SICP Section 1.1

By on

LISP stands for LISt Processing. Using Lisp requires you to make use of so many brackets that soon enough you abandon the language altogether, and switch to Python. A basic mathematical expression, say 3 + 4 is written in this way

(+ 3 4)

To assign a value, say 4, to a variable, say x, do the following

(define x 4)

Say we want to define a function that takes in a number and returns the square of that number. This is how we do it

(define (square x) (* x x))

The interpreter in our case uses applicative order evaluation, which means that it evaluates the arguments in the innermost bracket first, and then moves outwards. A different method of evaluation is normal order evaluation, where the interpreter evaluates arguments from left-to-right instead. The applicative order method is more efficient as compared to the normal order method, as the normal order method may end up evaluating the same thing multiple times.

Conditional Expressions

Now we come to conditional expressions. Conditional expressions follow this format

(cond (<p1> <e1>)
	(<p2> <e2>)
	(<p3> <e3>)
	...
	(<pn> <en>))

The ps are all predicates, ie, the expression whose value when interpreted returns a true or false. The es are the consequent expressions, ie, the values on which the predicate operates. An example mentioned in the SICP book is an absolute value function, ie, a function that returns the absolute value of the number passed in. It looks like this

(define (abs x)
	(cond ((> x 0) x)
		((= x 0) 0)
		((< x 0) (- x))))

Apart from the crazy number of brackets present in this declaration, everything else works. Look at the last expression: (- x). It tells the interpreter to return the negative of the value passed in.

Another conditional expression is an if expression, which has the form

(if <predicate> <consequent> <alternative>)

Read the general form in this way: if (this) (then this) (else this). With the if expression, our absolute value statement can be simplified, like so

(define (abs x)
	(if (< x 0)(- x) x))

We’ve lost most of the brackets, and almost all of the headache of the previous expression. Btw, in my DrRacket environment, when I chose R5RS as the language, it told me that it already had a library function called abs, so I had to name my function something else.

There are three other logical composition operations that are commonly used:

  1. (and <e1> ... <en>) If any of (e1 to en) evaluate to false, the expression returns false.
  2. (or <e1> ... <en>) If any of (e1 to en) evaluates to true, the expression returns true.
  3. (not <e>) If e is false, then the expression is true.

Exercise 1.2

(/ 
  (+ 5 4 (- 2 (- 3 (+ 6 4/5)))) 
  (* 3 (- 6 2) (- 2 7)))

Exercise 1.3

; STEP 1
; Define a function that squares a number
(define (sq x) (* x x))

; STEP 2
; Now use that to add up the numbers
; after finding the two largest numbers
(def (sum-sq-max x y z) 
  (if (and (> x z) (> y z)) (+ (sq x) (sq y)) 
    (if (and (> y x) (> z x)) (+ (sq z) (sq y)) (+ (sq x) (sq z)))
  )
)

Exercise 1.4

(define (a-plus-abs-b a b)
  ((if (> b 0) + -) a b)
)

This function adds the face value of a (i.e, considering the sign with the number) to the absolute value of b (i.e, discarding the sign).

Exercise 1.5

; Function one defined by Ben Bitdiddle
(define (p) (p))

; Function two defined by Ben Bitdiddle
(define (test x y)
  (if (= x 0) 0 y)
)