Comp 210 Lab 2: Data Definitions

Index: Simple data definitions, Donkey, Scheme style

Simple Data Definitions

In class we saw the data definition for a list of numbers:

A list of numbers is

null (the empty list), or
(cons f r), where f is a number and r is a list of numbers.

It is good practice always to write your data definitions. This will be expected to do this on most Comp210 homeworks. In Scheme, the data definitions are not part of your program, but it is good practice to include them as comments in your code, e.g.,

; A LoN (list of numbers) is one of
;   1) null
;   2) (cons f r), where f is a number, r is a LoN

In some programming languages, some form of data definitions are part of the program and used by the computer. Regardless of programming language, it will be important to clearly remember your data definition when writing your program.

What are some example lists of numbers?
What is the program template for lists of numbers?
Remember that the program template mimics the data definition. Also, the program template is not a completed function -- it is merely a skeleton of what most functions using this data will look like.

You should provide the template in your homeworks. Since a template isn't valid Scheme (it includes "holes" represented by ellipses), you need to put it in comments.
Make a couple functions using this template.
- Make one that computes the length of a list of numbers.
- Make one that computes the product of a list of numbers. (What's the product of an empty list?)
For a homework, you would now want to use some or all of your example lists of numbers as test cases for these functions.

Our five steps are

Make a data definition
Make a program template, including
1. Perform a case analysis
2. Extract the available data
3. Identify natural recursion
Describe each function to be defined and provide examples of what they should do
Write these functions, using the template
Test these functions, using the examples

For the beginning of this class, we will be very pedantic about following these steps. As these ideas become second nature, we can relax them.

Try some other examples:

How would you define a list of symbols?
How would you define a list that can contain both symbols and numbers?
Hint: as one option, you can either think of an empty list, or building a list with a symbol, or building a list with a number; as another option, you can think of an empty list, or building a list with a symbol or a number. Do you see the difference? There's nothing too mysterious -- they are equivalent, of course.
Sometimes you want to have a program that allows all lists, and for some reason check if a list has even length, for example. Other times you want to allow only even length lists.
How would you define even (0, 2, 4, ...) length lists of numbers?

Donkey

Like DrScheme, Donkey is a programming environment for Scheme. While DrScheme is generally better, Donkey has one important feature that DrScheme lacks: it allows you to see how your program is evaluated. This lab shows you how to use that feature.

To run Donkey, either

enter donkey in an xterm window, or
select Donkey from the Comp 210 menu.

(This assumes you have run register comp210. If not, you can enter /home/comp210/bin/donkey.)

As an example, type (if (= 1 2) (+ 1 2) (+ 1 3)) in the main window.

Press the Return key, or equivalently select the Eval button. This evaluates the expression to 4, just like DrScheme.
Put the cursor back on that expression by clicking in its box. This time select the Step button. Donkey highlights the first subexpression to evaluate, and up in the Next Reduction Rule textbox it displays the applicable rule for that subexpression. Selecting the Step button again evaluates that subexpression and goes on to the next subexpression to evaluate. Eventually, you evaluate the whole expression.
When stepping, you also have other options, e.g., selecting the Unstep button goes backwards one step in the evaluation.
Put the cursor back on the expression again. This time select the Step All button. This completely evaluates the expression, like the Eval button, but it builds up the extra information so that you can now Unstep, and then Step/Unstep like we just saw.

One main option you'll want in Donkey are to Load files (in the File menu). We assume you'll usually use DrScheme for writing your programs. Select Help from the Help menu to explain other options.

Try stepping through some examples. In particular, try a simple use of recursion:

(define length
   (lambda (l)
       (cond
           ((null? l) 0)
           (else      (+ 1 (length (cdr l)))))))
(length (cons 1 (cons 4 (cons 8 (cons 2)))))

When is the body of the lambda evaluated?
How are the pieces of the cond evaluated?
Observe how a bunch (hmm... a stack?) of additions pile up waiting for you to calculate the length of the rest of the list.

Since stepping through larger programs can be very tedious, you can indicate what kinds of subexpressions are "important" to show during stepping. In the Stop-at menu, currently All is selected, i.e., stepping stops at all subexpressions. If you select "if/cond/case", stepping will only stop and conditionals, but not at function applications. When stepping through recursive functions, you sometimes want to select only "apply" in the Stop-at menu, i.e., only indicate when it's applying a user-defined function and skip over the conditionals and primitive functions. Try the same example again and observe the difference.

Scheme style

Like any language, there are conventions for writing Scheme that help make it more readable. In this and the previous lab, we've discussed some conventions on providing supplementary information in comments. In class, we briefly discussed conventions for choosing between cond and if. Here, we will discuss layout and indenting conventions. Also of note, programmers vary widely in naming conventions, e.g., whether to name a list of numbers as l, lon, AListOfNumbers, nums, or something else.

The basic goals of spacing and indentation in Scheme include

making keywords stand out,
aligning related subexpressions, and
keeping blocks of code reasonably-sized -- not too horizontal or too vertical.

DrScheme will help you with the first two issues: selecting the Check Syntax button will highlight keywords, and DrScheme automatically aligns a line nicely when you use the Return key. The following are examples of good style.

```
(define afunction
   (lambda (x)
      body))
     
```
The define and lambda keywords are each on separate lines to point out that you are
1. making a definition and
2. creating a function with one argument.
```
(if (= 3 x)
    (f 5)
    (+ 7 y))
     
```
The "then" and "else" branches are on separate lines and aligned so that you can easily see them. The same idea holds for larger conditionals:
```
(cond
   ((null? l) 0)
   (else      (+ 1 (foo (cdr l)))))
     
```
(Note that I like to also align the result expressions in a cond, assuming the test expressions are reasonably short.)
When subexpressions are long, or so deeply nested that you're regularly using 60+ columns of characters, you may have to break lines more frequently, e.g.,
```
(cond
   ((null? l)
    0)
   (else
    (+ 1 (foo (cdr l)))))
     
```
or in function calls,
```
(myfunction (+ 3 (* 5 x) y)
            (- 3 (f 9 z)))
     
```
Note that using too many lines obscures structure:
```
(define
   afunction
   (lambda
      (l)
      (cond
         ((null? l)
          0)
         (else
          (+ 1
             (afunction
                (cdr l)))))))
     
```
It also makes you scroll vertically more. Unfortunately, sometimes you are forced into this if you want to be able to print your code on fixed-width paper, and you have really big complicated functions.