarity. You can type a string, or you can move
it to a character field.

To type a string is easy. Define an entry that uses the descriptor on
the stack to set parameters for the TYPE~N~ subroutine.

To move a string is harder, but still easy. You have 2 descriptors on
the stack: on top a field descriptor; below the string descriptor. Set
the input and output pointers, and do a character move of length the
smaller of the 2 field sizes. Space fill the remainder of the
destination field. Notice that you mustn't move more characters than you
have, or will fit. And of course, string descriptors will rarely have
the right size. Truncating a string is not an error condition!

If you can do the above, you can also move one character field to
another. That is, if you make your character string and field
descriptors compatible - which adds to the fun. You might want to
prevent moving a field to a string, but than who cares.

The problem is to reconcile all the above requirements. Not really to
produce optimum code, but even to produce code that is remotely
acceptable in size, speed, restrictions and correct operation.

We've slid into the subject of field descriptors. You might want to type
a character field, and of course the same code should work as for string
descriptors.

## Field entries

We've talked about the different kinds of numbers you might want, and
the different entries these require. However, all these entries dealt
with computation. Another kind of entry is useful for more sophisticated
output purposes. I call it a field-entry because its most common use is
to define a field in a data record.

In addition to the descriptor associated with a variable, a field entry
needs additional parameters that specify the output format. It is
extremely useful to be able to specify a field width for output once and
for all, and then use it automatically on all reports. Also it is useful
to be able to reference the name of the field - which of course is
contained in the dictionary entry.

So a useful convention is that a field entry puts the address of itself
- that is the dictionary entry - on the stack. Recall that a variable
entry places the address of the variable on the stack. If you want the
name of the entry, this address tells you where it is. If you want the
format, this address - offset by some constant - tells you where to find
it. And if you want the address of the field, you can get that too - a
process that is executed automatically for a variable.

These various capabilities require various entries to effect them. You
might define:

    ,NM - type out field name.
    F - extract field width.
    @F - obtain field address.

Depending (as usual) you might be able to make @F compatible with @. Or
make @ automatically work correctly for field entries. You may want to
distinguish addresses of variables from address of field entries. This
would be analogous to distinguishing different kinds of numbers, and for
the same reason - so that the same operations (in this case probably @
and =) will work on all.

Apply the Basic Principle.



# Programs that share

It is not obvious, but a program organised as we have discussed is
ideally suited to handling several users simultaneously. All of the
basic problems of interactive processing have been solved by interacting
with one user. The organization is such that all data is, or can be,
stored in the user's dictionary. To distinguish users merely requires
the program recognise the proper dictionary.

Of course the value of multiple users depends upon the application.
There appears to be a correlation between the complexity of an
application and the number of potential users. An application that
deserves a problem-oriented-language my well be of interest to many users
on a continuous basis.

Moreover, once the basic program is available, it is relatively simple
to add other, even unrelated, applications. The ability to control your
vocabulary by reading screens allows a terminal to be used by different
people with absolute minimum effort: each can have a personal screen
that will load his dictionary with the vocabulary he wants.

Providing the message traffic from any one terminal is low enough, as is
inevitably the case - for we have in effect slowed the computer down to
human speed - we can handle a much larger number of terminals than can
fit in core, hundreds, by storing inactive users on disk.

However there is a cost, primarily of assuring that re-entrant
programming rules are strictly followed. The additional code required to
switch the computer's attention among users and the additional core
required for disk buffers and user dictionaries demand that a single
user application by de-bugged first. And then the capacity of the
computer multiplied with a multiple-user control routine as the demand
develops. It is all too easy to get bogged down in the multiple-user
controller and never to perfect an application. Or to perfect a
multiple-user control and never to find a demand to justify it.

Given a successful single-user application, I will show how it can be
expanded to many users. If you plan to take this step, there are certain
precautions you should take with your original implementation. But mind
the Basic Principle!

### Non-user activities

Each user has a position in the ready table to identify his status. The
computer examines this table to decide what to do next. You may want to
add to the ready table entries not associated with users, but
representing tasks that must be performed by the computer.

For example, if you have to poll phone lines to acquire input, you want
to perform these polls asynchronously with whatever other work you're
doing. Since interrupt routines are best kept small, the task of
translating character sets, checking parity, distributing messages, etc.,
should be performed at lower priority. This is easy to do with an entry
in the ready table. The interrupt routine sets a message routine "ready"
and the computer will process it when possible.

Each such independent activity should have a ready table entry and a
(perhaps) small dictionary in which to store its parameters; return
address, register contents, etc. in the same format as a user activity.
In fact these activities are completely equivalent to users, except that
they don't process users. This is significant, for it means they never
generate error messages, they must handle their own errors, somehow.

If you haven't already noticed, we're now talking about operating
systems. I don't have much more to say on the subject, but there are
other asynchronous activities you might want:

  *  A clock to handle the timer interrupt and maintain a time and date
    in core and disk. It might ready other activities that relinquished
    control for a fixed time.
  *  A routine to write blocks on disk. Periodically it might scan the
    block buffers for blocks to copy. (however, writing blocks when the
    read routine needs a buffer seems simpler.)

Such activities cost little, and usually provide the simplest answer to
any asynchronous problem. Mind the Basic Principle, though!

### Message handling

If you can read input from one user, you can read input from many. You
must get an interrupt that tells you input is available and from whom it
comes. You simple direct it to the proper message buffer. Likewise with
output.

It needn't be simple, but it certainly depends on hardware exclusively.
If you have to poll terminals, it can become very interesting, indeed.
But the problem remains beyond the scope of this book.

If all your users are not core resident, it is better if none of them
are. Then any input message can be written into the message buffer area
on disk. And all output messages read from disk. The fact that some
users might reside in core, causes an unreasonable complication, and the
fact that disk access is fast compared to message transmission means
that to attempt to save such disk accesses is not efficient.

## User control

The fact that you have several users creates a new problem. Of course
the computer can only process one user at a time (we assume a single
processor). But when it's finished with one user, it must switch its
attention to another.

When is it finished with one user? Clearly, if a user is awaiting input
the computer is finished. We are talking about keyboard input, which
will take many seconds to arrive. Similarly if the user is sending
output, the computer may as well stop. Output will take several seconds,
especially if an acknowledgement from the device is anticipated. It
needn't stop. While sending one message, it could be composing the next.
But it's much simpler not to attempt such overlap. If the user is
reading disk, the computer can stop.

I want to define a single phrase to cover these situations. I shall say
that a user relinquishes control of the processor whenever he does
message or disk I/O. This is a voluntary action on his part, and those
are the only times he relinquishes control. In particular, there is no
time quantum that will take control from him. For this reason: With
several users, code must clearly be re-entrant. However, if a user is
promised that he will be allowed to finish what he starts, if he will
not lose control to someone else except when he relinquishes it, the
re-entrant requirements become much less onerous. The program need only
be re-entrant across I/O, which can save a lot of bother.

All right, what happens when a user relinquishes control? The computer
simple scans a table of users to see if anyone else is ready. The table
contains the address of the user's dictionary and a flag: ready or not?
The I/O complete interrupt routines simply mark the proper user ready.
And if no one is ready, the computer scans the table endlessly - it's
got nothing better to do. Naturally, upon program start-up, no one is
ready.

## Queing

You can save yourself a lot of trouble by putting some code in the user
controller. Two subroutines: QUE and UNQUE. When a user needs a facility
that might be in use by someone else, he calls QUE. If it's available,
he gets it. If it's not available, he joins the que of people waiting
for it. When it is released, and his turn, he will get it.

For example, he can't read disk if someone else if reading disk. Or at
least he can't use a particular channel or device. While he's waiting,
of course he relinquishes control. When he's through with the facility,
he calls UNQUE which passes it to someone else.

These are extremely valuable routines, for there are many facilities
that can be handled in the manner; each disk, each line (shared lines),
the printer, block 1 (disk allocation), non-re-entrant routines (SQRT).
An extension will even permit exclusive use of blocks.

Naturally, I have in mind a specific way to implement QUE and UNQUE. And
I caution you, more strongly than usual, that plausible modifications
won't work. I'll try to mention all the reasons.

In addition to the user's dictionary address and ready flag, each user
must have a link field - not in his dictionary, but in user control.
Each facility that is to be protected must have associated with it 2
fields: the owner, and the first person waiting. The best arrangement is
to have a table of such que-words, one for each facility. If a facility
is free, its owner is 0; otherwise its owner is the number of the user
owning it. A user's number is his position in the table of users,
starting at 1. If no one is waiting, a facility's waiter field is 0;
otherwise it is the number of the user waiting.

If I want a facility and its free:

  *  I place my number in the owner field and exit.

If it's busy, but no one's waiting:

  *  I place my number in the waiter field, 0 my link field, and
    relinquish control.

If someone's waiting:

  *  I follow the chain of links starting at the waiter's link field
    until I find a 0 link; I place my number there, 0 my link field, and
    relinquish control.

When I'm through with a facility (UNQUE):

  *  IF no one's waiting, I 0 the owner field, and exit.
  *  If someone's waiting, I move his number to the owner field, move his
    link field to the waiter field, mark him ready, and exit.

The whole procedure is simple and efficient. It handles a lot of
potential problems in a reasonable and effective way. Several comments:
The ques will probably be very short. In fact, facilities will usually
be free, unless the computer is over-loaded. A user can not be in more
than one que. However, a user can own more than one facility. Hence the
need for a waiter field with each facility: a que must descend from each
facility, and not from each owner; the two concepts are independent. You
must add to the error routine a loop to release any facilities held by
the current user. Since a user needs to know his own number in order to
que, this number must be stored in a field in his dictionary, and be set
by the re-initialize routine.

It's complicated, it's troublesome, and it's the price you must pay for
multiple users.

To gain exclusive use of a block, with the exception of block 1, best
handled as an exception, set aside some facility que-words for this
purpose. Find a free one and store the block number it represents
somewhere, then treat that block like any other facility. When the last
waiter releases the block, release the facility que-word for re-use.
Notice that this technique has no effect upon the block itself. It may
be resident in core, or not. Anyone may read or write it. However, no
one else may have exclusive use of it. If all users cooperate to request
exclusive use when the should, it works perfectly - with no extra cost
to ordinary reads/writes. Actually, exclusive use of a block is
necessary only under exceptional circumstances. Block 1 is an example of
such: The block may not be used by anyone else until another block has
been read, and the available space up-dated.

## Private dictionaries

The key to the case of conversion to multiple users is that all required
information about a user is stored in his dictionary - a single
contiguous area of core. He makes extensive use of code that belongs to
the system, and that does not reside in his dictionary. On the other
hand, code unique to his application may reside there. Here is the first
decision that you must make: What belongs in the user's private
dictionary?

Let us look at the arrangement of core. If we choose, and we should, it
follows dictionary format: each entry followed by the code it executes.
Each entry is linked to the previous so that the dictionary may be
searched backwards. Some entries are obviously of interest to all
applications: those that control the stack, that define dictionary
entries, that specify fields such as BASE, CONTEXT, etc. Other entries
are probably of local concern: the names of fields in records,
definitions used to edit text, special purpose code (random number
generator, square root, etc.). At some point you must separate the
system and user dictionaries.

If you establish several user dictionaries, the first entry in each will
link to the system dictionary (Fig 7.1) at the same point.Thus each user
is unaware of any other user, and his dictionary search is unaffected.

## Controlled access

It would appear that you want the system dictionary as large as possible
to avoid redundancy. That is not necessarily the case. There are some
entries that might go into the system dictionary - except that you
specifically want to deny them to some users. Prime examples are the GET
and DELETE entries that control disk allocation. Misuse of these words
by ignorant users can badly damage data stored on disk. The best
solution is to place the code in the system, without a dictionary entry.
Define a table of entry points into code of this nature. Then if a user
wants to use an entry point, he must first define it, perhaps:

    17 ENTRY GET 18 ENTRY RELEASE

establishing the words GET and RELEASE with the code identified in the
17th and 18th table positions. Library subroutines (FORTRAN arithmetic
subroutines) might be treated similarly.

Incidentally, this illustrates a general method of protection: In addition
to using a word, the user must define it correctly. Clearly you can
cascade the process. The value of such protection against malicious
mischief depends on secrecy, which is always the ultimate protection.
However even in the absence of secrecy, it provides valuable protection
against inadvertent damage.

## Memory protection

If all users will fit in core simultaneously, we are finished. You
divide memory into the appropriate dictionaries. You should provide
memory protection so that one user cannot damage another. The stack and
dictionary size checking discussed earlier, should be augmented by
checks on the = operator, so that a user cannot write outside his
dictionary, or outside a block he has read. If you have hardware memory
protect, you will find it difficult to take advantage of. The user must
be able to read his dictionary, the system dictionary and the block
buffers; he must be able to write his dictionary and the block buffers.
Several users might want to write the same block buffer; if not
simultaneously, at least consecutively. If your hardware can help, it's
better than any I've seen. But software protection can be made adequate
- except against malicious mischief.

Although a user cannot hurt anyone else, he is certainly capable of
destroying himself. Thus you should have a system entry that will
restore his dictionary to empty, with all control fields reset. Such an
entry will get heavy use, for it is a simple way to start over.

If you have implemented fixed-size entries, you have no links to lead to
the system dictionary. Your search routine must separately search the
user's dictionary and the system dictionary, since not all users can be
contiguous to the system. This should only cost a few instructions, but
is another reason to prefer the linked entries.

If you have multiple chains in your dictionary, each chain must jump
from the user's to the system dictionary. This is only a problem when
re-initializing the dictionary, and can be easily solved by keeping a
copy of the chain heads for the system dictionary.

## Disk buffers

The fact that you may have several users reading disk simultaneously has
no effect at all upon the disk-access subroutine. It can search the
block buffers and find an available buffer without concern as to who
asked for it. Of course you must have at least as many buffers as users.
In fact, all of core not required for dictionaries might as well be
devoted to block buffers, as left idle. However, if a block is being
read, you should mark the buffer busy some way, so someone else will not
assume it's there before it arrives. If you attempt to read a busy
block, you should relinquish control and try again when you're
re-started.

## User swapping

So far we've had all users resident in core. This is by far the best
arrangement for handling a small number of users. The step to allowing
more users than can be simultaneously resident is a small one
philosophically, but can be very difficult to implement. Suppose we had
room for 4 user's dictionaries in core, but we wanted to permit 40
users. Clearly we can store all 40 user dictionaries on disk and load
each one into core when he becomes active. Providing disk I/O is
substantially faster than message I/O there is not even a performance
penalty associated. When a user is awaiting message I/O we write him out
to disk. When he completes his message I/O we read him back into core.
Naturally, we do not move him from core when he is waiting for disk I/O,
since it would take unreasonably long to write him out and read him back
compared to the original delay.

So far there are no problems. The problem arises as to where to read him
back into. We have 4 buffers: if we load users always into the same
buffer we have 4 classes of users, each of which can go into a single
buffer. We are begging for delays at one buffer while another is empty.

If we are going to the trouble anyway, we should make all buffers
equivalent, and load a user into whichever one is free. However, now a
user's dictionary must be relocatable. That is, any references to his
dictionary must be relative to its origin, which is presumably stored in
an index register. This isn't too bad if we've planned from the start -
way back with a single-user program - to make all dictionary references
relative; it requires almost a complete re-write of the program if we
did not, for all dictionary references, and they're scattered all
through the program, must be indexed.

Actually, since any references to a block must be relative to the
(variable) origin of the block, we aren't introducing a new problem;
merely extending an old one. However, there's another complication. We
now have a real distinction between our 2 dictionaries: the system
dictionary is absolute and the user dictionary is relative. Therefore
the same kind of entry must be treated differently, depending on which
dictionary it's in.

For example, if we have compiled code in the parameter area, an absolute
user dictionary can store the code address in the address field. However
a relative user dictionary must store the address of a routine that
will, in turn, jump into the parameter field. Or else relative addresses
must be distinguished from absolute addresses, perhaps by size, and
treated properly.

To avoid impossible difficulties, you should be careful to write your
single-user program with the following constraints:

  *  Reserve an index register for a user pointer, the origin of the
    user's dictionary, andd *use* this index. That is, treat the
    dictionary as relative, even though you needn't.
  *  Make all code re-entrant. At least all code within which a user
    might relinquish control - which turns out to be most code.

Do this if you have the slightest intention of implementing a many-user
version. This violates the Basic Principle, but we're dealing with such
basic issues as to be worth it.

# Programs that think

The mystery of consciousness has intrigued philosophers for a long time.
It now seems apparent that just as life is a result of complex
organization, so is consciousness. It is somehow a byproduct of complex
interactions among data. Interactions so complex they only occur in
mammalian brains.

Therefore, one way of investigating the mind is to experiment with
manipulating data. The obvious way to do this is on a computer. We now
have a program with capabilities previously unattainable. Why not use it
in such a way as to probe the realm of 'thinking'? I don't propose that
you become a psychobiologist. But you can have a lot of fun, and do some
really impressive things with simple extensions to your program.

I will describe a number of entries of unusual capability. If you have
an application that can use them, or if you can create an application to
use them, by all means give them a try. However, the Basic Principle
forbids you including them without a purpose. They are sufficiently
elaborate and sufficiently specialized as to never prove unexpectedly
valuable.

I have had all the entries I describe in a single program. This program
had less than 1500 instructions so it is practical to include everything
in a single program. But I was experimenting, and never found an
application that needed a fraction of them.

## Word dissection

One of the most awkward characteristics of our program is that words
must be separated by spaces. Very often you'd like to suffix punctuation
or operator without an intervening space. And we will soon add abilities
that make prefixing desirable, too.

It is not difficult to modify the word subroutine to recognise
characters other than space as terminating characters. But it is
impossible to provide satisfying generality. Inevitably, you complicate
the word subroutine unduly by considering innumerable special cases.
And you can waste much ingenuity trying to achieve generality. For
example, there are no simple rules that permit all these to be words:

    HELLO GOOD-BY 3.14 I.B.M. -.5 1.E-3

Likewise, there are no simple rules that separate these strings into the
words intended:

    -ALPHA 1+ ALPHA+BETA +X\*\*-3 X,Y,Z; X.OR.Y

But don't despair! There is a general solution that can handle all these
cases. It is expensive in time, perhaps very expensive. But it solves
the problem so thoroughly, while demonstrating that no lesser solution
is possible, that I consider it well worth the price. Besides, the speed
of processing text is not a critical factor. We maximize speed precisely
so that we can afford extravagances such as this.

If you haven't already guessed: We read a word terminated by a space,
search the dictionary, convert it to a number. If it isn't a word by
this definition, we drop the last character and try again. Eventually we
strip off enough characters so that the remainder is a word.

Let me review the cost. We do as many dictionary searches (plus numeric
conversions) as there are letters to be dropped. This encourages fast
searches and quick recognition of non-numbers. It also encourages
minimizing the length of strings that must be dissected. But let's be
practical: The number of occasions when dissection is convenient are
few enough that you can afford the price. With the exception of compiler
source code. But I'm not writing a compiler, and if you are you can
probably make your word subroutine cope.

There are several things to be careful of: As you drop characters from
the aligned word, you must keep track of your current position within
this word. However, you must also back-up the input pointer so that you
can start the next word correctly. Incidentally this requires an initial
back-up over the terminal space that is not repeated.

Backing the input pointer is not possible with unbuffered input. This is
why I suggested that you buffer un-buffered devices back in Chapter 3.
If you aren't going to dissect, apply the Basic Principle.

You must also have a way to detect that you have dropped the last
character: a counter is one solution. Another is to place a space
immediately ahead of your aligned word, and to stop on the space. I
prefer the second, for I find I lack a convenient counter that is
preserved over dictionary search and numeric conversion. But this means
that I must fetch each character before I deposit a space over it. And
this means that my fetch subroutine must operate backwards, the only
place I ever need to fetch backwards. It depends on your hardware.

There are 2 things we can do to refine this dissection. They are
incompatible and the choice depends on your application: We don't need
to drop characters one-at-a-time. If you have several letters in
succession, or several digits, or perhaps a combination, you might drop
the all and then perform a single search/conversion. This means that you
must examine each character (which suggests the second termination
above). It also means that you must be able to distinguish alphanumerics
from special-characters. This requires a 64-character table of character
type tailored to your particular character set and application. If your
hardware permits, you may be able to use a 64-bit table - classic
trade-off of time vs. space.

However, this means you cannot dissect letter strings and you might want
to. Plurals, for instance, can be easily accommodated by dropping the
terminal 's'. On the other hand, you can easily mis-identify words by
dissecting letter strings: I once dissected the word SWAP: S was
defined, W was defined and my error message was AP ? Perhaps when
dropping a single letter you should replace it with a dash to indicate a
word stem. Or perhaps it doesn't matter if unidentifiable words are
mis-identified.

One further caution: If you are going to dissect, you must not discard
extra characters while initially aligning the word. Your input pointer
must be positioned so that you can backspace it correctly. If you exceed
maximum word size, stop immediately and supply a terminal space. This
means that no single word can exceed maximum size, which has now become
maximum string size.

Another optimization has to do with the size of words in the dictionary.
If you only match part of the word, you may as well start dropping
characters at that point, if number format permits.

What does word dissection mean to a program? How does it help it
'think'? It means that your program can read your mind. It means that no
matter how you type something, the computer will extract the meaning you
intended. It will use the meaning of the longest character string it
can, consistent with a left-to-right scan. It's not infallible: if you
define +1 and then type +1000 it will mis-understand. But if you use
your language consistently, it will follow.

I would like to be able to say that this ability will impress people. It
will impress you - at least it should. But ordinary people, like your
boss, expect this kind of ability from computers. They are only
impressed, negatively, if they discover its absence.

## Level definitions

I am embarrassed not to know the standard terminology for what I am
going to discuss. I have never heard it discussed and I have never
searched for it. But it must be a standard aspect of compiler writing -
discussed in courses dealing with compilers. If you know the
terminology, you also know most of what I'm going to say: although I
hope I can get you to stretch its application.

Our arithmetic operators have found their arguments already on the
stack. Conventional algebraic notation uses such operators as infixes,
and a left-right scan provides only 1 operand when the operator is
discovered. Consequently the operation must be deferred until the other
operand is available.

Moreover, we have a hierarchy of operations than control when that other
operator becomes available. For example:

    A+B\*C

the multiply must be done before the add. Moreover, parentheses are used
to modify the standard hierarchy:

    A\*(B+C)

Such a notation is completely equivalent to ours. It offers no advantages
over the operands-preceding-operator and has some limitations. But
people are accustomed to it and negatively-impressed by its absence. So
I will show you how to provide the capability.

However there is no reason to restrict our attention to the customary
arithmetic and/or logical operators. I will show you some other similar
hierarchies. The capability I describe will handle them all.

Let us establish a new kind of dictionary entry. It is identical to a
definition except that it has a number appended, a level number. So
let's call it a level-definition. The rule is that a level-definition is
not to be executed when it is encountered, but rather placed on a
push-down stack. It will be executed when another definition with a
equal or smaller level number is encountered.

A convenient format for level-definitions is:

    2 :L word . . . ;

The 2 is the level number, taken from the stack. :L declares the next
word as a level-definition. ';' marks the end.

Let's talk about + and \*:

    0 :L , ;
    1 :L + + ;
    2 :L \* \* ;

We have re-defined them in terms of their old definitions, but as
level-definitions. We defined ',' to have some way to stop. Now we can
say:

    3 + 4 \* 5 ,

What happened? 3 goes onto the parameter stack, + goes onto the
level-stack, 4 onto the parameter stack, \* onto the level-stack (since
it has a higher level number than the + already there), 5 onto the
parameter stack. Now ',' forces the \* to be executed (since its level
number is smaller) and \* finds 5 and 4 on the parameter stack. ',' also
forces + to be executed (with arguments 20 and 3) and then, because its
level number is 0, is itself executed and does nothing.

Clear? I would like to assume you're familiar with this technique, but I
don't quite dare. All I'm really contributing is a way to implement with
dictionary entries a technique usually built into compilers. Perhaps the
cop-out of suggesting you define the arithmetic operators and work out
some examples for yourself. Remember that *equal* level operators force
each other out, and that a *lower* level operator forces out a higher.
It is strangely easy to reason out the relative levels of operators
incorrectly.

What do we have so far? Why should you be interested in
level-definitions? You've seen a couple, their definitions are simple.
Level-definitions tend to be simple compared to ordinary definitions.
But given level-definitions you can write a compiler, for any language!
Level-definitions are necessary and sufficient to implement any
context-free grammar, not only the LR-1 grammars at the base of
contemporary languages. Frankly I don't know what to do with the power
they provide, but I'll toss out some suggestions later.

Now back to work. You've seen some level definitions. I hope you've
played with them some. How do we implement them? Well we don't. Rather
we implement a generalization: level-entries. When I found an
application for level-entries I also found out it was cheaper to
implement level-definitions as such than the way I was doing.

Every dictionary entry may be considered a virtual-computer instruction,
as discussed in Chapter 5. We consider a level-entry an instruction
whose execution can be delayed - after the fashion of a level
definition. Why not? A definition is, after all, only a particular sort
of instruction. If it may be profitably delayed, so might other
instructions.

I'm sorry if it seems complicated. It is! It's going to get more
complicated - you aren't getting something for nothing. But it's worth
it. However, notice that everything we're doing now builds on everything
we've done before. Notice that the concept of a special sort of entry
depends on having a dictionary available; and the extension of
definitions to include level numbers depends on having definitions. We
are gradually building a tree and are in the higher branches. We might
not depend on all the lower branches, but we have to have some.

How do you execute a level-entry? Exactly the same as any other.
However, the first thing the level-entry does is execute the LEVEL
routine, to give it a name, with its level number as parameter. LEVEL
tests this level number against the level-stack. 3 cases arise:

  *  It may place the level number and entry on the level-stack (higher
    level entry) and RETURN.
  *  It may replace the top of the level-stack with this entry, and
    execute the old top.
  *  If the level-stack is empty, and the level is 0, it will execute
    this entry.

All 3 cases are required!

Before actually executing an entry from the stack, LEVEL must set the
SOURCE address to reference another routine, FORCE. You recall that your
main control loop obtains its next entry either by reading a word and
searching, or by fetching from a definition. Well here is a third
source, the level-stack. As for a definition, the old value of SOURCE
and the virtual-IC must be saved - on the return-stack.

When you finally force execution of a level-entry, you must remember
that it has already been executed, and immediately jump to LEVEL. This
re-execution must start at a different place, 1 or 2 instructions below
the routine address, perhaps. Or you might include the re-start address
as a parameter, and keep it in the level-stack.

When a level-entry is done, it will RETURN and your control loop will go
to FORCE. The only way you can get to FORCE is by completing a
level-entry. Its function is to check the level stack and see if any
other entry can be forced off by the one on top. 3 cases arise:

  *  It may leave the level-stack alone (higher level on top), and
    restore SOURCE and virtual-IC from return-stack, and RETURN.
  *  It may execute the lower entry, replacing it with the top - thus
    dropping the level-stack.
  *  If there is no lower entry, and the level is 0, it will execute the
    top entry - thus emptying the level-stack. At this time it will
    restore from the return-stack.

Let me emphasize the importance of the return-stack, and the necessity
of saving SOURCE. If a level-entry is in fact a definition, SOURCE will
be reset yet again. It may be some time before we return and encounter
FORCE once again. For in fact, a level-definition may occur within a
definition; and it may execute other definitions - indeed, other level
definitions. The whole process may become incomprehensibly enmeshed, and
indeed it does in practice. But it will sort itself out. The beauty of
definitions, level-definitions particularly, is similar to that of
recursive functions. You need consider only the simple case when making
the definition; complex cases take care of themselves.

Now you should be able to implement level-entries, definitions among
them. What can you do with them?

  *  You can define the customary arithmetic operations: + - \* / MOD
    \*\*.
  *  You can define the customary logical operations: OR AND NOT IMPL.
  *  You can define infix relations: = < \> <= \>= /=.
  *  You can define an infix replacement: = := (one that works in either
    direction).
  *  You can define all the above.

It depends on your application.

  *  You can define words like PLUS MINUS TIMES DIVIDED-BY EQUALS; an
    English language arithmetic.
  *  You can define phrases like MOVE . . TO . . or DIVIDE . . INTO . .
    or ADD . . TO . . A COBOL language arithmetic.

But let me mention 2 particular uses:

  *  Consider a statement with the form
    -   IF relation THEN statement ELSE statement ;

    Define IF so it will be forced out by THEN and generate a
    conditional branch. Define THEN so it will be forced out by ELSE and
    fix-up the address left dangling by IF. Define ELSE so it will
    first generate an unconditional branch, then force out THEN, and
    then await being forced out itself. Define ; to force out ELSE and
    fix-up the forward branch.

With a few statements you can implement any such compiler construct.

  *  Consider a statement like

    1800. FT / SEC \*\* 2

    Define a kind of entry UNIT that puts a constant on the stack
    immediately and acts like a multiply when it's forced to. Define /
    to put a 1. on the stack immediately and divide when it's forced to.
    Define \*\* as an infix, and FT and SEC as UNITs.

This expression and any others you construct will be evaluated
correctly.

I pass the ball to you. If you have an application that could profit
from a natural language input format, you have the capability with level
definitions to implement it. For example, it would not be hard to teach
your program to solve the problems at the end of a high-school physics
text.

Keep in mind, that level-entries do not enhance the power of the
computer. They merely let you specify instructions in what, to the
computer, is an unnatural order. You are well advised to get your
application working, and *then* to append a fancy control language.

How does this relate to a program 'thinking'? Solely by deferring to the
human-oriented format of control languages. Not even this is impressive
to anyone but us! And even how impressed are you by FORTRAN's expression
evaluator any longer?

## Infinite dictionary

I would guess that your dictionary will average several hundred entries.
Even a small amount of data seems to generate a large number of fields -
to mention one source. However some applications need much larger
vocabularies. Perhaps you need to identify one of 10,000 customers; or
maybe you want the symbols for 104 elements available; or the names of
1000 approved additives.

Clearly such volume must be stored on disk. Also clearly, you don't want
to have to search disk explicitly. There is a gratifyingly effective
solution: If you can't find the word in the core dictionary, and it's
not a number, search a block on disk. Now the question reduces to: Which
block?

Establish a field called CONTEXT. Treat it like you did a block address:
it both identifies a block and suggests where it might be in core.
Search this block. By changing CONTEXT you can search different disk
dictionaries. By linking several blocks together, you can search larger
amounts of disk; or search several dictionaries in sequence.

You can afford to search a fair amount of disk, because if you can't
find the word you're going to generate an error message. A delay in
typing that message to make sure you can't find the word, is an
excellent investment. Still for really large vocabularies - thousands of
entries - such an approach is inadequate.

For very large dictionaries, scramble the word into a block address and
search that block. By that I mean compute a block address from the
letters in a word, just as we did for multiple chains in the core
dictionary, though you'll probably want a different algorithm. You can
search one of a thousand blocks and be assured that if the word is
anywhere, it's in that block. Because you used the same scramble
technique to put it there as you use to find it. Since many words will
scramble into the same block, you of course search for an exact match.
Again, just as in core. With such a large disk dictionary, you want to
be careful of several things. First, once you choose a scrambling
algorithm you can never change it; so make a good choice before you
define lots of entries. Second, try to keep the number of entries
roughly the same in all blocks; and roughly equal to half the capacity
of a block - to compensate for the first "roughly". Or else provide for
overflow by linking blocks together.

Such a disk dictionary can be really impressive - even to non-computer
folk - because you have fast access to a prodigious vocabulary. Fast
means you can search tens-of-thousands of entries in a single disk
access.

What do disk dictionary entries look like? I have found that 2 fields
are sufficient: the word field, the same size as the core dictionary
word field; and a parameter field, 1 word long. If you find a match on
disk, you put the parameter on the stack. Remember that you can't afford
to store absolute addresses on disk, so you can't have an address field
as in core. You could provide a coded address field, but it seems
adequate to treat disk entries as constants.

For instance you can name blocks. When you type the name of a block its
address is moved from the parameter field onto the stack. That is an
excellent place for it, because if you type the block number itself
that's where it would be placed. You can use block numbers and block
names interchangeably. Thus when you type an account number the block
associated with that account is placed onto the stack, whereupon you
store it into the base word that its fields reference. An illegal
account will cause an error message, in the ordinary way. Or you might
name the instructions for your computer. Then typing its name will place
a 1-word instruction on the stack, ready for further processing.

Although I spoke of account numbers, notice that you can't number
blocks. That is, the name of a disk dictionary entry cannot be a number.
For if you type a number it will be converted onto the stack, and never
sought on disk. And you must attempt to convert *before* searching disk
or you'll search disk for every literal you type. But then "numbers"
often don't look much like the numbers defined by NUMBER. They tend to
have embedded dashes, letters and such; or else you can prefix a letter
or suffix a \# character.

How do you put an entry on disk? A special defining entry:

    0 NAME ZERO

analogous to CONSTANT. Alternatively you might set a flag and let the
dictionary entry subroutine decide whether to use disk or core. This
latter is preferable if you have several different kinds of entries that
might go either to disk or core.

You will also need a way to forget disk entries:

    FORGET ZERO

FORGET must call WORD as defining entries do, since this is a
non-typical use of the word ZERO. When it finds the entry, it simple
clears it without trying to pack. Your entry routine should first search
disk to see if the word is already there. You don't want multiple
definitions on disk, even though there're useful in core. Then it should
search for a hole. If it finds the word already there, or if it can't
find a hole? You guessed it, an error message.

Let's talk about a refinement. With a thousand names on disk it's easy
to run out of mnemonics. Let's re-use the field CONTEXT: after you
scramble the word into a block address, add the contents of CONTEXT and
search that block. If CONTEXT is 0, no difference. But if CONTEXT is
non-zero, you're searching a different block. If CONTEXT can vary from 0
to 15, you can have 16 different definitions of the same word. You'll
find the one that had the same value of CONTEXT when you defined it. If
there is no entry for a word under a given CONTEXT, you won't get a
match. A block containing a definition for the same word under a
different CONTEXT won't be searched.

For example, stock numbers might look the same for different
sales-lines. By setting CONTEXT you can distinguish them. You can use
the same name for a report screen that you use for its instruction
screen; distinguish them by CONTEXT. If you're scrambling anyway, you
may as well add in CONTEXT (modulo a power of 2); it costs nothing, and
vastly extends the universe of names. In fact, you can use CONTEXT in
both the ways we've discussed, simultaneously. For as an additive
constant it tends to be small; and as a block number, large. So your
search routine can decide whether to scramble or not based on its size.

A problem arises if you plan to dissect words. All those extra
dictionary searches are augmented by disk searches and their attendant
disk accesses. Several solutions are possible: Scramble with only the
first couple of characters, so at least the disk searches are in the
same block - which will be in core. Or use only non-zero values of
CONTEXT and let 0 inhibit the disk search. That is, make dissection and
disk searching mutually exclusive. As is often the case, the problem is
serious only if you aren't aware of it.

## Infinite memory

Of course you can't really have infinite memory. Not even unlimited
memory. But you can access directly the entire random memory available
to your computer. A small augmentation of the field entries introduced
in Chapter 4 will do it. I postponed the discussion to here because it
has no particular connection with output, and because it's impressive
enough to relate to 'thinking'.

The problem of what to do with infinite memory, I leave up to you. You
will have to organize it somehow. Examine different parts of it, move
fields around, what you will. All I can do is show you how to eliminate
any explicit reference to disk.

Let's include in our field a parameter that points to a disk address.
The field is assumed to be relative to that address; that is, contained
in the disk block. The program will automatically read the block to
obtain the field. Of course a number of fields will point to the same
block address.

Before you start objecting, let me rush on. Stored with the block
address is the location of the core buffer that block last occupied. So
the program needn't actually read disk, or even search core buffers for
the block, unless the block has been overlaid. Hence repeated accesses
to the same block cost little.

Several trade-offs are involved: You should have a generous number of
core buffers to minimize overlays. You should choose you block size with
this use in mind. Accessing such disk-resident fields is slower than if
you deliberately read the block into a fixed location and access it
there; but the ease with which you can address data scattered on disk,
and the beauty of being able to forget that some data is on disk and
other data in core, to me make up for the loss in speed. Besides, it's
your problem to implement the feature in a way that is efficient.

Suppose you want to scan a portion of disk. All you have to do is define
the fields and establish a loop: start with the first block address,
store it in the base location where the fields expect it and increment
it each time through the loop. All right, your advantage is marginal.
All you save is a read instruction. But if that block links to another
one, all you need do is store the link in the base location for other
fields, and forget that a link is involved. If you access fields in the
link it will automatically be read. If not, it won't be. The more
complex your data, the greater the advantage.

Of course, you don't have to worry about writing blocks either. Chapter
6 talked about flagging blocks that need writing, rather than writing
them immediately. Pays off here! If you change a field, its block will
be re-written; if you don't, it won't. Just make sure that when you say
GOOD-BY your program writes all changed blocks.

You can make these field entries identical with those accessing core, by
making the pointer to the base address 0. If you don't point to a disk
address, you must mean core.

Notice that this addition of a base to a field entry defines a data
structure very much like the levels in COBOL's data division: 01 level
corresponding to the disk address; 02 levels to the fields themselves.
For a few extra instructions you can add higher levels: If the pointer
does not reference a disk address, but another field description, you
have the equivalent of 03 level, etc.

Consider how the field reference actually works. In the field entry you
have a word parameter that tells which word the field is in (or starts
in). If this field references another, you add the word parameters
together. When you find the core address of the disk block, you add the
word offset and voila': you have the word you want. Going through
intermediate fields has little advantage unless the intermediate fields
change. Why not? By incrementing a base field address, you can access
different rows of a matrix or different records in a block. Or you can
access different sub-records of a record. Very useful! It's enough to
make me think COBOL is a pretty good language. Of course you can do the
same thing with core fields, you just never point to a disk address at
the very end.

A word of warning! Don't try to gain efficiency by putting the core
address of a block in an index register. It's too hard to keep track of
which block, if any, the index is currently identifying. You simply have
to go through a fair bit of code to provide useful generality. Of
course, you hardware might have some special features: maybe
microprogramming? Even indirect addressing might be helpful.

Given such elaborate addressing capabilities, you can use some help
debugging your screens. Memory protection is easy to provide, and very
helpful. Include with each field entry a maximum size (in words) for
that field. When you calculate an address that purports to be in that
field, make sure it is. The upper limit for the final block reference is
of course the block size. The upper limit for a core reference is also
known. A simple error message stating OVERFLOW will catch trouble before
it has a chance to propagate.

You might want to implement an additional kind of field entry. This one
has a link. If you make a reference that lies outside the field, it will
follow this link and attempt to satisfy your request. In particular, a
record entry that points to a block: If you increment the record offset
beyond the end of the block, you can pick up a link from the block,
change the block address, reset the record offset and access the new,
overflow block. Automatically! This makes for a very attractive
implementation of variable length records (actually blocks), providing
the records are composed of fixed-length pieces.

If you want such an overflow capability, you must provide a way of
constructing the links. You need an entry that will search a block
(chain) for a record-size hole - of course all holes are the same size.
If you can't find a hold, you must GET a new block, link it, and then
you have a block full of holes. A hole should be identified by a 0 in
the first word, character or bit, so that when GET clears the new block
to 0, all record positions are empty. Naturally you have no guarantee
that overflow blocks will be near each other. Almost certainly they
won't be. Either you don't care, or you initially allocate each block
chain sequentially, up to mean size.

It is easy to remove a record. You create a hole by storing 0 in the
first word. It is hard to discover whether by doing this you have caused
an empty block which can be un-chained. Unless you expect your data to
shrink and need to recover space, don't bother. How can data shrink?
Also, don't move records around - to squeeze out holes perhaps. Just as
we want to use absolute block addresses, we want to use absolute record
addresses (if we use record addresses at all).

So, we can have automatic access to fields scattered all over disk and
in variable size records at that. Basic Principle!

One thing! If field entries can address other field entries, you need
some way to distinguish a field from a disk address. I have no
suggestion.

# Programs that bootstrap

It's sometimes hard to appreciate how it all gets started. We have been
tacitly assuming that your computer has a compiler and that you used it
to compile your program. But how did your compiler get written? Today
the answer is certainly that it was prepared by another compiler on
another computer. We've achieved parity with the biological maxim: all
life comes from previously existing life. For practical purposes, all
programs are prepared by previously existing programs.

Although this makes life somewhat easier for compiler writers,
especially when the target computer isn't built yet, it has a drawback.
You can never drop you ultimate dependence on the pre-existing program.
If you use a compiler that generates certain instructions, or assumes a
certain disk format, you are constrained to be compatible. Consider that
a simple version of our program, providing it includes compiler verbs,
is perfectly capable of compiling itself. It can do this with greater
freedom than the standard compiler, but more important, you can then
discard the standard compiler.

In Chapter 1, I discussed the sad state of software quality. Although we
can prepare an excellent object program, we are obliged to maintain it
as a source program for an unhappy compromise of a compiler. I must
admit that this is the most expedient way to get the program started.
However, I question whether it is most efficient over the long haul of
re-compiling and modifying.

Let us imagine a situation in which you have access to your computer. I
mean sole user sitting at the board with all the lights, for some hours
at a time. This is admittedly an a-typical situation, but one that can
always be arranged if you are competent, press hard, and will work odd
hours. Can you and the computer write a program? Can you write a program
that didn't descend from a pre-existing program? You can learn a bit and
have a lot of fun trying.

## Getting started

First you'll have to know some things: how to turn the computer on and
off (odd hours), how to enter and display data from the console
switches, and how to avoid damaging data stored on disk. You may have to
corner operators or engineers to discover such information; it is so
rarely of interest it doesn't get written down.

So now you're face to face with the computer. What do you do? First an
exercise. Initialize the interrupt locations in such a way that the
computer will run, will execute an endless loop, when you start it. OK?
Then modify your loop so that it will clear memory. OK? You've probably
learned a lot.

Now we're going to start for real. We're going to start building your
dictionary, even though you can't use it yet. You must choose your entry
format now; variable-sized entries are required, but you can decide
about word-size and layout. The first entry is SAVE; it will save your
program on disk. Lacking a control loop you'll have to jump to it
manually, but at least you can minimize re-doing a lot of work. The
second entry is LOAD; it will re-load your program from disk. You may
have a hardware load button, if you can store your program compatibly
with it, fine. You might want to punch a load card, to provide initial
load otherwise. But it's always convenient to be able to re-start from
core.

The third entry is DUMP; it will dump core onto the printer. It needn't
be very fast to be a lot faster than looking with the switches. This
probably isn't a trivial routine, but it oughtn't take more than a dozen
instructions. You might want to postpone it just a bit.

So, with a couple hours work - providing you read the manual first - you
have an operating system (SAVE, LOAD) and debugging package (DUMP). And
you know a lot about your computer.

## The roots

Lest you worry, I have gone through this process myself. I've done it
twice, actually, and I'm not describing it as I did it, but as I now
think I should have done it. So you've room for improvisation.

In a sense we're building a tree. We've now reached a point where we can
start making the roots. For a while everything will be concealed but
we'll eventually reach daylight and start on branches.

I presume you can LOAD your program and DUMP core. It's time to get away
from the switches and use the typewriter. So set up a message buffer
from which you can send and receive text. Presumably when awaiting text
your program sits in an endless loop somewhere. Learn to recognise that
loop. You'll spend most of your running time there and it's reassuring
to know that everything's all right.

No dictionary entry is associated with message I/O. You could define
one, but we won't need it. In general we will construct entries only
when they'll be needed. We can always add any entry we need, later.

You're doing great. Now establish the stacks, the dictionary search
subroutine and entries for WORD and NUMBER. Be very careful to do it
right the first time; that is, don't simplify NUMBER and plan to re-do
it later. The total amount of work is greater, even using the switches.

Now write a control loop. You might test the stack, but jump to an
unspecified error routine. And run. DUMP is still our only output
routine, but you should be able to read and execute words like DUMP,
SAVE and LOAD.

Write an entry for ENTRY, the subroutine that constructs dictionary
entries. I haven't specified the code executed for WORD, NUMBER and
ENTRY. These are subroutines, and the only time we'll use their names is
when compiling code. So they should execute code that generates a call
instruction. We haven't written that code yet.

Now define the code-entry, the word that names code; and the deposit
word, the word that places the stack in core. Now you can type octal
numbers and store them in the dictionary. No more switches. You can also
construct new dictionary entries, for code.

## The branches

We've reached a milestone. The invisible work is done and we can have a
written record of what remains. There are many things to do and the
order not so obvious. We've reached the position of having a source
language, and we need to be able to modify it and re-compile without
re-doing everything. Here we're forced to generate temporary code that
will become obsolete, but it will save a lot of effort.

First a READ and WRITE entry to provide disk-access to a single core
buffer. Then a simple T and R to type and replace lines of text in that
block. These entries will later become obsolete, so keep them simple.

We now need the READ and ;S verbs for screens. Specify a block number
and we can read the text in that block.

Now we write screens that provide definitions, an improved compiler,
improved block handler, improved text-editor and we can proceed with our
application. We want a REMEMBER entry. We haven't needed it so far
because we could always reach in and reset the dictionary manually.

I'm sure you've noticed the difficulty with modifying code in the root.
A powerful tool is to be able to shift the dictionary in core. If the
root doesn't use absolute addresses, define a SHIFT entry and use it.
Otherwise minimize the number of absolute addresses and define a more
elaborate SHIFT verb that adjusts them.

Be careful SAVEing your program. Keep a back-up of your old version
before SAVEing a new one, just in case. 

![image](./Fig123.jpg)

![image](./Fig62.jpg) 

![image](./Fig4.jpg)