Add remaining haskell book exercises

Haskell-book/21/instances/.gitignore

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

Haskell-book/21/instances/LICENSE

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+Copyright Author name here (c) 2018
+
+All rights reserved.
+
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are met:
+
+    * Redistributions of source code must retain the above copyright
+      notice, this list of conditions and the following disclaimer.
+
+    * Redistributions in binary form must reproduce the above
+      copyright notice, this list of conditions and the following
+      disclaimer in the documentation and/or other materials provided
+      with the distribution.
+
+    * Neither the name of Author name here nor the names of other
+      contributors may be used to endorse or promote products derived
+      from this software without specific prior written permission.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
+LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

Haskell-book/21/instances/Setup.hs

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+import Distribution.Simple
+main = defaultMain

Haskell-book/21/instances/package.yaml

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

Haskell-book/21/instances/src/Lib.hs

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+module Lib where
+
+import Data.Monoid
+import Data.Traversable
+import Test.QuickCheck
+import Test.QuickCheck.Checkers
+
+--
+-- Identity
+--
+newtype Identity a = Identity a
+    deriving (Eq, Ord, Show)
+
+instance Functor Identity where
+    fmap f (Identity x) = Identity $ f x
+
+instance Applicative Identity where
+    pure = Identity
+    (Identity f) <*> x = fmap f x
+
+instance Foldable Identity where
+    foldr f acc (Identity x) = f x acc
+
+instance Arbitrary a => Arbitrary (Identity a) where
+    arbitrary = fmap Identity $ arbitrary
+
+instance Eq a => EqProp (Identity a) where
+    (=-=) = eq
+
+instance Traversable Identity where
+    traverse f (Identity x) = Identity <$> f x
+
+--
+-- Constant
+--
+newtype Constant a b = Constant { getConstant :: a }
+    deriving (Eq, Ord, Show)
+
+instance Functor (Constant a) where
+    fmap _ (Constant x) = Constant x
+
+instance Monoid a => Applicative (Constant a) where
+    pure _ = Constant mempty
+    (Constant x) <*> (Constant y) = Constant $ mappend x y
+
+instance (Arbitrary a, Arbitrary b) => Arbitrary (Constant a b) where
+    arbitrary = do
+        x <- arbitrary
+        return $ Constant x
+
+instance (Eq a, Eq b) => EqProp (Constant a  b) where
+    (=-=) = eq
+
+instance Foldable (Constant a) where
+    foldMap _ (Constant _) = mempty
+
+instance Traversable (Constant a) where
+    traverse f (Constant x) = pure $ Constant x
+
+--
+-- Maybe
+--
+data Optional a = Nada | Yep a deriving (Show, Eq, Ord)
+
+instance Monoid a => Monoid (Optional a) where
+    mempty = Nada
+    mappend Nada _ = Nada
+    mappend _ Nada = Nada
+    mappend (Yep x) (Yep y) = Yep $ mappend x y
+
+instance Applicative Optional where
+    pure = Yep
+    (Yep f) <*> (Yep x) = Yep $ f x
+    Nada <*> (Yep x) = Nada
+    _ <*> Nada = Nada
+
+instance Functor Optional where
+    fmap _ Nada = Nada
+    fmap f (Yep x) = Yep $ f x
+
+instance Foldable Optional where
+    foldr f acc Nada = acc
+    foldr f acc (Yep x) = f x acc
+
+instance Traversable Optional where
+    traverse f Nada = pure Nada
+    traverse f (Yep x) = Yep <$> f x
+
+instance (CoArbitrary a, Arbitrary a) => Arbitrary (Optional a) where
+    arbitrary = do
+        x <- arbitrary
+        frequency [ (1, return Nada)
+                  , (2, return $ Yep x)
+                  ]
+
+instance (Eq a) => EqProp (Optional a) where
+    (=-=) = eq
+
+--
+-- List
+--
+data List a = Nil | Cons a (List a) deriving (Eq, Show)
+
+instance Functor List where
+    fmap _ Nil = Nil
+    fmap f (Cons x xs) = Cons (f x) (fmap f xs)
+
+instance Foldable List where
+    foldr _ acc Nil = acc
+    foldr f acc (Cons x xs) = f x (foldr f acc xs)
+
+instance Traversable List where
+    sequenceA Nil = pure Nil
+    sequenceA (Cons x xs) = Cons <$> x <*> (sequenceA xs)
+
+instance Arbitrary a => Arbitrary (List a) where
+    arbitrary = sized go
+        where go 0 = pure Nil
+              go n = do
+                  xs <- go (n - 1)
+                  x <- arbitrary
+                  return $ Cons x xs
+
+instance (Eq a) => EqProp (List a) where
+    (=-=) = eq
+
+--
+-- Three
+--
+data Three a b c = Three a b c deriving (Show, Eq)
+
+instance Functor (Three a b) where
+    fmap f (Three x y z) = Three x y (f z)
+
+instance Foldable (Three a b) where
+    foldr f acc (Three x y z) = (f z acc)
+
+instance Traversable (Three a b) where
+    traverse f (Three x y z) = fmap (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
+
+instance (Eq a, Eq b, Eq c) => EqProp (Three a b c) where
+    (=-=) = eq
+
+--
+-- Pair
+--
+data Pair a b = Pair a b deriving (Eq, Show)
+
+instance Functor (Pair a) where
+    fmap f (Pair x y) = Pair x (f y)
+
+instance Foldable (Pair a) where
+    foldr f acc (Pair x y) = (f y acc)
+
+instance Traversable (Pair a) where
+    traverse f (Pair x y) = fmap (Pair x) (f y)
+
+instance (Arbitrary a, Arbitrary b) => Arbitrary (Pair a b) where
+    arbitrary = do
+        x <- arbitrary
+        y <- arbitrary
+        return $ Pair x y
+
+instance (Eq a, Eq b) => EqProp (Pair a b) where
+    (=-=) = eq
+
+--
+-- Big
+--
+data Big a b = Big a b b deriving (Eq, Show)
+
+instance Functor (Big a) where
+    fmap f (Big x y z) = Big x (f y) (f z)
+
+instance Foldable (Big a) where
+    foldr f acc (Big _ y z) = (f y (f z acc)) 
+
+instance Traversable (Big a) where
+    traverse f (Big x y z) = (Big x) <$> (f y) <*> (f z)
+
+instance (Arbitrary a, Arbitrary b) => Arbitrary (Big a b) where
+    arbitrary = do
+        x <- arbitrary
+        y <- arbitrary
+        z <- arbitrary
+        return $ Big x y z
+
+instance (Eq a, Eq b) => EqProp (Big a b) where
+    (=-=) = eq
+
+--
+-- Bigger
+--
+data Bigger a b = Bigger a b b b deriving (Eq, Show)
+
+instance Functor (Bigger a) where
+    fmap f (Bigger x y z t) = Bigger x (f y) (f z) (f t)
+
+instance Foldable (Bigger a) where
+    foldr f acc (Bigger _ y z t) = f y $ f z $ f t acc
+
+instance Traversable (Bigger a) where
+    traverse f (Bigger x y z t) = (Bigger x) <$> (f y) <*> (f z) <*> (f t)
+
+instance (Arbitrary a, Arbitrary b) => Arbitrary (Bigger a b) where
+    arbitrary = do
+        x <- arbitrary
+        y <- arbitrary
+        z <- arbitrary
+        t <- arbitrary
+        return $ Bigger x y z t
+
+instance (Eq a, Eq b) => EqProp (Bigger a b) where
+    (=-=) = eq
+

Haskell-book/21/instances/src/SkiFree.hs

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+{-# LANGUAGE FlexibleContexts #-}
+
+module SkiFree where
+
+import Test.QuickCheck
+import Test.QuickCheck.Checkers
+
+data S n a = S (n a) a deriving (Eq, Show)
+
+instance ( Functor n
+         , Arbitrary (n a)
+         , Arbitrary a)
+  => Arbitrary (S n a) where
+      arbitrary = S <$> arbitrary <*> arbitrary
+
+--instance ( Applicative n
+--         , Testable (n Property)
+--         , EqProp a)
+--  => EqProp (S n a) where
+--    (S x y) =-= (S p q) =
+--        (property $ (=-=) <$> x <*> p) .&. (y =-= q)
+instance (Eq (n a), Eq a) => EqProp (S n a) where
+    (=-=) = eq
+
+instance Functor n => Functor (S n) where
+    fmap f (S x y) = S (fmap f x) (f y)
+
+instance Foldable n => Foldable (S n) where
+    foldMap f (S n a) = mappend (foldMap f n) (f a)
+
+instance Traversable n => Traversable (S n) where
+    traverse f (S x y) = S <$> (traverse f x) <*> (f y)

Haskell-book/21/instances/src/Tree.hs

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+module Tree where
+
+import Data.Monoid
+import Test.QuickCheck
+import Test.QuickCheck.Checkers
+import Test.QuickCheck.Classes
+
+-- Solution:
+-- https://www.reddit.com/r/HaskellBook/comments/7w7bqn/ch_21_is_this_a_sane_instance_of_traversable/
+
+data Tree a = Empty
+            | Leaf a
+            | Node (Tree a) a (Tree a)
+            deriving (Eq, Show)
+
+instance Functor Tree where
+    fmap _ Empty = Empty
+    fmap f (Leaf x) = Leaf $ f x
+    fmap f (Node x y z) = Node (fmap f x) (f y) (fmap f z)
+
+-- foldMap is a bit easier and looks more natural, but you can do
+-- foldr too for extra credit.
+instance Foldable Tree where
+    foldMap _ Empty = mempty
+    foldMap f (Leaf x) = f x
+    foldMap f (Node x y z) = (foldMap f x) <> (f y) <> (foldMap f z)
+
+instance Traversable Tree where
+    traverse f Empty = pure Empty
+    traverse f (Leaf x) = Leaf <$> f x
+    traverse f (Node x y z) = Node <$> (traverse f x) <*> (f y) <*> (traverse f z)
+
+instance Arbitrary a => Arbitrary (Tree a) where
+    arbitrary = do
+        x <- arbitrary
+        y <- arbitrary
+        z <- arbitrary
+        frequency [ (1, return Empty)
+                  , (2, return $ Leaf y)
+                  , (3, return $ Node x y z)
+                  ]
+
+instance Eq a => EqProp (Tree a) where
+    (=-=) = eq

Haskell-book/21/instances/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-10.5
+
+# 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/21/instances/test/Spec.hs

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+import Lib
+import Data.Monoid
+import Test.QuickCheck
+import Test.QuickCheck.Checkers
+import Test.QuickCheck.Classes
+import SkiFree
+import Tree
+
+main :: IO ()
+main = do
+    sample' (arbitrary :: Gen (S [] Int))
+
+    quickBatch $ traversable $ (Identity (['a'], ['b'], ['c']))
+
+    quickBatch $ applicative $ (undefined :: Constant (String, String, String) (String, String, String))
+    quickBatch $ traversable $ (undefined :: Constant (String, String, String) (String, String, String))
+
+    quickBatch $ traversable $ (undefined :: Optional (String, String, String))
+
+    quickBatch $ traversable $ (undefined :: List (String, String, String))
+
+    quickBatch $ traversable $ (undefined :: Three (String, String, String)
+                                                   (String, String, String)
+                                                   (String, String, String))
+    quickBatch $ traversable $ (undefined :: Pair (String, String, String)
+                                                  (String, String, String))
+    quickBatch $ traversable $ (undefined :: Big (String, String, String)
+                                                 (String, String, String))
+    quickBatch $ traversable $ (undefined :: Bigger (String, String, String)
+                                                    (String, String, String))
+
+    quickBatch $ functor $ S [("a", "q", "y")] ("a", "b", "c")
+    quickBatch $ traversable $ S [("a", "q", "y")] ("a", "b", "c")
+
+    quickBatch $ traversable $ Leaf ("a", "q", "y")