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Generic number type

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1 Problem


Can I have a generic numeric data type in Haskell which covers
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
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<hask>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 write
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 <hask>genericNumberLength
. However, there is already
and you can write
average :: Fractional a => [a] -> a
average xs = sum xs / genericlength xs

1.1 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
are interpreted as rationals itself. The second example fails, because
always returns an
number type, where
is not an instance. You should use
instead. This constructs a fraction out of two integers:
1 % 3 :: Rational
1 % floor pi :: Rational

2 See also