06.md

Code Club 6

Recap

Expressions are like little questions for Racket to answer. We have seen two ways to make expressions. An expression is either:

1. A value; or

2. ( function expression₁ expression₂ ... )

The value of the first kind of expression is itself. To evaluate the second kind of expression, Racket first evaluates all the sub-expressions, then applies the function to the values produced.

We also now know several kinds of value. A value is either:

1. A number (42);
2. A string ("Hello, World.");
3. A "Boolean" (either #true or #false); or
4. An image

And we know several built-in functions, for example:

1. Arithmetic functions like +, -, log and so on;
2. String functions like string-append, string->number and so on;
3. Boolean functions like and, or, and not; and
4. Image functions like circle.

And we have seen examples of defining new functions and new "global constants". For example:

(define THE-ANSWER 42)
(= (* 6 7) THE-ANSWER)

;; Number -> Number
;; Adds 2 to its argument
(check-expect (add2 3) 5)

(define (add2 x)
    (+ x 2))

What's missing?

1. Making decisions
2. Doing things over and over again

Exercises

1. Use place-image and empty-scene to write a function that places a circle in a blank scene of size 200 x 160 at a position halfway up and at a given distance from the left side.

Don't forget

(require 2htdp/image)

Here's the template for you (I'll explain later why it's called moving-ball :

;; number -> image
;; Place a circle at a specified location in an empty scene
(check-expect (moving-ball 80) 
              (place-image 
               (circle 10 "solid" "red") 
               80 80
               (empty-scene 200 160))) 

(define (moving-ball x) 
 ... )

2. Replace magic numbers with constants

For example,

(define BALL-RADIUS 40)

3. Make the ball move from left to right using animate.

Decisions

(if (> 3 2) 3 2)

or

(cond
    [(> 3 2) "three is bigger than two!"]
    [(< 3 2) "two is bigger than three!"]
    [else "three is the same size as two!"])

4. Write a function biggest which, given two numbers, returns the larger of the two, eg (biggest 3 2) should produce 2.

   (This function already exists: it is called max.)

5. Write a function income-tax which computes your income tax given a gross salary. The rule is as follows (this is slightly simplified)

   • Up to £11,500 : 0% (Personal allowance)
   • £11,501 - £45,000 : 20% (Basic rate)
   • £45,001 - £150,000 : 40% (Higher rate)
   • over £150,001 : 45% (Additional rate)

Hint: To start with, imagine there is only the personal allowance and the basic rate (no other tax brackets). Try to make that work.

Hint: It will be easier to define auxiliary functions that each do some part of the work.

Hint: You could also write a cond that starts at the top and works downwards.

4. Let's talk about world programs.