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Base.hs
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Base.hs
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{-
NOTA BENE: Do NOT use ($) anywhere in this module! The type of ($) is
slightly magical (it can return unlifted types), and it is wired in.
But, it is also *defined* in this module, with a non-magical type.
GHC gets terribly confused (and *hangs*) if you try to use ($) in this
module, because it has different types in different scenarios.
This is not a problem in general, because the type ($), being wired in, is not
written out to the interface file, so importing files don't get confused.
The problem is only if ($) is used here. So don't!
---------------------------------------------
The overall structure of the GHC Prelude is a bit tricky.
a) We want to avoid "orphan modules", i.e. ones with instance
decls that don't belong either to a tycon or a class
defined in the same module
b) We want to avoid giant modules
So the rough structure is as follows, in (linearised) dependency order
GHC.Prim Has no implementation. It defines built-in things, and
by importing it you bring them into scope.
The source file is GHC.Prim.hi-boot, which is just
copied to make GHC.Prim.hi
GHC.Base Classes: Eq, Ord, Functor, Monad
Types: list, (), Int, Bool, Ordering, Char, String
Data.Tuple Types: tuples, plus instances for GHC.Base classes
GHC.Show Class: Show, plus instances for GHC.Base/GHC.Tup types
GHC.Enum Class: Enum, plus instances for GHC.Base/GHC.Tup types
Data.Maybe Type: Maybe, plus instances for GHC.Base classes
GHC.List List functions
GHC.Num Class: Num, plus instances for Int
Type: Integer, plus instances for all classes so far (Eq, Ord, Num, Show)
Integer is needed here because it is mentioned in the signature
of 'fromInteger' in class Num
GHC.Real Classes: Real, Integral, Fractional, RealFrac
plus instances for Int, Integer
Types: Ratio, Rational
plus instances for classes so far
Rational is needed here because it is mentioned in the signature
of 'toRational' in class Real
GHC.ST The ST monad, instances and a few helper functions
Ix Classes: Ix, plus instances for Int, Bool, Char, Integer, Ordering, tuples
GHC.Arr Types: Array, MutableArray, MutableVar
Arrays are used by a function in GHC.Float
GHC.Float Classes: Floating, RealFloat
Types: Float, Double, plus instances of all classes so far
This module contains everything to do with floating point.
It is a big module (900 lines)
With a bit of luck, many modules can be compiled without ever reading GHC.Float.hi
Other Prelude modules are much easier with fewer complex dependencies.
-}
{-# LANGUAGE Unsafe #-}
{-# LANGUAGE CPP
, NoImplicitPrelude
, BangPatterns
, ExplicitForAll
, MagicHash
, UnboxedTuples
, ExistentialQuantification
, RankNTypes
, KindSignatures
, PolyKinds
, DataKinds
#-}
-- -Wno-orphans is needed for things like:
-- Orphan rule: "x# -# x#" ALWAYS forall x# :: Int# -# x# x# = 0
{-# OPTIONS_GHC -Wno-orphans #-}
{-# OPTIONS_HADDOCK not-home #-}
-----------------------------------------------------------------------------
-- |
-- Module : GHC.Base
-- Copyright : (c) The University of Glasgow, 1992-2002
-- License : see libraries/base/LICENSE
--
-- Maintainer : cvs-ghc@haskell.org
-- Stability : internal
-- Portability : non-portable (GHC extensions)
--
-- Basic data types and classes.
--
-----------------------------------------------------------------------------
#include "MachDeps.h"
module GHC.Base
(
module GHC.Base,
module GHC.Classes,
module GHC.CString,
module GHC.Magic,
module GHC.Types,
module GHC.Prim, -- Re-export GHC.Prim and [boot] GHC.Err,
module GHC.Prim.Ext, -- to avoid lots of people having to
module GHC.Err, -- import it explicitly
module GHC.Maybe
)
where
import GHC.Types
import GHC.Classes
import GHC.CString
import GHC.Magic
import GHC.Prim
import GHC.Prim.Ext
import GHC.Err
import GHC.Maybe
import {-# SOURCE #-} GHC.IO (mkUserError, mplusIO)
import GHC.Tuple () -- Note [Depend on GHC.Tuple]
import GHC.Integer () -- Note [Depend on GHC.Integer]
import GHC.Natural () -- Note [Depend on GHC.Natural]
-- for 'class Semigroup'
import {-# SOURCE #-} GHC.Real (Integral)
import {-# SOURCE #-} Data.Semigroup.Internal ( stimesDefault
, stimesMaybe
, stimesList
, stimesIdempotentMonoid
)
infixr 9 .
infixr 5 ++
infixl 4 <$
infixl 1 >>, >>=
infixr 1 =<<
infixr 0 $, $!
infixl 4 <*>, <*, *>, <**>
default () -- Double isn't available yet
{-
Note [Depend on GHC.Integer]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The Integer type is special because TidyPgm uses
GHC.Integer.Type.mkInteger to construct Integer literal values
Currently it reads the interface file whether or not the current
module *has* any Integer literals, so it's important that
GHC.Integer.Type (in package integer-gmp or integer-simple) is
compiled before any other module. (There's a hack in GHC to disable
this for packages ghc-prim, integer-gmp, integer-simple, which aren't
allowed to contain any Integer literals.)
Likewise we implicitly need Integer when deriving things like Eq
instances.
The danger is that if the build system doesn't know about the dependency
on Integer, it'll compile some base module before GHC.Integer.Type,
resulting in:
Failed to load interface for ‘GHC.Integer.Type’
There are files missing in the ‘integer-gmp’ package,
Bottom line: we make GHC.Base depend on GHC.Integer; and everything
else either depends on GHC.Base, or does not have NoImplicitPrelude
(and hence depends on Prelude).
Note [Depend on GHC.Tuple]
~~~~~~~~~~~~~~~~~~~~~~~~~~
Similarly, tuple syntax (or ()) creates an implicit dependency on
GHC.Tuple, so we use the same rule as for Integer --- see Note [Depend on
GHC.Integer] --- to explain this to the build system. We make GHC.Base
depend on GHC.Tuple, and everything else depends on GHC.Base or Prelude.
Note [Depend on GHC.Natural]
~~~~~~~~~~~~~~~~~~~~~~~~~~
Similar to GHC.Integer.
-}
#if 0
-- for use when compiling GHC.Base itself doesn't work
data Bool = False | True
data Ordering = LT | EQ | GT
data Char = C# Char#
type String = [Char]
data Int = I# Int#
data () = ()
data [] a = MkNil
not True = False
(&&) True True = True
otherwise = True
build = errorWithoutStackTrace "urk"
foldr = errorWithoutStackTrace "urk"
#endif
infixr 6 <>
-- | The class of semigroups (types with an associative binary operation).
--
-- Instances should satisfy the following:
--
-- [Associativity] @x '<>' (y '<>' z) = (x '<>' y) '<>' z@
--
-- @since 4.9.0.0
class Semigroup a where
-- | An associative operation.
--
-- >>> [1,2,3] <> [4,5,6]
-- [1,2,3,4,5,6]
(<>) :: a -> 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!"
sconcat :: NonEmpty a -> a
sconcat (a :| as) = go a as where
go b (c:cs) = b <> go c cs
go b [] = b
-- | 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 = 'Data.Semigroup.stimesIdempotent'@ or @stimes =
-- 'stimesIdempotentMonoid'@ respectively.
--
-- >>> stimes 4 [1]
-- [1,1,1,1]
stimes :: Integral b => b -> a -> a
stimes = stimesDefault
-- | The class of monoids (types with an associative binary operation that
-- has an identity). Instances should satisfy the following:
--
-- [Right identity] @x '<>' 'mempty' = x@
-- [Left identity] @'mempty' '<>' x = x@
-- [Associativity] @x '<>' (y '<>' z) = (x '<>' y) '<>' z@ ('Semigroup' law)
-- [Concatenation] @'mconcat' = 'foldr' ('<>') 'mempty'@
--
-- The method names refer to the monoid of lists under concatenation,
-- but there are many other instances.
--
-- Some types can be viewed as a monoid in more than one way,
-- e.g. both addition and multiplication on numbers.
-- In such cases we often define @newtype@s and make those instances
-- of 'Monoid', e.g. 'Data.Semigroup.Sum' and 'Data.Semigroup.Product'.
--
-- __NOTE__: 'Semigroup' is a superclass of 'Monoid' since /base-4.11.0.0/.
class Semigroup a => Monoid a where
-- | Identity of 'mappend'
--
-- >>> "Hello world" <> mempty
-- "Hello world"
mempty :: a
-- | An associative operation
--
-- __NOTE__: This method is redundant and has the default
-- implementation @'mappend' = ('<>')@ since /base-4.11.0.0/.
-- Should it be implemented manually, since 'mappend' is a synonym for
-- ('<>'), it is expected that the two functions are defined the same
-- way. In a future GHC release 'mappend' will be removed from 'Monoid'.
mappend :: a -> a -> a
mappend = (<>)
{-# INLINE mappend #-}
-- | Fold a list using the monoid.
--
-- For most types, the default definition for 'mconcat' will be
-- used, but the function is included in the class definition so
-- that an optimized version can be provided for specific types.
--
-- >>> mconcat ["Hello", " ", "Haskell", "!"]
-- "Hello Haskell!"
mconcat :: [a] -> a
mconcat = foldr mappend mempty
-- | @since 4.9.0.0
instance Semigroup [a] where
(<>) = (++)
{-# INLINE (<>) #-}
stimes = stimesList
-- | @since 2.01
instance Monoid [a] where
{-# INLINE mempty #-}
mempty = []
{-# INLINE mconcat #-}
mconcat xss = [x | xs <- xss, x <- xs]
-- See Note: [List comprehensions and inlining]
{-
Note: [List comprehensions and inlining]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The list monad operations are traditionally described in terms of concatMap:
xs >>= f = concatMap f xs
Similarly, mconcat for lists is just concat. Here in Base, however, we don't
have concatMap, and we'll refrain from adding it here so it won't have to be
hidden in imports. Instead, we use GHC's list comprehension desugaring
mechanism to define mconcat and the Applicative and Monad instances for lists.
We mark them INLINE because the inliner is not generally too keen to inline
build forms such as the ones these desugar to without our insistence. Defining
these using list comprehensions instead of foldr has an additional potential
benefit, as described in compiler/deSugar/DsListComp.hs: if optimizations
needed to make foldr/build forms efficient are turned off, we'll get reasonably
efficient translations anyway.
-}
-- | @since 4.9.0.0
instance Semigroup (NonEmpty a) where
(a :| as) <> ~(b :| bs) = a :| (as ++ b : bs)
-- | @since 4.9.0.0
instance Semigroup b => Semigroup (a -> b) where
f <> g = \x -> f x <> g x
stimes n f e = stimes n (f e)
-- | @since 2.01
instance Monoid b => Monoid (a -> b) where
mempty _ = mempty
-- | @since 4.9.0.0
instance Semigroup () where
_ <> _ = ()
sconcat _ = ()
stimes _ _ = ()
-- | @since 2.01
instance Monoid () where
-- Should it be strict?
mempty = ()
mconcat _ = ()
-- | @since 4.9.0.0
instance (Semigroup a, Semigroup b) => Semigroup (a, b) where
(a,b) <> (a',b') = (a<>a',b<>b')
stimes n (a,b) = (stimes n a, stimes n b)
-- | @since 2.01
instance (Monoid a, Monoid b) => Monoid (a,b) where
mempty = (mempty, mempty)
-- | @since 4.9.0.0
instance (Semigroup a, Semigroup b, Semigroup c) => Semigroup (a, b, c) where
(a,b,c) <> (a',b',c') = (a<>a',b<>b',c<>c')
stimes n (a,b,c) = (stimes n a, stimes n b, stimes n c)
-- | @since 2.01
instance (Monoid a, Monoid b, Monoid c) => Monoid (a,b,c) where
mempty = (mempty, mempty, mempty)
-- | @since 4.9.0.0
instance (Semigroup a, Semigroup b, Semigroup c, Semigroup d)
=> Semigroup (a, b, c, d) where
(a,b,c,d) <> (a',b',c',d') = (a<>a',b<>b',c<>c',d<>d')
stimes n (a,b,c,d) = (stimes n a, stimes n b, stimes n c, stimes n d)
-- | @since 2.01
instance (Monoid a, Monoid b, Monoid c, Monoid d) => Monoid (a,b,c,d) where
mempty = (mempty, mempty, mempty, mempty)
-- | @since 4.9.0.0
instance (Semigroup a, Semigroup b, Semigroup c, Semigroup d, Semigroup e)
=> Semigroup (a, b, c, d, e) where
(a,b,c,d,e) <> (a',b',c',d',e') = (a<>a',b<>b',c<>c',d<>d',e<>e')
stimes n (a,b,c,d,e) =
(stimes n a, stimes n b, stimes n c, stimes n d, stimes n e)
-- | @since 2.01
instance (Monoid a, Monoid b, Monoid c, Monoid d, Monoid e) =>
Monoid (a,b,c,d,e) where
mempty = (mempty, mempty, mempty, mempty, mempty)
-- | @since 4.9.0.0
instance Semigroup Ordering where
LT <> _ = LT
EQ <> y = y
GT <> _ = GT
stimes = stimesIdempotentMonoid
-- lexicographical ordering
-- | @since 2.01
instance Monoid Ordering where
mempty = EQ
-- | @since 4.9.0.0
instance Semigroup a => Semigroup (Maybe a) where
Nothing <> b = b
a <> Nothing = a
Just a <> Just b = Just (a <> b)
stimes = stimesMaybe
-- | Lift a semigroup into 'Maybe' forming a 'Monoid' according to
-- <http://en.wikipedia.org/wiki/Monoid>: \"Any semigroup @S@ may be
-- turned into a monoid simply by adjoining an element @e@ not in @S@
-- and defining @e*e = e@ and @e*s = s = s*e@ for all @s ∈ S@.\"
--
-- /Since 4.11.0/: constraint on inner @a@ value generalised from
-- 'Monoid' to 'Semigroup'.
--
-- @since 2.01
instance Semigroup a => Monoid (Maybe a) where
mempty = Nothing
-- | For tuples, the 'Monoid' constraint on @a@ determines
-- how the first values merge.
-- For example, 'String's concatenate:
--
-- > ("hello ", (+15)) <*> ("world!", 2002)
-- > ("hello world!",2017)
--
-- @since 2.01
instance Monoid a => Applicative ((,) a) where
pure x = (mempty, x)
(u, f) <*> (v, x) = (u <> v, f x)
liftA2 f (u, x) (v, y) = (u <> v, f x y)
-- | @since 4.9.0.0
instance Monoid a => Monad ((,) a) where
(u, a) >>= k = case k a of (v, b) -> (u <> v, b)
-- | @since 4.14.0.0
instance Functor ((,,) a b) where
fmap f (a, b, c) = (a, b, f c)
-- | @since 4.14.0.0
instance (Monoid a, Monoid b) => Applicative ((,,) a b) where
pure x = (mempty, mempty, x)
(a, b, f) <*> (a', b', x) = (a <> a', b <> b', f x)
-- | @since 4.14.0.0
instance (Monoid a, Monoid b) => Monad ((,,) a b) where
(u, v, a) >>= k = case k a of (u', v', b) -> (u <> u', v <> v', b)
-- | @since 4.14.0.0
instance Functor ((,,,) a b c) where
fmap f (a, b, c, d) = (a, b, c, f d)
-- | @since 4.14.0.0
instance (Monoid a, Monoid b, Monoid c) => Applicative ((,,,) a b c) where
pure x = (mempty, mempty, mempty, x)
(a, b, c, f) <*> (a', b', c', x) = (a <> a', b <> b', c <> c', f x)
-- | @since 4.14.0.0
instance (Monoid a, Monoid b, Monoid c) => Monad ((,,,) a b c) where
(u, v, w, a) >>= k = case k a of (u', v', w', b) -> (u <> u', v <> v', w <> w', b)
-- | @since 4.10.0.0
instance Semigroup a => Semigroup (IO a) where
(<>) = liftA2 (<>)
-- | @since 4.9.0.0
instance Monoid a => Monoid (IO a) where
mempty = pure mempty
{- | 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.
-}
class Functor f where
-- | Using @ApplicativeDo@: \'@'fmap' f as@\' can be understood as
-- the @do@ expression
--
-- @
-- do a <- as
-- pure (f a)
-- @
--
-- with an inferred @Functor@ constraint.
fmap :: (a -> b) -> f a -> f b
-- | 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 '<$' bs@\' can be understood as the
-- @do@ expression
--
-- @
-- do bs
-- pure a
-- @
--
-- with an inferred @Functor@ constraint.
(<$) :: a -> f b -> f a
(<$) = fmap . const
-- | A functor with application, providing operations to
--
-- * embed pure expressions ('pure'), and
--
-- * sequence computations and combine their results ('<*>' and 'liftA2').
--
-- A minimal complete definition must include implementations of 'pure'
-- and of either '<*>' or 'liftA2'. If it defines both, then they must behave
-- the same as their default definitions:
--
-- @('<*>') = 'liftA2' 'id'@
--
-- @'liftA2' f x y = f 'Prelude.<$>' 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).
class Functor f => Applicative f where
{-# MINIMAL pure, ((<*>) | liftA2) #-}
-- | Lift a value.
pure :: a -> f a
-- | 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)
-- @
(<*>) :: f (a -> b) -> f a -> f b
(<*>) = liftA2 id
-- | 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)
-- @
liftA2 :: (a -> b -> c) -> f a -> f b -> f c
liftA2 f x = (<*>) (fmap f x)
-- | 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 b
a1 *> a2 = (id <$ a1) <*> a2
-- This is essentially the same as liftA2 (flip const), but if the
-- Functor instance has an optimized (<$), it may be better to use
-- that instead. Before liftA2 became a method, this definition
-- was strictly better, but now it depends on the functor. For a
-- functor supporting a sharing-enhancing (<$), this definition
-- may reduce allocation by preventing a1 from ever being fully
-- realized. In an implementation with a boring (<$) but an optimizing
-- liftA2, it would likely be better to define (*>) using liftA2.
-- | 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
-- @
(<*) :: f a -> f b -> f a
(<*) = liftA2 const
-- | A variant of '<*>' with the arguments reversed.
--
-- Using @ApplicativeDo@: \'@as '<**>' fs@\' can be understood as the
-- @do@ expression
--
-- @
-- do a <- as
-- f <- fs
-- pure (f a)
-- @
(<**>) :: Applicative f => f a -> f (a -> b) -> f b
(<**>) = liftA2 (\a f -> f a)
-- Don't use $ here, see the note at the top of the page
-- | Lift a function to actions.
-- This function may be used as a value for `fmap` in a `Functor` instance.
--
-- | Using @ApplicativeDo@: \'@'liftA' f as@\' can be understood as the
-- @do@ expression
--
--
-- @
-- do a <- as
-- pure (f a)
-- @
--
-- with an inferred @Functor@ constraint, weaker than @Applicative@.
liftA :: Applicative f => (a -> b) -> f a -> f b
liftA f a = pure f <*> a
-- Caution: since this may be used for `fmap`, we can't use the obvious
-- definition of liftA = fmap.
-- | Lift a ternary function to actions.
--
-- Using @ApplicativeDo@: \'@'liftA3' f as bs cs@\' can be understood
-- as the @do@ expression
--
-- @
-- do a <- as
-- b <- bs
-- c <- cs
-- pure (f a b c)
-- @
liftA3 :: Applicative f => (a -> b -> c -> d) -> f a -> f b -> f c -> f d
liftA3 f a b c = liftA2 f a b <*> c
{-# INLINABLE liftA #-}
{-# SPECIALISE liftA :: (a1->r) -> IO a1 -> IO r #-}
{-# SPECIALISE liftA :: (a1->r) -> Maybe a1 -> Maybe r #-}
{-# INLINABLE liftA3 #-}
{-# SPECIALISE liftA3 :: (a1->a2->a3->r) -> IO a1 -> IO a2 -> IO a3 -> IO r #-}
{-# SPECIALISE liftA3 :: (a1->a2->a3->r) ->
Maybe a1 -> Maybe a2 -> Maybe a3 -> Maybe r #-}
-- | The 'join' function is the conventional monad join operator. It
-- is used to remove one level of monadic structure, projecting its
-- bound argument into the outer level.
--
--
-- \'@'join' bss@\' can be understood as the @do@ expression
--
-- @
-- do bs <- bss
-- bs
-- @
--
-- ==== __Examples__
--
-- A common use of 'join' is to run an 'IO' computation returned from
-- an 'GHC.Conc.STM' transaction, since 'GHC.Conc.STM' transactions
-- can't perform 'IO' directly. Recall that
--
-- @
-- 'GHC.Conc.atomically' :: STM a -> IO a
-- @
--
-- is used to run 'GHC.Conc.STM' transactions atomically. So, by
-- specializing the types of 'GHC.Conc.atomically' and 'join' to
--
-- @
-- 'GHC.Conc.atomically' :: STM (IO b) -> IO (IO b)
-- 'join' :: IO (IO b) -> IO b
-- @
--
-- we can compose them as
--
-- @
-- 'join' . 'GHC.Conc.atomically' :: STM (IO b) -> IO b
-- @
--
-- to run an 'GHC.Conc.STM' transaction and the 'IO' action it
-- returns.
join :: (Monad m) => m (m a) -> m a
join x = x >>= id
{- | 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, 'Data.Maybe.Maybe' and 'System.IO.IO'
defined in the "Prelude" satisfy these laws.
-}
class Applicative m => Monad m where
-- | 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
-- @
(>>=) :: forall a b. m a -> (a -> m b) -> m b
-- | 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
-- @
(>>) :: forall a b. m a -> m b -> m b
m >> k = m >>= \_ -> k -- See Note [Recursive bindings for Applicative/Monad]
{-# INLINE (>>) #-}
-- | Inject a value into the monadic type.
return :: a -> m a
return = pure
{- Note [Recursive bindings for Applicative/Monad]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The original Applicative/Monad proposal stated that after
implementation, the designated implementation of (>>) would become
(>>) :: forall a b. m a -> m b -> m b
(>>) = (*>)
by default. You might be inclined to change this to reflect the stated
proposal, but you really shouldn't! Why? Because people tend to define
such instances the /other/ way around: in particular, it is perfectly
legitimate to define an instance of Applicative (*>) in terms of (>>),
which would lead to an infinite loop for the default implementation of
Monad! And people do this in the wild.
This turned into a nasty bug that was tricky to track down, and rather
than eliminate it everywhere upstream, it's easier to just retain the
original default.
-}
-- | Same as '>>=', but with the arguments interchanged.
{-# SPECIALISE (=<<) :: (a -> [b]) -> [a] -> [b] #-}
(=<<) :: Monad m => (a -> m b) -> m a -> m b
f =<< x = x >>= f
-- | Conditional execution of 'Applicative' expressions. For example,
--
-- > when debug (putStrLn "Debugging")
--
-- will output the string @Debugging@ if the Boolean value @debug@
-- is 'True', and otherwise do nothing.
when :: (Applicative f) => Bool -> f () -> f ()
{-# INLINABLE when #-}
{-# SPECIALISE when :: Bool -> IO () -> IO () #-}
{-# SPECIALISE when :: Bool -> Maybe () -> Maybe () #-}
when p s = if p then s else pure ()
-- | Evaluate each action in the sequence from left to right,
-- and collect the results.
sequence :: Monad m => [m a] -> m [a]
{-# INLINE sequence #-}
sequence = mapM id
-- Note: [sequence and mapM]
-- | @'mapM' f@ is equivalent to @'sequence' . 'map' f@.
mapM :: Monad m => (a -> m b) -> [a] -> m [b]
{-# INLINE mapM #-}
mapM f as = foldr k (return []) as
where
k a r = do { x <- f a; xs <- r; return (x:xs) }
{-
Note: [sequence and mapM]
~~~~~~~~~~~~~~~~~~~~~~~~~
Originally, we defined
mapM f = sequence . map f
This relied on list fusion to produce efficient code for mapM, and led to
excessive allocation in cryptarithm2. Defining
sequence = mapM id
relies only on inlining a tiny function (id) and beta reduction, which tends to
be a more reliable aspect of simplification. Indeed, this does not lead to
similar problems in nofib.
-}
-- | Promote a function to a monad.
liftM :: (Monad m) => (a1 -> r) -> m a1 -> m r
liftM f m1 = do { x1 <- m1; return (f x1) }
-- | Promote a function to a monad, scanning the monadic arguments from
-- left to right. For example,
--
-- > liftM2 (+) [0,1] [0,2] = [0,2,1,3]
-- > liftM2 (+) (Just 1) Nothing = Nothing
--
liftM2 :: (Monad m) => (a1 -> a2 -> r) -> m a1 -> m a2 -> m r
liftM2 f m1 m2 = do { x1 <- m1; x2 <- m2; return (f x1 x2) }
-- Caution: since this may be used for `liftA2`, we can't use the obvious
-- definition of liftM2 = liftA2.
-- | Promote a function to a monad, scanning the monadic arguments from
-- left to right (cf. 'liftM2').
liftM3 :: (Monad m) => (a1 -> a2 -> a3 -> r) -> m a1 -> m a2 -> m a3 -> m r
liftM3 f m1 m2 m3 = do { x1 <- m1; x2 <- m2; x3 <- m3; return (f x1 x2 x3) }
-- | Promote a function to a monad, scanning the monadic arguments from
-- left to right (cf. 'liftM2').
liftM4 :: (Monad m) => (a1 -> a2 -> a3 -> a4 -> r) -> m a1 -> m a2 -> m a3 -> m a4 -> m r
liftM4 f m1 m2 m3 m4 = do { x1 <- m1; x2 <- m2; x3 <- m3; x4 <- m4; return (f x1 x2 x3 x4) }
-- | Promote a function to a monad, scanning the monadic arguments from
-- left to right (cf. 'liftM2').
liftM5 :: (Monad m) => (a1 -> a2 -> a3 -> a4 -> a5 -> r) -> m a1 -> m a2 -> m a3 -> m a4 -> m a5 -> m r
liftM5 f m1 m2 m3 m4 m5 = do { x1 <- m1; x2 <- m2; x3 <- m3; x4 <- m4; x5 <- m5; return (f x1 x2 x3 x4 x5) }
{-# INLINABLE liftM #-}
{-# SPECIALISE liftM :: (a1->r) -> IO a1 -> IO r #-}
{-# SPECIALISE liftM :: (a1->r) -> Maybe a1 -> Maybe r #-}
{-# INLINABLE liftM2 #-}
{-# SPECIALISE liftM2 :: (a1->a2->r) -> IO a1 -> IO a2 -> IO r #-}
{-# SPECIALISE liftM2 :: (a1->a2->r) -> Maybe a1 -> Maybe a2 -> Maybe r #-}
{-# INLINABLE liftM3 #-}
{-# SPECIALISE liftM3 :: (a1->a2->a3->r) -> IO a1 -> IO a2 -> IO a3 -> IO r #-}
{-# SPECIALISE liftM3 :: (a1->a2->a3->r) -> Maybe a1 -> Maybe a2 -> Maybe a3 -> Maybe r #-}
{-# INLINABLE liftM4 #-}
{-# SPECIALISE liftM4 :: (a1->a2->a3->a4->r) -> IO a1 -> IO a2 -> IO a3 -> IO a4 -> IO r #-}
{-# SPECIALISE liftM4 :: (a1->a2->a3->a4->r) -> Maybe a1 -> Maybe a2 -> Maybe a3 -> Maybe a4 -> Maybe r #-}
{-# INLINABLE liftM5 #-}
{-# SPECIALISE liftM5 :: (a1->a2->a3->a4->a5->r) -> IO a1 -> IO a2 -> IO a3 -> IO a4 -> IO a5 -> IO r #-}
{-# SPECIALISE liftM5 :: (a1->a2->a3->a4->a5->r) -> Maybe a1 -> Maybe a2 -> Maybe a3 -> Maybe a4 -> Maybe a5 -> Maybe r #-}
{- | In many situations, the 'liftM' operations can be replaced by uses of
'ap', which promotes function application.
> return f `ap` x1 `ap` ... `ap` xn
is equivalent to
> liftMn f x1 x2 ... xn
-}
ap :: (Monad m) => m (a -> b) -> m a -> m b
ap m1 m2 = do { x1 <- m1; x2 <- m2; return (x1 x2) }
-- Since many Applicative instances define (<*>) = ap, we
-- cannot define ap = (<*>)
{-# INLINABLE ap #-}
{-# SPECIALISE ap :: IO (a -> b) -> IO a -> IO b #-}
{-# SPECIALISE ap :: Maybe (a -> b) -> Maybe a -> Maybe b #-}
-- instances for Prelude types
-- | @since 2.01
instance Functor ((->) r) where
fmap = (.)
-- | @since 2.01
instance Applicative ((->) r) where
pure = const
(<*>) f g x = f x (g x)
liftA2 q f g x = q (f x) (g x)
-- | @since 2.01
instance Monad ((->) r) where
f >>= k = \ r -> k (f r) r
-- | @since 2.01
instance Functor ((,) a) where
fmap f (x,y) = (x, f y)
-- | @since 2.01
instance Functor Maybe where
fmap _ Nothing = Nothing
fmap f (Just a) = Just (f a)
-- | @since 2.01
instance Applicative Maybe where
pure = Just
Just f <*> m = fmap f m
Nothing <*> _m = Nothing
liftA2 f (Just x) (Just y) = Just (f x y)
liftA2 _ _ _ = Nothing