L      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~to be determined experimentalstephen.tetley@gmail.comJ  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJ  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJ  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJ  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIto be determined experimentalstephen.tetley@gmail.com1JI combinator - identity bird / idiot bird - Haskell . K!K combinator - kestrel - Haskell .  Corresponds to the encoding of true in the lambda calculus. Not interdefined. L#B combinator - bluebird - Haskell (). M"C combinator - cardinal - Haskell . NA combinator - apply / applicator - Haskell (). Note: the definition here is - C (B B I) I - and not the  familiar  - S (S K) -& which as far as Haskell is concerned  has a different type. , (S(SK)) :: ((a -> b) -> a) -> (a -> b) -> aO(Psi combinator - psi bird (?) - Haskell on. PB3 combinator - becard. Q"B1 combinator - blackbird - specs oo. RB' combinator - bluebird prime. S B2 combinator - bunting - specs ooo. TC' combinator - no name. U'C* combinator - cardinal once removed. V)C** combinator - cardinal twice removed. WD1 combinator - dickcissel. XD combinator - dove. YD2 combinator - dovekie. ZE combinator - eagle. [E ^ - bald eagle. > For alphabetical regularity it is somewhat misnamed here as  eaglebald. \F combinator - finch. ]$F* combinator - finch once removed. ^%F** combinator - finch once removed. _G combinator - goldfinch. `H combinator - hummingbird. a,I* combinator - identity bird once removed.  Alias of N , Haskell's ().  Type signature b.I** combinator - identity bird twice removed. c;Alternative J combinator - this is the J combintor of Joy, . Rayward-Smith and Burton (see. Antoni Diller ' Compiling  Functional Languages'# page 104). It is not the J - jay " combinator of the literature. dJ'2 combinator - from Joy, Rayward-Smith and Burton.  See the comment to c. eJ combinator - jay.  This is the usual J combinator. f Ki - kite.  Corresponds to the encoding of false in the lambda calculus. gO combinator - owl. h)(Big) Phi combinator - phoenix - Haskell liftM2. iQ4 combinator - quacky bird. jQ combinator - queer bird. Haskell (##) in Peter Thiemann's Wash, reverse composition. kQ3 combinator - quirky bird. lQ1 combinator - quixotic bird. m Q2 combinator - quizzical bird. nR combinator - robin. o$R* combinator - robin once removed. p&R** combinator - robin twice removed. qS combinator - starling. Haskell: Applicative's (<*>) on functions. Not interdefined. rS'% combinator - starling prime - Turner' s big phi.  Haskell: Applicative's liftA2 on functions. sT combinator - thrush.  Haskell (#) in Peter Thiemann's Wash, reverse application. tV combinator - vireo. u$V* combinator - vireo once removed. v&V** combinator - vireo twice removed. w0W combinator - warbler - elementary duplicator. x"W1 combinator - converse warbler.  w with the arguments reversed. y&W* combinator - warbler once removed. z(W** combinator - warbler twice removed. 1JKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz1JKLMNOPQRSTUVXWYZ[\]^_`abcdefghijklmnopqrstuvwxyz1JKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyzto be determined experimentalstephen.tetley@gmail.com1{I combinator - identity bird / idiot bird - Haskell . |!K combinator - kestrel - Haskell .  Corresponds to the encoding of true in the lambda calculus. }#B combinator - bluebird - Haskell (). ~"C combinator - cardinal - Haskell . A combinator - apply / applicator - Haskell (). (Psi combinator - psi bird (?) - Haskell . B3 combinator - becard. "B1 combinator - blackbird - specs oo. B' combinator - bluebird prime.  B2 combinator - bunting - specs ooo. C' combinator - no name. 'C* combinator - cardinal once removed. )C** combinator - cardinal twice removed. D1 combinator - dickcissel. D combinator - dove. D2 combinator - dovekie. E combinator - eagle. E ^ - bald eagle. > For alphabetical regularity it is somewhat misnamed here as  eaglebald. F combinator - finch. $F* combinator - finch once removed. %F** combinator - finch once removed. G combinator - goldfinch. H combinator - hummingbird. +I* combinator - identity bird once removed  Alias of  , Haskell's (). -I** combinator - identity bird twice removed ;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. J'2 combinator - from Joy, Rayward-Smith and Burton.  See the comment to . J combinator - jay.  This is the usual J combinator.  Ki - kite.  Corresponds to the encoding of false in the lambda calculus. O combinator - owl. )(Big) Phi combinator - phoenix - Haskell liftM2. Q4 combinator - quacky bird. Q combinator - queer bird. Haskell (##) in Peter Thiemann's Wash, reverse composition. Q3 combinator - quirky bird. Q1 combinator - quixotic bird.  Q2 combinator - quizzical bird. R combinator - robin. $R* combinator - robin once removed. %R* combinator - robin twice removed. S combinator - starling. Haskell: Applicative's (<*>) on functions. Substitution. S'% combinator - starling prime - Turner' s big phi.  Haskell: Applicative's liftA2 on functions. T combinator - thrush.  Haskell (#) in Peter Thiemann's Wash, reverse application. V combinator - vireo. $V* combinator - vireo once removed. &V** combinator - vireo twice removed. 0W combinator - warbler - elementary duplicator. "W1 combinator - converse warbler.   with the arguments reversed. &W* combinator - warbler once removed. (W** combinator - warbler twice removed. 1{|}~1{|}~1{|}~to be determined experimentalstephen.tetley@gmail.com T combinator - thrush (Reverse application - the T combinator.  Found in Peter Thiemann's WASH and the paper 'Client-Side Web  Scripting in Haskell' - Erik Meijer, Daan Leijen & James Hook. Q Combinator - the queer bitd. -Reverse composition - found in Peter Thiemann's WASH.  You might perfer to use (<<<) from Control.Categoty. S combinator - subst.  Familiar as Applicative's (<*>) operator, which itself is  fmap: ,f (b -> c) -> f b -> f c where f = ((->) a) The big Phi, or Turner's S' combinator. < Known to Haskell programmers as liftA2 and liftM2 for the * Applicative and Monad instances of (->).  ; (a1 -> a2 -> r) -> m a1 -> m a2 -> m r where m = ((->) a) 3Taste suggests you may prefer liftA2 especially as bigphi is  not a great name (calling it s' would take a very useful  variable name). A variant of the D2& or dovekie combinator - the argument > order has been changed to be more satisfying for Haskellers:   (appro comb f g) x y   (f x) `comb` (g y) on8 from Data.Function is similar but less general, where ? the two intermediate results are formed by applying the same % function to the supplied arguments:  on = (appro comb f f) 4dup - duplicator aka the W combinator aka Warbler.  dup f x = f x x 6Compose an arity 1 function with an arity 2 function.  B1 - blackbird 6Compose an arity 1 function with an arity 3 function.  B2 - bunting 6Compose an arity 1 function with an arity 4 function. #Combiners - similar to the cardinal' combinator. Mnemonically - comb(ine) after applying f to x and a  single identity: y.  " combfi comb f x y = comb (f x) y Equivalently:  ! combfi comb f = appro comb f id =But combfi is a useful introduction to the (somewhat manic, . but sometimes useful) higher arity versions. Extrapolation of  with another identity. (Mnemonically - comb(ine) after applying f to x and two  identities: y and z. ' combfii comb f x y z = comb (f x) y z Extrapolation of  with a further identity. (Mnemonically - comb(ine) after applying f to s and three  identities: t and u and v. + combfii comb f s t u v = comb (f s) t u v       !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~OPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~data-aviary-0.2.2Data.Aviary.FunctionalData.Aviary.BirdsInterData.Aviary.Birds Data.Aviaryfmap<$><$pure<*>*><*<**>liftAliftA2liftA3id.<<<>>>>>=>>returnfailmapMmapM_forMforM_sequence sequence_=<<>=><=<foreverjoinfilterM mapAndUnzipMzipWithM zipWithM_foldMfoldM_ replicateM replicateM_whenunlessliftMliftM2liftM3liftM4liftM5aparrfirstsecond***&&&returnA^>>>>^<<^^<<leftright+++|||appleftApploopextract duplicateextendliftW=>>.>>liftCtxmapW parallelWunfoldW sequenceWidiotkestrelbluebirdcardinal applicatorpsibecard blackbird bluebird'bunting cardinal' cardinalstarcardinalstarstar dickcisseldovedovekieeagle eaglebaldfinch finchstar finchstarstar goldfinch hummingbirdidstar idstarstarjaltjalt'jaykiteowlphoenixquackyqueerquirkyquixotic quizzicalrobin robinstar robinstarstarstarling starling'thrushvireo vireostar vireostarstarwarblerwarbler1 warblerstarwarblerstarstar###substbigphiapprodupooooooooocombficombfiicombfiiibaseGHC.Baseconstflip$ Data.Functionon