scala predicate basic -

i'm new scala may forgive me basic newbie question. have following code snippet.

type pred[a, b] = (a, b) => int; def abs[a, b](p: (a, b) => int): (a, b) => int =   (a, b) => if (p(a, b) < 0) -(p(a, b)) else (p(a, b)); def multiply(a: int, b: int): int =   * b; def subtract(a: int, b: int): int =   - b;  val absmultiply = abs(multiply); val abssubstract = abs(subtract);  println("abs(10 * 10) = " + absmultiply.apply(10, 10)); println("abs(10 - 100) = " + abssubstract.apply(10, 100)); 

so i've understand correctly should possible replace (a,b) => int pred[a, b].

def abs[a, b](p: pred[a, b]): pred[a, b] =   (a, b) => if (p(a, b) < 0) -(p(a, b)) else (p(a, b)); 

but compiler exception

type mismatch;  found   : (int, int) => int  required: (a, b) => int     type mismatch;  found   : (int, int) => int  required: (a, b) => int     

have misunderstood here wrong?

thank help.

cyrill

it works if declare , b contravariant types:

type pred[-a, -b] = (a, b) => int 

this necessary because multiply , subtract functions considered subtypes of pred[a, b], arguments must supertypes of , b. see this answer excellent explanation on subject.