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compose2 :: forall a b x y. (a -> b) -> (x -> y -> a) -> x -> y -> b

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

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

f (g x y) == g (f x) (f y)?

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

over2 :: forall t a s b. Newtype t a => Newtype s b => (a -> t) -> (a -> a -> b) -> t -> t -> s

Lifts a binary function to operate over newtypes.

newtype Meter = Meter Int
derive newtype instance newtypeMeter :: Newtype Meter _
newtype SquareMeter = SquareMeter Int
derive newtype instance newtypeSquareMeter :: Newtype SquareMeter _

area :: Meter -> Meter -> SquareMeter
area = over2 Meter (*)

The above example also demonstrates that the return type is polymorphic here too.

under2 :: forall t a s b. Newtype t a => Newtype s b => (a -> t) -> (t -> t -> s) -> a -> a -> b

The opposite of over2: lowers a binary function that operates on Newtyped values to operate on the wrapped value instead.

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

mapCopyAll :: forall a b p q. (String -> String) -> (a -> b) -> p -> q -> p

dimap :: forall a b. (a -> Number) -> (Number -> b) -> ContinuousScale -> (a -> b)

Transform both input and output (profunctor-like)

transformed = scale # dimap preprocess postprocess

insertByWith :: forall a. (a -> Boolean) -> (a -> a -> Ordering) -> a -> Array a -> Maybe (Array a)

Insert the element into a sorted array but only if the element can not be found by the predicate.

insertByWith (_ == 2) (\a b -> compare a b) 2 [1,3]  == Just [1,2,3]

compose3 :: forall a b x y z. (a -> b) -> (x -> y -> z -> a) -> x -> y -> z -> b

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

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

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

traverse :: forall f t a. Coercible (f a) (f t) => Newtype t a => (a -> t) -> (a -> f a) -> t -> f t

Similar to the function from the Traversable class, but operating within a newtype instead.

iterateUntilM :: forall a m. Monad m => (a -> Boolean) -> (a -> m a) -> a -> m a

Yields the result of applying f until p holds.

iterateUntilM :: forall m a. MonadRec m => (a -> Boolean) -> (a -> m a) -> a -> m a

Yields the result of applying f until p holds.

compose2SecondFlipped :: forall a b x y z. (y -> z -> b) -> (x -> b -> a) -> x -> y -> z -> a

retryUntilLoop :: forall m a. Monad m => (a -> Boolean) -> (a -> m a) -> a -> m a

Repeat a computation until the value satisfies a predicate, looping in the previous value

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

discard :: forall m a b c. Bind m => (a -> m b) -> (Unit -> (b -> m c)) -> (a -> m c)

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.

applyThirdFlipped :: forall x y z a. x -> (y -> z -> x -> a) -> y -> z -> a

composeKleisliFlipped :: forall a b c m. Bind m => (b -> m c) -> (a -> m b) -> a -> m c

Backwards Kleisli composition.

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)

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

B3 combinator - becard

B(BB)B

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

λ f g h x . f (g (h 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

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

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

A default implementation of bifoldr using bifoldMap.

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

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 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)

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)

composeKleisli :: forall a b c m. Bind m => (a -> m b) -> (b -> m c) -> a -> m c

Forwards Kleisli composition.

For example:

import Data.Array (head, tail)

third = tail >=> tail >=> head

applySecondFlipped :: forall x y a. x -> (y -> x -> a) -> y -> a

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

Returns a new function that calls the first function with the result of calling the second.

let addTwo x = x + 2
let double x = x * 2
let addTwoThenDouble x = addTwo :compose double
addTwoThenDouble 3 -- 10

This is function composition.

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

F combinator - finch

ETTET

Λ a b c . a → b → (b → a → c) → c

λ x y f . f y x

modifyOrCons :: forall a. (a -> Boolean) -> (a -> a) -> a -> Array a -> Array a

Modify an element when it was found by the predicate or push a new element to the front of the array.

modifyOrCons (_ == 2) (* 3) 11 [1,2,3] == Just [1,6,3]
modifyOrCons (_ == 4) (* 3) 11 [1,2,3] == Just [11,1,2,3]

modifyOrCons :: forall a. (a -> Boolean) -> (a -> a) -> a -> Array a -> Array a

Modify an element when it was found by the predicate or push a new element to the front of the array.

modifyOrCons (_ == 2) (* 3) 11 [1,2,3] == Just [1,6,3]
modifyOrCons (_ == 4) (* 3) 11 [1,2,3] == Just [11,1,2,3]

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

R combinator - robin

BBT

Λ a b c . a → (b → a → c) → b → c

λ x f y . f y x

on :: forall @sym f1 f2 a b r1 r2. Newtype f2 (Variant r2) => Newtype f1 (Variant r1) => Cons sym a r1 r2 => IsSymbol sym => (a -> b) -> (f1 -> b) -> f2 -> b

unsafeOptField_helper :: forall r val obj. r -> (val -> r) -> String -> obj -> r

caseDeposit :: forall a d. Deposit d => (Source -> a) -> (Mineral -> a) -> d -> a

fromKillSignal' :: forall r. (Int -> r) -> (String -> r) -> KillSignal -> r

modifyOrSnoc :: forall a. (a -> Boolean) -> (a -> a) -> Array a -> a -> Array a

Modify an element when it was found by the predicate or append a new element to the end of the array.

modifyOrSnoc (_ == 2) (* 3) [1,2,3] 11 == Just [1,6,3]
modifyOrSnoc (_ == 4) (* 3) [1,2,3] 11 == Just [1,2,3,11]

modifyOrSnoc :: forall a. (a -> Boolean) -> (a -> a) -> Array a -> a -> Array a

Modify an element when it was found by the predicate or append a new element to the end of the array.

modifyOrSnoc (_ == 2) (* 3) [1,2,3] 11 == Just [1,6,3]
modifyOrSnoc (_ == 4) (* 3) [1,2,3] 11 == Just [1,2,3,11]

while :: forall a. (a -> Boolean) -> (a -> a) -> a -> a

Keeps calling the function while the predicate is true.

1 :while (_ < 3) (_ + 1) -- 3
9 :while (_ < 3) (_ + 1) -- 9

alaF :: forall f g t a s b. Coercible (f t) (f a) => Coercible (g s) (g b) => Newtype t a => Newtype s b => (a -> t) -> (f t -> g s) -> f a -> g b

Similar to ala but useful for cases where you want to use an additional projection with the higher order function:

alaF Additive foldMap String.length ["hello", "world"] -- 10
alaF Multiplicative foldMap Math.abs [1.0, -2.0, 3.0, -4.0] -- 24.0

The type admits other possibilities due to the polymorphic Functor constraints, but the case described above works because ((->) a) is a Functor.

overF :: forall f g t a s b. Coercible (f a) (f t) => Coercible (g b) (g s) => Newtype t a => Newtype s b => (a -> t) -> (f a -> g b) -> f t -> g s

Much like over, but where the lifted function operates on values in a Functor:

findLabel :: String -> Array Label -> Maybe Label
findLabel s = overF Label (Foldable.find (_ == s))

The above example also demonstrates that the functor type is polymorphic here too, the input is an Array but the result is a Maybe.

underF :: forall f g t a s b. Coercible (f t) (f a) => Coercible (g s) (g b) => Newtype t a => Newtype s b => (a -> t) -> (f t -> g s) -> f a -> g b

Much like under, but where the lifted function operates on values in a Functor:

newtype EmailAddress = EmailAddress String
derive instance newtypeEmailAddress :: Newtype EmailAddress _

isValid :: EmailAddress -> Boolean
isValid x = false -- imagine a slightly less strict predicate here

findValidEmailString :: Array String -> Maybe String
findValidEmailString = underF EmailAddress (Foldable.find isValid)

The above example also demonstrates that the functor type is polymorphic here too, the input is an Array but the result is a Maybe.

imap :: forall f a b. Invariant f => (a -> b) -> (b -> a) -> f a -> f b

imapF :: forall f a b. Functor f => (a -> b) -> (b -> a) -> f a -> f b

As all Functors are also trivially Invariant, this function can be used as the imap implementation for any types that has an existing Functor instance.

imapC :: forall f a b. Contravariant f => (a -> b) -> (b -> a) -> f a -> f b

As all Contravariant functors are also trivially Invariant, this function can be used as the imap implementation for any types that have an existing Contravariant instance.

over :: forall t a s b. Newtype t a => Newtype s b => (a -> t) -> (a -> b) -> t -> s

Lifts a function operate over newtypes. This can be used to lift a function to manipulate the contents of a single newtype, somewhat like map does for a Functor:

newtype Label = Label String
derive instance newtypeLabel :: Newtype Label _

toUpperLabel :: Label -> Label
toUpperLabel = over Label String.toUpper

But the result newtype is polymorphic, meaning the result can be returned as an alternative newtype:

newtype UppercaseLabel = UppercaseLabel String
derive instance newtypeUppercaseLabel :: Newtype UppercaseLabel _

toUpperLabel' :: Label -> UppercaseLabel
toUpperLabel' = over Label String.toUpper

under :: forall t a s b. Newtype t a => Newtype s b => (a -> t) -> (t -> s) -> a -> b

The opposite of over: lowers a function that operates on Newtyped values to operate on the wrapped value instead.

newtype Degrees = Degrees Number
derive instance newtypeDegrees :: Newtype Degrees _

newtype NormalDegrees = NormalDegrees Number
derive instance newtypeNormalDegrees :: Newtype NormalDegrees _

normaliseDegrees :: Degrees -> NormalDegrees
normaliseDegrees (Degrees deg) = NormalDegrees (deg % 360.0)

asNormalDegrees :: Number -> Number
asNormalDegrees = under Degrees normaliseDegrees

As with over the Newtype is polymorphic, as illustrated in the example above - both Degrees and NormalDegrees are instances of Newtype, so even though normaliseDegrees changes the result type we can still put a Number in and get a Number out via under.

uncons' :: forall r. r -> (SourceToken -> TokenList -> r) -> TokenList -> r

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

Memoize the composition of two functions

subscriptionEventOpts :: forall opts c. SubscriptionClient c opts => (opts -> opts) -> c -> String -> Json -> Emitter Json

watchQueryEventOpts :: forall opts c. WatchQueryClient c opts => (opts -> opts) -> c -> String -> Json -> Emitter Json

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

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

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

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

f (g x y) == g' (f x) (f y)?

handle :: forall a' a p t s. RowCons t (Action t p) a a' => IsSymbol t => (s -> Action t p -> s) -> (Variant a -> s -> s) -> Variant a' -> s -> s

Converts a single action handler into an "action handler set" handlers = handle logIn. This "action handler set" can be combined with other action handlers using combine or >>=>>.

surroundMapWithIndex :: forall i f a m. FoldableWithIndex i f => Semigroup m => m -> (i -> a -> m) -> f a -> m

foldMapWithIndex but with each element surrounded by some fixed value.

For example:

> surroundMapWithIndex "*" (\i x -> show i <> x) []
= "*"

> surroundMapWithIndex "*" (\i x -> show i <> x) ["a"]
= "*0a*"

> surroundMapWithIndex "*" (\i x -> show i <> x) ["a", "b"]
= "*0a*1b*"

> surroundMapWithIndex "*" (\i x -> show i <> x) ["a", "b", "c"]
= "*0a*1b*2c*"

maybe' :: forall a b. (Unit -> b) -> (a -> b) -> Maybe a -> b

Similar to maybe but for use in cases where the default value may be expensive to compute. As PureScript is not lazy, the standard maybe has to evaluate the default value before returning the result, whereas here the value is only computed when the Maybe is known to be Nothing.

maybe' (\_ -> x) f Nothing == x
maybe' (\_ -> x) f (Just y) == f y

expectNotSatisfyM :: forall m a. MonadThrow Error m => Show a => a -> (a -> m Boolean) -> String -> m Unit

expectSatisfyM :: forall m a. MonadThrow Error m => Show a => a -> (a -> m Boolean) -> String -> m Unit

iterateN :: forall f a. Unfoldable1 f => (a -> a) -> a -> Int -> f a

forWithIndex :: forall i a b m t. Applicative m => TraversableWithIndex i t => t a -> (i -> a -> m b) -> m (t b)

A version of traverseWithIndex with its arguments flipped.

This can be useful when running an action written using do notation for every element in a data structure:

For example:

for [1, 2, 3] \i x -> do
  logShow i
  pure (x * x)

overF2 :: forall f g t a s b. Coercible (f a) (f t) => Coercible (g b) (g s) => Newtype t a => Newtype s b => (a -> t) -> (f a -> f a -> g b) -> f t -> f t -> g s

Much like over2, but where the lifted binary function operates on values in a Functor.

underF2 :: forall f g t a s b. Coercible (f t) (f a) => Coercible (g s) (g b) => Newtype t a => Newtype s b => (a -> t) -> (f t -> f t -> g s) -> f a -> f a -> g b

Much like under2, but where the lifted binary function operates on values in a Functor.

bitraverse_ :: forall t f a b c d. Bifoldable t => Applicative f => (a -> f c) -> (b -> f d) -> t a b -> f Unit

Traverse a data structure, accumulating effects using an Applicative functor, ignoring the final result.

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

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)

switchFoldOp :: forall s' s. Game s => GameBoot s' => (Input -> s -> s) -> (Input -> s' -> s') -> Input -> GameWithBoot s s' -> GameWithBoot s s'

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