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Changed directory: /home/hugo/Academic/Teaching/_Atual/Teoria de Categorias/Aulas/
λ> S $ S Zero
S (S Zero)
λ> :t produto
produto :: Natural -> Natural -> Natural
λ> fatorial $ S $ S $ S $ S Zero
S (S (S (S (S (S (S (S (S (S (S (S (S (S (S (S (S (S (S (S (S (S (S (S Zero)))))))))))))))))))))))
λ> paraInteiro $ fatorial $ S $ S $ S $ S Zero
24
λ> arv1
Raiz 10 Folha (Raiz 4 Folha Folha)
Aula10.hs:35:20-24: error: [GHC-88464] …
    Variable not in scope: arv1i :: ArvBin Integer
    Suggested fix: Perhaps use `arv1' (line 32)
   |
λ> arv2
Raiz 0 (Raiz 10 Folha (Raiz 4 Folha Folha)) (Raiz 10 Folha (Raiz 4 Folha Folha))
Aula10.hs:39:49-52: error: [GHC-39999] …
    * No instance for `Show a' arising from a use of `show'
      Possible fix:
        add (Show a) to the context of
          the type signature for:
            desenhaArvore :: forall a. ArvBin a -> String
    * In the first argument of `(++)', namely `(show x)'
      In the expression:
        (show x)
          ++ "\n" ++ desenhaArvore (subarv_esq) ++ desenhaArvore (subarv_dir)
      In an equation for `desenhaArvore':
          desenhaArvore (Raiz x subarv_esq subarv_dir)
            = (show x)
                ++ "\n" ++ desenhaArvore (subarv_esq) ++ desenhaArvore (subarv_dir)
   |
λ> desenhaArvore arv1
"10\n.4\n.."
λ> :t putStr
putStr :: String -> IO ()
λ> putStr $ desenhaArvore arv1
10
.4
..λ> putStr $ desenhaArvore arv1
10
.
4
.
.λ> putStr $ desenhaArvore arv1
10
.     4
.     .λ> putStr $ desenhaArvore arv1

<interactive>:97:10-27: error: [GHC-83865]
    * Couldn't match type: Integer -> String
                     with: [Char]
      Expected: String
        Actual: Integer -> String
    * In the second argument of `($)', namely `desenhaArvore arv1'
      In the expression: putStr $ desenhaArvore arv1
      In an equation for `it': it = putStr $ desenhaArvore arv1
λ> putStr $ desenhaArvore arv1

<interactive>:98:10-27: error: [GHC-83865]
    * Couldn't match type: Integer -> String
                     with: [Char]
      Expected: String
        Actual: Integer -> String
    * In the second argument of `($)', namely `desenhaArvore arv1'
      In the expression: putStr $ desenhaArvore arv1
      In an equation for `it': it = putStr $ desenhaArvore arv1
λ> putStr $ desenhaArvore arv1 0
10
 .
 4
  .
  .λ> putStr $ desenhaArvore arv1 0
10
 .
 4
  .
  .

λ> putStr $ desenhaArvore arv1 0
10
     .
     4
          .
          .

λ> putStr $ desenhaArvore arv2 0
0
     10
          .
          4
               .
               .


     10
          .
          4
               .
               .


λ> :t ArvBin

<interactive>:1:1-6: error: [GHC-31891]
    * Illegal term-level use of the type constructor or class `ArvBin'
    * defined at /home/hugo/Academic/Teaching/_Atual/Teoria de Categorias/Aulas/Aula10.hs:26:1
    * In the expression: ArvBin
λ> :i Arvbin

<interactive>:1:1-6: error: Not in scope: `Arvbin'
λ> :i ArvBin
type ArvBin :: * -> *
data ArvBin a where
  Folha :: ArvBin a
  Raiz :: a -> ArvBin a -> ArvBin a -> ArvBin a
  	-- Defined at /home/hugo/Academic/Teaching/_Atual/Teoria de Categorias/Aulas/Aula10.hs:26:1
instance Eq a => Eq (ArvBin a)
  -- Defined at /home/hugo/Academic/Teaching/_Atual/Teoria de Categorias/Aulas/Aula10.hs:29:19
instance Show a => Show (ArvBin a)
  -- Defined at /home/hugo/Academic/Teaching/_Atual/Teoria de Categorias/Aulas/Aula10.hs:29:13
λ> :i String
type String :: *
type String = [Char]
  	-- Defined in `GHC.Base'
λ> arv1
Raiz 10 Folha (Raiz 4 Folha Folha)
λ> fmap (^2) arv1
Raiz 100 Folha (Raiz 16 Folha Folha)
Aula10.hs:48:5-7: error: [GHC-54721] …
    `<$>' is not a (visible) method of class `Functor'
   |
λ> (+15) <$> [1, 2, 3]
[16,17,18]
λ> :i Semigroup
type Semigroup :: * -> Constraint
class Semigroup a where
  (<>) :: a -> a -> a
  GHC.Base.sconcat :: GHC.Base.NonEmpty a -> a
  GHC.Base.stimes :: Integral b => b -> a -> a
  {-# MINIMAL (<>) | sconcat #-}
  	-- Defined in `GHC.Base'
instance Semigroup () -- Defined in `GHC.Base'
instance (Semigroup a, Semigroup b) => Semigroup (a, b)
  -- Defined in `GHC.Base'
instance (Semigroup a, Semigroup b, Semigroup c) =>
         Semigroup (a, b, c)
  -- Defined in `GHC.Base'
instance (Semigroup a, Semigroup b, Semigroup c, Semigroup d) =>
         Semigroup (a, b, c, d)
  -- Defined in `GHC.Base'
instance (Semigroup a, Semigroup b, Semigroup c, Semigroup d,
          Semigroup e) =>
         Semigroup (a, b, c, d, e)
  -- Defined in `GHC.Base'
instance Semigroup b => Semigroup (a -> b) -- Defined in `GHC.Base'
instance Semigroup a => Semigroup (IO a) -- Defined in `GHC.Base'
instance Semigroup [a] -- Defined in `GHC.Base'
instance Semigroup a => Semigroup (Maybe a)
  -- Defined in `GHC.Base'
instance Semigroup Ordering -- Defined in `GHC.Base'
instance Semigroup a => Semigroup (Solo a) -- Defined in `GHC.Base'
instance Semigroup (Either a b) -- Defined in `Data.Either'
λ> :i Functor
type Functor :: (* -> *) -> Constraint
class Functor f where
  fmap :: (a -> b) -> f a -> f b
  (<$) :: a -> f b -> f a
  {-# MINIMAL fmap #-}
  	-- Defined in `GHC.Base'
instance Functor ((,) a) -- Defined in `GHC.Base'
instance Functor ((,,) a b) -- Defined in `GHC.Base'
instance Functor ((,,,) a b c) -- Defined in `GHC.Base'
instance Functor ((,,,,) a b c d) -- Defined in `GHC.Base'
instance Functor ((,,,,,) a b c d e) -- Defined in `GHC.Base'
instance Functor ((,,,,,,) a b c d e f) -- Defined in `GHC.Base'
instance Functor ((->) r) -- Defined in `GHC.Base'
instance Functor IO -- Defined in `GHC.Base'
instance Functor [] -- Defined in `GHC.Base'
instance Functor Maybe -- Defined in `GHC.Base'
instance Functor Solo -- Defined in `GHC.Base'
instance Functor (Either a) -- Defined in `Data.Either'
λ> :i Monoid
type Monoid :: * -> Constraint
class Semigroup a => Monoid a where
  mempty :: a
  mappend :: a -> a -> a
  mconcat :: [a] -> a
  {-# MINIMAL mempty | mconcat #-}
  	-- Defined in `GHC.Base'
instance Monoid () -- Defined in `GHC.Base'
instance (Monoid a, Monoid b) => Monoid (a, b)
  -- Defined in `GHC.Base'
instance (Monoid a, Monoid b, Monoid c) => Monoid (a, b, c)
  -- Defined in `GHC.Base'
instance (Monoid a, Monoid b, Monoid c, Monoid d) =>
         Monoid (a, b, c, d)
  -- Defined in `GHC.Base'
instance (Monoid a, Monoid b, Monoid c, Monoid d, Monoid e) =>
         Monoid (a, b, c, d, e)
  -- Defined in `GHC.Base'
instance Monoid b => Monoid (a -> b) -- Defined in `GHC.Base'
instance Monoid a => Monoid (IO a) -- Defined in `GHC.Base'
instance Monoid [a] -- Defined in `GHC.Base'
instance Semigroup a => Monoid (Maybe a) -- Defined in `GHC.Base'
instance Monoid Ordering -- Defined in `GHC.Base'
instance Monoid a => Monoid (Solo a) -- Defined in `GHC.Base'
Aula10.hs:58:10-23: error: [GHC-39999] …
    * No instance for `Semigroup Natural'
        arising from the superclasses of an instance declaration
    * In the instance declaration for `Monoid Natural'
   |
λ> (S Zero) <> (S $ S Zero)
S (S (S Zero))
λ> mempty :: Natural
Zero
λ> mconcat [Zero, S Zero, S (S (S (S Zero)))]
S (S (S (S (S Zero))))
λ> :i Foldable
type Foldable :: (* -> *) -> Constraint
class Foldable t where
  Data.Foldable.fold :: Monoid m => t m -> m
  foldMap :: Monoid m => (a -> m) -> t a -> m
  Data.Foldable.foldMap' :: Monoid m => (a -> m) -> t a -> m
  foldr :: (a -> b -> b) -> b -> t a -> b
  Data.Foldable.foldr' :: (a -> b -> b) -> b -> t a -> b
  foldl :: (b -> a -> b) -> b -> t a -> b
  Data.Foldable.foldl' :: (b -> a -> b) -> b -> t a -> b
  foldr1 :: (a -> a -> a) -> t a -> a
  foldl1 :: (a -> a -> a) -> t a -> a
  Data.Foldable.toList :: t a -> [a]
  null :: t a -> Bool
  length :: t a -> Int
  elem :: Eq a => a -> t a -> Bool
  maximum :: Ord a => t a -> a
  minimum :: Ord a => t a -> a
  sum :: Num a => t a -> a
  product :: Num a => t a -> a
  {-# MINIMAL foldMap | foldr #-}
  	-- Defined in `Data.Foldable'
instance Foldable ((,) a) -- Defined in `Data.Foldable'
instance Foldable (Either a) -- Defined in `Data.Foldable'
instance Foldable [] -- Defined in `Data.Foldable'
instance Foldable Maybe -- Defined in `Data.Foldable'
instance Foldable Solo -- Defined in `Data.Foldable'
λ> :i List

<interactive>:1:1-4: error: Not in scope: `List'
λ> :i ([])

<interactive>:1:2: error: [GHC-58481] parse error on input `['
λ> :i []

type List :: * -> *
data List a = [] | a : [a]
  	-- Defined in `GHC.Types'
instance Traversable [] -- Defined in `Data.Traversable'
instance MonadFail [] -- Defined in `Control.Monad.Fail'
instance Foldable [] -- Defined in `Data.Foldable'
instance Applicative [] -- Defined in `GHC.Base'
instance Functor [] -- Defined in `GHC.Base'
instance Monad [] -- Defined in `GHC.Base'
instance Monoid [a] -- Defined in `GHC.Base'
instance Semigroup [a] -- Defined in `GHC.Base'
instance Ord a => Ord [a] -- Defined in `GHC.Classes'
instance Read a => Read [a] -- Defined in `GHC.Read'
instance Show a => Show [a] -- Defined in `GHC.Show'
instance Eq a => Eq [a] -- Defined in `GHC.Classes'
λ> meu_foldr (*) 12 [3, 5, 2]
360
λ> meu_foldl (*) 12 [3, 5, 2]
360
λ> meu_foldl_em_cauda (*) 12 [3, 5, 2]
360
λ> :i Foldable
type Foldable :: (* -> *) -> Constraint
class Foldable t where
  Data.Foldable.fold :: Monoid m => t m -> m
  foldMap :: Monoid m => (a -> m) -> t a -> m
  Data.Foldable.foldMap' :: Monoid m => (a -> m) -> t a -> m
  foldr :: (a -> b -> b) -> b -> t a -> b
  Data.Foldable.foldr' :: (a -> b -> b) -> b -> t a -> b
  foldl :: (b -> a -> b) -> b -> t a -> b
  Data.Foldable.foldl' :: (b -> a -> b) -> b -> t a -> b
  foldr1 :: (a -> a -> a) -> t a -> a
  foldl1 :: (a -> a -> a) -> t a -> a
  Data.Foldable.toList :: t a -> [a]
  null :: t a -> Bool
  length :: t a -> Int
  elem :: Eq a => a -> t a -> Bool
  maximum :: Ord a => t a -> a
  minimum :: Ord a => t a -> a
  sum :: Num a => t a -> a
  product :: Num a => t a -> a
  {-# MINIMAL foldMap | foldr #-}
  	-- Defined in `Data.Foldable'
instance Foldable ((,) a) -- Defined in `Data.Foldable'
instance Foldable (Either a) -- Defined in `Data.Foldable'
instance Foldable [] -- Defined in `Data.Foldable'
instance Foldable Maybe -- Defined in `Data.Foldable'
instance Foldable Solo -- Defined in `Data.Foldable'
λ> :{
instance Foldable ArvBin where
  foldr _ x Folha = x
  foldr f x (Raiz r esq dir) =