Ord instance

From HaskellWiki

What is the meaning of the instance? Certainly most people agree that an instance shall provide an total ordering.

However opinions differ whether there shall be more in it:

• An
  Ord
  instance may also suggest a notion of magnitude
• An
  Ord
  instance may be free of any other association

Depending on these opinions we come to different conclusions

whether there should be instances for and numbers. In most circumstances expressions like are certainly a bug, when and are or numbers.

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 , or other functions that yield a real. The truth of relies on the encoding of by 0 and 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 such a language it is . If you use the numeric value of boolean values for arithmetics like in in order to map to -1 and to 1 without an ,

then porting a program between different representations of boolean values becomes error-prone.

However you like to work with s of boolean values and complex numbers, and requires an instance.

See also

• Haskell-Cafe on Unnecessarily strict implementations

Category: Style