Acme.Functors.Classes

Documentation

class Functor f => Applicative (f :: Type -> Type) where

A functor with application, providing operations to

• embed pure expressions (pure), and
• sequence computations and combine their results (<*> and liftA2).

A minimal complete definition must include implementations of pure and of either <*> or liftA2. If it defines both, then they must behave the same as their default definitions:

(<*>) = liftA2 id

liftA2 f x y = f <$> x <*> y

Further, any definition must satisfy the following:

Identity

pure id <*> v = v

Composition

pure (.) <*> u <*> v <*> w = u <*> (v <*> w)

Homomorphism

pure f <*> pure x = pure (f x)

Interchange

u <*> pure y = pure ($ y) <*> u

The other methods have the following default definitions, which may be overridden with equivalent specialized implementations:

• u *> v = (id <$ u) <*> v

• u <* v = liftA2 const u v

As a consequence of these laws, the Functor instance for f will satisfy

• fmap f x = pure f <*> x

It may be useful to note that supposing

forall x y. p (q x y) = f x . g y

it follows from the above that

liftA2 p (liftA2 q u v) = liftA2 f u . liftA2 g v

If f is also a Monad, it should satisfy

• pure = return

• m1 <*> m2 = m1 >>= (x1 -> m2 >>= (x2 -> return (x1 x2)))

• (*>) = (>>)

(which implies that pure and <*> satisfy the applicative functor laws).

Minimal complete definition

pure, ((<*>) | liftA2)

Methods

pure :: a -> f a

Lift a value.

(<*>) :: f (a -> b) -> f a -> f b infixl 4

Sequential application.

A few functors support an implementation of <*> that is more efficient than the default one.

Using ApplicativeDo: 'fs <*> as' can be understood as the do expression

do f <- fs
   a <- as
   pure (f a)

liftA2 :: (a -> b -> c) -> f a -> f b -> f c

Lift a binary function to actions.

Some functors support an implementation of liftA2 that is more efficient than the default one. In particular, if fmap is an expensive operation, it is likely better to use liftA2 than to fmap over the structure and then use <*>.

This became a typeclass method in 4.10.0.0. Prior to that, it was a function defined in terms of <*> and fmap.

Using ApplicativeDo: 'liftA2 f as bs' can be understood as the do expression

do a <- as
   b <- bs
   pure (f a b)

(*>) :: f a -> f b -> f b infixl 4

Sequence actions, discarding the value of the first argument.

'as *> bs' can be understood as the do expression

do as
   bs

This is a tad complicated for our ApplicativeDo extension which will give it a Monad constraint. For an Applicative constraint we write it of the form

do _ <- as
   b <- bs
   pure b

(<*) :: f a -> f b -> f a infixl 4

Sequence actions, discarding the value of the second argument.

Using ApplicativeDo: 'as <* bs' can be understood as the do expression

do a <- as
   bs
   pure a

Instances

Applicative []

Since: base-2.1

Defined in GHC.Base

Methods

pure :: a -> [a]

(<*>) :: [a -> b] -> [a] -> [b]

liftA2 :: (a -> b -> c) -> [a] -> [b] -> [c]

(*>) :: [a] -> [b] -> [b]

(<*) :: [a] -> [b] -> [a]

Applicative Maybe

Since: base-2.1

Defined in GHC.Base

Methods

pure :: a -> Maybe a

(<*>) :: Maybe (a -> b) -> Maybe a -> Maybe b

liftA2 :: (a -> b -> c) -> Maybe a -> Maybe b -> Maybe c

(*>) :: Maybe a -> Maybe b -> Maybe b

(<*) :: Maybe a -> Maybe b -> Maybe a

Applicative IO

Since: base-2.1

Defined in GHC.Base

Methods

pure :: a -> IO a

(<*>) :: IO (a -> b) -> IO a -> IO b

liftA2 :: (a -> b -> c) -> IO a -> IO b -> IO c

(*>) :: IO a -> IO b -> IO b

(<*) :: IO a -> IO b -> IO a

Applicative Min

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

pure :: a -> Min a

(<*>) :: Min (a -> b) -> Min a -> Min b

liftA2 :: (a -> b -> c) -> Min a -> Min b -> Min c

(*>) :: Min a -> Min b -> Min b

(<*) :: Min a -> Min b -> Min a

Applicative Max

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

pure :: a -> Max a

(<*>) :: Max (a -> b) -> Max a -> Max b

liftA2 :: (a -> b -> c) -> Max a -> Max b -> Max c

(*>) :: Max a -> Max b -> Max b

(<*) :: Max a -> Max b -> Max a

Applicative First

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

pure :: a -> First a

(<*>) :: First (a -> b) -> First a -> First b

liftA2 :: (a -> b -> c) -> First a -> First b -> First c

(*>) :: First a -> First b -> First b

(<*) :: First a -> First b -> First a

Applicative Last

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

pure :: a -> Last a

(<*>) :: Last (a -> b) -> Last a -> Last b

liftA2 :: (a -> b -> c) -> Last a -> Last b -> Last c

(*>) :: Last a -> Last b -> Last b

(<*) :: Last a -> Last b -> Last a

Applicative Option

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

pure :: a -> Option a

(<*>) :: Option (a -> b) -> Option a -> Option b

liftA2 :: (a -> b -> c) -> Option a -> Option b -> Option c

(*>) :: Option a -> Option b -> Option b

(<*) :: Option a -> Option b -> Option a

Applicative ZipList

f <$> ZipList xs1 <*> ... <*> ZipList xsN
    = ZipList (zipWithN f xs1 ... xsN)

where zipWithN refers to the zipWith function of the appropriate arity (zipWith, zipWith3, zipWith4, ...). For example:

(\a b c -> stimes c [a, b]) <$> ZipList "abcd" <*> ZipList "567" <*> ZipList [1..]
    = ZipList (zipWith3 (\a b c -> stimes c [a, b]) "abcd" "567" [1..])
    = ZipList {getZipList = ["a5","b6b6","c7c7c7"]}

Since: base-2.1

Defined in Control.Applicative

Methods

pure :: a -> ZipList a

(<*>) :: ZipList (a -> b) -> ZipList a -> ZipList b

liftA2 :: (a -> b -> c) -> ZipList a -> ZipList b -> ZipList c

(*>) :: ZipList a -> ZipList b -> ZipList b

(<*) :: ZipList a -> ZipList b -> ZipList a

Applicative NonEmpty

Since: base-4.9.0.0

Defined in GHC.Base

Methods

pure :: a -> NonEmpty a

(<*>) :: NonEmpty (a -> b) -> NonEmpty a -> NonEmpty b

liftA2 :: (a -> b -> c) -> NonEmpty a -> NonEmpty b -> NonEmpty c

(*>) :: NonEmpty a -> NonEmpty b -> NonEmpty b

(<*) :: NonEmpty a -> NonEmpty b -> NonEmpty a

Applicative OneOrMore

pure a = OneOrMore a ActuallyNone

OneOrMore f fs <*> OneOrMore x xs = OneOrMore (f x) (fs <*> xs)

Defined in Acme.Functors

Methods

pure :: a -> OneOrMore a

(<*>) :: OneOrMore (a -> b) -> OneOrMore a -> OneOrMore b

liftA2 :: (a -> b -> c) -> OneOrMore a -> OneOrMore b -> OneOrMore c

(*>) :: OneOrMore a -> OneOrMore b -> OneOrMore b

(<*) :: OneOrMore a -> OneOrMore b -> OneOrMore a

Applicative AnyNumberOf

You can use this to apply any number of functions to any number of arguments.

pure a = OneAndMaybeMore a ActuallyNone

OneAndMaybeMore f fs <*> OneAndMaybeMore x xs =
    OneAndMaybeMore (f x) (fs <*> xs)
_ <*> _ = ActuallyNone

Example:

    ( (+ 1) ~~ (* 2) ~~ (+ 5) ~~       ActuallyNone )
<*> (    1  ~~    6  ~~    4  ~~ 37 ~~ ActuallyNone )
 =  (    2  ~~   12  ~~    9  ~~       ActuallyNone )

This example demonstrates how when there are more arguments than functions, any excess arguments (in this case, the 37) are ignored.

Defined in Acme.Functors

Methods

pure :: a -> AnyNumberOf a

(<*>) :: AnyNumberOf (a -> b) -> AnyNumberOf a -> AnyNumberOf b

liftA2 :: (a -> b -> c) -> AnyNumberOf a -> AnyNumberOf b -> AnyNumberOf c

(*>) :: AnyNumberOf a -> AnyNumberOf b -> AnyNumberOf b

(<*) :: AnyNumberOf a -> AnyNumberOf b -> AnyNumberOf a

Applicative Two

If you have two functions f and g and two values a and a', then you can apply them with (<*>) to get two results f a and g a'.

pure a = Two a a

Two f g <*> Two a a' = Two (f a) (g a')

Defined in Acme.Functors

Methods

pure :: a -> Two a

(<*>) :: Two (a -> b) -> Two a -> Two b

liftA2 :: (a -> b -> c) -> Two a -> Two b -> Two c

(*>) :: Two a -> Two b -> Two b

(<*) :: Two a -> Two b -> Two a

Applicative OrNot

If you have a function f that might not actually be there, and a value a that might not actually be there, lifted application (<*>) gives you f a only if both of them are actually there.

pure = ActuallyYes

ActuallyYes f <*> ActuallyYes a = ActuallyYes (f a)
_             <*> _             = Nope

Defined in Acme.Functors

Methods

pure :: a -> OrNot a

(<*>) :: OrNot (a -> b) -> OrNot a -> OrNot b

liftA2 :: (a -> b -> c) -> OrNot a -> OrNot b -> OrNot c

(*>) :: OrNot a -> OrNot b -> OrNot b

(<*) :: OrNot a -> OrNot b -> OrNot a

Applicative LiftedButWhy

pure = LiftedButWhy

LiftedButWhy f <*> LiftedButWhy a = LiftedButWhy (f a)

Defined in Acme.Functors

Methods

pure :: a -> LiftedButWhy a

(<*>) :: LiftedButWhy (a -> b) -> LiftedButWhy a -> LiftedButWhy b

liftA2 :: (a -> b -> c) -> LiftedButWhy a -> LiftedButWhy b -> LiftedButWhy c

(*>) :: LiftedButWhy a -> LiftedButWhy b -> LiftedButWhy b

(<*) :: LiftedButWhy a -> LiftedButWhy b -> LiftedButWhy a

Monoid a => Applicative ((,) a)

For tuples, the Monoid constraint on a determines how the first values merge. For example, Strings concatenate:

("hello ", (+15)) <*> ("world!", 2002)
("hello world!",2017)

Since: base-2.1

Defined in GHC.Base

Methods

pure :: a0 -> (a, a0)

(<*>) :: (a, a0 -> b) -> (a, a0) -> (a, b)

liftA2 :: (a0 -> b -> c) -> (a, a0) -> (a, b) -> (a, c)

(*>) :: (a, a0) -> (a, b) -> (a, b)

(<*) :: (a, a0) -> (a, b) -> (a, a0)

Monad m => Applicative (WrappedMonad m)

Since: base-2.1

Defined in Control.Applicative

Methods

pure :: a -> WrappedMonad m a

(<*>) :: WrappedMonad m (a -> b) -> WrappedMonad m a -> WrappedMonad m b

liftA2 :: (a -> b -> c) -> WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m c

(*>) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m b

(<*) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m a

Applicative (DeterminedBy parameter)

pure a = Determination (\_ -> a)

Determination f <*> Determination a = Determination (\x -> f x (a x))

Defined in Acme.Functors

Methods

pure :: a -> DeterminedBy parameter a

(<*>) :: DeterminedBy parameter (a -> b) -> DeterminedBy parameter a -> DeterminedBy parameter b

liftA2 :: (a -> b -> c) -> DeterminedBy parameter a -> DeterminedBy parameter b -> DeterminedBy parameter c

(*>) :: DeterminedBy parameter a -> DeterminedBy parameter b -> DeterminedBy parameter b

(<*) :: DeterminedBy parameter a -> DeterminedBy parameter b -> DeterminedBy parameter a

Applicative (OrInsteadFirst otherThing)

pure = NotInsteadFirst

NotInsteadFirst f  <*> NotInsteadFirst a  = NotInsteadFirst (f a)
InsteadFirst other <*> _                  = InsteadFirst other
_                  <*> InsteadFirst other = InsteadFirst other

Defined in Acme.Functors

Methods

pure :: a -> OrInsteadFirst otherThing a

(<*>) :: OrInsteadFirst otherThing (a -> b) -> OrInsteadFirst otherThing a -> OrInsteadFirst otherThing b

liftA2 :: (a -> b -> c) -> OrInsteadFirst otherThing a -> OrInsteadFirst otherThing b -> OrInsteadFirst otherThing c

(*>) :: OrInsteadFirst otherThing a -> OrInsteadFirst otherThing b -> OrInsteadFirst otherThing b

(<*) :: OrInsteadFirst otherThing a -> OrInsteadFirst otherThing b -> OrInsteadFirst otherThing a

Semigroup otherThing => Applicative (OrInstead otherThing)

The possibility of having an otherThing obstructs this functor's ability to be applicative, much like the extra thing in Also extraThing does. In this case, since we do not need an empty value for the otherThing, it needs only a semigroup to be in compliance.

pure = NotInstead

NotInstead f   <*> NotInstead a   = NotInstead (f a)
Instead other1 <*> Instead other2 = Instead (other1 <> other2)
Instead other  <*> _              = Instead other
_              <*> Instead other  = Instead other

Defined in Acme.Functors

Methods

pure :: a -> OrInstead otherThing a

(<*>) :: OrInstead otherThing (a -> b) -> OrInstead otherThing a -> OrInstead otherThing b

liftA2 :: (a -> b -> c) -> OrInstead otherThing a -> OrInstead otherThing b -> OrInstead otherThing c

(*>) :: OrInstead otherThing a -> OrInstead otherThing b -> OrInstead otherThing b

(<*) :: OrInstead otherThing a -> OrInstead otherThing b -> OrInstead otherThing a

Monoid extraThing => Applicative (Also extraThing)

Dragging the extraThing along can be a bit of a burden. It prevents Also extraThing from being an applicative functor — unless the extraThing can pull its weight by bringing a monoid to the table.

pure = (`Also` mempty)

(f `Also` extra1) <*> (a `Also` extra2) = f a
                                          `Also` (extra1 <> extra2)

Defined in Acme.Functors

Methods

pure :: a -> Also extraThing a

(<*>) :: Also extraThing (a -> b) -> Also extraThing a -> Also extraThing b

liftA2 :: (a -> b -> c) -> Also extraThing a -> Also extraThing b -> Also extraThing c

(*>) :: Also extraThing a -> Also extraThing b -> Also extraThing b

(<*) :: Also extraThing a -> Also extraThing b -> Also extraThing a

(Monoid a, Monoid b) => Applicative ((,,) a b)

Since: base-4.14.0.0

Defined in GHC.Base

Methods

pure :: a0 -> (a, b, a0)

(<*>) :: (a, b, a0 -> b0) -> (a, b, a0) -> (a, b, b0)

liftA2 :: (a0 -> b0 -> c) -> (a, b, a0) -> (a, b, b0) -> (a, b, c)

(*>) :: (a, b, a0) -> (a, b, b0) -> (a, b, b0)

(<*) :: (a, b, a0) -> (a, b, b0) -> (a, b, a0)

Arrow a => Applicative (WrappedArrow a b)

Since: base-2.1

Defined in Control.Applicative

Methods

pure :: a0 -> WrappedArrow a b a0

(<*>) :: WrappedArrow a b (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0

liftA2 :: (a0 -> b0 -> c) -> WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b c

(*>) :: WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b b0

(<*) :: WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0

Applicative ((->) r :: Type -> Type)

Since: base-2.1

Defined in GHC.Base

Methods

pure :: a -> r -> a

(<*>) :: (r -> (a -> b)) -> (r -> a) -> r -> b

liftA2 :: (a -> b -> c) -> (r -> a) -> (r -> b) -> r -> c

(*>) :: (r -> a) -> (r -> b) -> r -> b

(<*) :: (r -> a) -> (r -> b) -> r -> a

(Monoid a, Monoid b, Monoid c) => Applicative ((,,,) a b c)

Since: base-4.14.0.0

Defined in GHC.Base

Methods

pure :: a0 -> (a, b, c, a0)

(<*>) :: (a, b, c, a0 -> b0) -> (a, b, c, a0) -> (a, b, c, b0)

liftA2 :: (a0 -> b0 -> c0) -> (a, b, c, a0) -> (a, b, c, b0) -> (a, b, c, c0)

(*>) :: (a, b, c, a0) -> (a, b, c, b0) -> (a, b, c, b0)

(<*) :: (a, b, c, a0) -> (a, b, c, b0) -> (a, b, c, a0)

class Applicative m => Monad (m :: Type -> Type) where

The Monad class defines the basic operations over a monad, a concept from a branch of mathematics known as category theory. From the perspective of a Haskell programmer, however, it is best to think of a monad as an abstract datatype of actions. Haskell's do expressions provide a convenient syntax for writing monadic expressions.

Instances of Monad should satisfy the following:

Left identity

return a >>= k = k a

Right identity

m >>= return = m

Associativity

m >>= (\x -> k x >>= h) = (m >>= k) >>= h

Furthermore, the Monad and Applicative operations should relate as follows:

• pure = return

• m1 <*> m2 = m1 >>= (x1 -> m2 >>= (x2 -> return (x1 x2)))

The above laws imply:

• fmap f xs  =  xs >>= return . f

• (>>) = (*>)

and that pure and (<*>) satisfy the applicative functor laws.

The instances of Monad for lists, Maybe and IO defined in the Prelude satisfy these laws.

Minimal complete definition

(>>=)

Methods

(>>=) :: m a -> (a -> m b) -> m b infixl 1

Sequentially compose two actions, passing any value produced by the first as an argument to the second.

'as >>= bs' can be understood as the do expression

do a <- as
   bs a

(>>) :: m a -> m b -> m b infixl 1

Sequentially compose two actions, discarding any value produced by the first, like sequencing operators (such as the semicolon) in imperative languages.

'as >> bs' can be understood as the do expression

do as
   bs

return :: a -> m a

Inject a value into the monadic type.

Instances

Monad []

Since: base-2.1

Defined in GHC.Base

Methods

(>>=) :: [a] -> (a -> [b]) -> [b]

(>>) :: [a] -> [b] -> [b]

return :: a -> [a]

Monad Maybe

Since: base-2.1

Defined in GHC.Base

Methods

(>>=) :: Maybe a -> (a -> Maybe b) -> Maybe b

(>>) :: Maybe a -> Maybe b -> Maybe b

return :: a -> Maybe a

Monad IO

Since: base-2.1

Defined in GHC.Base

Methods

(>>=) :: IO a -> (a -> IO b) -> IO b

(>>) :: IO a -> IO b -> IO b

return :: a -> IO a

Monad Min

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

(>>=) :: Min a -> (a -> Min b) -> Min b

(>>) :: Min a -> Min b -> Min b

return :: a -> Min a

Monad Max

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

(>>=) :: Max a -> (a -> Max b) -> Max b

(>>) :: Max a -> Max b -> Max b

return :: a -> Max a

Monad First

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

(>>=) :: First a -> (a -> First b) -> First b

(>>) :: First a -> First b -> First b

return :: a -> First a

Monad Last

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

(>>=) :: Last a -> (a -> Last b) -> Last b

(>>) :: Last a -> Last b -> Last b

return :: a -> Last a

Monad Option

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

(>>=) :: Option a -> (a -> Option b) -> Option b

(>>) :: Option a -> Option b -> Option b

return :: a -> Option a

Monad NonEmpty

Since: base-4.9.0.0

Defined in GHC.Base

Methods

(>>=) :: NonEmpty a -> (a -> NonEmpty b) -> NonEmpty b

(>>) :: NonEmpty a -> NonEmpty b -> NonEmpty b

return :: a -> NonEmpty a

Monad OrNot

Defined in Acme.Functors

Methods

(>>=) :: OrNot a -> (a -> OrNot b) -> OrNot b

(>>) :: OrNot a -> OrNot b -> OrNot b

return :: a -> OrNot a

Monad LiftedButWhy

LiftedButWhy a >>= f = f a

Defined in Acme.Functors

Methods

(>>=) :: LiftedButWhy a -> (a -> LiftedButWhy b) -> LiftedButWhy b

(>>) :: LiftedButWhy a -> LiftedButWhy b -> LiftedButWhy b

return :: a -> LiftedButWhy a

Monoid a => Monad ((,) a)

Since: base-4.9.0.0

Defined in GHC.Base

Methods

(>>=) :: (a, a0) -> (a0 -> (a, b)) -> (a, b)

(>>) :: (a, a0) -> (a, b) -> (a, b)

return :: a0 -> (a, a0)

Monad m => Monad (WrappedMonad m)

Since: base-4.7.0.0

Defined in Control.Applicative

Methods

(>>=) :: WrappedMonad m a -> (a -> WrappedMonad m b) -> WrappedMonad m b

(>>) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m b

return :: a -> WrappedMonad m a

Monad (DeterminedBy parameter)

Determination fa >>= ff =
    Determination (\x -> let Determination f = ff (fa x) in f x)

Defined in Acme.Functors

Methods

(>>=) :: DeterminedBy parameter a -> (a -> DeterminedBy parameter b) -> DeterminedBy parameter b

(>>) :: DeterminedBy parameter a -> DeterminedBy parameter b -> DeterminedBy parameter b

return :: a -> DeterminedBy parameter a

Monad (OrInsteadFirst otherThing)

InsteadFirst other >>= _ = InsteadFirst other
NotInsteadFirst a  >>= f = f a

Defined in Acme.Functors

Methods

(>>=) :: OrInsteadFirst otherThing a -> (a -> OrInsteadFirst otherThing b) -> OrInsteadFirst otherThing b

(>>) :: OrInsteadFirst otherThing a -> OrInsteadFirst otherThing b -> OrInsteadFirst otherThing b

return :: a -> OrInsteadFirst otherThing a

(Monoid a, Monoid b) => Monad ((,,) a b)

Since: base-4.14.0.0

Defined in GHC.Base

Methods

(>>=) :: (a, b, a0) -> (a0 -> (a, b, b0)) -> (a, b, b0)

(>>) :: (a, b, a0) -> (a, b, b0) -> (a, b, b0)

return :: a0 -> (a, b, a0)

Monad ((->) r :: Type -> Type)

Since: base-2.1

Defined in GHC.Base

Methods

(>>=) :: (r -> a) -> (a -> r -> b) -> r -> b

(>>) :: (r -> a) -> (r -> b) -> r -> b

return :: a -> r -> a

(Monoid a, Monoid b, Monoid c) => Monad ((,,,) a b c)

Since: base-4.14.0.0

Defined in GHC.Base

Methods

(>>=) :: (a, b, c, a0) -> (a0 -> (a, b, c, b0)) -> (a, b, c, b0)

(>>) :: (a, b, c, a0) -> (a, b, c, b0) -> (a, b, c, b0)

return :: a0 -> (a, b, c, a0)

class Eq a where

The Eq class defines equality (==) and inequality (/=). All the basic datatypes exported by the Prelude are instances of Eq, and Eq may be derived for any datatype whose constituents are also instances of Eq.

The Haskell Report defines no laws for Eq. However, == is customarily expected to implement an equivalence relationship where two values comparing equal are indistinguishable by "public" functions, with a "public" function being one not allowing to see implementation details. For example, for a type representing non-normalised natural numbers modulo 100, a "public" function doesn't make the difference between 1 and 201. It is expected to have the following properties:

Reflexivity

x == x = True

Symmetry

x == y = y == x

Transitivity

if x == y && y == z = True, then x == z = True

Substitutivity

if x == y = True and f is a "public" function whose return type is an instance of Eq, then f x == f y = True

Negation

x /= y = not (x == y)

Minimal complete definition: either == or /=.

Minimal complete definition

(==) | (/=)

Methods

(==) :: a -> a -> Bool infix 4

(/=) :: a -> a -> Bool infix 4

Instances

Eq Bool

Defined in GHC.Classes

Methods

(==) :: Bool -> Bool -> Bool

(/=) :: Bool -> Bool -> Bool

Eq Char

Defined in GHC.Classes

Methods

(==) :: Char -> Char -> Bool

(/=) :: Char -> Char -> Bool

Eq Double

Note that due to the presence of NaN, Double's Eq instance does not satisfy reflexivity.

>>> 0/0 == (0/0 :: Double)
False

Also note that Double's Eq instance does not satisfy substitutivity:

>>> 0 == (-0 :: Double)
True
>>> recip 0 == recip (-0 :: Double)
False

Defined in GHC.Classes

Methods

(==) :: Double -> Double -> Bool

(/=) :: Double -> Double -> Bool

Eq Float

Note that due to the presence of NaN, Float's Eq instance does not satisfy reflexivity.

>>> 0/0 == (0/0 :: Float)
False

Also note that Float's Eq instance does not satisfy substitutivity:

>>> 0 == (-0 :: Float)
True
>>> recip 0 == recip (-0 :: Float)
False

Defined in GHC.Classes

Methods

(==) :: Float -> Float -> Bool

(/=) :: Float -> Float -> Bool

Eq Int

Defined in GHC.Classes

Methods

(==) :: Int -> Int -> Bool

(/=) :: Int -> Int -> Bool

Eq Integer

Defined in GHC.Integer.Type

Methods

(==) :: Integer -> Integer -> Bool

(/=) :: Integer -> Integer -> Bool

Eq Natural

Since: base-4.8.0.0

Defined in GHC.Natural

Methods

(==) :: Natural -> Natural -> Bool

(/=) :: Natural -> Natural -> Bool

Eq Ordering

Defined in GHC.Classes

Methods

(==) :: Ordering -> Ordering -> Bool

(/=) :: Ordering -> Ordering -> Bool

Eq Word

Defined in GHC.Classes

Methods

(==) :: Word -> Word -> Bool

(/=) :: Word -> Word -> Bool

Eq ()

Defined in GHC.Classes

Methods

(==) :: () -> () -> Bool

(/=) :: () -> () -> Bool

Eq TyCon

Defined in GHC.Classes

Methods

(==) :: TyCon -> TyCon -> Bool

(/=) :: TyCon -> TyCon -> Bool

Eq Module

Defined in GHC.Classes

Methods

(==) :: Module -> Module -> Bool

(/=) :: Module -> Module -> Bool

Eq TrName

Defined in GHC.Classes

Methods

(==) :: TrName -> TrName -> Bool

(/=) :: TrName -> TrName -> Bool

Eq SrcLoc

Since: base-4.9.0.0

Defined in GHC.Stack.Types

Methods

(==) :: SrcLoc -> SrcLoc -> Bool

(/=) :: SrcLoc -> SrcLoc -> Bool

Eq BigNat

Defined in GHC.Integer.Type

Methods

(==) :: BigNat -> BigNat -> Bool

(/=) :: BigNat -> BigNat -> Bool

Eq a => Eq [a]

Defined in GHC.Classes

Methods

(==) :: [a] -> [a] -> Bool

(/=) :: [a] -> [a] -> Bool

Eq a => Eq (Maybe a)

Since: base-2.1

Defined in GHC.Maybe

Methods

(==) :: Maybe a -> Maybe a -> Bool

(/=) :: Maybe a -> Maybe a -> Bool

Eq a => Eq (Ratio a)

Since: base-2.1

Defined in GHC.Real

Methods

(==) :: Ratio a -> Ratio a -> Bool

(/=) :: Ratio a -> Ratio a -> Bool

Eq a => Eq (Min a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

(==) :: Min a -> Min a -> Bool

(/=) :: Min a -> Min a -> Bool

Eq a => Eq (Max a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

(==) :: Max a -> Max a -> Bool

(/=) :: Max a -> Max a -> Bool

Eq a => Eq (First a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

(==) :: First a -> First a -> Bool

(/=) :: First a -> First a -> Bool

Eq a => Eq (Last a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

(==) :: Last a -> Last a -> Bool

(/=) :: Last a -> Last a -> Bool

Eq m => Eq (WrappedMonoid m)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

(==) :: WrappedMonoid m -> WrappedMonoid m -> Bool

(/=) :: WrappedMonoid m -> WrappedMonoid m -> Bool

Eq a => Eq (Option a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

(==) :: Option a -> Option a -> Bool

(/=) :: Option a -> Option a -> Bool

Eq a => Eq (ZipList a)

Since: base-4.7.0.0

Defined in Control.Applicative

Methods

(==) :: ZipList a -> ZipList a -> Bool

(/=) :: ZipList a -> ZipList a -> Bool

Eq a => Eq (NonEmpty a)

Since: base-4.9.0.0

Defined in GHC.Base

Methods

(==) :: NonEmpty a -> NonEmpty a -> Bool

(/=) :: NonEmpty a -> NonEmpty a -> Bool

Eq a => Eq (OneOrMore a)

Defined in Acme.Functors

Methods

(==) :: OneOrMore a -> OneOrMore a -> Bool

(/=) :: OneOrMore a -> OneOrMore a -> Bool

Eq a => Eq (AnyNumberOf a)

Defined in Acme.Functors

Methods

(==) :: AnyNumberOf a -> AnyNumberOf a -> Bool

(/=) :: AnyNumberOf a -> AnyNumberOf a -> Bool

Eq a => Eq (Two a)

Defined in Acme.Functors

Methods

(==) :: Two a -> Two a -> Bool

(/=) :: Two a -> Two a -> Bool

Eq a => Eq (OrNot a)

Defined in Acme.Functors

Methods

(==) :: OrNot a -> OrNot a -> Bool

(/=) :: OrNot a -> OrNot a -> Bool

Eq a => Eq (LiftedButWhy a)

Defined in Acme.Functors

Methods

(==) :: LiftedButWhy a -> LiftedButWhy a -> Bool

(/=) :: LiftedButWhy a -> LiftedButWhy a -> Bool

(Eq a, Eq b) => Eq (a, b)

Defined in GHC.Classes

Methods

(==) :: (a, b) -> (a, b) -> Bool

(/=) :: (a, b) -> (a, b) -> Bool

Eq a => Eq (Arg a b)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

(==) :: Arg a b -> Arg a b -> Bool

(/=) :: Arg a b -> Arg a b -> Bool

(Eq a, Eq otherThing) => Eq (OrInsteadFirst otherThing a)

Defined in Acme.Functors

Methods

(==) :: OrInsteadFirst otherThing a -> OrInsteadFirst otherThing a -> Bool

(/=) :: OrInsteadFirst otherThing a -> OrInsteadFirst otherThing a -> Bool

(Eq a, Eq otherThing) => Eq (OrInstead otherThing a)

Defined in Acme.Functors

Methods

(==) :: OrInstead otherThing a -> OrInstead otherThing a -> Bool

(/=) :: OrInstead otherThing a -> OrInstead otherThing a -> Bool

(Eq a, Eq extraThing) => Eq (Also extraThing a)

Defined in Acme.Functors

Methods

(==) :: Also extraThing a -> Also extraThing a -> Bool

(/=) :: Also extraThing a -> Also extraThing a -> Bool

(Eq a, Eq b, Eq c) => Eq (a, b, c)

Defined in GHC.Classes

Methods

(==) :: (a, b, c) -> (a, b, c) -> Bool

(/=) :: (a, b, c) -> (a, b, c) -> Bool

(Eq a, Eq b, Eq c, Eq d) => Eq (a, b, c, d)

Defined in GHC.Classes

Methods

(==) :: (a, b, c, d) -> (a, b, c, d) -> Bool

(/=) :: (a, b, c, d) -> (a, b, c, d) -> Bool

(Eq a, Eq b, Eq c, Eq d, Eq e) => Eq (a, b, c, d, e)

Defined in GHC.Classes

Methods

(==) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool

(/=) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f) => Eq (a, b, c, d, e, f)

Defined in GHC.Classes

Methods

(==) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool

(/=) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g) => Eq (a, b, c, d, e, f, g)

Defined in GHC.Classes

Methods

(==) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool

(/=) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h) => Eq (a, b, c, d, e, f, g, h)

Defined in GHC.Classes

Methods

(==) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool

(/=) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i) => Eq (a, b, c, d, e, f, g, h, i)

Defined in GHC.Classes

Methods

(==) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool

(/=) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j) => Eq (a, b, c, d, e, f, g, h, i, j)

Defined in GHC.Classes

Methods

(==) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool

(/=) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k) => Eq (a, b, c, d, e, f, g, h, i, j, k)

Defined in GHC.Classes

Methods

(==) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool

(/=) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l) => Eq (a, b, c, d, e, f, g, h, i, j, k, l)

Defined in GHC.Classes

Methods

(==) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool

(/=) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m)

Defined in GHC.Classes

Methods

(==) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool

(/=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m, Eq n) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m, n)

Defined in GHC.Classes

Methods

(==) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool

(/=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m, Eq n, Eq o) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o)

Defined in GHC.Classes

Methods

(==) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool

(/=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool

class Functor (f :: Type -> Type) where

A type f is a Functor if it provides a function fmap which, given any types a and b lets you apply any function from (a -> b) to turn an f a into an f b, preserving the structure of f. Furthermore f needs to adhere to the following:

Identity

fmap id == id

Composition

fmap (f . g) == fmap f . fmap g

Note, that the second law follows from the free theorem of the type fmap and the first law, so you need only check that the former condition holds.

Minimal complete definition

fmap

Methods

fmap :: (a -> b) -> f a -> f b

Using ApplicativeDo: 'fmap f as' can be understood as the do expression

do a <- as
   pure (f a)

with an inferred Functor constraint.

(<$) :: a -> f b -> f a infixl 4

Replace all locations in the input with the same value. The default definition is fmap . const, but this may be overridden with a more efficient version.

Using ApplicativeDo: 'a <$ bs' can be understood as the do expression

do bs
   pure a

with an inferred Functor constraint.

Instances

Functor []

Since: base-2.1

Defined in GHC.Base

Methods

fmap :: (a -> b) -> [a] -> [b]

(<$) :: a -> [b] -> [a]

Functor Maybe

Since: base-2.1

Defined in GHC.Base

Methods

fmap :: (a -> b) -> Maybe a -> Maybe b

(<$) :: a -> Maybe b -> Maybe a

Functor IO

Since: base-2.1

Defined in GHC.Base

Methods

fmap :: (a -> b) -> IO a -> IO b

(<$) :: a -> IO b -> IO a

Functor Min

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

fmap :: (a -> b) -> Min a -> Min b

(<$) :: a -> Min b -> Min a

Functor Max

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

fmap :: (a -> b) -> Max a -> Max b

(<$) :: a -> Max b -> Max a

Functor First

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

fmap :: (a -> b) -> First a -> First b

(<$) :: a -> First b -> First a

Functor Last

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

fmap :: (a -> b) -> Last a -> Last b

(<$) :: a -> Last b -> Last a

Functor Option

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

fmap :: (a -> b) -> Option a -> Option b

(<$) :: a -> Option b -> Option a

Functor ZipList

Since: base-2.1

Defined in Control.Applicative

Methods

fmap :: (a -> b) -> ZipList a -> ZipList b

(<$) :: a -> ZipList b -> ZipList a

Functor NonEmpty

Since: base-4.9.0.0

Defined in GHC.Base

Methods

fmap :: (a -> b) -> NonEmpty a -> NonEmpty b

(<$) :: a -> NonEmpty b -> NonEmpty a

Functor OneOrMore

Defined in Acme.Functors

Methods

fmap :: (a -> b) -> OneOrMore a -> OneOrMore b

(<$) :: a -> OneOrMore b -> OneOrMore a

Functor AnyNumberOf

Defined in Acme.Functors

Methods

fmap :: (a -> b) -> AnyNumberOf a -> AnyNumberOf b

(<$) :: a -> AnyNumberOf b -> AnyNumberOf a

Functor Two

Defined in Acme.Functors

Methods

fmap :: (a -> b) -> Two a -> Two b

(<$) :: a -> Two b -> Two a

Functor OrNot

Defined in Acme.Functors

Methods

fmap :: (a -> b) -> OrNot a -> OrNot b

(<$) :: a -> OrNot b -> OrNot a

Functor LiftedButWhy

Defined in Acme.Functors

Methods

fmap :: (a -> b) -> LiftedButWhy a -> LiftedButWhy b

(<$) :: a -> LiftedButWhy b -> LiftedButWhy a

Functor ((,) a)

Since: base-2.1

Defined in GHC.Base

Methods

fmap :: (a0 -> b) -> (a, a0) -> (a, b)

(<$) :: a0 -> (a, b) -> (a, a0)

Functor (Arg a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

fmap :: (a0 -> b) -> Arg a a0 -> Arg a b

(<$) :: a0 -> Arg a b -> Arg a a0

Monad m => Functor (WrappedMonad m)

Since: base-2.1

Defined in Control.Applicative

Methods

fmap :: (a -> b) -> WrappedMonad m a -> WrappedMonad m b

(<$) :: a -> WrappedMonad m b -> WrappedMonad m a

Functor (DeterminedBy parameter)

Defined in Acme.Functors

Methods

fmap :: (a -> b) -> DeterminedBy parameter a -> DeterminedBy parameter b

(<$) :: a -> DeterminedBy parameter b -> DeterminedBy parameter a

Functor (OrInsteadFirst otherThing)

Defined in Acme.Functors

Methods

fmap :: (a -> b) -> OrInsteadFirst otherThing a -> OrInsteadFirst otherThing b

(<$) :: a -> OrInsteadFirst otherThing b -> OrInsteadFirst otherThing a

Functor (OrInstead otherThing)

Defined in Acme.Functors

Methods

fmap :: (a -> b) -> OrInstead otherThing a -> OrInstead otherThing b

(<$) :: a -> OrInstead otherThing b -> OrInstead otherThing a

Functor (Also extraThing)

Defined in Acme.Functors

Methods

fmap :: (a -> b) -> Also extraThing a -> Also extraThing b

(<$) :: a -> Also extraThing b -> Also extraThing a

Functor ((,,) a b)

Since: base-4.14.0.0

Defined in GHC.Base

Methods

fmap :: (a0 -> b0) -> (a, b, a0) -> (a, b, b0)

(<$) :: a0 -> (a, b, b0) -> (a, b, a0)

Arrow a => Functor (WrappedArrow a b)

Since: base-2.1

Defined in Control.Applicative

Methods

fmap :: (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0

(<$) :: a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0

Functor ((->) r :: Type -> Type)

Since: base-2.1

Defined in GHC.Base

Methods

fmap :: (a -> b) -> (r -> a) -> r -> b

(<$) :: a -> (r -> b) -> r -> a

Functor ((,,,) a b c)

Since: base-4.14.0.0

Defined in GHC.Base

Methods

fmap :: (a0 -> b0) -> (a, b, c, a0) -> (a, b, c, b0)

(<$) :: a0 -> (a, b, c, b0) -> (a, b, c, a0)

class Semigroup a => Monoid a where

Methods

mempty :: a

Instances

Monoid a => Monoid (OneOrMore a)

mempty = OneOrMore mempty ActuallyNone

Defined in Acme.Functors

Methods

mempty :: OneOrMore a

Monoid a => Monoid (AnyNumberOf a)

mempty = mempty ~~ mempty

Defined in Acme.Functors

Methods

mempty :: AnyNumberOf a

Monoid a => Monoid (Two a)

mempty = Two mempty mempty

Defined in Acme.Functors

Methods

mempty :: Two a

Monoid a => Monoid (OrNot a)

mempty = ActuallyYes mempty

Defined in Acme.Functors

Methods

mempty :: OrNot a

Monoid a => Monoid (LiftedButWhy a)

mempty = LiftedButWhy mempty

Defined in Acme.Functors

Methods

mempty :: LiftedButWhy a

Monoid a => Monoid (DeterminedBy parameter a)

mempty = Determination (\_ -> mempty)

Defined in Acme.Functors

Methods

mempty :: DeterminedBy parameter a

(Semigroup otherThing, Monoid a) => Monoid (OrInsteadFirst otherThing a)

mempty = NotInsteadFirst mempty

Defined in Acme.Functors

Methods

mempty :: OrInsteadFirst otherThing a

(Semigroup otherThing, Monoid a) => Monoid (OrInstead otherThing a)

Defined in Acme.Functors

Methods

mempty :: OrInstead otherThing a

(Monoid extraThing, Monoid a) => Monoid (Also extraThing a)

mempty = Also mempty mempty

Defined in Acme.Functors

Methods

mempty :: Also extraThing a

class Semigroup a where

The class of semigroups (types with an associative binary operation).

Instances should satisfy the following:

Associativity

x <> (y <> z) = (x <> y) <> z

Since: base-4.9.0.0

Minimal complete definition

(<>)

Methods

(<>) :: a -> a -> a infixr 6

An associative operation.

>>> [1,2,3] <> [4,5,6]
[1,2,3,4,5,6]

sconcat :: NonEmpty a -> a

Reduce a non-empty list with <>

The default definition should be sufficient, but this can be overridden for efficiency.

>>> import Data.List.NonEmpty
>>> sconcat $ "Hello" :| [" ", "Haskell", "!"]
"Hello Haskell!"

stimes :: Integral b => b -> a -> a

Repeat a value n times.

Given that this works on a Semigroup it is allowed to fail if you request 0 or fewer repetitions, and the default definition will do so.

By making this a member of the class, idempotent semigroups and monoids can upgrade this to execute in \(\mathcal{O}(1)\) by picking stimes = stimesIdempotent or stimes = stimesIdempotentMonoid respectively.

>>> stimes 4 [1]
[1,1,1,1]

Instances

Semigroup Ordering

Since: base-4.9.0.0

Defined in GHC.Base

Methods

(<>) :: Ordering -> Ordering -> Ordering

sconcat :: NonEmpty Ordering -> Ordering

stimes :: Integral b => b -> Ordering -> Ordering

Semigroup ()

Since: base-4.9.0.0

Defined in GHC.Base

Methods

(<>) :: () -> () -> ()

sconcat :: NonEmpty () -> ()

stimes :: Integral b => b -> () -> ()

Semigroup [a]

Since: base-4.9.0.0

Defined in GHC.Base

Methods

(<>) :: [a] -> [a] -> [a]

sconcat :: NonEmpty [a] -> [a]

stimes :: Integral b => b -> [a] -> [a]

Semigroup a => Semigroup (Maybe a)

Since: base-4.9.0.0

Defined in GHC.Base

Methods

(<>) :: Maybe a -> Maybe a -> Maybe a

sconcat :: NonEmpty (Maybe a) -> Maybe a

stimes :: Integral b => b -> Maybe a -> Maybe a

Semigroup a => Semigroup (IO a)

Since: base-4.10.0.0

Defined in GHC.Base

Methods

(<>) :: IO a -> IO a -> IO a

sconcat :: NonEmpty (IO a) -> IO a

stimes :: Integral b => b -> IO a -> IO a

Ord a => Semigroup (Min a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

(<>) :: Min a -> Min a -> Min a

sconcat :: NonEmpty (Min a) -> Min a

stimes :: Integral b => b -> Min a -> Min a

Ord a => Semigroup (Max a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

(<>) :: Max a -> Max a -> Max a

sconcat :: NonEmpty (Max a) -> Max a

stimes :: Integral b => b -> Max a -> Max a

Semigroup (First a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

(<>) :: First a -> First a -> First a

sconcat :: NonEmpty (First a) -> First a

stimes :: Integral b => b -> First a -> First a

Semigroup (Last a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

(<>) :: Last a -> Last a -> Last a

sconcat :: NonEmpty (Last a) -> Last a

stimes :: Integral b => b -> Last a -> Last a

Monoid m => Semigroup (WrappedMonoid m)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

(<>) :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m

sconcat :: NonEmpty (WrappedMonoid m) -> WrappedMonoid m

stimes :: Integral b => b -> WrappedMonoid m -> WrappedMonoid m

Semigroup a => Semigroup (Option a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

(<>) :: Option a -> Option a -> Option a

sconcat :: NonEmpty (Option a) -> Option a

stimes :: Integral b => b -> Option a -> Option a

Semigroup (NonEmpty a)

Since: base-4.9.0.0

Defined in GHC.Base

Methods

(<>) :: NonEmpty a -> NonEmpty a -> NonEmpty a

sconcat :: NonEmpty (NonEmpty a) -> NonEmpty a

stimes :: Integral b => b -> NonEmpty a -> NonEmpty a

Semigroup a => Semigroup (OneOrMore a)

OneOrMore a more <> OneOrMore a' more' =
    OneOrMore a (more <> OneAndMaybeMore a' more')

Defined in Acme.Functors

Methods

(<>) :: OneOrMore a -> OneOrMore a -> OneOrMore a

sconcat :: NonEmpty (OneOrMore a) -> OneOrMore a

stimes :: Integral b => b -> OneOrMore a -> OneOrMore a

Semigroup a => Semigroup (AnyNumberOf a)

The operation of combining some number of a with some other number of a is sometimes referred to as zipping.

OneAndMaybeMore x xs <> OneAndMaybeMore y ys =
    OneAndMaybeMore (x <> y) (xs <> ys)
_ <> _ = ActuallyNone

Defined in Acme.Functors

Methods

(<>) :: AnyNumberOf a -> AnyNumberOf a -> AnyNumberOf a

sconcat :: NonEmpty (AnyNumberOf a) -> AnyNumberOf a

stimes :: Integral b => b -> AnyNumberOf a -> AnyNumberOf a

Semigroup a => Semigroup (Two a)

Two x y <> Two x' y' = Two (x <> x') (y <> y')

Defined in Acme.Functors

Methods

(<>) :: Two a -> Two a -> Two a

sconcat :: NonEmpty (Two a) -> Two a

stimes :: Integral b => b -> Two a -> Two a

Semigroup a => Semigroup (OrNot a)

If you have value a that may not actually be there, and another value a' that might not actually be there, the lifted semigroup operation (<>) gives you a <> a' only if both of them are actually there.

ActuallyYes a <> ActuallyYes a' = ActuallyYes (a <> a')
_             <> _              = Nope

Defined in Acme.Functors

Methods

(<>) :: OrNot a -> OrNot a -> OrNot a

sconcat :: NonEmpty (OrNot a) -> OrNot a

stimes :: Integral b => b -> OrNot a -> OrNot a

Semigroup a => Semigroup (LiftedButWhy a)

LiftedButWhy x <> LiftedButWhy y = LiftedButWhy (x <> y)

Defined in Acme.Functors

Methods

(<>) :: LiftedButWhy a -> LiftedButWhy a -> LiftedButWhy a

sconcat :: NonEmpty (LiftedButWhy a) -> LiftedButWhy a

stimes :: Integral b => b -> LiftedButWhy a -> LiftedButWhy a

Semigroup b => Semigroup (a -> b)

Since: base-4.9.0.0

Defined in GHC.Base

Methods

(<>) :: (a -> b) -> (a -> b) -> a -> b

sconcat :: NonEmpty (a -> b) -> a -> b

stimes :: Integral b0 => b0 -> (a -> b) -> a -> b

(Semigroup a, Semigroup b) => Semigroup (a, b)

Since: base-4.9.0.0

Defined in GHC.Base

Methods

(<>) :: (a, b) -> (a, b) -> (a, b)

sconcat :: NonEmpty (a, b) -> (a, b)

stimes :: Integral b0 => b0 -> (a, b) -> (a, b)

Semigroup a => Semigroup (DeterminedBy parameter a)

Determination f <> Determination g = Determination (\x -> f x <> g x)

Defined in Acme.Functors

Methods

(<>) :: DeterminedBy parameter a -> DeterminedBy parameter a -> DeterminedBy parameter a

sconcat :: NonEmpty (DeterminedBy parameter a) -> DeterminedBy parameter a

stimes :: Integral b => b -> DeterminedBy parameter a -> DeterminedBy parameter a

(Semigroup otherThing, Semigroup a) => Semigroup (OrInsteadFirst otherThing a)

NotInsteadFirst a  <> NotInsteadFirst a' = NotInsteadFirst (a <> a')
InsteadFirst other <> _                  = InsteadFirst other
_                  <> InsteadFirst other = InsteadFirst other

Defined in Acme.Functors

Methods

(<>) :: OrInsteadFirst otherThing a -> OrInsteadFirst otherThing a -> OrInsteadFirst otherThing a

sconcat :: NonEmpty (OrInsteadFirst otherThing a) -> OrInsteadFirst otherThing a

stimes :: Integral b => b -> OrInsteadFirst otherThing a -> OrInsteadFirst otherThing a

(Semigroup otherThing, Semigroup a) => Semigroup (OrInstead otherThing a)

NotInstead a   <> NotInstead a'  = NotInstead (a <> a')
Instead other1 <> Instead other2 = Instead (other1 <> other2)
Instead other  <> _              = Instead other
_              <> Instead other  = Instead other

Defined in Acme.Functors

Methods

(<>) :: OrInstead otherThing a -> OrInstead otherThing a -> OrInstead otherThing a

sconcat :: NonEmpty (OrInstead otherThing a) -> OrInstead otherThing a

stimes :: Integral b => b -> OrInstead otherThing a -> OrInstead otherThing a

(Semigroup extraThing, Semigroup a) => Semigroup (Also extraThing a)

(a `Also` extra1) <> (a' `Also` extra2) = (a <> a')
                                          `Also` (extra1 <> extra2)

Defined in Acme.Functors

Methods

(<>) :: Also extraThing a -> Also extraThing a -> Also extraThing a

sconcat :: NonEmpty (Also extraThing a) -> Also extraThing a

stimes :: Integral b => b -> Also extraThing a -> Also extraThing a

(Semigroup a, Semigroup b, Semigroup c) => Semigroup (a, b, c)

Since: base-4.9.0.0

Defined in GHC.Base

Methods

(<>) :: (a, b, c) -> (a, b, c) -> (a, b, c)

sconcat :: NonEmpty (a, b, c) -> (a, b, c)

stimes :: Integral b0 => b0 -> (a, b, c) -> (a, b, c)

(Semigroup a, Semigroup b, Semigroup c, Semigroup d) => Semigroup (a, b, c, d)

Since: base-4.9.0.0

Defined in GHC.Base

Methods

(<>) :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d)

sconcat :: NonEmpty (a, b, c, d) -> (a, b, c, d)

stimes :: Integral b0 => b0 -> (a, b, c, d) -> (a, b, c, d)

(Semigroup a, Semigroup b, Semigroup c, Semigroup d, Semigroup e) => Semigroup (a, b, c, d, e)

Since: base-4.9.0.0

Defined in GHC.Base

Methods

(<>) :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e)

sconcat :: NonEmpty (a, b, c, d, e) -> (a, b, c, d, e)

stimes :: Integral b0 => b0 -> (a, b, c, d, e) -> (a, b, c, d, e)

class Show a where

Conversion of values to readable Strings.

Derived instances of Show have the following properties, which are compatible with derived instances of Read:

• The result of show is a syntactically correct Haskell expression containing only constants, given the fixity declarations in force at the point where the type is declared. It contains only the constructor names defined in the data type, parentheses, and spaces. When labelled constructor fields are used, braces, commas, field names, and equal signs are also used.
• If the constructor is defined to be an infix operator, then showsPrec will produce infix applications of the constructor.
• the representation will be enclosed in parentheses if the precedence of the top-level constructor in x is less than d (associativity is ignored). Thus, if d is 0 then the result is never surrounded in parentheses; if d is 11 it is always surrounded in parentheses, unless it is an atomic expression.
• If the constructor is defined using record syntax, then show will produce the record-syntax form, with the fields given in the same order as the original declaration.

For example, given the declarations

infixr 5 :^:
data Tree a =  Leaf a  |  Tree a :^: Tree a

the derived instance of Show is equivalent to

instance (Show a) => Show (Tree a) where

       showsPrec d (Leaf m) = showParen (d > app_prec) $
            showString "Leaf " . showsPrec (app_prec+1) m
         where app_prec = 10

       showsPrec d (u :^: v) = showParen (d > up_prec) $
            showsPrec (up_prec+1) u .
            showString " :^: "      .
            showsPrec (up_prec+1) v
         where up_prec = 5

Note that right-associativity of :^: is ignored. For example,

• show (Leaf 1 :^: Leaf 2 :^: Leaf 3) produces the string "Leaf 1 :^: (Leaf 2 :^: Leaf 3)".

Minimal complete definition

showsPrec | show

Methods

showsPrec

Arguments

:: Int

the operator precedence of the enclosing context (a number from 0 to 11). Function application has precedence 10.

-> a

the value to be converted to a String

-> ShowS

Convert a value to a readable String.

showsPrec should satisfy the law

showsPrec d x r ++ s  ==  showsPrec d x (r ++ s)

Derived instances of Read and Show satisfy the following:

• (x,"") is an element of (readsPrec d (showsPrec d x "")).

That is, readsPrec parses the string produced by showsPrec, and delivers the value that showsPrec started with.

show :: a -> String

A specialised variant of showsPrec, using precedence context zero, and returning an ordinary String.

showList :: [a] -> ShowS

The method showList is provided to allow the programmer to give a specialised way of showing lists of values. For example, this is used by the predefined Show instance of the Char type, where values of type String should be shown in double quotes, rather than between square brackets.

Instances

Show Bool

Since: base-2.1

Defined in GHC.Show

Methods

showsPrec :: Int -> Bool -> ShowS

show :: Bool -> String

showList :: [Bool] -> ShowS

Show Char

Since: base-2.1

Defined in GHC.Show

Methods

showsPrec :: Int -> Char -> ShowS

show :: Char -> String

showList :: [Char] -> ShowS

Show Int

Since: base-2.1

Defined in GHC.Show

Methods

showsPrec :: Int -> Int -> ShowS

show :: Int -> String

showList :: [Int] -> ShowS

Show Integer

Since: base-2.1

Defined in GHC.Show

Methods

showsPrec :: Int -> Integer -> ShowS

show :: Integer -> String

showList :: [Integer] -> ShowS

Show Natural

Since: base-4.8.0.0

Defined in GHC.Show

Methods

showsPrec :: Int -> Natural -> ShowS

show :: Natural -> String

showList :: [Natural] -> ShowS

Show Ordering

Since: base-2.1

Defined in GHC.Show

Methods

showsPrec :: Int -> Ordering -> ShowS

show :: Ordering -> String

showList :: [Ordering] -> ShowS

Show Word

Since: base-2.1

Defined in GHC.Show

Methods

showsPrec :: Int -> Word -> ShowS

show :: Word -> String

showList :: [Word] -> ShowS

Show RuntimeRep

Since: base-4.11.0.0

Defined in GHC.Show

Methods

showsPrec :: Int -> RuntimeRep -> ShowS

show :: RuntimeRep -> String

showList :: [RuntimeRep] -> ShowS

Show VecCount

Since: base-4.11.0.0

Defined in GHC.Show

Methods

showsPrec :: Int -> VecCount -> ShowS

show :: VecCount -> String

showList :: [VecCount] -> ShowS

Show VecElem

Since: base-4.11.0.0

Defined in GHC.Show

Methods

showsPrec :: Int -> VecElem -> ShowS

show :: VecElem -> String

showList :: [VecElem] -> ShowS

Show CallStack

Since: base-4.9.0.0

Defined in GHC.Show

Methods

showsPrec :: Int -> CallStack -> ShowS

show :: CallStack -> String

showList :: [CallStack] -> ShowS

Show ()

Since: base-2.1

Defined in GHC.Show

Methods

showsPrec :: Int -> () -> ShowS

show :: () -> String

showList :: [()] -> ShowS

Show TyCon

Since: base-2.1

Defined in GHC.Show

Methods

showsPrec :: Int -> TyCon -> ShowS

show :: TyCon -> String

showList :: [TyCon] -> ShowS

Show Module

Since: base-4.9.0.0

Defined in GHC.Show

Methods

showsPrec :: Int -> Module -> ShowS

show :: Module -> String

showList :: [Module] -> ShowS

Show TrName

Since: base-4.9.0.0

Defined in GHC.Show

Methods

showsPrec :: Int -> TrName -> ShowS

show :: TrName -> String

showList :: [TrName] -> ShowS

Show KindRep

Defined in GHC.Show

Methods

showsPrec :: Int -> KindRep -> ShowS

show :: KindRep -> String

showList :: [KindRep] -> ShowS

Show TypeLitSort

Since: base-4.11.0.0

Defined in GHC.Show

Methods

showsPrec :: Int -> TypeLitSort -> ShowS

show :: TypeLitSort -> String

showList :: [TypeLitSort] -> ShowS

Show SrcLoc

Since: base-4.9.0.0

Defined in GHC.Show

Methods

showsPrec :: Int -> SrcLoc -> ShowS

show :: SrcLoc -> String

showList :: [SrcLoc] -> ShowS

Show a => Show [a]

Since: base-2.1

Defined in GHC.Show

Methods

showsPrec :: Int -> [a] -> ShowS

show :: [a] -> String

showList :: [[a]] -> ShowS

Show a => Show (Maybe a)

Since: base-2.1

Defined in GHC.Show

Methods

showsPrec :: Int -> Maybe a -> ShowS

show :: Maybe a -> String

showList :: [Maybe a] -> ShowS

Show a => Show (Ratio a)

Since: base-2.0.1

Defined in GHC.Real

Methods

showsPrec :: Int -> Ratio a -> ShowS

show :: Ratio a -> String

showList :: [Ratio a] -> ShowS

Show a => Show (Min a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

showsPrec :: Int -> Min a -> ShowS

show :: Min a -> String

showList :: [Min a] -> ShowS

Show a => Show (Max a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

showsPrec :: Int -> Max a -> ShowS

show :: Max a -> String

showList :: [Max a] -> ShowS

Show a => Show (First a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

showsPrec :: Int -> First a -> ShowS

show :: First a -> String

showList :: [First a] -> ShowS

Show a => Show (Last a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

showsPrec :: Int -> Last a -> ShowS

show :: Last a -> String

showList :: [Last a] -> ShowS

Show m => Show (WrappedMonoid m)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

showsPrec :: Int -> WrappedMonoid m -> ShowS

show :: WrappedMonoid m -> String

showList :: [WrappedMonoid m] -> ShowS

Show a => Show (Option a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

showsPrec :: Int -> Option a -> ShowS

show :: Option a -> String

showList :: [Option a] -> ShowS

Show a => Show (ZipList a)

Since: base-4.7.0.0

Defined in Control.Applicative

Methods

showsPrec :: Int -> ZipList a -> ShowS

show :: ZipList a -> String

showList :: [ZipList a] -> ShowS

Show a => Show (NonEmpty a)

Since: base-4.11.0.0

Defined in GHC.Show

Methods

showsPrec :: Int -> NonEmpty a -> ShowS

show :: NonEmpty a -> String

showList :: [NonEmpty a] -> ShowS

Show a => Show (OneOrMore a)

Defined in Acme.Functors

Methods

showsPrec :: Int -> OneOrMore a -> ShowS

show :: OneOrMore a -> String

showList :: [OneOrMore a] -> ShowS

Show a => Show (AnyNumberOf a)

Defined in Acme.Functors

Methods

showsPrec :: Int -> AnyNumberOf a -> ShowS

show :: AnyNumberOf a -> String

showList :: [AnyNumberOf a] -> ShowS

Show a => Show (Two a)

Defined in Acme.Functors

Methods

showsPrec :: Int -> Two a -> ShowS

show :: Two a -> String

showList :: [Two a] -> ShowS

Show a => Show (OrNot a)

Defined in Acme.Functors

Methods

showsPrec :: Int -> OrNot a -> ShowS

show :: OrNot a -> String

showList :: [OrNot a] -> ShowS

Show a => Show (LiftedButWhy a)

Defined in Acme.Functors

Methods

showsPrec :: Int -> LiftedButWhy a -> ShowS

show :: LiftedButWhy a -> String

showList :: [LiftedButWhy a] -> ShowS

(Show a, Show b) => Show (a, b)

Since: base-2.1

Defined in GHC.Show

Methods

showsPrec :: Int -> (a, b) -> ShowS

show :: (a, b) -> String

showList :: [(a, b)] -> ShowS

(Show a, Show b) => Show (Arg a b)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

showsPrec :: Int -> Arg a b -> ShowS

show :: Arg a b -> String

showList :: [Arg a b] -> ShowS

(Show a, Show otherThing) => Show (OrInsteadFirst otherThing a)

Defined in Acme.Functors

Methods

showsPrec :: Int -> OrInsteadFirst otherThing a -> ShowS

show :: OrInsteadFirst otherThing a -> String

showList :: [OrInsteadFirst otherThing a] -> ShowS

(Show a, Show otherThing) => Show (OrInstead otherThing a)

Defined in Acme.Functors

Methods

showsPrec :: Int -> OrInstead otherThing a -> ShowS

show :: OrInstead otherThing a -> String

showList :: [OrInstead otherThing a] -> ShowS

(Show a, Show extraThing) => Show (Also extraThing a)

Defined in Acme.Functors

Methods

showsPrec :: Int -> Also extraThing a -> ShowS

show :: Also extraThing a -> String

showList :: [Also extraThing a] -> ShowS

(Show a, Show b, Show c) => Show (a, b, c)

Since: base-2.1

Defined in GHC.Show

Methods

showsPrec :: Int -> (a, b, c) -> ShowS

show :: (a, b, c) -> String

showList :: [(a, b, c)] -> ShowS

(Show a, Show b, Show c, Show d) => Show (a, b, c, d)

Since: base-2.1

Defined in GHC.Show

Methods

showsPrec :: Int -> (a, b, c, d) -> ShowS

show :: (a, b, c, d) -> String

showList :: [(a, b, c, d)] -> ShowS

(Show a, Show b, Show c, Show d, Show e) => Show (a, b, c, d, e)

Since: base-2.1

Defined in GHC.Show

Methods

showsPrec :: Int -> (a, b, c, d, e) -> ShowS

show :: (a, b, c, d, e) -> String

showList :: [(a, b, c, d, e)] -> ShowS

(Show a, Show b, Show c, Show d, Show e, Show f) => Show (a, b, c, d, e, f)

Since: base-2.1

Defined in GHC.Show

Methods

showsPrec :: Int -> (a, b, c, d, e, f) -> ShowS

show :: (a, b, c, d, e, f) -> String

showList :: [(a, b, c, d, e, f)] -> ShowS

(Show a, Show b, Show c, Show d, Show e, Show f, Show g) => Show (a, b, c, d, e, f, g)

Since: base-2.1

Defined in GHC.Show

Methods

showsPrec :: Int -> (a, b, c, d, e, f, g) -> ShowS

show :: (a, b, c, d, e, f, g) -> String

showList :: [(a, b, c, d, e, f, g)] -> ShowS

(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h) => Show (a, b, c, d, e, f, g, h)

Since: base-2.1

Defined in GHC.Show

Methods

showsPrec :: Int -> (a, b, c, d, e, f, g, h) -> ShowS

show :: (a, b, c, d, e, f, g, h) -> String

showList :: [(a, b, c, d, e, f, g, h)] -> ShowS

(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i) => Show (a, b, c, d, e, f, g, h, i)

Since: base-2.1

Defined in GHC.Show

Methods

showsPrec :: Int -> (a, b, c, d, e, f, g, h, i) -> ShowS

show :: (a, b, c, d, e, f, g, h, i) -> String

showList :: [(a, b, c, d, e, f, g, h, i)] -> ShowS

(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j) => Show (a, b, c, d, e, f, g, h, i, j)

Since: base-2.1

Defined in GHC.Show

Methods

showsPrec :: Int -> (a, b, c, d, e, f, g, h, i, j) -> ShowS

show :: (a, b, c, d, e, f, g, h, i, j) -> String

showList :: [(a, b, c, d, e, f, g, h, i, j)] -> ShowS

(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k) => Show (a, b, c, d, e, f, g, h, i, j, k)

Since: base-2.1

Defined in GHC.Show

Methods

showsPrec :: Int -> (a, b, c, d, e, f, g, h, i, j, k) -> ShowS

show :: (a, b, c, d, e, f, g, h, i, j, k) -> String

showList :: [(a, b, c, d, e, f, g, h, i, j, k)] -> ShowS

(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k, Show l) => Show (a, b, c, d, e, f, g, h, i, j, k, l)

Since: base-2.1

Defined in GHC.Show

Methods

showsPrec :: Int -> (a, b, c, d, e, f, g, h, i, j, k, l) -> ShowS

show :: (a, b, c, d, e, f, g, h, i, j, k, l) -> String

showList :: [(a, b, c, d, e, f, g, h, i, j, k, l)] -> ShowS

(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k, Show l, Show m) => Show (a, b, c, d, e, f, g, h, i, j, k, l, m)

Since: base-2.1

Defined in GHC.Show

Methods

showsPrec :: Int -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> ShowS

show :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> String

showList :: [(a, b, c, d, e, f, g, h, i, j, k, l, m)] -> ShowS

(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k, Show l, Show m, Show n) => Show (a, b, c, d, e, f, g, h, i, j, k, l, m, n)

Since: base-2.1

Defined in GHC.Show

Methods

showsPrec :: Int -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> ShowS

show :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> String

showList :: [(a, b, c, d, e, f, g, h, i, j, k, l, m, n)] -> ShowS

(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k, Show l, Show m, Show n, Show o) => Show (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o)

Since: base-2.1

Defined in GHC.Show

Methods

showsPrec :: Int -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> ShowS

show :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> String

showList :: [(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o)] -> ShowS