Add remaining haskell book exercises

9 files changed, 209 insertions, 0 deletions

diff --git a/Haskell-book/15/semigroup/src/Bool.hs b/Haskell-book/15/semigroup/src/Bool.hs
new file mode 100644
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+++ b/Haskell-book/15/semigroup/src/Bool.hs
@@ -0,0 +1,30 @@
+module Bool where
+
+import Data.Semigroup
+import Test.QuickCheck
+
+newtype BoolConj = BoolConj Bool deriving (Eq, Show)
+
+instance Semigroup BoolConj where
+    (BoolConj True) <> (BoolConj True) = BoolConj True
+    _ <> _ = BoolConj False
+
+instance Monoid BoolConj where
+    mempty = BoolConj True
+    mappend = (<>)
+
+instance Arbitrary BoolConj where
+    arbitrary = fmap BoolConj arbitrary
+
+newtype BoolDisj = BoolDisj Bool deriving (Eq, Show)
+
+instance Semigroup BoolDisj where
+    (BoolDisj False) <> (BoolDisj False) = BoolDisj False
+    _ <> _ = BoolDisj True
+
+instance Monoid BoolDisj where
+    mempty = BoolDisj False
+    mappend = (<>)
+
+instance Arbitrary BoolDisj where
+    arbitrary = fmap BoolDisj arbitrary
diff --git a/Haskell-book/15/semigroup/src/Combine.hs b/Haskell-book/15/semigroup/src/Combine.hs
new file mode 100644
index 0000000..fe420dd
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+++ b/Haskell-book/15/semigroup/src/Combine.hs
@@ -0,0 +1,25 @@
+{-# LANGUAGE FlexibleInstances #-}
+module Combine where
+
+import Data.Semigroup
+import Test.QuickCheck
+
+newtype Combine a b =
+    Combine { unCombine :: (a -> b) }
+
+instance Semigroup b => Semigroup (Combine a b) where
+    (Combine f1) <> (Combine f2) = Combine f
+        where f x = (f1 x) <> (f2 x)
+
+instance (Monoid b) => Monoid (Combine a b) where
+    mempty = Combine $ \_ -> mempty
+    mappend (Combine f1) (Combine f2) = Combine f
+        where f x = mappend (f1 x) (f2 x)
+
+instance (Num a, CoArbitrary a, Arbitrary b) => Arbitrary (Combine a b) where
+    arbitrary = do
+        f <- arbitrary
+        return $ Combine (\n -> f n)
+
+instance (Show a, Show b) => Show (Combine a b) where
+    show _ = "a -> b"
diff --git a/Haskell-book/15/semigroup/src/Comp.hs b/Haskell-book/15/semigroup/src/Comp.hs
new file mode 100644
index 0000000..f7224da
--- /dev/null
+++ b/Haskell-book/15/semigroup/src/Comp.hs
@@ -0,0 +1,22 @@
+module Comp where
+
+import Data.Semigroup
+import Test.QuickCheck
+
+newtype Comp a =
+    Comp { unComp :: (a -> a) }
+
+instance Semigroup a => Semigroup (Comp a) where
+    (Comp f1) <> (Comp f2) = Comp f
+        where f x = (f1 x) <> (f2 x)
+
+instance Monoid a => Monoid (Comp a) where
+    mempty = Comp $ \_ -> mempty
+    mappend (Comp f1) (Comp f2) = Comp f
+        where f x = mappend (f1 x) (f2 x)
+
+instance (Arbitrary a, CoArbitrary a) => Arbitrary (Comp a) where
+    arbitrary = fmap Comp arbitrary
+
+instance Show (Comp a) where
+    show _ = "a -> a"
diff --git a/Haskell-book/15/semigroup/src/Identity.hs b/Haskell-book/15/semigroup/src/Identity.hs
new file mode 100644
index 0000000..cb7180a
--- /dev/null
+++ b/Haskell-book/15/semigroup/src/Identity.hs
@@ -0,0 +1,16 @@
+module Identity where
+
+import Data.Semigroup
+import Test.QuickCheck
+
+newtype Identity a = Identity a deriving (Show, Eq)
+
+instance Semigroup a => Semigroup (Identity a) where
+    (Identity x) <> (Identity y) = Identity (x <> y)
+
+instance Monoid a => Monoid (Identity a) where
+    mempty = Identity mempty
+    mappend (Identity x) (Identity y) = Identity $ mappend x y
+
+instance Arbitrary a => Arbitrary (Identity a) where
+    arbitrary = fmap Identity arbitrary
diff --git a/Haskell-book/15/semigroup/src/Mem.hs b/Haskell-book/15/semigroup/src/Mem.hs
new file mode 100644
index 0000000..575e82d
--- /dev/null
+++ b/Haskell-book/15/semigroup/src/Mem.hs
@@ -0,0 +1,11 @@
+module Mem where
+
+newtype Mem s a =
+    Mem {
+        runMem :: s -> (a,s)
+    }
+
+instance Monoid a => Monoid (Mem s a) where
+    mempty = Mem $ \x -> (mempty, x)
+    mappend (Mem f1) (Mem f2) = Mem f
+        where f x = ((mappend (fst $ f1 x) (fst $ f2 x)), snd $ f2 $ snd $ f1 x)
diff --git a/Haskell-book/15/semigroup/src/Or.hs b/Haskell-book/15/semigroup/src/Or.hs
new file mode 100644
index 0000000..17d4801
--- /dev/null
+++ b/Haskell-book/15/semigroup/src/Or.hs
@@ -0,0 +1,19 @@
+module Or where
+
+import Data.Semigroup
+import Test.QuickCheck
+
+data Or a b =
+    Fst a
+  | Snd b
+  deriving (Eq, Show)
+
+instance Semigroup (Or a b) where
+    (Snd x) <> _ = Snd x
+    _ <> x = x
+
+instance (Arbitrary a, Arbitrary b) => Arbitrary (Or a b) where
+    arbitrary = do
+        x <- arbitrary
+        y <- arbitrary
+        frequency [ (1, return $ Fst x), (1, return $ Snd y) ]
diff --git a/Haskell-book/15/semigroup/src/Trivial.hs b/Haskell-book/15/semigroup/src/Trivial.hs
new file mode 100644
index 0000000..de9a1ad
--- /dev/null
+++ b/Haskell-book/15/semigroup/src/Trivial.hs
@@ -0,0 +1,16 @@
+module Trivial where
+
+import Data.Semigroup
+import Test.QuickCheck
+
+data Trivial = Trivial deriving (Eq, Show)
+
+instance Semigroup Trivial where
+    _ <> _ = Trivial
+
+instance Arbitrary Trivial where
+    arbitrary = return Trivial
+
+instance Monoid Trivial where
+    mempty = undefined
+    mappend = (<>)
diff --git a/Haskell-book/15/semigroup/src/Two.hs b/Haskell-book/15/semigroup/src/Two.hs
new file mode 100644
index 0000000..70c2760
--- /dev/null
+++ b/Haskell-book/15/semigroup/src/Two.hs
@@ -0,0 +1,53 @@
+module Two where
+
+import Data.Semigroup
+import Test.QuickCheck
+
+data Two a b = Two a b deriving (Eq, Show)
+
+data Three a b c = Three a b c deriving (Eq, Show)
+
+data Four a b c d = Four a b c d deriving (Eq, Show)
+
+instance (Semigroup a, Semigroup b) => Semigroup (Two a b) where
+    (Two x1 y1) <> (Two x2 y2) = Two (x1 <> x2) (y1 <> y2)
+
+instance (Monoid a, Monoid b) => Monoid (Two a b) where
+    mempty = Two mempty mempty
+    mappend (Two x1 y1) (Two x2 y2) = Two (mappend x1 x2) (mappend y1 y2)
+
+instance (Arbitrary a, Arbitrary b) => Arbitrary (Two a b) where
+    arbitrary = do
+        x <- arbitrary
+        y <- arbitrary
+        return $ Two x y
+
+instance (Semigroup a, Semigroup b, Semigroup c) => Semigroup (Three a b c) where
+    (Three x1 y1 z1) <> (Three x2 y2 z2) = Three (x1 <> x2) (y1 <> y2) (z1 <> z2)
+
+instance (Monoid a, Monoid b, Monoid c) => Monoid (Three a b c) where
+    mempty = Three mempty mempty mempty
+    mappend (Three x1 y1 z1) (Three x2 y2 z2) = Three (mappend x1 x2) (mappend y1 y2) (mappend z1 z2)
+
+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 (Semigroup a, Semigroup b, Semigroup c, Semigroup d) => Semigroup (Four a b c d) where
+    (Four x1 y1 z1 t1) <> (Four x2 y2 z2 t2) = Four (x1 <> x2) (y1 <> y2) (z1 <> z2) (t1 <> t2)
+
+instance (Monoid a, Monoid b, Monoid c, Monoid d) => Monoid (Four a b c d) where
+    mempty = Four mempty mempty mempty mempty
+    mappend (Four x1 y1 z1 t1) (Four x2 y2 z2 t2) =
+        Four (mappend x1 x2) (mappend y1 y2) (mappend z1 z2) (mappend t1 t2)
+
+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
diff --git a/Haskell-book/15/semigroup/src/Validation.hs b/Haskell-book/15/semigroup/src/Validation.hs
new file mode 100644
index 0000000..a5d1c9c
--- /dev/null
+++ b/Haskell-book/15/semigroup/src/Validation.hs
@@ -0,0 +1,17 @@
+module Validation where
+
+import Data.Semigroup
+import Test.QuickCheck (arbitrary, Arbitrary(..), frequency)
+
+data Validation a b = Failure a | Success b deriving (Eq, Show)
+
+instance Semigroup a => Semigroup (Validation a b) where
+    (Success x) <> _ = Success x
+    _ <> (Success x) = Success x
+    (Failure x) <> (Failure y) = Failure $ x <> y
+
+instance (Arbitrary a, Arbitrary b) => Arbitrary (Validation a b) where
+    arbitrary = do
+        x <- arbitrary
+        y <- arbitrary
+        frequency [ (1, return $ Success x), (1, return $ Failure y) ]