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


-- | Type-threaded list
--   
--   Thrist 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.
--   
--   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>http://omega.googlecode.com/files/Thrist-draft-2011-11-20.pdf</a>
@package thrist
@version 0.2.2

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

module Data.Thrist

-- | A type-threaded list of binary polymorphic types.
data Thrist :: (* -> * -> *) -> * -> * -> *
Nil :: Thrist ~> a a
Cons :: (a ~> b) -> Thrist ~> b c -> Thrist ~> a c

-- | A newtype wrapper, defined for convenience, that <a>swaps</a> 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 +> j) -> (i ~> j)) -> Thrist +> a b -> Thrist ~> 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 ~> j) -> (j +> c) -> (i +> c)) -> (b +> c) -> Thrist ~> a b -> (a +> c)

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

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

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

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

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

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

-- | Returns <a>True</a> when the Thrist is <a>Nil</a>.
nullThrist :: Thrist ~> a b -> Bool
instance Category (Thrist (~>))
instance Arrow (~>) => Arrow (Thrist (~>))
instance Monoid (Thrist (~>) a a)

module Data.Thrist.List
data List :: * -> * -> *
El :: a -> List a a
instance Monad List'