# Generic number type

### From HaskellWiki

## Contents |

## 1 Problem

Question:

Can I have a generic numeric data type in Haskell which coversAnswer: In principle you can define a type like

data GenericNumber = Integer Integer | Rational Rational | Double Double

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 usingthat all scripting language users have encountered so far (or ignored :-).

A## 2 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.

### 2.1 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

average :: Fractional a => [a] -> a average xs = sum xs / genericLength xs

### 2.2 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 literals1 % 3 :: Rational 1 % floor pi :: Rational

### 2.3 isSquare

It may seem irksome thatisSquare :: (Integral a) => a -> Bool isSquare n = (floor . sqrt $ fromIntegral n) ^ 2 == n

isSquare :: GenericNumber -> Bool isSquare n = (floor . sqrt $ n) ^ 2 == n

## 3 See also

- The discussion on haskell-cafe which provided the impetus for this page: http://www.haskell.org/pipermail/haskell-cafe/2007-June/027092.html