Question

I want to make a function in standard ml that checks if a tree is complete or not, the function somehow works, but its giving me the wrong type and a warning of non-exhaustive cases

The tree code:

datatype 'data tree = 
  EMPTY
| NODE of 'data tree * 'data * 'data tree;

fun isComplete EMPTY = true
  | isComplete (NODE(x, y, z)) = if (x = EMPTY andalso z <> EMPTY) orelse (x <> EMPTY andalso z = EMPTY) then false else true;

Now the above function’s type is: ''a tree -> bool but the required type is 'a tree -> bool

The warning I’m having is:

stdIn:169.8 Warning: calling polyEqual
stdIn:169.26 Warning: calling polyEqual
stdIn:169.45-169.47 Warning: calling polyEqual
stdIn:169.64-169.66 Warning: calling polyEqual
stdIn:124.1-169.94 Warning: match nonexhaustive
          NODE (x,y,z) => ...

What is the problem I’m having?

EDIT:

Thanks to Michael, I fixed the code and now it works:

- fun isComplete EMPTY = true
    | isComplete (NODE(EMPTY, _, EMPTY)) = true
    | isComplete (NODE(NODE(x, y, z), _, NODE(a, b, c))) = true
    | isComplete (EMPTY, _, NODE(x, y, z)) = false
    | isComplete (NODE(x, y, z), _, EMPTY) = false;

Answer 1

The ''a tree -> bool type indicates that a is an equality type: it must be a type that supports testing with equals. Since you are using = and <> to test x and z, the tree data must support equality (even though you’re not doing anything interesting with the values). This is the root of the polyEqual warning.

The nonexhaustive match warning is more puzzling. When I paste your datatype and function definitions into Moscow ML, I do not get a warning. I don’t think I’d worry about it too much, as I’d expect fixing the type to also take care of the warning.

To get the desired type 'a tree -> bool, I’d suggest getting rid of the if in favor of pattern matching. E.g.:

fun isComplete EMPTY = true
  | isComplete (NODE(EMPTY, _, EMPTY)) = true
  | isComplete (NODE(EMPTY, _, NODE(x,y,z))) = false
  | ... (* fill out the rest of the cases *)

I’ll leave it to you to figure out the full set of cases, as this looks like homework.

Incidentally, I don’t think your test for completeness is correct. Consider what happens when neither subtree is EMPTY: you call the tree complete without considering the contents. This doesn’t have anything to do with the warnings you’re seeing, though.