Problem 1. see:

http://www.cs.bu.edu/~hwxi/academic/courses/CS320/Fall06/solutions/01/solution1.perl

Problem 2.

fun fact n =
   new_if (n > 0, n * fact (n-1), 1)

Since Standard ML is call-by-value, it evaluates the terms "n > 0", "n * 
fact (n-1)", and "1" to values before it calls new_if. Therefore, a 
recursive call to fact is made regardless of the terminating condition n 
<= 0, so "fact" loops forever (or more precisely, "fact" loops until
memory is consumed up, which should happen given that "fact" is not
tail-recursive).

Problem 3.

fun is_triangle (a: real, b: real , c: real): bool =
   a + b > c andalso a + c > b andalso b + c > a