What is the meaning of the
Certainly most people agree that an
Ord instance shall provide an total ordering.
However opinions differ whether there shall be more in it:
Ordinstance may also suggest a notion of magnitude
Ordinstance may be free of any other association
Depending on these opinions we come to different conclusions
whether there should be
Ord instances for
In most circumstances expressions like
a < b are certainly a bug,
Consider someone rewrites an algorithm for real numbers to complex numbers
and he relies on the type system to catch all inconsistencies.
The field operations can remain the same, but
(<) has to be applied to results of
realPart or other functions that yield a real.
The truth of
False < True relies on the encoding of
False by 0 and
True by 1.
However there are also programming languages that represent "true" by -1, because this has bit pattern 1....1.
The CPU has an instruction to fill a byte with the content of a flag
and you can use this bit pattern for bitwise AND and OR operations.
This makes that representation very efficient.
In principle we could also provide machine dependent efficient representations of boolean values in Haskell.
If "true" is associated with -1 then it holds
False > True.
If you use the numeric value of boolean values for arithmetics like in
2 * fromEnum bool - 1
in order to map
False to -1 and
True to 1 without an
then porting a program between different representations of boolean values becomes error-prone.
However you like to work with
Sets of boolean values and complex numbers,
Set requires an
You may consider using the
Ord instance by
Set operations an abuse,
since they do not require a particular ordering.
Ordering is only needed for implementation of efficient
and the operations would be as efficient, if the order is reversed or otherwise modified.
But we would certainly not like to have
1 < 2 for
1 > 2 for, say,
The solution might be a type class especially for
However it would miss automatic instance deriving.
- Haskell-Cafe on Unnecessarily strict implementations