Question

Write a function isaset which takes a list of any equality type² and returns true if the list is a set (each element appears exactly once). So, the type of isaset is ' 'a list -> bool.

Here are a few examples of expected behavior - isaset nil; * the empty set is definitly val it true : bool - isaset ["foo", "bar", "baz"]; val it true : bool - isaset [1,2,3,4,4,5,6]; val it false : bool special name! a set; it even has a

Hints:

• Do not try for efficiency. A brute-force O(n2 ) solution is appropriate to this exercise. 3

• You might find it easier to develop an algorithm if you consider how to determine the list is not a set.

• A recursive helper function is needed; again, hide it inside let … in … end;

• isaset is recursive.

• Use appropriate pattern matching in your parameters.

• Trying hard, I found a use for defining a val inside the let … in … end;, but it was a bit contrived; don’t worry if your solution doesn’t have one.

Answer 1

-fun notfound(x,[])=true

| notfound(x,b::y)

if x=b then false

else notfound(x,y);

val notfound = fn : ' ' a* ' ' a list ->bool

-fun isaset [ ]=true

| isaset (c::y)=

if notfound (c,y) then isaset(c::y)

else false;

val isaset =fn : ' ' a list -> bool