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{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE RankNTypes #-}
{-# LANGUAGE GADTs #-}
module Exercises where
-- Rearrange.
--
-- 1
--
data Sum a b =
First b
| Second a
instance Functor (Sum e) where
fmap f (First a) = First (f a)
fmap f (Second b) = Second b
--
-- 2
--
data Company a c b =
DeepBlue a c
| Something b
instance Functor (Company e e') where
fmap f (Something b) = Something (f b)
fmap _ (DeepBlue a c) = DeepBlue a c
--
-- 3
--
data More b a =
L a b a
| R b a b
deriving (Eq, Show)
instance Functor (More x) where
fmap f (L a b a') = L (f a) b (f a')
fmap f (R b a b') = R b (f a) b'
-- Write Functor instances.
--
-- 1
--
data Quant a b =
Finance
| Desk a
| Bloor b
instance Functor (Quant a) where
fmap f (Bloor b) = Bloor (f b)
fmap _ Finance = Finance
fmap _ (Desk x) = Desk x
--
-- 2
--
newtype K a b =
K a
instance Functor (K a) where
fmap _ (K x) = K x
--
-- 3
--
newtype Flip f a b =
Flip (f b a)
deriving (Eq, Show)
instance Functor (Flip K a) where
fmap f (Flip (K a))= Flip $ K $ f a
--
-- 4
--
data EvilGoateeConst a b =
GoatyConst b
instance Functor (EvilGoateeConst a) where
fmap f (GoatyConst x) = GoatyConst $ f x
--
-- 5
--
data LiftItOut f a = LiftItOut (f a)
instance Functor f => Functor (LiftItOut f) where
fmap f (LiftItOut g) = LiftItOut $ fmap f $ g
--
-- 6
--
data Parappa f g a =
DaWrappa (f a) (g a)
instance (Functor f, Functor g) => Functor (Parappa f g) where
fmap f (DaWrappa f1 f2) = DaWrappa (fmap f f1) (fmap f f2)
--
-- 7
--
data IgnoreOne f g a b =
IgnoringSomething (f a) (g b)
instance Functor g => Functor (IgnoreOne f g a) where
fmap f (IgnoringSomething f1 f2) = IgnoringSomething f1 $ fmap f f2
--
-- 8
--
data Notorious g o a t =
Notorious (g o) (g a) (g t)
instance Functor g => Functor (Notorious g o a) where
fmap f (Notorious f1 f2 f3) = Notorious f1 f2 $ fmap f f3
--
-- 9
--
data List a = Nil | Cons a (List a)
instance Functor List where
fmap f (Cons x y) = Cons (f x) (fmap f y)
fmap _ Nil = Nil
--
-- 10
--
data GoatLord a =
NoGoat
| OneGoat a
| MoreGoats (GoatLord a)
(GoatLord a)
(GoatLord a)
instance Functor GoatLord where
fmap _ NoGoat = NoGoat
fmap f (OneGoat x) = OneGoat $ f x
fmap f (MoreGoats x y z) = MoreGoats (g x) (g y) (g z)
where g t = fmap f t
--
-- 11
--
data TalkToMe a =
Halt
| Print String a
| Read (String -> a)
instance Functor TalkToMe where
fmap _ Halt = Halt
fmap f (Print x y) = Print x $ f y
fmap f (Read g) = Read (f . g)
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