Define the behavior of:
1 2 | (define (a-plus-abs-b a b) ((if (> b 0) + -) a b)) |
When a-plus-abs-b is invoked, all the subexpressions are evaluated. Thus, the if special form is evaluated to + when b > 0, otherwise evaluated to -, and applied to the values of a and b.
The equivalent case analysis is:
Which simplified is:
Given three numbers, the procedure should return the sum of the square of the two larger numbers:
1 2 3 4 5 6 7 8 9 10 11 | (define (>= x y) (not (< x y))) (define (max x y) (if (>= x y) x y)) (define (square x) (* x x)) (define (squares-sum x y) (+ (square x) (square y))) (define (sum-larger x y z) (cond ((>= x (max y z)) (squares-sum x (max y z))) ((>= y (max x z)) (squares-sum y (max x z))) ((>= z (max x y)) (squares-sum z (max x y))))) |
1 | (sum-larger 5 6 9) |
Value: 117
1 | (sum-larger -2 -4 -5) |
Value: 20
This expression
1 2 | (/ (+ 5 4 (- 2 (- 3 (+ 6 (/ 4 5))))) (* 3 (- 6 2) (- 2 7))) |
I’m yet to learn how to pretty-print code in Scheme.
Evaluation of a numeral:
1 | 10 |
Value: 10
–
Prefix notation allows to pass a slew of arguments:
1 | (+ 5 3 4) |
Value: 12
–
A simple combination applying an operator to two operands:
1 | (- 9 1) |
Value: 8
–
1 | (/ 6 2) |
Value: 3
–
Nested combinations are also allowed by the prefix notation:
1 | (+ (* 2 4) (- 4 6)) |
Value: 6
–
define is a special form that does not follow the read-eval-print loop (REPL):
1 | (define a 3) |
Value: a
–
1 | (define b (+ a 1)) |
Value: b
–
1 | (+ a b (* a b)) |
Value: 19
–
= is a primitive predicate. A predicate evaluates to either to the constant #f or the constant #t:
1 | (= a b) |
Value: #f
–
if is a special form also:
1 2 3 | (if (and (> b a) (< b (* a b))) b a) |
Value: 4
–
cond is a conditional expression used in case analysis:
1 2 3 | (cond ((= a 4) 6) ((= b 4) (+ 6 7 a)) (else 25)) |
Value: 16
--
1 | (+ 2 (if (> b a) b a)) |
Value: 6
--
1 2 3 4 | (* (cond ((> a b) a) ((< a b) b) (else -1)) (+ a 1)) |
Value: 16
Reading now:
SICP
1 2 3 | (define pi 3.141516) (define radius 10) (* pi (* radius radius)) |
This is an example of awesome 
