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


-- | Type-threaded list
--   
--   <tt>Thrist</tt> is a list-like data structure (GADT) whose elements
--   are values of a two-parameter datatype. The typing constraint ensures
--   that the second type parameter of a former value unifies with the
--   first type parameter of the latter.
--   
--   This threading of types is the foundation for thrists' nice
--   properties. E.g., paired with a suitable semantics, function
--   composition $(.)$ can be embedded.
--   
--   Technically a thrist is embodying the concept of a <i>free
--   category</i>.
--   
--   Sub-modules demonstrate the power of the thrist idea by emulating some
--   familiar data structures.
--   
--   For further ideas, please consult the companion (draft) paper
--   "Thrists: Dominoes of Data" at
--   <a>https://github.com/ggreif/omega/blob/master/doc/Thrist-draft-2011-11-20.pdf</a>
@package thrist
@version 0.4

module Data.Thrist

-- | A type-threaded list of binary polymorphic types.
data Thrist :: (k -> k -> *) -> k -> k -> *
[Nil] :: Thrist arr a a
[Cons] :: (a `arr` b) -> Thrist arr b c -> Thrist arr a c

-- | A newtype wrapper, defined for convenience, that "swaps" the two type
--   variables of a binary type. Can be used to reverse a Thrist using
--   <a>foldlThrist</a>. See examples.
newtype Flipped m a b
Flipped :: m b a -> Flipped m a b
[unflip] :: Flipped m a b -> m b a

-- | Equivalent to <a>map</a> for thrists. Takes a function from one binary
--   type to another and applies it to each thrist element. For example
--   this could convert a thrist of (a,b) into a thrist of Either a b:
mapThrist :: (forall i j. (i `brr` j) -> i `arr` j) -> Thrist brr a b -> Thrist arr a b

-- | Equivalent to <a>foldr</a> for thrists. Takes a combining function, a
--   value to replace Nil, and a thrist, returning some new binary type.
foldrThrist :: (forall i j. (i `arr` j) -> (j `brr` c) -> i `brr` c) -> (b `brr` c) -> Thrist arr a b -> a `brr` c

-- | Equivalent to <a>foldl</a> for <a>Thrist</a>s.
foldlThrist :: (forall j k. (a `brr` j) -> (j `arr` k) -> a `brr` k) -> (a `brr` b) -> Thrist arr b c -> a `brr` c

-- | Equivalent to <a>foldr1</a> for <a>Thrist</a>s.
foldr1Thrist :: (forall i j k. (i `arr` j) -> (j `arr` k) -> i `arr` k) -> Thrist arr a b -> a `arr` b

-- | Equivalent to <a>foldl1</a> for <a>Thrist</a>s.
foldl1Thrist :: (forall i j k. (i `arr` j) -> (j `arr` k) -> i `arr` k) -> Thrist arr a b -> a `arr` b

-- | Equivalent to <a>mapM</a> on <a>Thrist</a>s.
mapMThrist :: Monad m => (forall i j. (i `brr` j) -> m (i `arr` j)) -> Thrist brr a b -> m (Thrist arr a b)

-- | Equivalent to <a>foldM</a> on <a>Thrist</a>s.
foldMThrist :: Monad m => (forall j k. (a `brr` j) -> (j `arr` k) -> m (a `brr` k)) -> (a `brr` b) -> Thrist arr b c -> m (a `brr` c)

-- | Equivalent to (++) for thrists.
appendThrist :: Thrist arr a b -> Thrist arr b c -> Thrist arr a c

-- | Returns <a>True</a> when the Thrist is <a>Nil</a>.
nullThrist :: Thrist arr a b -> Bool

-- | Returns the length of the Thrist.
lengthThrist :: Thrist arr a b -> Int
instance forall k (arr :: k -> k -> *) (a :: k). GHC.Base.Semigroup (Data.Thrist.Thrist arr a a)
instance forall k (arr :: k -> k -> *) (a :: k). GHC.Base.Monoid (Data.Thrist.Thrist arr a a)
instance Control.Arrow.Arrow arr => Control.Arrow.Arrow (Data.Thrist.Thrist arr)
instance forall k (arr :: k -> k -> *). Control.Category.Category (Data.Thrist.Thrist arr)

module Data.Thrist.List
data List :: * -> * -> *
[El] :: a -> List a a
instance GHC.Base.Functor Data.Thrist.List.List'
instance GHC.Base.Applicative Data.Thrist.List.List'
instance GHC.Base.Monad Data.Thrist.List.List'

module Data.Thrist.Monad
data Monad' :: (* -> *) -> * -> * -> *
[Feed] :: Monad m => m b -> Monad' m a b
[Digest] :: Monad m => (a -> m b) -> Monad' m a b