Force equality for real numbers in Real in SML

Question

As explained in the REAL signature, real type defined in SML is not an equality type and hence the following expression does not reduces

> 1.0 = 1.0;
poly: : error: Type error in function application.
   Function: = : ''a * ''a -> bool
   Argument: (1.0, 1.0) : real * real
   Reason: Can't unify ''a to real (Requires equality type)

However, this is not handy as datatypes and lists containing reals, lose equality too. I would need to overload polymorphic equality = with Real.== so it could approximately consider reals too.

Is that possible ?

EDIT: Edited question to be more clear

Answer 1

Did you read Why can't I compare reals in Standard ML and consider the Real.== operator or perform an epsilon test? Have you considered a type like Haskell's Data.Decimal (in which the mantissa and exponent are handled as a pair of Integer)?

Answer 2

The simple answer is: no, you can't.