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


-- | Combinator birds.
--   
--   A catalogue of the combinator birds (Data.Aviary.Birds etc.) - these
--   modules are intended for illustration and-or reference (i.e. looking
--   up combinators by their type signature).
--   
--   Using <tt>Data.Aviary</tt> as a library (i.e. depending on it for
--   other packages) is not recommended: combinator-mania leads to
--   inscrutable code.
--   
--   Changelog
--   
--   v0.4.0:
--   
--   <ul>
--   <li>Removed the "useful" combinators (to emphasize that Data.Aviary is
--   not a utility library).</li>
--   <li>Fixed typos in Haddock docs - thanks to Christopher Young for
--   spotting them.</li>
--   </ul>
--   
--   v0.3.0:
--   
--   <ul>
--   <li>Added Monadic variations.</li>
--   </ul>
--   
--   v0.2.3:
--   
--   <ul>
--   <li>Added Data.Aviary.BirdsVersion - same as the original Birds
--   module, but with type signatures following a revised naming
--   scheme.</li>
--   </ul>
--   
--   v0.2.2:
--   
--   <ul>
--   <li>Added Data.Aviary.Functional - the Applicative, Monad etc.
--   combinatorswith implementations and signatures specialized to the
--   (simple) functional type cf. the Reader monad.</li>
--   </ul>
--   
--   v0.2.1:
--   
--   <ul>
--   <li>Added <tt>dup</tt> and the <i>combiner</i> variants of
--   cardinal-prime.</li>
--   </ul>
--   
--   v0.2.0:
--   
--   <ul>
--   <li>Added Haddock docs for <tt>(##)</tt>.</li>
--   </ul>
@package data-aviary
@version 0.4.0


-- | Functor, Applicative, Monad operations <i>specialized</i> to the
--   functional type.
--   
--   This catalogue is for reference and is not intended for use.
module Data.Aviary.Functional

-- | <a>fmap</a> for the function instance of Functor is <i>compose</i>
--   (<a>.</a>) which in turn is <a>bluebird</a>.
fmap :: (a -> b) -> (r -> a) -> (r -> b)

-- | The Applicative combinator (<a>&lt;$&gt;</a>) is a synonym for
--   <a>fmap</a>, so for the function instance of of Applicative it is
--   <i>compose</i> (<a>.</a>) which is <a>bluebird</a>.
(<$>) :: (a -> b) -> (r -> a) -> (r -> b)

-- | Applicative (<a>&lt;$</a>).
(<$) :: a -> (r -> b) -> (r -> a)

-- | The function instance of Applicative <a>pure</a> is <tt>const</tt>
--   which is <a>kestrel</a>.
pure :: a -> (r -> a)

-- | The combinator (<a>&lt;*&gt;</a>) for the function instance of
--   Applicative is the S combinator aka <a>starling</a>.
(<*>) :: (r -> a -> b) -> (r -> a) -> (r -> b)
(*>) :: (r -> a) -> (r -> b) -> (r -> b)
(<*) :: (r -> a) -> (r -> b) -> (r -> a)
(<**>) :: (r -> a) -> (r -> a -> b) -> (r -> b)

-- | The Applicative function <a>liftA</a> is a synonym for <a>fmap</a>, so
--   for the function instance of of Applicative it is <i>compose</i>
--   (<a>.</a>) which is <a>bluebird</a>.
liftA :: (a -> b) -> (r -> a) -> (r -> b)

-- | <a>liftA2</a> for the function instance of Applicative is the
--   <a>phoenix</a> combinator, also called big Phi and
--   <i>starling-prime</i>.
liftA2 :: (a -> b -> c) -> (r -> a) -> (r -> b) -> (r -> c)
liftA3 :: (a -> b -> c -> d) -> (r -> a) -> (r -> b) -> (r -> c) -> (r -> d)

-- | For the function instance of Category <tt>id</tt> is just the identity
--   function (Haskell's <a>id</a>).
id :: a -> a

-- | For the function instance of Category composition is just regular
--   function composition aka <a>bluebird</a>.
(.) :: (b -> c) -> (a -> b) -> (a -> c)

-- | For the function instance of Category right-to-left composition is
--   just regular function composition aka <a>bluebird</a>.
(<<<) :: (b -> c) -> (a -> b) -> (a -> c)

-- | For the function instance of Category left-to-right composition is the
--   <a>queer</a> bird.
(>>>) :: (a -> b) -> (b -> c) -> (a -> c)
(>>=) :: (r -> a) -> (a -> r -> b) -> (r -> b)
(>>) :: (r -> a) -> (r -> b) -> (r -> b)

-- | The function instance of Monadic <a>return</a> is equal to the
--   constant function (<tt>const</tt>) aka <a>kestrel</a>.
return :: a -> (r -> a)
fail :: String -> (r -> a)
mapM :: (a -> r -> b) -> [a] -> r -> [b]
mapM_ :: (a -> r -> b) -> [a] -> r -> ()
forM :: [a] -> (a -> r -> b) -> r -> [b]
forM_ :: [a] -> (a -> r -> b) -> r -> ()
sequence :: [r -> a] -> r -> [a]
sequence_ :: [r -> a] -> r -> ()
(=<<) :: (a -> r -> b) -> (r -> a) -> r -> b
(>=>) :: (a -> r -> b) -> (b -> r -> c) -> a -> r -> c
(<=<) :: (b -> r -> c) -> (a -> r -> b) -> a -> r -> c
forever :: (r -> a) -> (r -> b)
join :: (r -> (r -> a)) -> r -> a
filterM :: (a -> r -> Bool) -> [a] -> r -> [a]
mapAndUnzipM :: (a -> r -> (b, c)) -> [a] -> r -> ([b], [c])
zipWithM :: (a -> b -> r -> c) -> [a] -> [b] -> r -> [c]
zipWithM_ :: (a -> b -> r -> c) -> [a] -> [b] -> r -> ()
foldM :: (a -> b -> r -> a) -> a -> [b] -> r -> a
foldM_ :: (a -> b -> r -> a) -> a -> [b] -> r -> ()
replicateM :: Int -> (r -> a) -> r -> [a]
replicateM_ :: Int -> (r -> a) -> r -> ()
when :: Bool -> (r -> ()) -> r -> ()
unless :: Bool -> (r -> ()) -> r -> ()

-- | The Monadic function <a>liftM</a> would ideally be a synonym for
--   <a>fmap</a>, so for the function instance of of Monad it corresponds
--   to composition - Haskell's (<a>.</a>) and the <a>bluebird</a>
--   combinator.
liftM :: (a -> b) -> (r -> a) -> r -> b

-- | <a>liftM2</a> for the function instance of Monad is the <a>phoenix</a>
--   combinator, also called big Phi and <i>starling-prime</i>.
liftM2 :: (a -> b -> c) -> (r -> a) -> (r -> b) -> r -> c
liftM3 :: (a -> b -> c -> d) -> (r -> a) -> (r -> b) -> (r -> c) -> r -> d
liftM4 :: (a -> b -> c -> d -> e) -> (r -> a) -> (r -> b) -> (r -> c) -> (r -> d) -> r -> e
liftM5 :: (a -> b -> c -> d -> e -> f) -> (r -> a) -> (r -> b) -> (r -> c) -> (r -> d) -> (r -> e) -> r -> f

-- | <a>ap</a> is the Monadic equivalent of the Applicative operator
--   (<a>&lt;*&gt;</a>). So for the function instance of Monad it
--   corresponds to the S combinator aka <a>starling</a>.
ap :: (r -> a -> b) -> (r -> a) -> r -> b

-- | The Arrow operation <a>arr</a> corresponds to function application for
--   the function instance of Arrow - i.e. Haskell's (<tt>$</tt>) operator.
--   
--   This is the <a>applicator</a> combinator in Data.Aviary.
arr :: (b -> c) -> b -> c
first :: (b -> c) -> (b, d) -> (c, d)
second :: (b -> c) -> (d, b) -> (d, c)
(***) :: (b -> c) -> (b' -> c') -> (b, b') -> (c, c')
(&&&) :: (b -> c) -> (b -> c') -> b -> (c, c')

-- | For the function instance of Arrow, <a>returnA</a> is the identity
--   function aka <a>idiot</a>.
returnA :: b -> b

-- | The Arrow operation <i>precomposition with a pure function</i>
--   (left-to-right) is equal to the left-to-right composition operator
--   (<a>&gt;&gt;&gt;</a>) for function Arrows.
--   
--   This corresponds to <a>queer</a>.
(^>>) :: (b -> c) -> (c -> d) -> (b -> d)

-- | The Arrow operation <i>postcomposition with a pure function</i>
--   (left-to-right) is equal to the left-to-right composition operator
--   (<a>&gt;&gt;&gt;</a>) for function Arrows.
--   
--   This corresponds to <a>queer</a>.
(>>^) :: (b -> c) -> (c -> d) -> (b -> d)

-- | The Arrow operation <i>precomposition with a pure function</i>
--   (right-to-left) is equal to the right-to-left composition operator
--   (<a>&lt;&lt;&lt;</a>) for function Arrows, which in turn is equal to
--   regular function composition.
--   
--   This corresponds to <a>bluebird</a>.
(<<^) :: (c -> d) -> (b -> c) -> (b -> d)

-- | The Arrow operation <i>postcomposition with a pure function</i>
--   (right-to-left) is equal to the right-to-left composition operator
--   (<a>&lt;&lt;&lt;</a>) for function Arrows, which in turn is equal to
--   regular function composition.
--   
--   This corresponds to <a>bluebird</a>.
(^<<) :: (c -> d) -> (b -> c) -> (b -> d)
left :: (b -> c) -> (Either b d) -> (Either c d)
right :: (b -> c) -> (Either d b) -> (Either d c)
(+++) :: (b -> c) -> (b' -> c') -> (Either b b') -> (Either c c')
(|||) :: (b -> d) -> (c -> d) -> (Either b c) -> d
app :: (b -> c, b) -> c
leftApp :: (b -> c) -> (Either b d) -> (Either c d)
loop :: ((b, d) -> (c, d)) -> b -> c
extract :: Monoid m => (m -> a) -> a
duplicate :: Monoid m => (m -> a) -> m -> (m -> a)
extend :: Monoid m => ((m -> a) -> b) -> (m -> a) -> m -> b
liftW :: Monoid m => (a -> b) -> (m -> a) -> m -> b
(=>>) :: Monoid m => (m -> a) -> ((m -> a) -> b) -> m -> b
(.>>) :: Monoid m => (m -> a) -> b -> m -> b
liftCtx :: Monoid m => (a -> b) -> (m -> a) -> b
mapW :: Monoid m => ((m -> a) -> b) -> (m -> [a]) -> [b]
parallelW :: Monoid m => (m -> [a]) -> [m -> a]
unfoldW :: Monoid m => ((m -> b) -> (a, b)) -> (m -> b) -> [a]
sequenceW :: Monoid m => [(m -> a) -> b] -> (m -> a) -> [b]


-- | Bird monickered combinators - different naming scheme for the type
--   signatures to Data.Aviary.Birds.
--   
--   This module is intended for illustration (the type signatures!) rather
--   than utility.
--   
--   The 'long reach' Turner set { S, K, I, B, C, S', B', C' }
--   
--   The Joy et al. set { S, I, B, C, J(alt), S', B', C', J(alt)' }
module Data.Aviary.BirdsVersion

-- | I combinator - identity bird / idiot bird - Haskell <a>id</a>.
idiot :: ans -> ans

-- | K combinator - kestrel - Haskell <a>const</a>. Corresponds to the
--   encoding of <tt>true</tt> in the lambda calculus.
kestrel :: ans -> r1 -> ans

-- | B combinator - bluebird - Haskell (<a>.</a>).
bluebird :: (a -> ans) -> (r1 -> a) -> r1 -> ans

-- | C combinator - cardinal - Haskell <a>flip</a>.
cardinal :: (r2 -> r1 -> ans) -> r1 -> r2 -> ans

-- | A combinator - apply / applicator - Haskell (<a>$</a>)
--   
--   This is also called <tt>i-star</tt>.
applicator :: (r1 -> ans) -> r1 -> ans

-- | Psi combinator - psi bird (?) - Haskell <a>on</a>.
psi :: (a -> a -> ans) -> (r1 -> a) -> r1 -> r1 -> ans

-- | B3 combinator - becard.
becard :: (b -> ans) -> (a -> b) -> (r1 -> a) -> r1 -> ans

-- | B1 combinator - blackbird - specs <tt>oo</tt>.
blackbird :: (a -> ans) -> (r1 -> r2 -> a) -> r1 -> r2 -> ans

-- | B' combinator - bluebird prime.
bluebird' :: (r1 -> a -> ans) -> r1 -> (r2 -> a) -> r2 -> ans

-- | B2 combinator - bunting - specs <tt>ooo</tt>.
bunting :: (a -> ans) -> (r1 -> r2 -> r3 -> a) -> r1 -> r2 -> r3 -> ans

-- | C' combinator - no name.
cardinal' :: (a -> r1 -> ans) -> (r2 -> a) -> r1 -> r2 -> ans

-- | C* combinator - cardinal once removed.
cardinalstar :: (r1 -> r3 -> r2 -> ans) -> r1 -> r2 -> r3 -> ans

-- | C** combinator - cardinal twice removed.
cardinalstarstar :: (r1 -> r2 -> r4 -> r3 -> ans) -> r1 -> r2 -> r3 -> r4 -> ans

-- | D combinator - dove.
dove :: (r1 -> a -> ans) -> r1 -> (r2 -> a) -> r2 -> ans

-- | D1 combinator - dickcissel.
dickcissel :: (r1 -> r2 -> a -> ans) -> r1 -> r2 -> (r3 -> a) -> r3 -> ans

-- | D2 combinator - dovekie.
dovekie :: (a -> b -> ans) -> (r1 -> a) -> r1 -> (r2 -> b) -> r2 -> ans

-- | E combinator - eagle.
eagle :: (a -> d -> ans) -> a -> (b -> c -> d) -> b -> c -> ans

-- | E ^ - bald eagle. For alphabetical regularity it is somewhat misnamed
--   here as eaglebald.
eaglebald :: (a -> b -> ans) -> (r1 -> r2 -> a) -> r1 -> r2 -> (r3 -> r4 -> b) -> r3 -> r4 -> ans

-- | F combinator - finch.
finch :: r1 -> r2 -> (r2 -> r1 -> ans) -> ans

-- | F* combinator - finch once removed.
finchstar :: (r3 -> r2 -> r1 -> ans) -> r1 -> r2 -> r3 -> ans

-- | F** combinator - finch twice removed.
finchstarstar :: (r1 -> r4 -> r3 -> r2 -> ans) -> r1 -> r2 -> r3 -> r4 -> ans

-- | G combinator - goldfinch.
goldfinch :: (r2 -> a -> ans) -> (r1 -> a) -> r1 -> r2 -> ans

-- | H combinator - hummingbird.
hummingbird :: (r1 -> r2 -> r1 -> ans) -> r1 -> r2 -> ans

-- | I* combinator - identity bird once removed Alias of <a>applicator</a>,
--   Haskell's (<a>$</a>).
idstar :: (r1 -> ans) -> r1 -> ans

-- | I** combinator - identity bird twice removed
idstarstar :: (r1 -> r2 -> ans) -> r1 -> r2 -> ans

-- | Alternative J combinator - this is the J combintor of Joy,
--   Rayward-Smith and Burton (see. Antoni Diller 'Compiling Functional
--   Languages' page 104). It is not the J - jay combinator of the
--   literature.
jalt :: (r1 -> ans) -> r1 -> r2 -> ans

-- | J' combinator - from Joy, Rayward-Smith and Burton. See the comment to
--   <a>jalt</a>.
jalt' :: (r1 -> r2 -> ans) -> r1 -> r2 -> r3 -> ans

-- | J combinator - jay.
--   
--   This is the usual J combinator.
jay :: (r1 -> ans -> ans) -> r1 -> ans -> r1 -> ans

-- | Ki - kite. Corresponds to the encoding of <tt>false</tt> in the lambda
--   calculus.
kite :: r1 -> ans -> ans

-- | O combinator - owl.
owl :: ((a -> ans) -> a) -> (a -> ans) -> ans

-- | (Big) Phi combinator - phoenix - Haskell <tt>liftM2</tt>.
phoenix :: (a -> b -> ans) -> (r1 -> a) -> (r1 -> b) -> r1 -> ans

-- | Q4 combinator - quacky bird.
quacky :: r1 -> (r1 -> a) -> (a -> ans) -> ans

-- | Q combinator - queer bird.
--   
--   Haskell <tt>(##)</tt> in Peter Thiemann's Wash, reverse composition.
queer :: (r1 -> a) -> (a -> ans) -> r1 -> ans

-- | Q3 combinator - quirky bird.
quirky :: (r1 -> a) -> r1 -> (a -> ans) -> ans

-- | Q1 combinator - quixotic bird.
quixotic :: (a -> ans) -> r1 -> (r1 -> a) -> ans

-- | Q2 combinator - quizzical bird.
quizzical :: r1 -> (a -> ans) -> (r1 -> a) -> ans

-- | R combinator - robin.
robin :: r1 -> (r2 -> r1 -> ans) -> r2 -> ans

-- | R* combinator - robin once removed.
robinstar :: (r2 -> r3 -> r1 -> ans) -> r1 -> r2 -> r3 -> ans

-- | R** combinator - robin twice removed.
robinstarstar :: (r1 -> r3 -> r4 -> r2 -> ans) -> r1 -> r2 -> r3 -> r4 -> ans

-- | S combinator - starling.
--   
--   Haskell: Applicative's <tt>(&lt;*&gt;)</tt> on functions.
--   
--   (Substitution / composition).
starling :: (r1 -> a -> ans) -> (r1 -> a) -> r1 -> ans

-- | S' combinator - starling prime - Turner's big phi. Haskell:
--   Applicative's liftA2 on functions.
starling' :: (a -> b -> ans) -> (r1 -> a) -> (r1 -> b) -> r1 -> ans

-- | T combinator - thrush. Haskell <tt>(#)</tt> in Peter Thiemann's Wash,
--   reverse application.
thrush :: r1 -> (r1 -> ans) -> ans

-- | V combinator - vireo.
vireo :: r1 -> r2 -> (r1 -> r2 -> ans) -> ans

-- | V* combinator - vireo once removed.
vireostar :: (r2 -> r1 -> r2 -> ans) -> r1 -> r2 -> r2 -> ans

-- | V** combinator - vireo twice removed.
vireostarstar :: (r1 -> r3 -> r2 -> r3 -> ans) -> r1 -> r2 -> r3 -> r3 -> ans

-- | W combinator - warbler - elementary duplicator.
warbler :: (r1 -> r1 -> ans) -> r1 -> ans

-- | W1 combinator - converse warbler. <a>warbler</a> with the arguments
--   reversed.
warbler1 :: r1 -> (r1 -> r1 -> ans) -> ans

-- | W* combinator - warbler once removed.
warblerstar :: (r1 -> r2 -> r2 -> ans) -> r1 -> r2 -> ans

-- | W** combinator - warbler twice removed.
warblerstarstar :: (r1 -> r2 -> r3 -> r3 -> ans) -> r1 -> r2 -> r3 -> ans


-- | Bird monickered combinators interdefined.
--   
--   This module is intended for illustration rather than utility.
--   
--   The 'long reach' Turner set { S, K, I, B, C, S', B', C' }
--   
--   The Joy et al. set { S, I, B, C, J(alt), S', B', C', J(alt)' }
module Data.Aviary.BirdsInter

-- | I combinator - identity bird / idiot bird - Haskell <a>id</a>.
idiot :: a -> a

-- | K combinator - kestrel - Haskell <a>const</a>. Corresponds to the
--   encoding of <tt>true</tt> in the lambda calculus.
--   
--   Not interdefined.
kestrel :: a -> b -> a

-- | B combinator - bluebird - Haskell (<a>.</a>).
bluebird :: (b -> c) -> (a -> b) -> a -> c

-- | C combinator - cardinal - Haskell <a>flip</a>.
cardinal :: (a -> b -> c) -> b -> a -> c

-- | A combinator - apply / applicator - Haskell (<a>$</a>).
--   
--   This is also called <tt>i-star</tt>.
--   
--   Note: the (inter-) definition here is <tt>- C (B B I) I -</tt> and not
--   the familiar <tt>- S (S K) -</tt> which as far as Haskell is concerned
--   has a different type:
--   
--   <pre>
--   (S(SK)) :: ((a -&gt; b) -&gt; a) -&gt; (a -&gt; b) -&gt; a 
--   </pre>
applicator :: (a -> b) -> a -> b

-- | Psi combinator - psi bird (?) - Haskell <tt>on</tt>.
psi :: (b -> b -> c) -> (a -> b) -> a -> a -> c

-- | B3 combinator - becard.
becard :: (c -> d) -> (b -> c) -> (a -> b) -> a -> d

-- | B1 combinator - blackbird - specs <tt>oo</tt>.
blackbird :: (c -> d) -> (a -> b -> c) -> a -> b -> d

-- | B' combinator - bluebird prime.
bluebird' :: (a -> c -> d) -> a -> (b -> c) -> b -> d

-- | B2 combinator - bunting - specs <tt>ooo</tt>.
bunting :: (d -> e) -> (a -> b -> c -> d) -> a -> b -> c -> e

-- | C' combinator - no name.
cardinal' :: (c -> a -> d) -> (b -> c) -> a -> b -> d

-- | C* combinator - cardinal once removed.
cardinalstar :: (a -> c -> b -> d) -> a -> b -> c -> d

-- | C** combinator - cardinal twice removed.
cardinalstarstar :: (a -> b -> d -> c -> e) -> a -> b -> c -> d -> e

-- | D combinator - dove.
dove :: (a -> c -> d) -> a -> (b -> c) -> b -> d

-- | D1 combinator - dickcissel.
dickcissel :: (a -> b -> d -> e) -> a -> b -> (c -> d) -> c -> e

-- | D2 combinator - dovekie.
dovekie :: (c -> d -> e) -> (a -> c) -> a -> (b -> d) -> b -> e

-- | E combinator - eagle.
eagle :: (a -> d -> e) -> a -> (b -> c -> d) -> b -> c -> e

-- | E ^ - bald eagle. For alphabetical regularity it is somewhat misnamed
--   here as eaglebald.
eaglebald :: (e -> f -> g) -> (a -> b -> e) -> a -> b -> (c -> d -> f) -> c -> d -> g

-- | F combinator - finch.
finch :: a -> b -> (b -> a -> c) -> c

-- | F* combinator - finch once removed.
finchstar :: (c -> b -> a -> d) -> a -> b -> c -> d

-- | F** combinator - finch twice removed.
finchstarstar :: (a -> d -> c -> b -> e) -> a -> b -> c -> d -> e

-- | G combinator - goldfinch.
goldfinch :: (b -> c -> d) -> (a -> c) -> a -> b -> d

-- | H combinator - hummingbird.
hummingbird :: (a -> b -> a -> c) -> a -> b -> c

-- | I* combinator - identity bird once removed. Alias of
--   <a>applicator</a>, Haskell's (<a>$</a>). Type signature
idstar :: (a -> b) -> a -> b

-- | I** combinator - identity bird twice removed.
idstarstar :: (a -> b -> c) -> a -> b -> c

-- | Alternative J combinator - this is the J combintor of Joy,
--   Rayward-Smith and Burton (see. Antoni Diller 'Compiling Functional
--   Languages' page 104). It is not the J - jay combinator of the
--   literature.
jalt :: (a -> c) -> a -> b -> c

-- | J' combinator - from Joy, Rayward-Smith and Burton. See the comment to
--   <a>jalt</a>.
jalt' :: (a -> b -> d) -> a -> b -> c -> d

-- | J combinator - jay.
--   
--   This is the usual J combinator.
jay :: (a -> b -> b) -> a -> b -> a -> b

-- | Ki - kite. Corresponds to the encoding of <tt>false</tt> in the lambda
--   calculus.
kite :: a -> b -> b

-- | O combinator - owl.
owl :: ((a -> b) -> a) -> (a -> b) -> b

-- | (Big) Phi combinator - phoenix - Haskell <tt>liftM2</tt>.
phoenix :: (b -> c -> d) -> (a -> b) -> (a -> c) -> a -> d

-- | Q4 combinator - quacky bird.
quacky :: a -> (a -> b) -> (b -> c) -> c

-- | Q combinator - queer bird.
--   
--   Haskell <tt>(##)</tt> in Peter Thiemann's Wash, reverse composition.
queer :: (a -> b) -> (b -> c) -> a -> c

-- | Q3 combinator - quirky bird.
quirky :: (a -> b) -> a -> (b -> c) -> c

-- | Q1 combinator - quixotic bird.
quixotic :: (b -> c) -> a -> (a -> b) -> c

-- | Q2 combinator - quizzical bird.
quizzical :: a -> (b -> c) -> (a -> b) -> c

-- | R combinator - robin.
robin :: a -> (b -> a -> c) -> b -> c

-- | R* combinator - robin once removed.
robinstar :: (b -> c -> a -> d) -> a -> b -> c -> d

-- | R** combinator - robin twice removed.
robinstarstar :: (a -> c -> d -> b -> e) -> a -> b -> c -> d -> e

-- | S combinator - starling.
--   
--   Haskell: Applicative's <tt>(&lt;*&gt;)</tt> on functions.
--   
--   Not interdefined.
starling :: (a -> b -> c) -> (a -> b) -> a -> c

-- | S' combinator - starling prime - Turner's big phi. Haskell:
--   Applicative's liftA2 on functions.
starling' :: (b -> c -> d) -> (a -> b) -> (a -> c) -> a -> d

-- | T combinator - thrush. Haskell <tt>(#)</tt> in Peter Thiemann's Wash,
--   reverse application.
thrush :: a -> (a -> b) -> b

-- | V combinator - vireo.
vireo :: a -> b -> (a -> b -> b) -> b

-- | V* combinator - vireo once removed.
vireostar :: (b -> a -> b -> d) -> a -> b -> b -> d

-- | V** combinator - vireo twice removed.
vireostarstar :: (a -> c -> b -> c -> e) -> a -> b -> c -> c -> e

-- | W combinator - warbler - elementary duplicator.
warbler :: (a -> a -> b) -> a -> b

-- | W1 combinator - converse warbler. <a>warbler</a> with the arguments
--   reversed.
warbler1 :: a -> (a -> a -> b) -> b

-- | W* combinator - warbler once removed.
warblerstar :: (a -> b -> b -> c) -> a -> b -> c

-- | W** combinator - warbler twice removed.
warblerstarstar :: (a -> b -> c -> c -> d) -> a -> b -> c -> d


-- | Bird monickered combinators
--   
--   This module is intended for illustration (the type signatures!) rather
--   than utility.
--   
--   The 'long reach' Turner set { S, K, I, B, C, S', B', C' }
--   
--   The Joy et al. set { S, I, B, C, J(alt), S', B', C', J(alt)' }
module Data.Aviary.Birds

-- | I combinator - identity bird / idiot bird - Haskell <a>id</a>.
idiot :: a -> a

-- | K combinator - kestrel - Haskell <a>const</a>. Corresponds to the
--   encoding of <tt>true</tt> in the lambda calculus.
kestrel :: a -> b -> a

-- | B combinator - bluebird - Haskell (<a>.</a>).
bluebird :: (b -> c) -> (a -> b) -> a -> c

-- | C combinator - cardinal - Haskell <a>flip</a>.
cardinal :: (a -> b -> c) -> b -> a -> c

-- | A combinator - apply / applicator - Haskell (<a>$</a>).
--   
--   This is also called <tt>i-star</tt>.
applicator :: (a -> b) -> a -> b

-- | Psi combinator - psi bird (?) - Haskell <a>on</a>.
psi :: (b -> b -> c) -> (a -> b) -> a -> a -> c

-- | B3 combinator - becard.
becard :: (c -> d) -> (b -> c) -> (a -> b) -> a -> d

-- | B1 combinator - blackbird - specs <tt>oo</tt>.
blackbird :: (c -> d) -> (a -> b -> c) -> a -> b -> d

-- | B' combinator - bluebird prime.
bluebird' :: (a -> c -> d) -> a -> (b -> c) -> b -> d

-- | B2 combinator - bunting - specs <tt>ooo</tt>.
bunting :: (d -> e) -> (a -> b -> c -> d) -> a -> b -> c -> e

-- | C' combinator - no name.
cardinal' :: (c -> a -> d) -> (b -> c) -> a -> b -> d

-- | C* combinator - cardinal once removed.
cardinalstar :: (a -> c -> b -> d) -> a -> b -> c -> d

-- | C** combinator - cardinal twice removed.
cardinalstarstar :: (a -> b -> d -> c -> e) -> a -> b -> c -> d -> e

-- | D combinator - dove.
dove :: (a -> c -> d) -> a -> (b -> c) -> b -> d

-- | D1 combinator - dickcissel.
dickcissel :: (a -> b -> d -> e) -> a -> b -> (c -> d) -> c -> e

-- | D2 combinator - dovekie.
dovekie :: (c -> d -> e) -> (a -> c) -> a -> (b -> d) -> b -> e

-- | E combinator - eagle.
eagle :: (a -> d -> e) -> a -> (b -> c -> d) -> b -> c -> e

-- | E ^ - bald eagle. For alphabetical regularity it is somewhat misnamed
--   here as eaglebald.
eaglebald :: (e -> f -> g) -> (a -> b -> e) -> a -> b -> (c -> d -> f) -> c -> d -> g

-- | F combinator - finch.
finch :: a -> b -> (b -> a -> c) -> c

-- | F* combinator - finch once removed.
finchstar :: (c -> b -> a -> d) -> a -> b -> c -> d

-- | F** combinator - finch twice removed.
finchstarstar :: (a -> d -> c -> b -> e) -> a -> b -> c -> d -> e

-- | G combinator - goldfinch.
goldfinch :: (b -> c -> d) -> (a -> c) -> a -> b -> d

-- | H combinator - hummingbird.
hummingbird :: (a -> b -> a -> c) -> a -> b -> c

-- | I* combinator - identity bird once removed Alias of <a>applicator</a>,
--   Haskell's (<a>$</a>).
idstar :: (a -> b) -> a -> b

-- | I** combinator - identity bird twice removed
idstarstar :: (a -> b -> c) -> a -> b -> c

-- | Alternative J combinator - this is the J combintor of Joy,
--   Rayward-Smith and Burton (see. Antoni Diller 'Compiling Functional
--   Languages' page 104). It is not the J - jay combinator of the
--   literature.
jalt :: (a -> c) -> a -> b -> c

-- | J' combinator - from Joy, Rayward-Smith and Burton. See the comment to
--   <a>jalt</a>.
jalt' :: (a -> b -> d) -> a -> b -> c -> d

-- | J combinator - jay.
--   
--   This is the usual J combinator.
jay :: (a -> b -> b) -> a -> b -> a -> b

-- | Ki - kite. Corresponds to the encoding of <tt>false</tt> in the lambda
--   calculus.
kite :: a -> b -> b

-- | O combinator - owl.
owl :: ((a -> b) -> a) -> (a -> b) -> b

-- | (Big) Phi combinator - phoenix - Haskell <tt>liftM2</tt>.
--   
--   This is the same function as <a>starling'</a>.
phoenix :: (b -> c -> d) -> (a -> b) -> (a -> c) -> a -> d

-- | Q4 combinator - quacky bird.
quacky :: a -> (a -> b) -> (b -> c) -> c

-- | Q combinator - queer bird.
--   
--   Haskell <tt>(##)</tt> in Peter Thiemann's Wash, reverse composition.
queer :: (a -> b) -> (b -> c) -> a -> c

-- | Q3 combinator - quirky bird.
quirky :: (a -> b) -> a -> (b -> c) -> c

-- | Q1 combinator - quixotic bird.
quixotic :: (b -> c) -> a -> (a -> b) -> c

-- | Q2 combinator - quizzical bird.
quizzical :: a -> (b -> c) -> (a -> b) -> c

-- | R combinator - robin.
robin :: a -> (b -> a -> c) -> b -> c

-- | R* combinator - robin once removed.
robinstar :: (b -> c -> a -> d) -> a -> b -> c -> d

-- | R** combinator - robin twice removed.
robinstarstar :: (a -> c -> d -> b -> e) -> a -> b -> c -> d -> e

-- | S combinator - starling.
--   
--   Haskell: Applicative's <tt>(&lt;*&gt;)</tt> on functions.
--   
--   Substitution.
starling :: (a -> b -> c) -> (a -> b) -> a -> c

-- | S' combinator - starling prime - Turner's big phi. Haskell:
--   Applicative's <tt>liftA2</tt> on functions (and similarly Monad's
--   <tt>liftM2</tt>).
--   
--   This is the same function as <a>phoenix</a>.
starling' :: (b -> c -> d) -> (a -> b) -> (a -> c) -> a -> d

-- | T combinator - thrush. Haskell <tt>(#)</tt> in Peter Thiemann's Wash,
--   reverse application.
thrush :: a -> (a -> b) -> b

-- | V combinator - vireo (pairing).
vireo :: a -> b -> (a -> b -> c) -> c

-- | V* combinator - vireo once removed.
vireostar :: (b -> a -> b -> d) -> a -> b -> b -> d

-- | V** combinator - vireo twice removed.
vireostarstar :: (a -> c -> b -> c -> e) -> a -> b -> c -> c -> e

-- | W combinator - warbler - elementary duplicator.
warbler :: (a -> a -> b) -> a -> b

-- | W1 combinator - converse warbler. <a>warbler</a> with the arguments
--   reversed.
warbler1 :: a -> (a -> a -> b) -> b

-- | W* combinator - warbler once removed.
warblerstar :: (a -> b -> b -> c) -> a -> b -> c

-- | W** combinator - warbler twice removed.
warblerstarstar :: (a -> b -> c -> c -> d) -> a -> b -> c -> d