Question

I’m having trouble with pattern matching with lists in SML. I’m trying to create a function that takes a 2×2 real matrix (defined as 'a list list) and creates a complex (real * real). The matrix is formatted as a list of lists(that are made with reals) with each list being a row. I know that I have to pattern match but I’m unsure how to implement my understanding into actual code. My code thus far is:

fun fromMatrix ((a::M):real matrix) : complex =  (hd a, tl M);

I keep getting this error:

stdIn:1.5-13.32 Error: right-hand-side of clause doesn't agree with function result type [tycon mismatch]
  expression:  real * real list list
  result type:  complex
  in declaration:
    fromMatrix =
      (fn <pat> :: <pat> : real matrix => (hd <exp>,tl <exp>): complex)

Answer 1

Okay so if (a::M) has type real matrix (or real list list), then that means a (head) has type real list and M (tail) has type real list list. Then hd a has type real, and tl M has type real list list. So putting them together, (hd a, tl M) has type real * real list list, probably not what you want.

You probably want to understand that for lists, x :: y means that x is the first element, and y is the rest of the list (not the second element), which is a list. Similarly, the hd function returns the first element of a list, and the tl function returns the rest of the list. If you want to extract the first two elements, you could use the pattern x :: y :: z (where z is the rest of the list after the first 2 elements). If you know it’s going to be a 2-element list, you could match x :: y :: [], or equivalently, [x, y]. You can nest patterns, so if you have a 2-element list of 2-element lists, you could directly match [[a, b], [c, d]]. However, using a fixed-size list is a sign of bad design. You probably want to use a tuple instead.