Argthtjtr

I want to write a function in SML/NJ which will take 2 matrices as an arguments and it will multiply them.

I can only use:

• 
  

  function dot, which take 2 vectors and calculate scalar product:

  
  
  

  fun dot (xs: int list, ys: int list): int =
  
      List.foldl (fn (x,y) => x+y)
  
         0
  
         (ListPair.map (fn (x,y) => x*y) (xs, ys))
  
  

  
  


• 
  

  function transpose, which take 1 matrix and calculate transpose of this matrix:

  
  
  

  fun transpose (m: 'a list list): 'a list list =
  
      List.tabulate (List.length (List.nth (m, 0)),
  
             fn x => List.map (fn y => (List.nth (y, x))) m)
  
  

  
  
  
  
  

  • anonymous function

  
  

  • structures List, ListPair and Math

  
  
  
  

The function I want to write should be like this:

fun multiply (a: int list list, b: int list list): int list list

So far I have done this:

fun multiply (a: int list list, b: int list list): int list list =

case a of

 => 

  | g::rep => [(List.map (fn y => dot(g, y)) transpose(b))] @ (multiply(rep, b))

But I got this error:

test.sml:66.21-66.62 Error: operator and operand do not agree [tycon mismatch]

  operator domain: int list list

  operand:         'Z list list -> 'Z list list

  in expression:

(List.map (fn y => dot <exp>)) transpose

I get no errors, if in the last line of function multiply I write b instead of tranpose(b), but of course, if I do this, I don't the the resoult I want:

fun multiply (a: int list list, b: int list list): int list list =

case a of

 => 

  | g::rep => [(List.map (fn y => dot(g, y)) b)] @ (multiply(rep, b))

I don't know what else should I do. Can anybody pease help me?