Add remaining haskell book exercises

7 files changed, 227 insertions, 0 deletions

diff --git a/Haskell-book/26/MaybeT/src/Either.hs b/Haskell-book/26/MaybeT/src/Either.hs
new file mode 100644
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+++ b/Haskell-book/26/MaybeT/src/Either.hs
@@ -0,0 +1,56 @@
+module Either where
+
+import Control.Monad (liftM)
+import MonadTrans
+import MonadIO
+
+newtype EitherT e m a =
+    EitherT { runEitherT :: m (Either e a) }
+
+-- 1
+instance Functor m => Functor (EitherT e m) where
+    fmap f (EitherT x) = EitherT $ (fmap . fmap) f x
+
+-- 2
+instance Applicative m => Applicative (EitherT e m) where
+    pure x = EitherT $ pure $ pure x
+
+    (EitherT f) <*> (EitherT a) = EitherT $ (<*>) <$> f <*> a
+
+-- 3
+instance Monad m => Monad (EitherT e m) where
+    return = pure
+
+    (EitherT em) >>= f = EitherT $ do
+        v <- em
+        case v of
+            Left y -> return $ Left y
+            Right y -> runEitherT (f y)
+
+
+-- 4
+-- transformer version of swapEither.
+-- Hint: write swapEither first, then swapEitherT in terms of the former.
+swapEither :: Either e a -> Either a e
+swapEither (Left x) = Right x
+swapEither (Right y) = Left y
+
+swapEitherT :: (Functor m)
+            => EitherT e m a
+            -> EitherT a m e
+swapEitherT (EitherT x) = EitherT $ fmap swapEither x
+
+-- 5. Write the transformer variant of the either catamorphism.
+eitherT :: Monad m
+        => (a -> m c)
+        -> (b -> m c)
+        -> EitherT a m b
+        -> m c
+eitherT f g (EitherT x) = x >>= (either f g)
+
+instance MonadTrans (EitherT e) where
+    lift = EitherT . liftM Right
+
+instance (MonadIO m)
+  => MonadIO (EitherT e m) where
+      liftIO = lift . liftIO
diff --git a/Haskell-book/26/MaybeT/src/Identity.hs b/Haskell-book/26/MaybeT/src/Identity.hs
new file mode 100644
index 0000000..8189c18
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+++ b/Haskell-book/26/MaybeT/src/Identity.hs
@@ -0,0 +1,43 @@
+module Identity where
+
+import MonadIO
+import MonadTrans
+
+newtype Identity a =
+    Identity { runIdentity :: a }
+    deriving (Eq, Show)
+
+instance Functor Identity where
+    fmap f (Identity a) = Identity (f a)
+
+instance Applicative Identity where
+    pure = Identity
+    (Identity f) <*> (Identity a) = Identity (f a)
+
+newtype IdentityT f a =
+    IdentityT { runIdentityT :: f a }
+    deriving (Eq, Show)
+
+instance (Functor m)
+  => Functor (IdentityT m) where
+      fmap f (IdentityT fa) = IdentityT (fmap f fa)
+
+instance (Applicative m)
+  => Applicative (IdentityT m) where
+      pure x = IdentityT (pure x)
+
+      (IdentityT fab) <*> (IdentityT fa) =
+          IdentityT (fab <*> fa)
+
+instance (Monad m)
+  => Monad (IdentityT m) where
+      return = pure
+
+      (IdentityT ma) >>= f = IdentityT $ ma >>= runIdentityT . f
+
+instance (MonadIO m)
+  => MonadIO (IdentityT m) where
+      liftIO = IdentityT . liftIO
+
+instance MonadTrans IdentityT where
+    lift = IdentityT
diff --git a/Haskell-book/26/MaybeT/src/Maybe.hs b/Haskell-book/26/MaybeT/src/Maybe.hs
new file mode 100644
index 0000000..4d6c9b7
--- /dev/null
+++ b/Haskell-book/26/MaybeT/src/Maybe.hs
@@ -0,0 +1,40 @@
+module Maybe where
+
+import Control.Monad
+import MonadIO
+import MonadTrans
+
+newtype MaybeT m a =
+    MaybeT { runMaybeT :: m (Maybe a) }
+
+-- compare to the instance for MaybeT
+instance (Functor m)
+      => Functor (MaybeT m) where
+        fmap f (MaybeT ma) =
+            MaybeT $ (fmap . fmap) f ma
+
+instance (Applicative m)
+      => Applicative (MaybeT m) where
+        pure x = MaybeT (pure (pure x))
+
+        (MaybeT fab) <*> (MaybeT mma) = MaybeT $ (<*>) <$> fab <*> mma
+
+instance (Monad m)
+      => Monad (MaybeT m) where
+        return = pure
+
+        -- (>>=) :: MaybeT m a -> (a -> MaybeT m b) -> MaybeT m b
+        (MaybeT ma) >>= f = MaybeT $ do
+            -- ma :: m (Maybe a)
+            -- v :: Maybe a
+            v <- ma
+            case v of
+                Nothing -> return Nothing
+                Just y -> runMaybeT (f y)
+
+instance MonadTrans MaybeT where
+    lift = MaybeT . liftM Just
+
+instance (MonadIO m)
+  => MonadIO (MaybeT m) where
+      liftIO = lift . liftIO
diff --git a/Haskell-book/26/MaybeT/src/MonadIO.hs b/Haskell-book/26/MaybeT/src/MonadIO.hs
new file mode 100644
index 0000000..93244dd
--- /dev/null
+++ b/Haskell-book/26/MaybeT/src/MonadIO.hs
@@ -0,0 +1,5 @@
+module MonadIO where
+
+class (Monad m) => MonadIO m where
+    -- | Lift a computation from the 'IO' monad.
+    liftIO :: IO a -> m a
diff --git a/Haskell-book/26/MaybeT/src/MonadTrans.hs b/Haskell-book/26/MaybeT/src/MonadTrans.hs
new file mode 100644
index 0000000..7954164
--- /dev/null
+++ b/Haskell-book/26/MaybeT/src/MonadTrans.hs
@@ -0,0 +1,7 @@
+module MonadTrans where
+
+class MonadTrans t where
+    -- | Lift a computation from
+    -- the argument monad to
+    -- the constructed monad.
+    lift :: (Monad m) => m a -> t m a
diff --git a/Haskell-book/26/MaybeT/src/Reader.hs b/Haskell-book/26/MaybeT/src/Reader.hs
new file mode 100644
index 0000000..38fded9
--- /dev/null
+++ b/Haskell-book/26/MaybeT/src/Reader.hs
@@ -0,0 +1,35 @@
+module Reader where
+
+import MonadIO
+import MonadTrans
+
+newtype ReaderT r m a =
+    ReaderT { runReaderT :: r -> m a }
+
+instance (Functor m)
+      => Functor (ReaderT r m) where
+    fmap f (ReaderT rma) =
+        ReaderT $ (fmap . fmap) f rma
+
+instance (Applicative m)
+      => Applicative (ReaderT r m) where
+    pure a = ReaderT (pure (pure a))
+
+    (ReaderT fmab) <*> (ReaderT rma) =
+        ReaderT $ (<*>) <$> fmab <*> rma
+
+instance (Monad m)
+      => Monad (ReaderT r m) where
+    return = pure
+
+    (ReaderT rma) >>= f =
+        ReaderT $ \r -> do
+            a <- rma r
+            runReaderT (f a) r
+
+instance MonadTrans (ReaderT r) where
+    lift = ReaderT . const
+
+instance (MonadIO m)
+  => MonadIO (ReaderT r m) where
+      liftIO = lift . liftIO
diff --git a/Haskell-book/26/MaybeT/src/State.hs b/Haskell-book/26/MaybeT/src/State.hs
new file mode 100644
index 0000000..d30fdd5
--- /dev/null
+++ b/Haskell-book/26/MaybeT/src/State.hs
@@ -0,0 +1,41 @@
+module State where
+
+import MonadIO
+import MonadTrans
+
+newtype StateT s m a =
+    StateT { runStateT :: s -> m (a, s) }
+
+-- 1
+instance (Functor m)
+      => Functor (StateT s m) where
+    fmap f (StateT m) = StateT $ \s -> fmap first $ m s
+            where first = uncurry (\t1 t2 -> ((f t1), t2))
+            
+-- 2
+-- Links:
+--   http://stackoverflow.com/questions/18673525/is-it-possible-to-implement-applicative-m-applicative-statet-s-m
+--   https://github.com/NICTA/course/issues/134
+instance (Monad m)
+      => Applicative (StateT s m) where
+    pure x = StateT $ (\s -> pure (x, s))
+    StateT g <*> StateT h = StateT $ \s -> keepFirst <$> g s <*> h s
+        where keepFirst (f, s') (x, _) = (f x, s')
+  
+
+-- 3
+instance (Monad m)
+      => Monad (StateT s m) where
+    return = pure
+
+    (StateT sma) >>= f =
+        StateT $ \s -> do
+            a <- sma s
+            runStateT (f $ fst a) s
+
+instance MonadTrans (StateT s) where
+    lift c = StateT $ \s -> c >>= (\x -> return (x, s))
+
+instance (MonadIO m)
+  => MonadIO (StateT s m) where
+      liftIO = lift . liftIO