Control.Alternative
- Package
- purescript-control
- Repository
- purescript/purescript-control
#Alternative Source
class Alternative :: (Type -> Type) -> Constraintclass (Applicative f, Plus f) <= Alternative f
The Alternative type class has no members of its own; it just specifies
that the type constructor has both Applicative and Plus instances.
Types which have Alternative instances should also satisfy the following
laws:
- Distributivity:
(f <|> g) <*> x == (f <*> x) <|> (g <*> x) - Annihilation:
empty <*> f = empty
Instances
#guard Source
guard :: forall m. Alternative m => Boolean -> m UnitFail using Plus if a condition does not hold, or
succeed using Applicative if it does.
For example:
import Prelude
import Control.Alternative (guard)
import Data.Array ((..))
factors :: Int -> Array Int
factors n = do
a <- 1..n
b <- 1..n
guard $ a * b == n
pure a
Re-exports from Control.Alt
#Alt Source
class Alt :: (Type -> Type) -> Constraintclass (Functor f) <= Alt f where
The Alt type class identifies an associative operation on a type
constructor. It is similar to Semigroup, except that it applies to
types of kind * -> *, like Array or List, rather than concrete types
String or Number.
Alt instances are required to satisfy the following laws:
- Associativity:
(x <|> y) <|> z == x <|> (y <|> z) - Distributivity:
f <$> (x <|> y) == (f <$> x) <|> (f <$> y)
For example, the Array ([]) type is an instance of Alt, where
(<|>) is defined to be concatenation.
A common use case is to select the first "valid" item, or, if all items are "invalid", the last "invalid" item.
For example:
import Control.Alt ((<|>))
import Data.Maybe (Maybe(..)
import Data.Either (Either(..))
Nothing <|> Just 1 <|> Just 2 == Just 1
Left "err" <|> Right 1 <|> Right 2 == Right 1
Left "err 1" <|> Left "err 2" <|> Left "err 3" == Left "err 3"
Members
alt :: forall a. f a -> f a -> f a
Instances
Re-exports from Control.Applicative
#Applicative Source
class Applicative :: (Type -> Type) -> Constraintclass (Apply f) <= Applicative f where
The Applicative type class extends the Apply type class
with a pure function, which can be used to create values of type f a
from values of type a.
Where Apply provides the ability to lift functions of two or
more arguments to functions whose arguments are wrapped using f, and
Functor provides the ability to lift functions of one
argument, pure can be seen as the function which lifts functions of
zero arguments. That is, Applicative functors support a lifting
operation for any number of function arguments.
Instances must satisfy the following laws in addition to the Apply
laws:
- Identity:
(pure identity) <*> v = v - Composition:
pure (<<<) <*> f <*> g <*> h = f <*> (g <*> h) - Homomorphism:
(pure f) <*> (pure x) = pure (f x) - Interchange:
u <*> (pure y) = (pure (_ $ y)) <*> u
Members
pure :: forall a. a -> f a
Instances
#when Source
when :: forall m. Applicative m => Boolean -> m Unit -> m UnitPerform an applicative action when a condition is true.
#unless Source
unless :: forall m. Applicative m => Boolean -> m Unit -> m UnitPerform an applicative action unless a condition is true.
#liftA1 Source
liftA1 :: forall f a b. Applicative f => (a -> b) -> f a -> f bliftA1 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
Re-exports from Control.Apply
#Apply Source
class Apply :: (Type -> Type) -> Constraintclass (Functor f) <= Apply f where
The Apply class provides the (<*>) which is used to apply a function
to an argument under a type constructor.
Apply can be used to lift functions of two or more arguments to work on
values wrapped with the type constructor f. It might also be understood
in terms of the lift2 function:
lift2 :: forall f a b c. Apply f => (a -> b -> c) -> f a -> f b -> f c
lift2 f a b = f <$> a <*> b
(<*>) is recovered from lift2 as lift2 ($). That is, (<*>) lifts
the function application operator ($) to arguments wrapped with the
type constructor f.
Put differently...
foo =
functionTakingNArguments <$> computationProducingArg1
<*> computationProducingArg2
<*> ...
<*> computationProducingArgN
Instances must satisfy the following law in addition to the Functor
laws:
- Associative composition:
(<<<) <$> f <*> g <*> h = f <*> (g <*> h)
Formally, Apply represents a strong lax semi-monoidal endofunctor.
Members
apply :: forall a b. f (a -> b) -> f a -> f b
Instances
Re-exports from Control.Plus
#Plus Source
class Plus :: (Type -> Type) -> Constraintclass (Alt f) <= Plus f where
The Plus type class extends the Alt type class with a value that
should be the left and right identity for (<|>).
It is similar to Monoid, except that it applies to types of
kind * -> *, like Array or List, rather than concrete types like
String or Number.
Plus instances should satisfy the following laws:
- Left identity:
empty <|> x == x - Right identity:
x <|> empty == x - Annihilation:
f <$> empty == empty
Members
empty :: forall a. f a
Instances
Re-exports from Data.Functor
#Functor Source
class Functor :: (Type -> Type) -> Constraintclass Functor f where
A Functor is a type constructor which supports a mapping operation
map.
map can be used to turn functions a -> b into functions
f a -> f b whose argument and return types use the type constructor f
to represent some computational context.
Instances must satisfy the following laws:
- Identity:
map identity = identity - Composition:
map (f <<< g) = map f <<< map g
Members
map :: forall a b. (a -> b) -> f a -> f b
Instances
#void Source
void :: forall f a. Functor f => f a -> f UnitThe void function is used to ignore the type wrapped by a
Functor, replacing it with Unit and keeping only the type
information provided by the type constructor itself.
void is often useful when using do notation to change the return type
of a monadic computation:
main = forE 1 10 \n -> void do
print n
print (n * n)