Generic number type
Can I have a generic numeric data type in Haskell which covers
Double and so on, like it is done in scripting languages like Perl and MatLab?
Answer: In principle you can define a type like
data GenericNumber = Integer Integer | Rational Rational | Double Double
and define appropriate instances for
Num class et. al.
However you will find that it is difficult to implement these methods in a way that is appropriate for each use case.
There is simply no type that can emulate the others.
Floating point numbers are imprecise - a/b*b=a does not hold in general.
Rationals are precise but pi and sqrt 2 are not rational.
That is, when using
GenericNumbers you will encounter exactly the problems
that all scripting language users have encountered so far (or ignored :-).
It is strongly advised to carefully check whether a GenericNumber is indeed useful for your application. So let's revisit some examples and their idiomatic solutions in plain Haskell 98.
You may find it cumbersome to manually convert integers to fractional number types like in
average :: Fractional a => [a] -> a average xs = sum xs / fromIntegral (length xs)
and you may prefer
average :: [GenericNumber] -> GenericNumber average xs = sum xs / genericNumberLength xs
with an appropriate implementation of
However, there is already
Data.List.genericLength and you can write
average :: Fractional a => [a] -> a average xs = sum xs / genericlength xs
You find it easy to write
1 / 3 :: Rational
but uncomfortable that
1 / floor pi :: Rational
does not work.
The first example works, because the numeric literals
3 are interpreted as rationals itself.
The second example fails, because
floor always returns an
Integral number type, where
Rational is not an instance.
You should use
% instead. This constructs a fraction out of two integers:
1 % 3 :: Rational 1 % floor pi :: Rational
- Suggestions for implementing a generic number type: http://www.haskell.org/pipermail/haskell-cafe/2007-June/027092.html