Hi,
I'm trying to set up some operators for applicative versions of prelude
types. For instance:
-- | Applicative Equality.
class (Eq a) => AppEq f a where
(.==.), (./=.) :: f a -> f a -> f Bool
instance (Applicative f, Eq a) => AppEq f a where
(.==.) = liftA2 (==)
(./=.) = liftA2 (/=)
Hopefully the intention is fairly straightforward: if "f" is an instance
of Applicative then the lifted implementation of the underlying type.
Otherwise I can just give my own instance, which is useful for things
that "wrap" prelude types but where "fmap" doesn't work. For instance:
data (Ord a) => Interval a = Interval a a
instance (Ord a) => AppEq Interval a where
i1@(Interval _ u1) .==. i2@(Interval _ u2)
| isSingleton i1 && isSingleton i2 && u1 == u2 = Interval True True
| has i1 u2 || has i2 u1 = Interval False True
| otherwise = Interval False
False
i1 ./=. i2 = let Interval b1 b2 = (i1 .==. i2) in Interval (not b2)
(not b1)
isSingleton :: (Ord a) => Interval a -> Bool
isSingleton (Interval lower upper) = lower == upper
has :: (Ord a) => Interval a -> a -> Bool
has (Interval lower upper) v = v >= lower && v <= upper
You can't (easily) define fmap for Interval because the function given
as an argument might not be monotonic. So instead you have to write
custom implementations for each lifted function, as shown here for
(.==.) and (./=.) . The same principle works for AppOrd, AppNum etc,
but I'm trying to solve the problem for just AppEq for now.
This compiles, but when I try to use it I get this in ghci:
*Interval> let i1 = Interval 4 5
*Interval> let i2 = Interval 4 6
*Interval> i1 .==. i2
<interactive>:1:0:
Overlapping instances for AppEq Interval Integer
arising from a use of `.==.' at <interactive>:1:0-9
Matching instances:
instance (Ord a) => AppEq Interval a
-- Defined at Interval.hs:(22,0)-(27,78)
instance (Control.Applicative.Applicative f, Eq a) => AppEq f a
-- Defined at AppPrelude.hs:(32,0)-(34,23)
In the expression: i1 .==. i2
In the definition of `it': it = i1 .==. i2
I'm puzzled, because Interval is not an instance of Applicative, so the
second instance doesn't apply. Can anyone help me out?
I'm using ghc 6.8.3, so its possible that this was a bug fixed in 6.10.
Paul.
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