6.001 Recitation #2 – Sept 6, 2002

RI: Konrad Tollmar, NE43-V608

konrad@ai.mit.edu, http://www.ai..mit.edu/~konrad/6001

The MIT Scheme programming environment

Basic Scheme

- primitives

- combinations

- abstractions

- lambda

- special form cond

- special form if

1. Evaluate these expressions

(+ 2 3)

-> 5

(+ (* (/ 12 2) 1000) 1)

-> 6001

(+ 4)

-> 4

(- 3)

-> -3

(/ 5)

-> 0.2

(/ 60 5 2 3)

-> 2

(+)

-> 0

(*)

-> 1

(-)

-> error

(define a 1)

-> undef

(define a+1 (+ a 1))

-> undef

a

-> 1

a+1

-> 2

(define a 2)

-> undef

a+1

-> 2

(define four 4)

-> undef

four

-> 4

(+ four 1)

-> 5

(+ (four) 1)

-> error

2. Lambda

A. Evaluate these lambda procedures

(define six (lambda () 6))

-> undef

six

-> 6

(+ six 1)

-> error

(+ (six) 1)

-> 7

(define inc

(lambda (x) (+ x 1)))

-> undef

B. Define the lambda procedures twice and second.

(define (twice x)

(* 2 x))

(define (second a b c)

(b))

C. What is difference?

Plus take any number of arguments, add take only two arguments

D. Define an abs function

(define abs (lambda (x)

(cons ((> x 0) x)

((< x 0) (- x))

(else 0)))

(define abs (lambda (x)

(if (< x 0) (- x) x)))

E. Procedure abstractions

(define avarage (lambda (x y) (/ (+ x y) 2)))

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

(define avsq (lambda (x y) (avarage (square x) (square y))))

F. Procedure abstractions

(define convert (lambda (currency amount)

(cond ((string=? currency "USD") (/ amount RATE))

((string=? currency "SEK") (* amount RATE))

(else "error"))))

(define convert (lambda (currency amount)

(cond ((string=? currency "USD")

(begin

(display (string-append "USD->SEK: " (number->string (/ amount RATE))))

(/ amount RATE)))

((string=? currency "SEK") (* amount RATE))

(else "error"))))