Generic number type
Problem
Question:
Can I have a generic numeric data type in Haskell which covers Integer
, Rational
, 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 GenericNumber
s you will encounter exactly the problems
that all scripting language users have encountered so far (or ignored :-).
Solutions
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.
average
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 genericNumberLength
.
However, there is already Data.List.genericLength
and you can write
average :: Fractional a => [a] -> a
average xs = sum xs / genericlength xs
ratios
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 1
and 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
See also
- Suggestions for implementing a generic number type: http://www.haskell.org/pipermail/haskell-cafe/2007-June/027092.html