librarylib/Combinators.xtl

source

ˡI̲ : a -> a

function · line 11
ˡI̲ ← { x → x }                                      ⍝ Idiot Bird (identity)

ˡK̲ : a -> b -> a

function · line 12
ˡK̲ ← { x y → x }                                    ⍝ Kestrel

ˡT̲ : a -> (a -> b) -> b

function · line 13
ˡT̲ ← { x y̲ → y̲ x }                                  ⍝ Thrush

ˡW̲ : (a -> a -> b) -> a -> b

function · line 14
ˡW̲ ← { x̲ y → y x̲ y }                                ⍝ Warbler

ˡW̲1 : a -> (a -> a -> b) -> b

function · line 15
ˡW̲1 ← { x y̲ → x y̲ x }                               ⍝ Converse Warbler

ˡB̲ : (a -> b) -> (c -> a) -> c -> b

function · line 17
ˡB̲ ← { x̲ y̲ z → x̲ y̲ z }                              ⍝ Bluebird: compose

ˡB̲1 : (a -> b) -> (c -> d -> a) -> c -> d -> b

function · line 18
ˡB̲1 ← { x̲ y̲ z w → x̲ z y̲ w }                         ⍝ Blackbird

ˡB̲2 : (a -> b) -> (c -> d -> e -> a) -> c -> d -> e -> b

function · line 19
ˡB̲2 ← { x̲ y̲ z w v → x̲ (z y̲ w)_ v }                  ⍝ Bunting

ˡB̲3 : (a -> b) -> (c -> a) -> (d -> c) -> d -> b

function · line 20
ˡB̲3 ← { x̲ y̲ z̲ w → x̲ y̲ z̲ w }                         ⍝ Becard

ˡC̲ : (a -> b -> c) -> b -> a -> c

function · line 21
ˡC̲ ← { x̲ y z → z x̲ y }                              ⍝ Cardinal: swap

ˡD̲ : (a -> b -> c) -> a -> (d -> b) -> d -> c

function · line 22
ˡD̲ ← { x̲ y z̲ w → y x̲ z̲ w }                          ⍝ Dove

ˡD̲1 : (a -> b -> c -> d) -> a -> b -> (e -> c) -> e -> d

function · line 23
ˡD̲1 ← { x̲ y z w̲ v → (y x̲ z)_ w̲ v }                  ⍝ Dickcissel

ˡD̲2 : (a -> b -> c) -> (d -> a) -> d -> (e -> b) -> e -> c

function · line 24
ˡD̲2 ← { x̲ y̲ z w̲ v → (y̲ z) x̲ w̲ v }                   ⍝ Dovekie

ˡE̲ : (a -> b -> c) -> a -> (d -> e -> b) -> d -> e -> c

function · line 25
ˡE̲ ← { x̲ y z̲ w v → y x̲ w z̲ v }                      ⍝ Eagle

ˡE̲h : (a -> b -> c) -> (d -> e -> a) -> d -> e -> (f -> g -> b) -> f -> g -> c

function · line 26
ˡE̲h ← { x̲ a̲ b c d̲ e f → (b a̲ c) x̲ e d̲ f }           ⍝ Bald Eagle

ˡF̲ : a -> b -> (b -> a -> c) -> c

function · line 27
ˡF̲ ← { x y z̲ → y z̲ x }                              ⍝ Finch

ˡG̲ : (a -> b -> c) -> (d -> b) -> d -> a -> c

function · line 28
ˡG̲ ← { x̲ y̲ z w → w x̲ y̲ z }                          ⍝ Goldfinch

ˡH̲ : (a -> b -> a -> c) -> a -> b -> c

function · line 29
ˡH̲ ← { x̲ y z → (y x̲ z)_ y }                         ⍝ Hummingbird

ˡJ̲ : (a -> b -> b) -> a -> b -> a -> b

function · line 30
ˡJ̲ ← { x̲ y z w → y x̲ w x̲ z }                        ⍝ Jay

ˡO̲ : ((a -> b) -> a) -> (a -> b) -> b

function · line 31
ˡO̲ ← { x̲ y̲ → y̲ x̲ 'y̲ }                               ⍝ Owl

ˡQ̲ : (a -> b) -> (b -> c) -> a -> c

function · line 32
ˡQ̲ ← { x̲ y̲ z → y̲ x̲ z }                              ⍝ Queer Bird

ˡQ̲1 : (a -> b) -> c -> (c -> a) -> b

function · line 33
ˡQ̲1 ← { x̲ y z̲ → x̲ z̲ y }                             ⍝ Quixotic Bird

ˡQ̲2 : a -> (b -> c) -> (a -> b) -> c

function · line 34
ˡQ̲2 ← { x y̲ z̲ → y̲ z̲ x }                             ⍝ Quizzical Bird

ˡQ̲3 : (a -> b) -> a -> (b -> c) -> c

function · line 35
ˡQ̲3 ← { x̲ y z̲ → z̲ x̲ y }                             ⍝ Quirky Bird

ˡQ̲4 : a -> (a -> b) -> (b -> c) -> c

function · line 36
ˡQ̲4 ← { x y̲ z̲ → z̲ y̲ x }                             ⍝ Quacky Bird

ˡR̲ : a -> (b -> a -> c) -> b -> c

function · line 37
ˡR̲ ← { x y̲ z → z y̲ x }                              ⍝ Robin

ˡS̲ : (a -> b -> c) -> (a -> b) -> a -> c

function · line 38
ˡS̲ ← { x̲ y̲ z → z x̲ y̲ z }                            ⍝ Starling

ˡV̲ : a -> b -> (a -> b -> c) -> c

function · line 39
ˡV̲ ← { x y z̲ → x z̲ y }                              ⍝ Vireo: a pair

ˡC̲s : (a -> b -> c -> d) -> a -> c -> b -> d

function · line 42
ˡC̲s ← { x̲ y z w → (y x̲ w)_ z }

ˡR̲s : (a -> b -> c -> d) -> c -> a -> b -> d

function · line 43
ˡR̲s ← { x̲ y z w → (z x̲ w)_ y }

ˡF̲s : (a -> b -> c -> d) -> c -> b -> a -> d

function · line 44
ˡF̲s ← { x̲ y z w → (w x̲ z)_ y }

ˡV̲s : (a -> b -> c -> d) -> b -> c -> a -> d

function · line 45
ˡV̲s ← { x̲ y z w → (w x̲ y)_ z }

ˡW̲s : (a -> b -> b -> c) -> a -> b -> c

function · line 46
ˡW̲s ← { x̲ y z → (y x̲ z)_ z }

ˡC̲ss : (a -> b -> c -> d -> e) -> a -> b -> d -> c -> e

function · line 49
ˡC̲ss ← { x̲ y z w v → ((y x̲ z)_ v)_ w }

ˡR̲ss : (a -> b -> c -> d -> e) -> a -> d -> b -> c -> e

function · line 50
ˡR̲ss ← { x̲ y z w v → ((y x̲ w)_ v)_ z }

ˡF̲ss : (a -> b -> c -> d -> e) -> a -> d -> c -> b -> e

function · line 51
ˡF̲ss ← { x̲ y z w v → ((y x̲ v)_ w)_ z }

ˡV̲ss : (a -> b -> c -> d -> e) -> a -> c -> d -> b -> e

function · line 52
ˡV̲ss ← { x̲ y z w v → ((y x̲ v)_ z)_ w }

ˡW̲ss : (a -> b -> c -> c -> d) -> a -> b -> c -> d

function · line 53
ˡW̲ss ← { x̲ y z w → ((y x̲ z)_ w)_ w }

ˡY̲ : (a -> a) -> a

function · line 57
ˡY̲ ← { f̲ → f̲ ˡY̲ 'f̲ }
Used in: ˡY̲