Program as Data

Brian Harvey
University of California, Berkeley

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MIT Press web page for Computer Science Logo Style

In most programming languages there is a sharp distinction between program and data. Data are the things you can manipulate in your program, things like numbers and letters. These things live in variables, which can be given new values by your program. But the program itself is not subject to manipulation; it's something you write ahead of time, and then it remains fixed.

In Logo the distinction is not so sharp. We've made extensive use of one mechanism by which a program can manipulate itself: the instruction lists that are used as inputs to run, if, and so on are data that can be computed by a program. For example, the solitaire program in Chapter 4 constructs a list of Logo instruction lists, each of which would move a card to some other legal position, and then says

run first :onto

to move the card to the first such position.

`Text` and `Define`

In this chapter we'll use a pair of more advanced tools that allow a program to create more program. Run deals with a single instruction; now we'll be able to examine and create procedures.

Text is an operation that takes one input, a word. That word must be the name of a user-defined procedure. The output from text is a list. The first member of that list is a list containing the names of the inputs to the chosen procedure. (If the procedure has no inputs, the list will be empty.)* The remaining members of the output list are instruction lists, one for each line in the definition of the procedure.

^*Berkeley Logo allows user-defined procedures with optional inputs. For such a procedure, this first sublist may contain lists, representing optional inputs, as well as words, representing required inputs.

Here is an example. Suppose we've defined the procedure

to opinion :yes :no
print sentence [I like] :yes
print sentence [I hate] :no
end

Here's what the text of that procedure looks like:

? show text "opinion
[[yes no] [print sentence [I like] :yes] [print sentence [I hate] :no]]

In this example the output from text is a list with three members. The first member is a list containing the words yes and no, the names of opinion's inputs. (Note that the colons that are used to indicate inputs in a title line are not used here.) The second and third members of the output list are instruction lists, one for each line in the definition. (Note that there is no end line in the definition; as I've remarked before, that line isn't an instruction in the procedure because end isn't a command.)

The opposite of text is the command define. This command takes two inputs. The first must be a word and the second a list. The effect of define is to define a procedure whose name is the first input and whose text is the second input. You can use define to define a new procedure or to change the definition of an old one. For example, I might redefine opinion:

? define "opinion [[yes no] [print sentence :yes [is yummy.]]
                            [print sentence :no [is yucky.]]]
? opinion [Ice cream] "Cheese
Ice cream is yummy.
Cheese is yucky.
? po "opinion
to opinion :yes :no
print sentence :yes [is yummy.]
print sentence :no [is yucky.]
end

Instead of replacing an old definition with an entirely new one, we can use define and text together to change a procedure's definition:

? define "opinion lput [print sentence :no "stinks!] ~
                       butlast text "opinion
? opinion "Logo "Basic
Logo is yummy.
Basic stinks!

(Of course, I didn't have to redefine the same procedure name. I could have said

? define "strong.opinion ~
         lput [print sentence :no "stinks!] butlast text "opinion

and then I would have had two procedures, the unchanged opinion and the new version named strong.opinion.)

It may be instructive to consider the analogy between variables, which hold data, and procedures, which hold instructions. Variables are given values with the make command and examined with the operation thing. Procedures are given definitions with the define command and examined with the operation text. (There is no abbreviation for text-quote, however, like the dots abbreviation for thing-quote.)

To illustrate define and text, I've used them in instructions typed in at top level. In practice, you wouldn't use them that way; it's easier to examine a procedure with po and to change its definition with edit. Text and define are meant to be used not at top level but inside a program.

Automated Definition

Early in the first volume I defined the operation second this way:

to second :thing
output first butfirst :thing
end

Suppose I want more operations following this model, to be called third, fourth, and so on. I could define them all by hand or I could write a program to do it for me:

to ordinals
ord1 [second third fourth fifth sixth seventh] [output first butfirst]
end

to ord1 :names :instr
if emptyp :names [stop]
define first :names list [thing] (lput ":thing :instr)
ord1 (butfirst :names) (lput "butfirst :instr)
end

? ordinals
? po "fifth
to fifth :thing
output first butfirst butfirst butfirst butfirst :thing
end

(The name ordinals comes from the phrase ordinal numbers, which is what things like "third" are called. Regular numbers like "three" are called cardinal numbers.) This procedure automatically defined new procedures named second through seventh, each with one more butfirst in its instruction line.

A Single-Keystroke Program Generator

A fairly common thing to do in Logo is to write a little program that lets you type a single character on the keyboard to carry out some instruction. For example, teachers of very young children sometimes use a program that accepts F to move the turtle forward some distance, B for back, and L and R for left and right. What I want to write is a program-writing program that will accept a name and a list of keystrokes and instructions as inputs and define a procedure with that name that understands those instructions.

to onekey :name :list
local "text
make "text [[] [local "char] [print [Type ? for help]]
            [make "char readchar]]
foreach :list [make "text lput (sentence [if equalp :char]
                                         (word "" first ?)
                                         butfirst ?)
                               :text]
make "text lput (lput (list "foreach :list ""print)
                      [if equalp :char "?]) ~
                :text
make "text lput (list :name) :text
define :name :text
end

If we use this program with the instruction

onekey "instant [[F [forward 20]] [B [back 20]]
                 [L [left 15]] [R [right 15]]]

then it creates the following procedure:

to instant
local "char
print [type ? for help]
make "char readchar
if equalp :char "F [forward 20]
if equalp :char "B [back 20]
if equalp :char "L [left 15]
if equalp :char "R [right 15]
if equalp :char "? [foreach [[F [forward 20]] [B [back 20]]
                             [L [left 15]] [R [right 15]]]
                            "print]
instant
end

In addition to illustrating the use of define, this program demonstrates how sentence, list, and lput can all be useful in constructing lists, when you have to combine some constant members with some variable members.

Of course, if we only want to make one instant program, it's easier just to type it in. An automatic procedure like onekey is useful when you want to create several different procedures like instant, each with a different "menu" of characters. For example, consider these instructions:

onekey "instant [[F [forward 20]] [B [back 20]]
                 [L [left 15]] [R [right 15]] [P [pens]]]
onekey "pens [[U [penup stop]] [D [pendown stop]] [E [penerase stop]]]

With these definitions, typing P to instant prepares to accept a pen command from the second list. In effect, instant recognizes two-letter commands PU for penup and so on, except that the sequence P? will display the help information for just the pen commands. Here's another example:

onekey "tinyturns [[F [forward 20]] [B [back 20]]
                   [L [left 5]] [R [right 5]] [H [hugeturns]]]
onekey "hugeturns [[F [forward 20]] [B [back 20]]
                   [L [left 45]] [R [right 45]] [T [tinyturns]]]

Procedure Cross-Reference Listings

When you're working on a very large project, it's easy to lose track of which procedure invokes which other one. We can use the computer to help solve this problem by creating a cross-reference listing for all the procedures in a project. For every procedure in the project, a cross-reference listing tells which other procedures invoke that one. If you write long procedures, it can also be helpful to list which instruction line in procedure A invokes procedure B.

The general strategy will be to look through the text of every procedure, looking for the name of the procedure we're interested in. Suppose we're finding all the references to procedure X and we're looking through procedures A, B, and C. For each line of each procedure, we want to know whether the word X appears in that line. (Of course you would not really name a procedure A or X. You'd use meaningful names. This is just an example.) We can't, however, just test

memberp "x :instr

(I'm imagining that the variable instr contains an instruction line.) The reason is that a procedure invocation can be part of a sublist of the instruction list if X is invoked by way of something like if. For example, the word X is not a member of the list

[if emptyp :list [x :foo stop]]

But it's a member of a member. (Earlier I made a big fuss about the fact that if that instruction were part of procedure A, it's actually if that invokes X, not A. That's the true story, for the Logo interpreter. But for purposes of a cross-reference listing, it does us no good to know that if invokes X; what we want to know is which procedure definition to look at if we want to find the instruction that uses X.)

So the first thing we need is a procedure submemberp that takes inputs like those of memberp but outputs true if the first input is a member of the second, or a member of a member, and so on.

to submemberp :thing :list
if emptyp :list [output "false]
if equalp :thing first :list [output "true]
if listp first :list ~
   [if submemberp :thing first :list [output "true]]
output submemberp :thing butfirst :list
end

Now we want a procedure that will take two words as input, both of which are the names of procedures, and will print a list of all the references to the first procedure in the text of the second.

to reference :target :examinee
ref1 :target :examinee butfirst text :examinee 1
end

to ref1 :target :examinee :instrs :linenum
if emptyp :instrs [stop]
if submemberp :target first :instrs ~
   [print sentence "|   | (word :examinee "\( :linenum "\) )]
ref1 :target :examinee butfirst :instrs :linenum+1
end

Reference uses butfirst text :examinee as the third input to ref1 to avoid the list of inputs to the procedure we're examining. That's because one of those inputs might have the same name as the target procedure, and we'd get a false indication of success. (In the body of the definition of :examinee, any reference to a variable named X will not use the word X but rather the word "X or the word :X. You may find that statement confusing. When you type an instruction like

print "foo

the Logo evaluator interprets "foo as a request for the word foo, quoted (as opposed to evaluated). So print won't print a quotation mark. But if we look at the list

[print "foo]

then we are not, right now, evaluating it as a Logo instruction. The second member of that list is the word "foo, quote mark and all.)

We can still get "false hits," finding the word X (or whatever procedure name we're looking for) in an instruction list, but not being used as a procedure name:

print [w x y z]

But cases like that will be relatively rare compared to the cases of variables and procedures with the same name.

The reason I'm printing spaces before the information is that I'm working toward a listing that will look like this:

target1
   proca(3)
   procb(1)
   procc(4)
target2
   procb(3)
   procb(4)

This means that the procedure named target1 is invoked in each of the procedures proca, procb, and procc; procedure target2 is invoked by procb on two different instruction lines.

Okay, now we can find references to one specific procedure within the text of another specific procedure. Now we want to look for references to one procedure within all the procedures making up a project.

to xref :target :list
print :target
foreach :list [reference :target ?]
end

We're almost done. Now we want to apply xref to every procedure in the project. This involves another run through the list of projects:

to xrefall :list
foreach :list [xref ? :list]
end

To use this program to make a cross-reference listing of itself, you'd say

xrefall [xrefall xref reference ref1 submemberp]

To cross-reference all of the procedures in your workspace, you'd say

xrefall procedures

If you try this program on a project with a large number of procedures, you should expect it to take a long time. If there are five procedures, we have to examine each of them for references to each of them, so we invoke reference 25 times. If there are 10 procedures, we invoke reference 100 times! In general, the number of invocations is the square of the number of procedures. The fancy way to say this is that the program "takes quadratic time" or that it "behaves quadratically."

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