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An abbreviated introduction to Racket

Monday, 28 January 2019
We begin to explore the Racket programming language and some of the capabilities of that language. We consider some basic issues of the the structure of expressions in Racket, the syntax of the language.
Algorithm building blocks. The DrRacket programming environment (see that reading for the “chicken and egg” problem).

Introduction: Algorithms and programming languages

While our main goals in this course are for you to develop your skills in “algorithmic thinking” and apply algorithmic techniques to problems in the digital humanities, you will find it equally useful to learn how to direct computers to perform these algorithms. Programming languages provide a formal notation for expressing algorithms that can be read by both humans and computers. We will use the Racket programming language, a dialect of the Scheme programming language, itself a dialect of the Lisp programming language, one of the first important programming languages.

One thing that sets these languages apart from most other languages is a simple, but non-traditional, syntax. To tell the computer to apply a procedure (subroutine, function) to some arguments, you write an open parenthesis, the name of the procedure, the arguments separated by spaces, and a close parenthesis. For example, here’s how you add 2 and 3.

> (+ 2 3)

One advantage of this parenthesized notation is that it eliminates the need for the reader or the computer to know a set of precedence rules for operations. Consider, for example, the expression 2+3x5. Do you add first or multiply first? Different programming languages may interpret it differently. On the other hand, we have to explicitly state the order, writing either (+ 2 (* 3 5)) or ((+ 2 3) 5), using * as the multiplication symbol.

> (+ 2 (* 3 5))
> (* (+ 2 3) 5)

As this example suggests, we have already started to explore both basic operations (addition and multiplication) and sequencing (through nesting) in Racket. You should keep three points in mind when writing and reading Racket expressions.

  • Parenthesize all non-trivial expressions. Parentheses tell Racket that you want to apply a procedure to some values.
  • Do not parenthesize basic values. Since there’s no procedure call involved with a basic value, we do not write parentheses.
  • Write expressions in prefix order. That is, you write the procedure (function, operation, subroutine) before the arguments, even if it’s something like + that you would normally put between arguments.
  • Sequence computations by nesting. If you have intermediate computations that you need to do, you can parenthesize them and put them within another rexpression.

Beyond numeric expressions

Of course, you can use Racket for more than arithmetic computations. Here are some examples working with text.

We can find the length of a string.

> (string-length "Jabberwocky")

We can break a string apart into a list of string.

> (string-split "Twas brillig and the slithy toves" " ")
'("Twas" "brillig" "and" "the" "slithy" "toves")

We can find out how many words there are once we’ve split it apart.

> (length (string-split "Twas brillig and the slithy toves" " "))

This operation returned a list, an ordered collection of values. Note that lists are also surrounded by parentheses. Racket distinguishes lists, which should not be evaluated, from expressions, which should be evaluated, by including a tick mark, ', before the parenthesis in most lists.

Once we have a list of words, we can find out how long each word is.

> (map string-length
       (string-split "Twas brillig and the slithy toves" " "))
'(4 7 3 3 6 5)

We can even split in strange ways, such as at the vowels. (We’ll explain the strange #px"[aeiou]" in a subsequent reading.)

> (string-split "Twas brillig and the slithy toves" #px"[aeiou]")
'("Tw" "s br" "ll" "g " "nd th" " sl" "thy t" "v" "s")

Computing with images

You’ve already seen a few of Racket’s basic types. Racket supports numbers, strings (text), and lists of values. Of course, these are not the only types it supports. Some additional types are available through separate libraries. For example, it is comparatively straightforward to get Racket to draw simple shapes.

> (circle 15 'outline "blue")
A white circle of radius 15 designated by a thin blue line along its circumference
> (circle 10 'solid "red")
A red disc of radius 10

We can also combine shapes by putting them above or beside each other.

> (above (circle 10 'outline "blue")
         (circle 15 'outline "red"))
Two circles stacked on top of each other.  The top one, which is smaller, is outlined in blue.  The bottom one is outlined in red.
> (beside (circle 10 'solid "blue")
          (circle 10 'outline "blue"))
Two identical-size circles next to each other.  The first is a solid blue disc.  The second is a white circle outlined in blue.
> (above (rectangle 15 10 'solid "red")
         (beside (rectangle 15 10 'solid "blue")
                 (rectangle 15 10 'solid "black")))
Three rectangles in a pyramid.  The top rectangle is red.  The lower-left one is blue.  The lower-right one is black.  The red rectangle is centered over the other two rectangles.

As you may have discovered in your youth, there are a wide variety of interesting images we can make by just combining simple colored shapes. You’ll have an opportunity to do so in [the corresponding lab].

Self Checks

Check 1: Reflect on procedures

Make a list of five or so procedures you’ve encountered in this reading, the number and types of the parameters (e.g., do they require numbers or strings), and their behavior.

Check 2: Some other examples

Predict the output for each of the following expressions. Be prepared to discuss them in class.

(* (+ 4 2) 2)
(- 1 (/ 1 2))
(string-length "Snicker snack")
(string-split "Snicker snack" "ck")
(circle 10 'solid "teal")

Check 3: Precedence

Consider the expression 3-4x5-6.

If we did not have rules for order of evaluation, one possible way to evaluate the expression would be to subtract six from five (giving us negative one), then subtract four from three (giving us negative one), and then multiply those two numbers together (giving us one). We’d express that in Racket as (* (- 5 6) (- 3 4)).

a. What is the “official” way to evaluate that expression?

b. How would you express that in Racket?

c. Come up with at least two other orders in which to evaluate that expression.

d. Express those other two orders in Racket.