Search results

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

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

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 m r a. MonadReader r m => (r -> r) -> m a -> m a

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.

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

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

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

foldMap1Default :: forall t m a. Warn (Text "\'foldMap1Default\' is deprecated, use \'foldMap1DefaultL\' instead") => Foldable1 t => Functor t => Semigroup m => (a -> m) -> t a -> m

Deprecated previous name of foldMap1DefaultL.

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.

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.

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

Get a value which depends on the environment.

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.

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

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

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.

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

Ignore the return value of a computation, using the specified return value instead.

seek :: forall s a w. ComonadStore s w => s -> w a -> w a

Reposition the focus at the specified position.

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.

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

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

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

A version of voidRight with its arguments flipped.

duplicate :: forall a w. Extend w => w a -> w (w a)

Duplicate a comonadic context.

duplicate is dual to Control.Bind.join.

intercalate :: forall f m. Foldable f => Monoid m => m -> f m -> m

Fold a data structure, accumulating values in some Monoid, combining adjacent elements using the specified separator.

For example:

> intercalate ", " ["Lorem", "ipsum", "dolor"]
= "Lorem, ipsum, dolor"

> intercalate "*" ["a", "b", "c"]
= "a*b*c"

> intercalate [1] [[2, 3], [4, 5], [6, 7]]
= [2, 3, 1, 4, 5, 1, 6, 7]

intercalate :: forall f m. Foldable1 f => Semigroup m => m -> f m -> m

Fold a data structure using a Semigroup instance, combining adjacent elements using the specified separator.

surround :: forall f m. Foldable f => Semigroup m => m -> f m -> m

fold but with each element surrounded by some fixed value.

For example:

> surround "*" []
= "*"

> surround "*" ["1"]
= "*1*"

> surround "*" ["1", "2"]
= "*1*2*"

> surround "*" ["1", "2", "3"]
= "*1*2*3*"

unfoldable :: forall m f a. MonadRec m => MonadGen m => Unfoldable f => m a -> m (f a)

Creates a generator that produces unfoldable structures based on an existing generator for the elements.

The size of the unfoldable will be determined by the current size state for the generator. To generate an unfoldable structure of a particular size, use the resize function from the MonadGen class first.

enumFromTo :: forall a u. Enum a => Unfoldable1 u => a -> a -> u a

Returns a contiguous sequence of elements from the first value to the second value (inclusive).

enumFromTo 0 3 = [0, 1, 2, 3]
enumFromTo 'c' 'a' = ['c', 'b', 'a']

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

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.

peek :: forall s w a. ComonadStore s w => s -> w a -> a

track :: forall t w a. ComonadTraced t w => t -> w a -> a

unwrapCofree :: forall f w a. ComonadCofree f w => w a -> f (w a)

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.

add :: forall a. Semiring a => a -> a -> a

append :: forall a. Semigroup a => a -> a -> a

conj :: forall a. HeytingAlgebra a => a -> a -> a

const :: forall a b. a -> b -> a

Returns its first argument and ignores its second.

const 1 "hello" = 1

It can also be thought of as creating a function that ignores its argument:

const 1 = \_ -> 1

disj :: forall a. HeytingAlgebra a => a -> a -> a

div :: forall a. EuclideanRing a => a -> a -> a

gcd :: forall a. Eq a => EuclideanRing a => a -> a -> a

The greatest common divisor of two values.

genericAdd :: forall a rep. Generic a rep => GenericSemiring rep => a -> a -> a

A Generic implementation of the add member from the Semiring type class.

genericAdd' :: forall a. GenericSemiring a => a -> a -> a

genericAppend :: forall a rep. Generic a rep => GenericSemigroup rep => a -> a -> a

A Generic implementation of the append member from the Semigroup type class.

genericAppend' :: forall a. GenericSemigroup a => a -> a -> a

genericConj :: forall a rep. Generic a rep => GenericHeytingAlgebra rep => a -> a -> a

A Generic implementation of the conj member from the HeytingAlgebra type class.

genericConj' :: forall a. GenericHeytingAlgebra a => a -> a -> a

genericDisj :: forall a rep. Generic a rep => GenericHeytingAlgebra rep => a -> a -> a

A Generic implementation of the disj member from the HeytingAlgebra type class.

genericDisj' :: forall a. GenericHeytingAlgebra a => a -> a -> a

genericImplies :: forall a rep. Generic a rep => GenericHeytingAlgebra rep => a -> a -> a

A Generic implementation of the implies member from the HeytingAlgebra type class.

genericImplies' :: forall a. GenericHeytingAlgebra a => a -> a -> a

genericMul :: forall a rep. Generic a rep => GenericSemiring rep => a -> a -> a

A Generic implementation of the mul member from the Semiring type class.

genericMul' :: forall a. GenericSemiring a => a -> a -> a

genericSub :: forall a rep. Generic a rep => GenericRing rep => a -> a -> a

A Generic implementation of the sub member from the Ring type class.

genericSub' :: forall a. GenericRing a => a -> a -> a

implies :: forall a. HeytingAlgebra a => a -> a -> a

lcm :: forall a. Eq a => EuclideanRing a => a -> a -> a

The least common multiple of two values.

leftDiv :: forall a. DivisionRing a => a -> a -> a

Left division, defined as leftDiv a b = recip b * a. Left and right division are distinct in this module because a DivisionRing is not necessarily commutative.

If the type a is also a EuclideanRing, then this function is equivalent to div from the EuclideanRing class. When working abstractly, div should generally be preferred, unless you know that you need your code to work with noncommutative rings.

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

Take the maximum of two values. If they are considered equal, the first argument is chosen.

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

Take the minimum of two values. If they are considered equal, the first argument is chosen.

mod :: forall a. EuclideanRing a => a -> a -> a

mul :: forall a. Semiring a => a -> a -> a

rightDiv :: forall a. DivisionRing a => a -> a -> a

Right division, defined as rightDiv a b = a * recip b. Left and right division are distinct in this module because a DivisionRing is not necessarily commutative.

If the type a is also a EuclideanRing, then this function is equivalent to div from the EuclideanRing class. When working abstractly, div should generally be preferred, unless you know that you need your code to work with noncommutative rings.

sub :: forall a. Ring a => a -> a -> a

extract :: forall w a. Comonad w => w a -> a

proof :: forall a b p. TypeEquals a b => p a -> p b

coerce :: forall f a b. Contravariant f => Functor f => f a -> f b

and :: forall a f. Foldable f => HeytingAlgebra a => f a -> a

The conjunction of all the values in a data structure. When specialized to Boolean, this function will test whether all of the values in a data structure are true.

fold :: forall f m. Foldable f => Monoid m => f m -> m

Fold a data structure, accumulating values in some Monoid.

fold1 :: forall t m. Foldable1 t => Semigroup m => t m -> m

Fold a data structure, accumulating values in some Semigroup.

inj :: forall f g a. Inject f g => f a -> g a

length :: forall a b f. Foldable f => Semiring b => f a -> b

Returns the size/length of a finite structure. Optimized for structures that are similar to cons-lists, because there is no general way to do better.

maximum :: forall f a. Ord a => Foldable1 f => f a -> a

minimum :: forall f a. Ord a => Foldable1 f => f a -> a

or :: forall a f. Foldable f => HeytingAlgebra a => f a -> a

The disjunction of all the values in a data structure. When specialized to Boolean, this function will test whether any of the values in a data structure is true.

product :: forall a f. Foldable f => Semiring a => f a -> a

Find the product of the numeric values in a data structure.

sum :: forall a f. Foldable f => Semiring a => f a -> a

Find the sum of the numeric values in a data structure.

forever :: forall m a b. MonadRec m => m a -> m b

forever runs an action indefinitely, using the MonadRec instance to ensure constant stack usage.

For example:

main = forever $ trace "Hello, World!"

elements :: forall m f a. MonadGen m => Foldable1 f => f a -> m a

Creates a generator that outputs a value chosen from a selection with uniform probability.

ask :: forall e w a. ComonadAsk e w => w a -> e

cleared :: forall f a b. Filterable f => f a -> f b

Filter out all values.

pos :: forall s w a. ComonadStore s w => w a -> s

convertOptions :: forall i o t. ConvertOptions t i o => t -> i -> o

defaults :: forall all defaults provided. Defaults defaults provided all => defaults -> provided -> all

hmap :: forall a b f. HMap f a b => f -> a -> b

hmapWithIndex :: forall a b f. HMapWithIndex f a b => f -> a -> b

mapping :: forall a b f. Mapping f a b => f -> a -> b

addNextEvent :: forall builder event. SupportsNextEvent builder event => event -> builder -> builder

genericAdd :: forall rep a. Generic a rep => GenericSemiring rep => a -> a -> a

A Generic implementation of the add member from the Semiring type class.

genericAdd' :: forall a. GenericSemiring a => a -> a -> a