SML list equality oddness

Question

I have this bit of code:

fun foldr2(f, x::xs) =
    if xs = [] then
      x
    else
      f(x, foldr2(f, xs))

With the type signature

(''a * ''a -> ''a) * ''a list -> ''a

Looks pretty straight-forward, it takes a function that works over equality types and a list of equality type as arguments, because of the xs = [] comparison. However, for some reason it works on input such as (op +, [2.3, 2.7, 4.0]), when in SML/NJ reals are not an equality type. Can anyone help me shed some light on why this magic occurs?

Answer 1

I believe it's to do with the magical way in which + is overloaded for reals. To me, this almost verges on being a compiler bug, although I would have to look at the SML97 definition to see exactly what the correct behaviour is meant to be. The overloading over + is something of a nasty dark corner in SML, IMHO.

For example, if you define a function that is of type real * real -> real and pass that as an argument to foldr2 you get the type error you were expecting:

fun f (x : real * real) = 134.5
foldr2 (f, [1.4, 2.25, 7.0])
  stdIn:8.1-8.29 Error: operator and operand don't agree [equality type required]

You can even induce the type error if you just add a type annotation to op +, which basically led me to the conclusion that it is the overloading of + that is causing the mysterious effect.