CSE341 Section #6 Problems

Summary of basic Scheme features:

    Types:
    numbers: integers (3, 802), reals (3.4), rationals (3/4), complex (2+3.4i)
    symbols: x, y, hello, r2d2
    booleans: #t, #f
    strings: "hello", "how are you?"
    lists: (3 4 5) (98.5 "hello" (3 82.9) 73)

    Constructs:
    function call: (f arg1 arg2 arg3 ... arg-n)
    variable binding: (define sym expr)
    function binding: (define (f p1 p2 ... pn) expr)
    function binding with helper functions:
        (define (f p1 p2 ... pn) (define ...) (define ...) expr)
    let binding: (let ((sym1 e1) (sym2 e2) ... (sym-n en)) expr)
    let* binding: (let* ((sym1 e1) (sym2 e2) ... (sym-n en)) expr)
    if expression: (if test e1 e2)
    cond expression: (cond (test1 e1) (test2 e2) ... (test-n e-n))
                     (cond (test1 e1) (test2 e2) ... (else e-n))

    Useful functions
    arithmetic: +, -, *, /, modulo, quotient, remainder
    mathematical: abs, sin, cos, max, min, expt (exponent), sqrt, floor,
                  ceiling, truncate, round
    relational (for numbers): =, <, >, <=, >=
    equality (for other structures): eq?, eqv?, equal?
    logical: and, or, not
    type predicates: number? integer? symbol? boolean? string? list?
    higher-order: map, filter, foldl, foldr, sort
    list operations:
        length -- length of a list
        car -- first element of a list
        cdr -- rest of the list
        cons -- takes a value and a list and constructs a new list with the
                value at the front and the list after
        append -- joins lists together
        list -- forms a list from a sequence of values
        null? -- is something an empty list?
        pair? -- is something a nonempty list?

1. For each of the following definitions of a factorial function, identify the
   parenthesis error:

     (define (fact n) (if (= n 0) (1) (* n (fact (- n 1)))))
     (define (fact n) (if = n 0 1 (* n (fact (- n 1)))))
     (define fact (n) (if (= n 0) 1 (* n (fact (- n 1)))))
     (define (fact n) (if (= n 0) 1 (* n fact (- n 1))))
     (define (fact n) (if (= n 0) 1 (* n ((fact) (- n 1)))))

2. How do you form a comment in Scheme?  Is there a syntax for multi-line
   comments?  How is the expression (/ a b c d) evaluated (i.e., left-to-right
   or right-to-left)?  How would you compare to see if one string is less than
   another?

3. Define a function stutter that takes a list as an argument and that returns
   the list obtained by replacing every value in the list with two of that
   value.

4. Define a function sum that takes a list as an argument and that returns the
   sum of the numbers in the list.  Don't worry about embedded numbers (numbers
   in inner lists).  For example, (sum '(1 3.4 a b "hello" (2 3))) should
   return 4.4.

5. Define a function (multiples n m) that returns a list of the first n
   multiples of m.  For example, (multiples 3 5) should return (5 10 15).

6. Define a function flatten that takes a list as an argument and that returns
   the list obtained by eliminating internal list structures.  For example:

        (flatten '(1 2 a (b c (d e (f)) g) () () 13)) should return
        (1 2 a b c d e f g 13)