What's the type of function "abs"?

I'm a newbie, knowing a little about Haskell, and hope my question isn't very silly... ===================================================================== My absolute value function looks like this: abs2 :: Num a => a -> a abs2 n = if n >= 0 then n else 0 - n GHCi tells me that I should add Ord type class to its definition. Well, it's true. It has used relational operators and Num isn't a subclass of Ord. However, when I input ":t abs" in GHCi, the interpreter shows "abs :: Num a => a -> a". I read GHC/Num.lhs and find that abs is defined as "abs :: a -> a" and has no concrete content. So I think the abs function is written in C as a module to implement directly and the type of abs just follows its class GHC.Num. Is it right? Or there are any other reasons? Thanks, Hengruo

Hi, On 2015-03-11 14:21, Zhang Hengruo wrote:
My absolute value function looks like this:
abs2 :: Num a => a -> a abs2 n = if n >= 0 then n else 0 - n
GHCi tells me that I should add Ord type class to its definition. Well, it's true. It has used relational operators and Num isn't a subclass of Ord. However, when I input ":t abs" in GHCi, the interpreter shows "abs :: Num a => a -> a". I read GHC/Num.lhs and find that abs is defined as "abs :: a -> a" and has no concrete content. So I think the abs function is written in C as a module to implement directly and the type of abs just follows its class GHC.Num. Is it right? Or there are any other reasons?
'abs' is a function defined on the 'Num' class, i.e. any instance of 'Num' (such as 'Num Int') may define 'abs' as it pleases. See http://hackage.haskell.org/package/base-4.7.0.2/docs/src/GHC-Num.html#abs for a few instantiations of the 'Num' class. In particular, concrete instances of the class know the actual type of 'a'. For instance, the definition of 'Num Int' could actually use '>=' because there's indeed an Ord instance for Int. In other cases, e.g. 'Num Word', 'abs' is just the identity function, i.e. 'abs x = x' since there are no non-positive Word values. -- Frerich Raabe - raabe@froglogic.com www.froglogic.com - Multi-Platform GUI Testing

One nice thing about haskell is that the source to most things is available on hackage. If you look at abs, here:
https://hackage.haskell.org/package/base-4.7.0.2/docs/src/GHC-Num.html#abs
You will see two things:
1) abs is actually part of the Num typeclass, so can be defined differently for the different numerical types
2) the definition for Int is similar to yours:
abs n = if n `geInt` 0 then n else negate n
Notice `geInt` is just an int-specific (>=) operator. Because we're defining an instance we know the concrete type we're dealing with (the type is Int -> Int by this point, rather than a -> a), so we don't need to make use of Ord in this case.
11 Mar 2015 22:21、Zhang Hengruo
I'm a newbie, knowing a little about Haskell, and hope my question isn't very silly... ===================================================================== My absolute value function looks like this:
abs2 :: Num a => a -> a abs2 n = if n >= 0 then n else 0 - n
GHCi tells me that I should add Ord type class to its definition. Well, it's true. It has used relational operators and Num isn't a subclass of Ord. However, when I input ":t abs" in GHCi, the interpreter shows "abs :: Num a => a -> a". I read GHC/Num.lhs and find that abs is defined as "abs :: a -> a" and has no concrete content. So I think the abs function is written in C as a module to implement directly and the type of abs just follows its class GHC.Num. Is it right? Or there are any other reasons?
Thanks,
Hengruo _______________________________________________ Beginners mailing list Beginners@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/beginners

Oh! Thank you very much! I took notice of instances of Num just now... You
two are so kind!
2015-03-11 21:30 GMT+08:00 Daniel P. Wright
One nice thing about haskell is that the source to most things is available on hackage. If you look at abs, here:
https://hackage.haskell.org/package/base-4.7.0.2/docs/src/GHC-Num.html#abs
You will see two things:
1) abs is actually part of the Num typeclass, so can be defined differently for the different numerical types 2) the definition for Int is similar to yours:
abs n = if n `geInt` 0 then n else negate n
Notice `geInt` is just an int-specific (>=) operator. Because we're defining an instance we know the concrete type we're dealing with (the type is Int -> Int by this point, rather than a -> a), so we don't need to make use of Ord in this case.
11 Mar 2015 22:21、Zhang Hengruo
のメッセージ: I'm a newbie, knowing a little about Haskell, and hope my question isn't very silly... ===================================================================== My absolute value function looks like this:
abs2 :: Num a => a -> a abs2 n = if n >= 0 then n else 0 - n
GHCi tells me that I should add Ord type class to its definition. Well, it's true. It has used relational operators and Num isn't a subclass of Ord. However, when I input ":t abs" in GHCi, the interpreter shows "abs :: Num a => a -> a". I read GHC/Num.lhs and find that abs is defined as "abs :: a -> a" and has no concrete content. So I think the abs function is written in C as a module to implement directly and the type of abs just follows its class GHC.Num. Is it right? Or there are any other reasons?
Thanks,
Hengruo
_______________________________________________ Beginners mailing list Beginners@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/beginners
_______________________________________________ Beginners mailing list Beginners@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/beginners
participants (3)
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Daniel P. Wright
-
Frerich Raabe
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Zhang Hengruo