Reputation: 43
I tried the following code
class Group a where
(.+.) :: a -> a -> a
(.-.) :: a -> a -> a
zero :: a
opposite :: a -> a
x .-. y = x .+. opposite y
opposite x = zero .-. x
{-# MINIMAL (.+.), zero, (opposite | (.-.)) #-}
instance Fractional a => Group a where
x .+. y = x + y
zero = 0 :: a
opposite = negate :: a -> a
But on loading into GHCi, I get the following error:
group1.hs:11:26: error:
• Illegal instance declaration for ‘Group a’
(All instance types must be of the form (T a1 ... an)
where a1 ... an are *distinct type variables*,
and each type variable appears at most once in the instance head.
Use FlexibleInstances if you want to disable this.)
• In the instance declaration for ‘Group a’
|
11 | instance Fractional a => Group a where
|
What am I doing wrong?
Upvotes: 1
Views: 653
Reputation: 20566
I was able to compile your example:
{-# LANGUAGE FlexibleInstances, UndecidableInstances #-}
class Group a where
(.+.) :: a -> a -> a
(.-.) :: a -> a -> a
zero :: a
opposite :: a -> a
x .-. y = x .+. opposite y
opposite x = zero .-. x
{-# MINIMAL (.+.), zero, (opposite | (.-.)) #-}
-- data Fractional a = Fractional a a
instance (Fractional a, Num a) => Group a where
x .+. y = x + y
zero = 0
opposite = negate
FlexibleInstances
allow instance of unknown type with constraints. Basically allow instance X a
UndecidableInstances
we need because we declare that any a
belong to class Group
and it could (inevitable?) lead to a
belong to Group
thru several different instance
declarations.Upvotes: 2
Reputation: 43
Ah! I have finally understood, what is wrong. In Haskell, a class can be instantiated for an ADT only. So, the only reasonable solution is to declare something as follows:
class Group a where
(.+.) :: a -> a -> a
(.-.) :: a -> a -> a
zero :: a
opposite :: a -> a
x .-. y = x .+. opposite y
opposite x = zero .-. x
{-# MINIMAL (.+.), zero, (opposite | (.-.)) #-}
newtype GroupType a = GroupType a
instance Fractional a => Group (GroupType a) where
GroupType x .+. GroupType y = GroupType $ x + y
zero = GroupType 0
opposite (GroupType x) = GroupType $ negate x
Upvotes: 3