CODEWITHSUNDEEP
haskellfloating-pointfunctional-programming
Mystery
Mystery

Reputation: 35

Can data ord be replaced with only RealFloat in comparing numbers in Haskell?

maxs :: (RealFloat a) => a -> a -> a
maxs a b
    | a>b = a
    | otherwise = b


maxs :: (Ord a) => a -> a -> a
maxs a b
    | a>b = a
    | otherwise = b

I'm trying to write a max function using Haskell. These two seem to work both. I wrote the first one and the latter one comes from the book. My question is, what's the difference between them? Can they replace each other?

The ord class is used for totally ordered datatypes. But in this case, order doesn't seem to matter.

Upvotes: 1

Views: 87

Answers (2)

MathematicalOrchid
MathematicalOrchid

Reputation: 62848

RealFloat implies RealFrac which implies Real which in turn implies Ord.

In other words, every type that is an instance of RealFloat must also be an instance of Ord. So both of these functions require Ord (which is what defines the "<" operator that you're trying to use). But the first one pointlessly also requires a bunch of stuff to do with floating-point numbers (e.g., the cos function).

Order most certainly does matter; that's the whole point of a max function. It's to find the maximum value. Without an ordering, there is no maximum value!

By using RealFrac, on the other hand, you are prevented from (for example) finding the maximum String, since a String clearly isn't any kind of floating-point number.

Upvotes: 1

Andrej Bauer
Andrej Bauer

Reputation: 2477

Suppose I write two functions:

f :: (a, b) -> a
f (x, y) = x

g :: (Int, Bool) -> Int
g (x, y) = x

What is the difference? Function g is less general because its type is more precise than the type of f. In a sense g is "artificially restricted" to work only on (Int, Bool) when it could work on any product type.

The situation with your two definitions of $\max$ is similar. One is more general than the other, but not because it does anything smarter, but because you declared one of them to work on any Ord instance, while the other works only on the RealFloat instances.

By the way, Ord is more or less unavoidable here because if you have max you can define $\leq$ by $$x \leq y \iff \max(x,y) = y.$$

Upvotes: 4

Related Questions