-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/


-- | A Category typeclass hierarchy powerful enough to encode full programs.
--   
--   Please see the README on GitHub at
--   <a>https://github.com/githubuser/catalyst#readme</a>
@package catalyst
@version 0.0.0.0

module Control.Category.Closed

module Control.Category.Monoidal
class SymmetricProduct k => MonoidalProduct k
(***) :: MonoidalProduct k => (al `k` bl) -> (ar `k` br) -> (al, ar) `k` (bl, br)
first' :: MonoidalProduct k => (a `k` b) -> (a, c) `k` (b, c)
second' :: MonoidalProduct k => (a `k` b) -> (c, a) `k` (c, b)
class SymmetricSum k => MonoidalSum k
(+++) :: MonoidalSum k => (al `k` bl) -> (ar `k` br) -> Either al ar `k` Either bl br
left :: MonoidalSum k => (a `k` b) -> Either a c `k` Either b c
right :: MonoidalSum k => (a `k` b) -> Either c a `k` Either c b
class Category k => SymmetricProduct k
swap :: SymmetricProduct k => (l, r) `k` (r, l)
reassoc :: SymmetricProduct k => (a, (b, c)) `k` ((a, b), c)
class Category k => SymmetricSum k
swapE :: SymmetricSum k => Either l r `k` Either r l
reassocE :: SymmetricSum k => Either a (Either b c) `k` Either (Either a b) c
class CategoryPlus k => CategoryZero k
zeroC :: CategoryZero k => k a b
class Category k => CategoryPlus k
(<+>) :: CategoryPlus k => k a b -> k a b -> k a b
instance Control.Category.Monoidal.MonoidalSum (->)
instance Control.Category.Monoidal.SymmetricSum (->)
instance Control.Category.Monoidal.MonoidalProduct (->)
instance Control.Category.Monoidal.SymmetricProduct (->)

module Control.Category.Cartesian
class MonoidalProduct k => Cartesian k
(&&&) :: Cartesian k => (a `k` l) -> (a `k` r) -> a `k` (l, r)
consume :: Cartesian k => a `k` ()
copy :: Cartesian k => a `k` (a, a)
fst' :: Cartesian k => (l, r) `k` l
snd' :: Cartesian k => (l, r) `k` r
class MonoidalSum k => Cocartesian k
(|||) :: Cocartesian k => (al `k` b) -> (ar `k` b) -> Either al ar `k` b
injectL :: Cocartesian k => a `k` Either a b
injectR :: Cocartesian k => a `k` Either b a
unify :: Cocartesian k => Either a a `k` a

-- | tags <a>Right</a> when <a>True</a>, <a>Left</a> when <a>False</a>
tag :: Cocartesian k => k (Bool, a) (Either a a)
instance Control.Category.Cartesian.Cocartesian (->)
instance Control.Category.Cartesian.Cartesian (->)

module Control.Category.Numeric

module Control.Category.Recursive
class Category k => Recursive k
recurseL :: Recursive k => (Either a s `k` Either b s) -> a `k` b
recurseR :: Recursive k => (Either s a `k` Either s b) -> a `k` b
class Category k => Fixed k
fixL :: Fixed k => ((a, s) `k` (b, s)) -> a `k` b
fixR :: Fixed k => ((s, a) `k` (s, b)) -> a `k` b
instance Control.Category.Recursive.Fixed (->)
instance Control.Category.Recursive.Recursive (->)

module Control.Category.Free
data IsCategory
HasCategory :: IsCategory
NoCategory :: IsCategory
data IsSymmetricProduct
HasSymmetricProduct :: IsSymmetricProduct
NoSymmetricProduct :: IsSymmetricProduct
data IsSymmetricSum
HasSymmetricSum :: IsSymmetricSum
NoSymmetricSum :: IsSymmetricSum
data IsMonoidalProduct
HasMonoidalProduct :: IsMonoidalProduct
NoMonoidalProduct :: IsMonoidalProduct
data IsMonoidalSum
HasMonoidalSum :: IsMonoidalSum
NoMonoidalSum :: IsMonoidalSum
data IsCartesian
HasCartesian :: IsCartesian
NoCartesian :: IsCartesian
data IsCocartesian
HasCocartesian :: IsCocartesian
NoCocartesian :: IsCocartesian
data IsRecursive
HasRecursive :: IsRecursive
NoRecursive :: IsRecursive
data IsFixed
HasFixed :: IsFixed
NoFixed :: IsFixed
data Requirements
Req :: IsCategory -> IsSymmetricProduct -> IsSymmetricSum -> IsMonoidalProduct -> IsMonoidalSum -> IsCartesian -> IsCocartesian -> IsRecursive -> IsFixed -> Requirements
type family ConstraintsOf (x :: anykind) (k :: * -> * -> *) = (c :: Constraint)
type FreeFunction c a b = Catalyst ('Req 'HasCategory 'HasSymmetricProduct 'HasSymmetricSum 'HasMonoidalProduct 'HasMonoidalSum 'HasCartesian 'HasCocartesian 'HasRecursive 'HasFixed) c
data Catalyst (r :: Requirements) (p :: * -> * -> *) a b
[ID] :: r ~ 'Req 'HasCategory symP symS monP monS cart cocart rec fix => Catalyst r p x x
[Comp] :: Catalyst ('Req 'HasCategory symP symS monP monS cart cocart rec fix) p x y -> Catalyst ('Req 'HasCategory symP symS monP monS cart cocart rec fix) p y z -> Catalyst ('Req 'HasCategory symP symS monP monS cart cocart rec fix) p x z
[Swap] :: r ~ 'Req 'HasCategory 'HasSymmetricProduct symS monP monS cart cocart rec fix => Catalyst r p (a, b) (b, a)
[Reassoc] :: r ~ 'Req 'HasCategory 'HasSymmetricProduct symS monP monS cart cocart rec fix => Catalyst r p (a, (b, c)) ((a, b), c)
[SwapE] :: r ~ 'Req cat symP 'HasSymmetricSum monP monS cart cocart rec fix => Catalyst r p (Either a b) (Either b a)
[ReassocE] :: r ~ 'Req cat symP 'HasSymmetricSum monP monS cart cocart rec fix => Catalyst r p (Either a (Either b c)) (Either (Either a b) c)
[First] :: r ~ 'Req cat symP symS 'HasMonoidalProduct monS cart cocart rec fix => Catalyst r p a b -> Catalyst r p (a, m) (b, m)
[Second] :: r ~ 'Req cat symP symS 'HasMonoidalProduct monS cart cocart rec fix => Catalyst r p a b -> Catalyst r p (m, a) (m, b)
[Alongside] :: r ~ 'Req cat symP symS 'HasMonoidalProduct monS cart cocart rec fix => Catalyst r p a b -> Catalyst r p a' b' -> Catalyst r p (a, a') (b, b')
[Fanout] :: r ~ 'Req cat symP symS monP monS 'HasCartesian cocart rec fix => Catalyst r p a b -> Catalyst r p a b' -> Catalyst r p a (b, b')
[Left'] :: r ~ 'Req cat symP symS monP 'HasMonoidalSum cart cocart rec fix => Catalyst r p a b -> Catalyst r p (Either a x) (Either b x)
[Right'] :: r ~ 'Req cat symP symS monP 'HasMonoidalSum cart cocart rec fix => Catalyst r p a b -> Catalyst r p (Either x a) (Either x b)
[EitherOf] :: r ~ 'Req cat symP symS monP 'HasMonoidalSum cart cocart rec fix => Catalyst r p a b -> Catalyst r p a' b' -> Catalyst r p (Either a a') (Either b b')
[Fanin] :: r ~ 'Req cat symP symS monP monS cart 'HasCocartesian rec fix => Catalyst r p a b -> Catalyst r p a' b -> Catalyst r p (Either a a') b
[Copy] :: r ~ 'Req cat symP symS monP monS 'HasCartesian cocart rec fix => Catalyst r p x (x, x)
[Consume] :: r ~ 'Req cat symP symS monP monS 'HasCartesian cocart rec fix => Catalyst r p x ()
[Fst] :: r ~ 'Req cat symP symS monP monS 'HasCartesian cocart rec fix => Catalyst r p (a, b) a
[Snd] :: r ~ 'Req cat symP symS monP monS 'HasCartesian cocart rec fix => Catalyst r p (a, b) b
[InjectL] :: r ~ 'Req cat symP symS monP monS cart 'HasCocartesian rec fix => Catalyst r p a (Either a b)
[InjectR] :: r ~ 'Req cat symP symS monP monS cart 'HasCocartesian rec fix => Catalyst r p b (Either a b)
[Unify] :: r ~ 'Req cat symP symS monP monS cart 'HasCocartesian rec fix => Catalyst r p (Either a a) a
[Tag] :: r ~ 'Req cat symP symS monP monS cart 'HasCocartesian rec fix => Catalyst r p (Bool, a) (Either a a)
[RecurseL] :: r ~ 'Req cat symP symS monP monS cart cocart 'HasRecursive fix => Catalyst r p (Either a d) (Either b d) -> Catalyst r p a b
[RecurseR] :: r ~ 'Req cat symP symS monP monS cart cocart 'HasRecursive fix => Catalyst r p (Either d a) (Either d b) -> Catalyst r p a b
[FixL] :: r ~ 'Req cat symP symS monP monS cart cocart rec 'HasFixed => Catalyst r p (a, d) (b, d) -> Catalyst r p a b
[FixR] :: r ~ 'Req cat symP symS monP monS cart cocart rec 'HasFixed => Catalyst r p (d, a) (d, b) -> Catalyst r p a b
[LiftC] :: p a b -> Catalyst r p a b
runFree :: forall r p c a b. ConstraintsOf r p => (forall x y. c x y -> p x y) -> Catalyst r c a b -> p a b
liftC :: c a b -> Catalyst r c a b
instance (forall x y. GHC.Show.Show (c x y)) => GHC.Show.Show (Control.Category.Free.Catalyst r c a b)
instance (r GHC.Types.~ 'Control.Category.Free.Req 'Control.Category.Free.HasCategory symP symS monP monS cart cocart rec fix) => Control.Category.Category (Control.Category.Free.Catalyst r c)
instance (r GHC.Types.~ 'Control.Category.Free.Req 'Control.Category.Free.HasCategory 'Control.Category.Free.HasSymmetricProduct symS 'Control.Category.Free.HasMonoidalProduct monS 'Control.Category.Free.HasCartesian cocart rec fix) => Control.Category.Cartesian.Cartesian (Control.Category.Free.Catalyst r c)
instance (r GHC.Types.~ 'Control.Category.Free.Req 'Control.Category.Free.HasCategory symP 'Control.Category.Free.HasSymmetricSum monP 'Control.Category.Free.HasMonoidalSum cart 'Control.Category.Free.HasCocartesian rec fix) => Control.Category.Cartesian.Cocartesian (Control.Category.Free.Catalyst r c)
instance (r GHC.Types.~ 'Control.Category.Free.Req 'Control.Category.Free.HasCategory 'Control.Category.Free.HasSymmetricProduct symS monP monS cart cocart rec fix) => Control.Category.Monoidal.SymmetricProduct (Control.Category.Free.Catalyst r c)
instance (r GHC.Types.~ 'Control.Category.Free.Req 'Control.Category.Free.HasCategory symP 'Control.Category.Free.HasSymmetricSum monP monS cart cocart rec fix) => Control.Category.Monoidal.SymmetricSum (Control.Category.Free.Catalyst r c)
instance (r GHC.Types.~ 'Control.Category.Free.Req 'Control.Category.Free.HasCategory 'Control.Category.Free.HasSymmetricProduct symS 'Control.Category.Free.HasMonoidalProduct monS cart cocart rec fix) => Control.Category.Monoidal.MonoidalProduct (Control.Category.Free.Catalyst r c)
instance (r GHC.Types.~ 'Control.Category.Free.Req 'Control.Category.Free.HasCategory symP 'Control.Category.Free.HasSymmetricSum monP 'Control.Category.Free.HasMonoidalSum cart cocart rec fix) => Control.Category.Monoidal.MonoidalSum (Control.Category.Free.Catalyst r c)
instance (r GHC.Types.~ 'Control.Category.Free.Req 'Control.Category.Free.HasCategory symP symS monP monS cart cocart 'Control.Category.Free.HasRecursive fix) => Control.Category.Recursive.Recursive (Control.Category.Free.Catalyst r c)
instance (r GHC.Types.~ 'Control.Category.Free.Req 'Control.Category.Free.HasCategory symP symS monP monS cart cocart rec 'Control.Category.Free.HasFixed) => Control.Category.Recursive.Fixed (Control.Category.Free.Catalyst r c)