CSE341 Section #1 Problems

Summary of ML features so far:

        types: int, real, bool, string, char, tuple, list, function

        Constructs:
        val <variable> = <expression>;
        fun <name>(<type> : <name>, ..., <type> : <name>) = <expression>;
        if <boolean expression> then <expression> else <expression>
            
        operator    example                   description
        --------------------------------------------------------------------
           +        2 + 2                       addition
           -        18.4 - 3.8                  subtraction
           *        3 * 18                      multiplication
           /        14.5 / 3.4                  real division
          div       88 div 10                   integer (truncated) division
          mod       88 mod 10                   modulus function
           ~        ~18                         arithmetic negation
           ^        "hello" ^ "there"           string concatenation
          ::        3 :: [1, 2, 3]              construct a list from head/tail
           @        [1, 2] @ [3, 4]             append two lists together
           <        4 < 19                      less than
           >        2.4 > 3.8                   greater than
          <=        "ab" <= "cd"                less than or equal
          >=        1.7 >= 4.7                  greater than or equal
           =        [1, 2] = [1, 1+1]           equals
          <>        3 <> 4                      not equal
        andalso     2 + 2 = 4 andalso 3 < 4     logical and (short circuited)
        orelse      8 > 9 orelse 1.4 < 2.8      logical or (short circuited)
          not       not (8 < 9)                 logical negation

        Function        Description
        --------------------------------------------------
        abs             absolute value of int or real
        real            convert int to real
        floor/ceil      integer just lower or higher than a real
        trunc/round     convert real to int
        hd              head (first element) of a list
        tl              tail (elements after first) of a list
        length          length of a list

1. What is the type of each of the following expressions?
        (3, 4.5)
        [4.5, 3.8]
        ((3, 4), 18.5)
        [[3, 4], [7]]
        [("hello", 3)]

2. For each of the following types, give an expression of that type:
        int * string * real
        string list
        int * string list
        (int * string) list
        (int * string) list list
        (int * string list) list

3. Write a function called gcd that returns the greatest common divisor of two
   integers.  You can take advantage of the fact that:

        gcd(n, 0) = n for all n
        gcd(x, y) = gcd(x mod y, y) for all x, y

   Using the gcd function, write a function lcm that returns the least common
   multiple of two integers.

4. Write a function called sum that returns the sum of a list of integers.  How
   would you change it to make it sum a list of reals?

5. Write a function called toReal that takes a list of ints as an argument and
   that returns the result of converting each int to a real.  For example,
   toReal([3, 5, ~7]) should return [3.0, 5.0, ~7.0].

6. Write a function called switchPairs that takes a list as an argument and
   that returns the list formed by switching the order of successive pairs of
   elements in the list.  For example:

        switchPairs([3, 7, 4, 9, 8, 12]) should return [7,3,9,4,12,8]

   If the list has an odd number of values, then the final element should not
   be moved.  For example:

        switchPairs([3, 7, 4, 9, 8, 12, 2])  should return [7,3,9,4,12,8,2]