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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)

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.

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.

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

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

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.

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

Memoize the composition of two functions

foldingWithIndex :: forall f i x y z. FoldingWithIndex f i x y z => f -> i -> x -> y -> z

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

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

foldingWithIndex :: forall f i x y z. FoldingWithIndex f i x y z => f -> i -> x -> y -> z

new3 :: forall b a3 a2 a1 o. o -> a1 -> a2 -> a3 -> b

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

W1 combinator - converse warbler

CW

Λ a b . a → (a → a → b) → b

λ x f = f x x

for :: forall a b m t. Applicative m => Traversable t => t a -> (a -> m b) -> m (t b)

A version of traverse 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] \n -> do
  print n
  return (n * n)

mkQ :: forall a b r. Typeable a => Typeable b => r -> (b -> r) -> a -> r

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

discard :: forall a f b. Discard a => Bind f => f a -> (a -> f b) -> f b

catchError :: forall e m a. MonadError e m => m a -> (e -> m a) -> m a

apApplyFlipped :: forall f b a. Apply f => f a -> f (a -> b) -> f b

applyOp :: forall event a b. Applicative event => event a -> event (a -> b) -> event b

sampleOnLeft :: forall event a b. IsEvent event => event a -> event (a -> b) -> event b

sampleOnRight :: forall event a b. IsEvent event => event a -> event (a -> b) -> event b

sampleOn :: forall event b a. IsEvent event => event a -> event (a -> b) -> event b

bind' :: forall v1 v0 m c. HasBind c m => ObjectOf c v0 => ObjectOf c (m v1) => Restrictable Function c => m v0 -> (v0 -> (m v1)) -> m v1

bind :: forall c b a. HasChain a => a b -> (b -> a c) -> a c

A version of chain with the arguments flipped. This is provided only to support desugaring do notation. It is not recommended to use explicitly.

controlError :: forall f g e a. ErrorControl f g e => f a -> (e -> g a) -> g a

fairConjunction :: forall b a m. MonadLogic m => m a -> (a -> m b) -> m b

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

H combinator - hummingbird

BW(BC)

Λ a b c (a → b → a → c) → a → b → c

λ f x y . f x y x

when :: forall b a m. MonadLogic m => m a -> (a -> m b) -> m b

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

Applies a function to an argument. This is primarily used as the operator ($) which allows parentheses to be omitted in some cases, or as a natural way to apply a chain of composed functions to a value.

liftA1 :: forall f a b. Applicative f => (a -> b) -> f a -> f b

liftA1 provides a default implementation of (<$>) for any Applicative functor, without using (<$>) as provided by the Functor-Applicative superclass relationship.

liftA1 can therefore be used to write Functor instances as follows:

instance functorF :: Functor F where
  map = liftA1

liftM1 :: forall m a b. Monad m => (a -> b) -> m a -> m b

liftM1 provides a default implementation of (<$>) for any Monad, without using (<$>) as provided by the Functor-Monad superclass relationship.

liftM1 can therefore be used to write Functor instances as follows:

instance functorF :: Functor F where
  map = liftM1

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

un :: forall t a. Newtype t a => (a -> t) -> t -> a

Given a constructor for a Newtype, this returns the appropriate unwrap function.

all :: forall a b f. Foldable f => HeytingAlgebra b => (a -> b) -> f a -> b

all f is the same as and <<< map f; map a function over the structure, and then get the conjunction of the results.

any :: forall a b f. Foldable f => HeytingAlgebra b => (a -> b) -> f a -> b

any f is the same as or <<< map f; map a function over the structure, and then get the disjunction of the results.

foldMap :: forall f a m. Foldable f => Monoid m => (a -> m) -> f a -> m

foldMap1 :: forall t a m. Foldable1 t => Semigroup m => (a -> m) -> t a -> m

foldMap1DefaultL :: forall t m a. Foldable1 t => Functor t => Semigroup m => (a -> m) -> t a -> m

A default implementation of foldMap1 using foldl1.

Note: when defining a Foldable1 instance, this function is unsafe to use in combination with foldl1Default.

foldMap1DefaultR :: forall t m a. Foldable1 t => Functor t => Semigroup m => (a -> m) -> t a -> m

A default implementation of foldMap1 using foldr1.

Note: when defining a Foldable1 instance, this function is unsafe to use in combination with foldr1Default.

foldMapDefault :: forall i f a m. FoldableWithIndex i f => Monoid m => (a -> m) -> f a -> m

A default implementation of foldMap using foldMapWithIndex

foldMapDefaultL :: forall f a m. Foldable f => Monoid m => (a -> m) -> f a -> m

A default implementation of foldMap using foldl.

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

foldMapDefaultR :: forall f a m. Foldable f => Monoid m => (a -> m) -> f a -> m

A default implementation of foldMap using foldr.

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

mapDefault :: forall i f a b. FunctorWithIndex i f => (a -> b) -> f a -> f b

A default implementation of Functor's map in terms of mapWithIndex

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

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

cmapFlipped is cmap with its arguments reversed.

asks :: forall e1 e2 w a. ComonadAsk e1 w => (e1 -> e2) -> w a -> e2

Get a value which depends on the environment.

tracks :: forall w a t. ComonadTraced t w => (a -> t) -> w a -> a

Extracts a value at a relative position which depends on the current value.

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

memoize :: forall a b. Tabulate a => (a -> b) -> a -> b

Memoize a function of one argument

delay :: forall m a b. Delay m => a -> (a -> m b) -> m b

map :: forall p q a b. Dissect p q => (a -> b) -> p a -> p b

A tail-recursive map operation, implemented in terms of Dissect.

memoize :: forall b a. Tabulate a => (a -> b) -> a -> b

Memoize a function of one argument

over :: forall s t a b @sym lenses. IsSymbol sym => ParseSymbol sym lenses => ConstructBarlow lenses Function s t a b => (a -> b) -> s -> t

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

A combinator - applicator

Λ a b . (a → b) → a → b

λ f x . f x

defaultFilter :: forall a h f. BooleanEq h => Applicative f => Foldable f => Monoid (f a) => (a -> h) -> f a -> f a

filter :: forall f h a. Filterable f => BooleanEq h => (a -> h) -> f a -> f a

foldMap :: forall a b s. Convert s (Statements a) => Monoid b => (a -> b) -> s -> b

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

I* combinator - id bird once removed

S(SK)

Λ a b . (a → b) → a → b

λ f x . f x

intercept :: forall a e g f. ErrorControl f g e => f a -> (e -> a) -> g a

liftF :: forall b a f. Applicative f => (a -> b) -> a -> f b

local :: forall a b r. (a -> b) -> (Ask b => r) -> (Ask a => r)

Run a function over an implicit parameter

Note: Be careful while using this to map over the value without updating the type.

-- evaluates to `1`, not `2`
provide 1 (local ((*) 2) (ask @Int))

map :: forall a c b. HasMap a => (b -> c) -> a b -> a c

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

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

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

Memoize the function f. If the argument of f differs from the previous call, then f is recomputed.

moldMap :: forall t e m. Moldable t e => Monoid m => (e -> m) -> t -> m

moldMapDefaultL :: forall m e t. Moldable t e => Monoid m => (e -> m) -> t -> m

moldMapDefaultR :: forall m e t. Moldable t e => Monoid m => (e -> m) -> t -> m

A default implementation of moldMap based on moldr

nmap :: forall fa fb a b. NestedFunctor fa fb a b => (a -> b) -> fa -> fb

on :: forall evt obj callback out proxy. On evt obj callback out => proxy evt -> obj -> callback -> out

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

mapFlipped is map with its arguments reversed. For example:

[1, 2, 3] <#> \n -> n * n

modify :: forall t a. Newtype t a => (a -> a) -> t -> t

This combinator unwraps the newtype, applies a monomorphic function to the contained value and wraps the result back in the newtype

enumFromThenTo :: forall f a. Unfoldable f => Functor f => BoundedEnum a => a -> a -> a -> f a

Returns a sequence of elements from the first value, taking steps according to the difference between the first and second value, up to (but not exceeding) the third value.

enumFromThenTo 0 2 6 = [0, 2, 4, 6]
enumFromThenTo 0 3 5 = [0, 3]

Note that there is no BoundedEnum instance for integers, they're just being used here for illustrative purposes to help clarify the behaviour.

The example shows Array return values, but the result can be any type with an Unfoldable1 instance.

censor :: forall w m a. MonadWriter w m => (w -> w) -> m a -> m a

Modify the final accumulator value by applying a function.

local :: forall e w a. ComonadEnv e w => (e -> e) -> w a -> w a

local :: forall r m a. MonadReader r m => (r -> r) -> m a -> m a

peeks :: forall s a w. ComonadStore s w => (s -> s) -> w a -> a

Extract a value from a position which depends on the current position.

seeks :: forall s a w. ComonadStore s w => (s -> s) -> w a -> w a

Reposition the focus at the specified position, which depends on the current position.

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

transAnaT :: forall t f. Recursive t f => Corecursive t f => (t -> t) -> t -> t

transCataT :: forall t f. Recursive t f => Corecursive t f => (t -> t) -> t -> t

censorAccum :: forall acc html a. Accum acc html => (acc -> acc) -> html a -> html a

setCtx :: forall ctx html a. Ctx ctx html => (ctx -> ctx) -> html a -> html a

mapErr :: forall e m a. MonadError e m => (e -> e) -> m a -> m a

everywhere :: forall a. Data a => (forall b. Data b => b -> b) -> a -> a

Apply a transformation everywhere, bottom-up

everywhere' :: forall a. Data a => (forall b. Data b => b -> b) -> a -> a

Apply a transformation everywhere, top-down

gmapT :: forall a. Data a => (forall b. Data b => b -> b) -> a -> a

A generic transformation that maps over the immediate subterms

iterate :: forall a u. Unfoldable1 u => (a -> a) -> a -> u a

Create an infinite Unfoldable1 by repeated application of a function to a seed value. Analogous to iterateN, but with no iteration limit.

This should only be used to produce either lazy types (like lazy Lists) or types with truncating Unfoldable1 instances (like Maybe).

mkT :: forall a b. Typeable a => Typeable b => (b -> b) -> a -> a

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

Applies an argument to a function. This is primarily used as the (#) operator, which allows parentheses to be omitted in some cases, or as a natural way to apply a value to a chain of composed functions.

clamp :: forall a. Ord a => a -> a -> a -> a

Clamp a value between a minimum and a maximum. For example:

let f = clamp 0 10
f (-5) == 0
f 5    == 5
f 15   == 10

asks :: forall r m a. MonadAsk r m => (r -> a) -> m a

Projects a value from the global context in a MonadAsk.

gets :: forall s m a. MonadState s m => (s -> a) -> m a

Get a value which depends on the current state.

folding :: forall f x y z. Folding f x y z => f -> x -> y -> z

hfoldl :: forall f x a b. HFoldl f x a b => f -> x -> a -> b

hfoldlWithIndex :: forall f x a b. HFoldlWithIndex f x a b => f -> x -> a -> b

mappingWithIndex :: forall f i a b. MappingWithIndex f i a b => f -> i -> a -> b

convertOptionsWithDefaults :: forall t defaults provided all. ConvertOptionsWithDefaults t defaults provided all => t -> defaults -> provided -> all

applyTo :: forall f this a b. f -> this -> a -> b

Apply a function to a this object with the given arguments

buildNode :: forall e f p v. ElementBuilder e f p v => e -> f p -> v -> v

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

bind :: forall a. Semigroup a => a -> (a -> a) -> a

clamp :: forall a. HasGreater a => HasLess a => a -> a -> a -> a

Clamps a value between some bounds. If the lower bound is greater than the upper bound, they will be swapped.

2 :clamp 3 5 -- 3
4 :clamp 3 5 -- 4
6 :clamp 3 5 -- 5
6 :clamp 5 3 -- 5

extract :: forall r x a. TypeEquals r x => r -> (x -> a) -> a

foldEnum :: forall a b. BoundedEnum a => Semigroup b => (a -> b) -> b

Map each element of a BoundedEnum into a semigroup, and combine the results through refold1.

folding :: forall f x y z. Folding f x y z => f -> x -> y -> z

hfoldl :: forall f x a b. HFoldl f x a b => f -> x -> a -> b

hfoldlWithIndex :: forall f x a b. HFoldlWithIndex f x a b => f -> x -> a -> b

mappingWithIndex :: forall f i a b. MappingWithIndex f i a b => f -> i -> a -> b

new2 :: forall b a2 a1 o. o -> a1 -> a2 -> b

nmapFlipped :: forall b a fb fa. NestedFunctor fa fb a b => fa -> (a -> b) -> fb

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

Reverse application which is probably exist inside Lens module

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

tabulate :: forall f a b. Representable f a => (a -> b) -> f b

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

T combinator - thrush

CI

Λ a b . a → (a → b) → b

λ x f . f x

fix :: forall l. Lazy l => (l -> l) -> l

fix defines a value as the fixed point of a function.

The Lazy instance allows us to generate the result lazily.

modify :: forall s m. MonadState s m => (s -> s) -> m s

Modify the state by applying a function to the current state. The returned value is the new state value.

fix :: forall a. (a -> a) -> a

Fixed point Y combinator

Λ a . (a → a) → a

λ f . (λ x. f (x x)) (λ x . f (x x))

fix :: forall a. (a -> a) -> a

applyFirst :: forall a b f. Apply f => f a -> f b -> f a

Combine two effectful actions, keeping only the result of the first.

applySecond :: forall a b f. Apply f => f a -> f b -> f b

Combine two effectful actions, keeping only the result of the second.

voidLeft :: forall f a b. Functor f => f a -> b -> f b

A version of voidRight with its arguments flipped.

alt :: forall f a. Alt f => f a -> f a -> f a

choose :: forall m a. MonadGen m => m a -> m a -> m a

Creates a generator that outputs a value chosen from one of two existing existing generators with even probability.

mulNat :: forall proxy a b c. ProductNat a b c => proxy a -> proxy b -> proxy c

plus :: forall proxy a b c. SumInt a b c => proxy a -> proxy b -> proxy c

plusNat :: forall proxy a b c. SumNat a b c => proxy a -> proxy b -> proxy c

powNat :: forall proxy a b c. ExponentiationNat a b c => proxy a -> proxy b -> proxy c

> powNat d2 d3
8 -- : NProxy D8

a raised to the power of b a^b = c

prod :: forall proxy a b c. ProductInt a b c => proxy a -> proxy b -> proxy c

sampleOnLeft_ :: forall event a b. IsEvent event => event a -> event b -> event b

sampleOnRight_ :: forall event a b. IsEvent event => event a -> event b -> event a

Create an Event which samples the latest values from the first event at the times when the second event fires, ignoring the values produced by the second event.

sampleOn_ :: forall b a event. IsEvent event => event a -> event b -> event a

Create an Event which samples the latest values from the first event at the times when the second event fires, ignoring the values produced by the second event.

applyFirst :: forall v1 v0 f c. HasApply c f => HasConst c => HasMap c f => ObjectOf c v0 => ObjectOf c v1 => ObjectOf c (c v1 v0) => f v0 -> f v1 -> f v0

applySecond :: forall v1 v0 f c. HasApply c f => HasConst c => HasIdentity c => HasMap c f => ObjectOf c v0 => ObjectOf c v1 => ObjectOf c (c v1 v1) => ObjectOf c (c v0 (c v1 v1)) => ObjectOf c (c (c v1 v1) (c v0 (c v1 v1))) => f v0 -> f v1 -> f v1

concat :: forall xs ys zs lproxy. Concat xs ys zs => lproxy xs -> lproxy ys -> lproxy zs

drop :: forall n xs ys lproxy iproxy. Drop n xs ys => iproxy n -> lproxy xs -> lproxy ys

map :: forall f xs ys fproxy kproxy lproxy. Map f xs ys => fproxy f -> kproxy xs -> lproxy ys

take :: forall n xs ys lproxy iproxy. Take n xs ys => iproxy n -> lproxy xs -> lproxy ys

zip :: forall x y z lproxy. Zip x y z => lproxy x -> lproxy y -> lproxy z

flipScalarMul :: forall k f. VectorField f k => f k -> k -> f k

get :: forall v s r' r l g f. Cons s v r' r => RGet f g s l r => RowToList r l => g s -> f r -> v

getOrAlt :: forall v s r' r l h g f. Alternative h => Cons s v r' r => RowToList r l => RGetOrAlt f g s l r => g s -> f r -> h v

match :: forall v r1 r0 l1 l0 g f. RMatch f g v l0 r0 l1 r1 => RowToList r0 l0 => RowToList r1 l1 => f r0 -> g r1 -> v

max1 :: forall f a. Ord1 f => f a -> f a -> f a