Cannot justify constraints in explicitly typed binding error in Haskell

Question

quadraticRoots :: Floating t => t -> t -> t -> (t, t)
quadraticRoots a b c = if d < 0 then error "0" else (x, y)
                          where
                            x = e + sqrt d / (2 * a)
                            y = e - sqrt d / (2 * a)
                            d = b * b - 4 * a * c
                            e = - b / (2 * a)

The above code gives the following error in Hugs:

Cannot justify constraints in explicitly typed binding
*** Expression    : quadraticRoots
*** Type          : Floating a => a -> a -> a -> (a,a)
*** Given context : Floating a
*** Constraints   : Ord a

Can anyone help me interpret this?

mnoronha · Accepted Answer · 2016-11-07 00:07:11Z

4

In order to make a comparison like d < 0, the thing you are comparing must be a member of the Ord typeclass. Thus, we need to amend our type signature to include the additional constraint Ord:

quadraticRoots :: (Ord t, Floating t) => t -> t -> t -> (t, t)

answered Nov 7, 2016 at 0:07

mnoronha

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Comments

Will Ness · Accepted Answer · 2016-11-07 09:14:20Z

Your type signature says t is in Floating type class, but compiler found it must also be in Ord.

Were Ord a superclass of Floating, all would be good. But it's not.

To see the type the compiler derives (infers), just omit the explicit type signature. Then, after defining the function in GHCi, ask

~> :t quadraticRoots
quadraticRoots :: (Ord t, Floating t) => t -> t -> t -> (t, t)

< is in Ord, sqrt is in Floating, and / is in Fractional. But Floating is a subclass of Fractional, so specifying it alone is enough for the both of them:

~> :i sqrt
class Fractional a => Floating a where
  ...
  sqrt :: a -> a
  ...

~> :i /
class Num a => Fractional a where
  (/) :: a -> a -> a
  ...
infixl 7 /

~> :i <
class Eq a => Ord a where
  ...
  (<) :: a -> a -> Bool
  ...
infix 4 <

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