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compose2Flipped :: forall a b x y. (x -> y -> a) -> (a -> b) -> x -> y -> b

composeSecond :: forall a b x y. (x -> b -> a) -> (y -> b) -> x -> y -> a

\f g x y -> f x (g y)

goldfinch :: forall d c b a. (b -> c -> d) -> (a -> c) -> a -> b -> d

G combinator - goldfinch

BBC

Λ a b c d . (b → c → d) → (a → c) → a → b → d

λ f g x y . f y (g x)

on :: forall a b c. (b -> b -> c) -> (a -> b) -> a -> a -> c

The on function is used to change the domain of a binary operator.

For example, we can create a function which compares two records based on the values of their x properties:

compareX :: forall r. { x :: Number | r } -> { x :: Number | r } -> Ordering
compareX = compare `on` _.x

on :: forall c b a. (b -> b -> c) -> (a -> b) -> a -> a -> c

Psi combinator - psi bird - on

Λ a b . (b → b → c) → (a → b) → a → a → c

λ f g . λ x y . f (g x) (g y)

on :: forall c b a. (a -> a -> b) -> (c -> a) -> c -> c -> b

psi :: forall c b a. (a -> a -> b) -> (c -> a) -> (c -> c -> b)

verifyScannable :: forall b a f. Eq (f b) => Functor f => Foldable f => Scannable f => (b -> a -> b) -> (a -> b) -> b -> f a -> Boolean

absorbtion :: forall a. Eq a => (a -> a -> a) -> (a -> a -> a) -> a -> a -> Boolean

absorbtion :: forall a. Eq a => (a -> a -> a) -> (a -> a -> a) -> a -> a -> Boolean

onemore :: forall t24 t25 t27 t28. (t25 -> t27 -> t28) -> (t24 -> t25) -> (t24 -> t27) -> t24 -> t28

antitransitive :: forall b a. HeytingAlgebra b => (a -> a -> b) -> a -> a -> a -> b

intransitive :: forall b a. HeytingAlgebra b => (a -> a -> b) -> a -> a -> a -> b

transitive :: forall b a. HeytingAlgebra b => (a -> a -> b) -> a -> a -> a -> b

antitransitive :: forall b a. HeytingAlgebra b => (a -> a -> b) -> a -> a -> a -> b

intransitive :: forall b a. HeytingAlgebra b => (a -> a -> b) -> a -> a -> a -> b

transitive :: forall b a. HeytingAlgebra b => (a -> a -> b) -> a -> a -> a -> b

associative :: forall a. Eq a => (a -> a -> a) -> a -> a -> a -> Boolean

cancellative :: forall a. Eq a => (a -> a -> a) -> a -> a -> a -> Boolean

leftCancellative :: forall a. Eq a => (a -> a -> a) -> a -> a -> a -> Boolean

leftUnar :: forall a. Eq a => (a -> a -> a) -> a -> a -> a -> Boolean

rightCancellative :: forall a. Eq a => (a -> a -> a) -> a -> a -> a -> Boolean

rightUnar :: forall a. Eq a => (a -> a -> a) -> a -> a -> a -> Boolean

associative :: forall a. Eq a => (a -> a -> a) -> a -> a -> a -> Boolean

cancellative :: forall a. Eq a => (a -> a -> a) -> a -> a -> a -> Boolean

leftCancellative :: forall a. Eq a => (a -> a -> a) -> a -> a -> a -> Boolean

leftUnar :: forall a. Eq a => (a -> a -> a) -> a -> a -> a -> Boolean

rightCancellative :: forall a. Eq a => (a -> a -> a) -> a -> a -> a -> Boolean

rightUnar :: forall a. Eq a => (a -> a -> a) -> a -> a -> a -> Boolean

verifySemilattice :: forall a. Eq a => (a -> a -> a) -> a -> a -> a -> Boolean

associative :: forall a. Eq a => (a -> a -> a) -> a -> a -> a -> Boolean

f (f x y) z == f x (f y z)?

splay1 :: forall a b c. (a -> b -> c) -> (a -> b) -> a -> c

verifySemilattice :: forall a. Eq a => (a -> a -> a) -> a -> a -> a -> Boolean

s :: forall c b a. (a -> b -> c) -> (a -> b) -> (a -> c)

monotonic :: forall a. HeytingAlgebra a => Eq a => (a -> a -> a) -> a -> a -> a -> a

monotonic :: forall a. HeytingAlgebra a => Eq a => (a -> a -> a) -> a -> a -> a -> a

everything :: forall a r. Data a => (r -> r -> r) -> (forall b. Data b => b -> r) -> a -> r

Summarise all nodes in top-down, left-to-right

compose3Flipped :: forall a b x y z. (x -> y -> z -> a) -> (a -> b) -> x -> y -> z -> b

composeThird :: forall a b x y z. (x -> y -> b -> a) -> (z -> b) -> x -> y -> z -> a

\f g x y z -> f x y (g z)

jay :: forall b a. (a -> b -> b) -> a -> b -> a -> b

J combinator - Jay

B(BC)(W(BC(B(BBB))))

Λ a b c d . (a → b → b) → a → b → a → b

λ f x y z . f x (f z y)

splay2 :: forall a b c d. (a -> b -> c -> d) -> (a -> b -> c) -> a -> b -> d

compose2Second :: forall a b x y z. (x -> b -> a) -> (y -> z -> b) -> x -> y -> z -> a

\f g x y z -> f x (g y z)

distributive :: forall a. Eq a => (a -> a -> a) -> (a -> a -> a) -> a -> a -> a -> Boolean

leftDistributive :: forall a. Eq a => (a -> a -> a) -> (a -> a -> a) -> a -> a -> a -> Boolean

rightDistributive :: forall a. Eq a => (a -> a -> a) -> (a -> a -> a) -> a -> a -> a -> Boolean

distributive :: forall a. Eq a => (a -> a -> a) -> (a -> a -> a) -> a -> a -> a -> Boolean

leftDistributive :: forall a. Eq a => (a -> a -> a) -> (a -> a -> a) -> a -> a -> a -> Boolean

rightDistributive :: forall a. Eq a => (a -> a -> a) -> (a -> a -> a) -> a -> a -> a -> Boolean

bifoldl :: forall p a b c. Bifoldable p => (c -> a -> c) -> (c -> b -> c) -> c -> p a b -> c

bifoldlDefault :: forall p a b c. Bifoldable p => (c -> a -> c) -> (c -> b -> c) -> c -> p a b -> c

A default implementation of bifoldl using bifoldMap.

Note: when defining a Bifoldable instance, this function is unsafe to use in combination with bifoldMapDefaultL.