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.
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:
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 capabililties, 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 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: Now we get down the the nitty-gritty. This is our first clash with the establishment. The conventionsl 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.
Moreovere, 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 millenium 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.
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.
First consider the word "input". I want to use it in a specific sense:
- Input is information that controls a program.
- 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:
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.
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 acess 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.
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.
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.
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 consistant and be accurate. Sloppy indenting is obvious.
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 occassion.
So let me suggest a compromise: abbreviate in some consistant 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: 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.
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.
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.
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: 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.
- 4837 758 + -338 + 23 + 4457 + -8354 + ,
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.
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.
Another way of distinguishing verbs is:
- Destructive verb removes its arguments from the stack.
- Non-destructive verb leaves its arguments on the stack.
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.
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.
- @ replace the address on the stack with its contents.
- = Store into the address on the stack, the value just beneath it on the stack.
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. Incidently, 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 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.
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 preceeding 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.
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 insistance 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
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 everytime) 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 noticable increase in speed is available. And it complicates the program considerably.
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.
We will discuss the stack in the next section. First let's define a number more precisely.
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
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
- 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
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 106 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 - 1043 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
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.
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.
- 0- 3.14. +17 -.5Z X 6.-3 1.E3
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.
In NATURAL the number-so-far is multipled by 10. Don't use a literal 10, but rathere 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.
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 TYPEB 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.
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 TYPEB. In determining spaces, remember that TYPEB 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 buffeer 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 TYPEB. A tab entry might calculate the amount to space in order to reach a specific position on the stack.
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.
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 religously 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.
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.
- 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.
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 apparant 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.
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.
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 probablity 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).
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.
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
- LIST SORT EQUAL GREATER LESS
List in alphabetical order all employees in dept 6:
- 6 DEPT EQUAL NAME SORT LIST
List twice, by seniority, all employees holding job 17 in dept 3:
- 17 JOB EQUAL 3 DEPT EQUAL SENIORITY SORT LIST LIST
- 10000 SALARY GREATER AGE SORT LIST 3 SENIORITY LESS LIST
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.
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 constsitute 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 compiler-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?
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 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.
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.
- 3 VECTOR X 3 VECTOR Y 9 VECTOR Z
- X Z = Z Y + add X and Y, store in Z.
- X Y Z *C multiply X and Y (outer product), store in Z.
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 thie, 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 preceeds 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, 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.