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)

Haskell-book/16/HeavyLifting.hs

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+module HeavyLifting where
+
+a = fmap (+1) $ read "[1]" :: [Int]
+
+b = (fmap . fmap) (++ "lol") (Just ["Hi,", "Hello"])
+
+c = fmap (*2) (\x -> x - 2)
+
+d =
+    fmap ((return '1' ++) . show)
+    (\x -> [x, 1..3])
+
+e :: IO Integer
+e = let ioi = readIO "1" :: IO Integer
+        changed = fmap read $ fmap ("123" ++) $ fmap show ioi
+     in fmap (*3) changed

Haskell-book/16/Possibly.hs

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+module Possibly where
+
+data Possibly a =
+    LolNope
+  | Yeppers a
+  deriving (Eq, Show)
+
+instance Functor Possibly where
+    fmap f LolNope = LolNope
+    fmap f (Yeppers x) = Yeppers $ f x

Haskell-book/16/Short.hs

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+module Short where
+
+data Sum a b =
+    First a
+  | Second b
+  deriving (Eq, Show)
+
+instance Functor (Sum a) where
+    fmap f (Second x) = Second $ f x
+    fmap f (First x) = First x

Haskell-book/16/func/.gitignore

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+.stack-work/
+func.cabal
+*~

Haskell-book/16/func/Setup.hs

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+import Distribution.Simple
+main = defaultMain

Haskell-book/16/func/app/Main.hs

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+module Main where
+
+import Lib
+
+main :: IO ()
+main = someFunc

Haskell-book/16/func/package.yaml

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+name:                func
+version:             0.1.0.0
+author:              "Eugen Wissner"
+maintainer:          "belka@caraus.de"
+copyright:           "2018 Eugen Wissner"
+
+dependencies:
+- base >= 4.7 && < 5
+- QuickCheck
+
+library:
+  source-dirs: src
+
+# executables:
+#  func-exe:
+#    main:                Main.hs
+#    source-dirs:         app
+#    ghc-options:
+#    - -threaded
+#    - -rtsopts
+#    - -with-rtsopts=-N
+#    dependencies:
+#    - func
+
+tests:
+  func-test:
+    main:                Spec.hs
+    source-dirs:         test
+    ghc-options:
+    - -threaded
+    - -rtsopts
+    - -with-rtsopts=-N
+    dependencies:
+    - func

Haskell-book/16/func/src/Func.hs

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+module Func where
+
+import Test.QuickCheck
+
+-- class Functor f where
+--     fmap :: (a -> b) -> f a -> f b
+
+newtype Identity a = Identity a deriving (Eq, Show)
+
+instance Functor Identity where
+    fmap f (Identity a) = Identity $ f a
+
+instance Arbitrary a => Arbitrary (Identity a) where
+    arbitrary = fmap Identity arbitrary
+
+data Pair a = Pair a a deriving (Eq, Show)
+
+instance Functor Pair where
+    fmap f (Pair x y) = Pair (f x) (f y)
+
+instance Arbitrary a => Arbitrary (Pair a) where
+    arbitrary = do
+        x <- arbitrary
+        y <- arbitrary
+        return $ Pair x y
+
+data Two a b = Two a b deriving (Eq, Show)
+
+instance Functor (Two a) where
+    fmap f (Two x y) = Two x (f y)
+
+instance (Arbitrary a, Arbitrary b) => Arbitrary (Two a b) where
+    arbitrary = do
+        x <- arbitrary
+        y <- arbitrary
+        return $ Two x y
+
+data Three a b c = Three a b c deriving (Eq, Show)
+
+instance Functor (Three a b) where
+    fmap f (Three x y z) = Three x y (f z)
+
+instance (Arbitrary a, Arbitrary b, Arbitrary c) => Arbitrary (Three a b c) where
+    arbitrary = do
+        x <- arbitrary
+        y <- arbitrary
+        z <- arbitrary
+        return $ Three x y z
+
+data Three' a b = Three' a b b deriving (Eq, Show)
+
+instance Functor (Three' a) where
+    fmap f (Three' x y z) = Three' x (f y) (f z)
+
+instance (Arbitrary a, Arbitrary b) => Arbitrary (Three' a b) where
+    arbitrary = do
+        x <- arbitrary
+        y <- arbitrary
+        z <- arbitrary
+        return $ Three' x y z
+
+data Four a b c d = Four a b c d deriving (Eq, Show)
+
+instance Functor (Four a b c) where
+    fmap f (Four x y z t) = Four x y z (f t)
+
+instance (Arbitrary a, Arbitrary b, Arbitrary c, Arbitrary d)
+  => Arbitrary (Four a b c d) where
+      arbitrary = do
+        x <- arbitrary
+        y <- arbitrary
+        z <- arbitrary
+        t <- arbitrary
+        return $ Four x y z t
+
+data Four' a b = Four' a a a b deriving (Eq, Show)
+
+instance Functor (Four' a) where
+    fmap f (Four' x y z t) = Four' x y z (f t)
+
+instance (Arbitrary a, Arbitrary b) => Arbitrary (Four' a b) where
+      arbitrary = do
+        x <- arbitrary
+        y <- arbitrary
+        z <- arbitrary
+        t <- arbitrary
+        return $ Four' x y z t
+
+data Trivial = Trivial

Haskell-book/16/func/stack.yaml

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+# This file was automatically generated by 'stack init'
+#
+# Some commonly used options have been documented as comments in this file.
+# For advanced use and comprehensive documentation of the format, please see:
+# https://docs.haskellstack.org/en/stable/yaml_configuration/
+
+# Resolver to choose a 'specific' stackage snapshot or a compiler version.
+# A snapshot resolver dictates the compiler version and the set of packages
+# to be used for project dependencies. For example:
+#
+# resolver: lts-3.5
+# resolver: nightly-2015-09-21
+# resolver: ghc-7.10.2
+# resolver: ghcjs-0.1.0_ghc-7.10.2
+# resolver:
+#  name: custom-snapshot
+#  location: "./custom-snapshot.yaml"
+resolver: lts-10.3
+
+# User packages to be built.
+# Various formats can be used as shown in the example below.
+#
+# packages:
+# - some-directory
+# - https://example.com/foo/bar/baz-0.0.2.tar.gz
+# - location:
+#    git: https://github.com/commercialhaskell/stack.git
+#    commit: e7b331f14bcffb8367cd58fbfc8b40ec7642100a
+# - location: https://github.com/commercialhaskell/stack/commit/e7b331f14bcffb8367cd58fbfc8b40ec7642100a
+#   extra-dep: true
+#  subdirs:
+#  - auto-update
+#  - wai
+#
+# A package marked 'extra-dep: true' will only be built if demanded by a
+# non-dependency (i.e. a user package), and its test suites and benchmarks
+# will not be run. This is useful for tweaking upstream packages.
+packages:
+- .
+# Dependency packages to be pulled from upstream that are not in the resolver
+# (e.g., acme-missiles-0.3)
+# extra-deps: []
+
+# Override default flag values for local packages and extra-deps
+# flags: {}
+
+# Extra package databases containing global packages
+# extra-package-dbs: []
+
+# Control whether we use the GHC we find on the path
+# system-ghc: true
+#
+# Require a specific version of stack, using version ranges
+# require-stack-version: -any # Default
+# require-stack-version: ">=1.6"
+#
+# Override the architecture used by stack, especially useful on Windows
+# arch: i386
+# arch: x86_64
+#
+# Extra directories used by stack for building
+# extra-include-dirs: [/path/to/dir]
+# extra-lib-dirs: [/path/to/dir]
+#
+# Allow a newer minor version of GHC than the snapshot specifies
+# compiler-check: newer-minor

Haskell-book/16/func/test/Spec.hs

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+{-# LANGUAGE ViewPatterns #-}
+
+import Func
+import Test.QuickCheck
+import Test.QuickCheck.Function
+
+functorIdentity :: (Functor f, Eq (f a)) => f a -> Bool
+functorIdentity f = fmap id f == f
+
+functorCompose :: (Eq (f c), Functor f) =>
+       (a -> b)
+    -> (b -> c)
+    -> f a
+    -> Bool
+functorCompose f g x =
+    (fmap g (fmap f x)) == (fmap (g . f) x)
+
+functorCompose' :: (Eq (f c), Functor f) =>
+        f a
+    -> Fun a b
+    -> Fun b c
+    -> Bool
+functorCompose' x (Fun _ f) (Fun _ g) =
+    (fmap (g . f) x) == (fmap g . fmap f $ x)
+
+main :: IO ()
+main = do
+    quickCheck (functorIdentity :: Identity Int -> Bool)
+    quickCheck ((functorCompose (+1) (*2)) :: Identity Int -> Bool)
+    quickCheck (functorCompose' :: Identity Int -> Fun Int Int -> Fun Int Int -> Bool)
+
+    quickCheck (functorIdentity :: Pair Int -> Bool)
+    quickCheck ((functorCompose (+1) (*2)) :: Pair Int -> Bool)
+    quickCheck (functorCompose' :: Pair Int -> Fun Int Int -> Fun Int Int -> Bool)
+
+    quickCheck (functorIdentity :: Two Int Int -> Bool)
+    quickCheck ((functorCompose (+1) (*2)) :: Two Int Int -> Bool)
+    quickCheck (functorCompose' :: Two Int Int -> Fun Int Int -> Fun Int Int -> Bool)
+
+    quickCheck (functorIdentity :: Three Int Int Int -> Bool)
+    quickCheck ((functorCompose (+1) (*2)) :: Three Int Int Int -> Bool)
+    quickCheck (functorCompose' :: Three Int Int Int -> Fun Int Int -> Fun Int Int -> Bool)
+
+    quickCheck (functorIdentity :: Three' Int Int -> Bool)
+    quickCheck ((functorCompose (+1) (*2)) :: Three' Int Int -> Bool)
+    quickCheck (functorCompose' :: Three' Int Int -> Fun Int Int -> Fun Int Int -> Bool)
+
+    quickCheck (functorIdentity :: Four Int Int Int Int -> Bool)
+    quickCheck ((functorCompose (+1) (*2)) :: Four Int Int Int Int -> Bool)
+    quickCheck (functorCompose' :: Four Int Int Int Int -> Fun Int Int -> Fun Int Int -> Bool)
+
+    quickCheck (functorIdentity :: Four' Int Int -> Bool)
+    quickCheck ((functorCompose (+1) (*2)) :: Four' Int Int -> Bool)
+    quickCheck (functorCompose' :: Four' Int Int -> Fun Int Int -> Fun Int Int -> Bool)