Key to CSE341 Section #3 Problems

1.  One possible solution to each appears below.
        fun isPrime(n) =
            let fun isFactor(m) = n mod m = 0
                val factors = filter(isFactor, 2--trunc(Math.sqrt(real(n))))
            in n > 1 andalso factors = []
            end;

        fun isPrime(n) = 
            n > 1 andalso
            filter(fn(x) => n mod x = 0, 2--trunc(Math.sqrt(real(n))) = [];

2. One possible solution appears below.
        (* sum of squares of values from a list *)
        fun sumOfSquares(lst) = reduce(op +, map(fn x => x * x, lst));

3. One possible solution appears below.
        (* sum of squares of 1 through n *)
        fun sumOfSquares2(n) = reduce(op +, map(fn x => x * x, 1--n));

4. One possible solution appears below.
        (* product of first n odd numbers *)
        fun oddProduct(n) = reduce(op *, map(fn x => 2 * x + 1, 1--n));

5. One possible solution appears below.
        (* length of a list *)
        fun len(lst) = reduce(op +, 0::map(fn x => 1, lst));

6. One possible solution for each appears below.
        a) val double = curry op* 2;
        b) val prependStar = curry op ^ "*";
        c) val oneTo = curry op-- 1;
        d) val addOne = map2 (curry op+ 1)
        e) val f = abs o curry op+ 10 o curry op* 2;
        f) val primeProduct = reduce2 op* o filter2 isPrime;

7.     a) fun f c:char = 1.0 is interpreted as fun (f c):char = 1.0
          should be fun f (c:char) = 1.0
       b) fun f x::xs = [] is interpreted as fun (f x)::xs = []
          should be fun f (x::xs) = []
       c) print Int.toString 123 is interpreted as (print Int.toString) 123
          should be print (Int.toString 123)
       d) val add2 = map2 curry op+ 2 is interpreted as
          val add2 = (map2 curry) op+ 2
          should be val add2 = map2 (curry op+ 2)