Add remaining haskell book exercises

Haskell-book/16/Exercises.hs

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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)