operator and operand don't agree [equality type required]

Question

This function calculate count element y in list

fun func y xs=List.length(List.filter(fn x => x=y) xs);

val countElement = fn : ''a -> ''a ?.list -> int
func 1 [1,2,3,4];
val it = 1 : int

But, when I write func 1.1 [1.1,2.1,3.1,4.1]; I get error:

stdIn:64.1-64.35 Error: operator and operand don't agree [equality type required]
operator domain: ''Z
operand:         real
in expression:
countElement 1.1

How can I solve it problem ?

Answer 1

real is not an equality type in SML 97. That means you cannot use = to compare two reals.

Answer 2

Standard ML has a concept of "equality types", or types that "admit equality"; or, more to the point, it has a concept of types that do not admit equality. You can only use = on types that do admit equality. (This is why its type is ''a * ''a -> bool rather than 'a * 'a -> bool. Type variables that start with '' can only be instantiated to equality types.)

In SML '97, real is one type that does not admit equality; so, the following code will not type-check:

val oneIsOne = (1.0 = 1.0)    (* FAIL! *)

The reason for this design decision is that IEEE 754 (the standard that defines floating-point numbers) defines "equality" in a rather strange way — NaN is not equal to itself, and 0.0 is equal to ~0.0 even though 1 / 0.0 is not equal to 1 / ~0.0. The language designers decided that they didn't want = to differ from the semantics specified by IEEE 754, but that they also didn't want the semantics of = to be different for real than for all other types in the language. Instead, they completely eliminated = for real, and made the IEEE 754 definition semantics available as Real.== [link]. So, you can write:

fun countRealElement y xs = List.length (List.filter (fn x => Real.== (x,y)) xs)

val it = countRealElement 1.1 [1.1,2.1,3.1,4.1]    (* 1 *)

(where countRealElement has type real -> real list -> int).