lecture_01b.md

SICP Lecture 1B

Substitution Model

Gerald Jay Sussman

(define (sos x y)
  (+ (sq x) (sq y)))
(define (sq x)
  (* x x))

kinds of expressions:

• numbers
• symbols
• lambda expressions
• definitions
• conditionals
• combinations

Substitution rule:

1. evaluate the operator to get procedure
2. evaluation the operands to get arguments
3. apply the procedure to the arguments

• copy the body of the procedure, substituting the argument supplied (reduction)
• evaluate the new body

"The key to understanding complicated things is to know where not to look at, what not to compute, what not to think"

(if )

"one of the thing every sorcerer will tell you: if you have the name of the spirit you have the power over it"

iteration:

(define (+ x y)
  (if (= x 0)
    y
    (+ (-1+ x) (1+ y))))

-> time = O(x), space = O(1)

linear recursion:

(define (+ x y)
  (if (= x 0)
    y
    (1+ (+ (-1+ x) y))))

-> time = O(x), space = O(x)

(define (fib n)
  (if (< n 2)
    n
    (+ fib((-n 1)) fib((-n 2)))))

-> time = O(fib(n)), space = O(n)

(define (move n from to spare)
  (cond ((n = 0) "done")
    (else
        (move (-1+ n) from spare to)
        (print-move from to)
        (move (-1+ n) spare to from))))