{- 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, -- 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.Err import GHC.Maybe import {-# SOURCE #-} GHC.IO (failIO,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. (<>) :: a -> a -> a -- | Reduce a non-empty list with '<>' -- -- The default definition should be sufficient, but this can be -- overridden for efficiency. -- 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 /O(1)/ by -- picking @stimes = 'Data.Semigroup.stimesIdempotent'@ or @stimes = -- 'stimesIdempotentMonoid'@ respectively. 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' mempty :: a -- | An associative operation -- -- __NOTE__: This method is redundant and has the default -- implementation @'mappend' = ('<>')@ since /base-4.11.0.0/. 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 :: [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 4.10.0.0 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 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. (<$) :: 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'@ -- -- * @('<*>') = 'ap'@ -- -- * @('*>') = ('>>')@ -- -- (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. (<*>) :: 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 '<*>'. 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. (*>) :: 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. (<*) :: f a -> f b -> f a (<*) = liftA2 const -- | A variant of '<*>' with the arguments reversed. (<**>) :: 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. 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. 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. -- -- ==== __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'@ * @('<*>') = 'ap'@ 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. (>>=) :: 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. (>>) :: 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 ((->) a) 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 Just _m1 *> m2 = m2 Nothing *> _m2 = Nothing -- | @since 2.01 instance Monad Maybe where (Just x) >>= k = k x Nothing >>= _ = Nothing (>>) = (*>) -- ----------------------------------------------------------------------------- -- The Alternative class definition infixl 3 <|> -- | A monoid on applicative functors. -- -- If defined, 'some' and 'many' should be the least solutions -- of the equations: -- -- * @'some' v = (:) 'Prelude.<$>' v '<*>' 'many' v@ -- -- * @'many' v = 'some' v '<|>' 'pure' []@ class Applicative f => Alternative f where -- | The identity of '<|>' empty :: f a -- | An associative binary operation (<|>) :: f a -> f a -> f a -- | One or more. some :: f a -> f [a] some v = some_v where many_v = some_v <|> pure [] some_v = liftA2 (:) v many_v -- | Zero or more. many :: f a -> f [a] many v = many_v where many_v = some_v <|> pure [] some_v = liftA2 (:) v many_v -- | @since 2.01 instance Alternative Maybe where empty = Nothing Nothing <|> r = r l <|> _ = l -- ----------------------------------------------------------------------------- -- The MonadPlus class definition -- | Monads that also support choice and failure. class (Alternative m, Monad m) => MonadPlus m where -- | The identity of 'mplus'. It should also satisfy the equations -- -- > mzero >>= f = mzero -- > v >> mzero = mzero -- -- The default definition is -- -- @ -- mzero = 'empty' -- @ mzero :: m a mzero = empty -- | An associative operation. The default definition is -- -- @ -- mplus = ('<|>') -- @ mplus :: m a -> m a -> m a mplus = (<|>) -- | @since 2.01 instance MonadPlus Maybe --------------------------------------------- -- The non-empty list type infixr 5 :| -- | Non-empty (and non-strict) list type. -- -- @since 4.9.0.0 data NonEmpty a = a :| [a] deriving ( Eq -- ^ @since 4.9.0.0 , Ord -- ^ @since 4.9.0.0 ) -- | @since 4.9.0.0 instance Functor NonEmpty where fmap f ~(a :| as) = f a :| fmap f as b <$ ~(_ :| as) = b :| (b <$ as) -- | @since 4.9.0.0 instance Applicative NonEmpty where pure a = a :| [] (<*>) = ap liftA2 = liftM2 -- | @since 4.9.0.0 instance Monad NonEmpty where ~(a :| as) >>= f = b :| (bs ++ bs') where b :| bs = f a bs' = as >>= toList . f toList ~(c :| cs) = c : cs ---------------------------------------------- -- The list type -- | @since 2.01 instance Functor [] where {-# INLINE fmap #-} fmap = map -- See Note: [List comprehensions and inlining] -- | @since 2.01 instance Applicative [] where {-# INLINE pure #-} pure x = [x] {-# INLINE (<*>) #-} fs <*> xs = [f x | f <- fs, x <- xs] {-# INLINE liftA2 #-} liftA2 f xs ys = [f x y | x <- xs, y <- ys] {-# INLINE (*>) #-} xs *> ys = [y | _ <- xs, y <- ys] -- See Note: [List comprehensions and inlining] -- | @since 2.01 instance Monad [] where {-# INLINE (>>=) #-} xs >>= f = [y | x <- xs, y <- f x] {-# INLINE (>>) #-} (>>) = (*>) -- | @since 2.01 instance Alternative [] where empty = [] (<|>) = (++) -- | @since 2.01 instance MonadPlus [] {- A few list functions that appear here because they are used here. The rest of the prelude list functions are in GHC.List. -} ---------------------------------------------- -- foldr/build/augment ---------------------------------------------- -- | 'foldr', applied to a binary operator, a starting value (typically -- the right-identity of the operator), and a list, reduces the list -- using the binary operator, from right to left: -- -- > foldr f z [x1, x2, ..., xn] == x1 `f` (x2 `f` ... (xn `f` z)...) foldr :: (a -> b -> b) -> b -> [a] -> b -- foldr _ z [] = z -- foldr f z (x:xs) = f x (foldr f z xs) {-# INLINE [0] foldr #-} -- Inline only in the final stage, after the foldr/cons rule has had a chance -- Also note that we inline it when it has *two* parameters, which are the -- ones we are keen about specialising! foldr k z = go where go [] = z go (y:ys) = y `k` go ys -- | A list producer that can be fused with 'foldr'. -- This function is merely -- -- > build g = g (:) [] -- -- but GHC's simplifier will transform an expression of the form -- @'foldr' k z ('build' g)@, which may arise after inlining, to @g k z@, -- which avoids producing an intermediate list. build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a] {-# INLINE [1] build #-} -- The INLINE is important, even though build is tiny, -- because it prevents [] getting inlined in the version that -- appears in the interface file. If [] *is* inlined, it -- won't match with [] appearing in rules in an importing module. -- -- The "1" says to inline in phase 1 build g = g (:) [] -- | A list producer that can be fused with 'foldr'. -- This function is merely -- -- > augment g xs = g (:) xs -- -- but GHC's simplifier will transform an expression of the form -- @'foldr' k z ('augment' g xs)@, which may arise after inlining, to -- @g k ('foldr' k z xs)@, which avoids producing an intermediate list. augment :: forall a. (forall b. (a->b->b) -> b -> b) -> [a] -> [a] {-# INLINE [1] augment #-} augment g xs = g (:) xs {-# RULES "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) . foldr k z (build g) = g k z "foldr/augment" forall k z xs (g::forall b. (a->b->b) -> b -> b) . foldr k z (augment g xs) = g k (foldr k z xs) "foldr/id" foldr (:) [] = \x -> x "foldr/app" [1] forall ys. foldr (:) ys = \xs -> xs ++ ys -- Only activate this from phase 1, because that's -- when we disable the rule that expands (++) into foldr -- The foldr/cons rule looks nice, but it can give disastrously -- bloated code when commpiling -- array (a,b) [(1,2), (2,2), (3,2), ...very long list... ] -- i.e. when there are very very long literal lists -- So I've disabled it for now. We could have special cases -- for short lists, I suppose. -- "foldr/cons" forall k z x xs. foldr k z (x:xs) = k x (foldr k z xs) "foldr/single" forall k z x. foldr k z [x] = k x z "foldr/nil" forall k z. foldr k z [] = z "foldr/cons/build" forall k z x (g::forall b. (a->b->b) -> b -> b) . foldr k z (x:build g) = k x (g k z) "augment/build" forall (g::forall b. (a->b->b) -> b -> b) (h::forall b. (a->b->b) -> b -> b) . augment g (build h) = build (\c n -> g c (h c n)) "augment/nil" forall (g::forall b. (a->b->b) -> b -> b) . augment g [] = build g #-} -- This rule is true, but not (I think) useful: -- augment g (augment h t) = augment (\cn -> g c (h c n)) t ---------------------------------------------- -- map ---------------------------------------------- -- | /O(n)/. 'map' @f xs@ is the list obtained by applying @f@ to each element -- of @xs@, i.e., -- -- > map f [x1, x2, ..., xn] == [f x1, f x2, ..., f xn] -- > map f [x1, x2, ...] == [f x1, f x2, ...] -- -- >>> map (+1) [1, 2, 3] --- [2,3,4] map :: (a -> b) -> [a] -> [b] {-# NOINLINE [0] map #-} -- We want the RULEs "map" and "map/coerce" to fire first. -- map is recursive, so won't inline anyway, -- but saying so is more explicit, and silences warnings map _ [] = [] map f (x:xs) = f x : map f xs -- Note eta expanded mapFB :: (elt -> lst -> lst) -> (a -> elt) -> a -> lst -> lst {-# INLINE [0] mapFB #-} -- See Note [Inline FB functions] in GHC.List mapFB c f = \x ys -> c (f x) ys {- Note [The rules for map] ~~~~~~~~~~~~~~~~~~~~~~~~~~~ The rules for map work like this. * Up to (but not including) phase 1, we use the "map" rule to rewrite all saturated applications of map with its build/fold form, hoping for fusion to happen. In phase 1 and 0, we switch off that rule, inline build, and switch on the "mapList" rule, which rewrites the foldr/mapFB thing back into plain map. It's important that these two rules aren't both active at once (along with build's unfolding) else we'd get an infinite loop in the rules. Hence the activation control below. * This same pattern is followed by many other functions: e.g. append, filter, iterate, repeat, etc. in GHC.List See also Note [Inline FB functions] in GHC.List * The "mapFB" rule optimises compositions of map * The "mapFB/id" rule gets rid of 'map id' calls. You might think that (mapFB c id) will turn into c simply when mapFB is inlined; but before that happens the "mapList" rule turns (foldr (mapFB (:) id) [] a back into map id Which is not very clever. * Any similarity to the Functor laws for [] is expected. -} {-# RULES "map" [~1] forall f xs. map f xs = build (\c n -> foldr (mapFB c f) n xs) "mapList" [1] forall f. foldr (mapFB (:) f) [] = map f "mapFB" forall c f g. mapFB (mapFB c f) g = mapFB c (f.g) "mapFB/id" forall c. mapFB c (\x -> x) = c #-} -- See Breitner, Eisenberg, Peyton Jones, and Weirich, "Safe Zero-cost -- Coercions for Haskell", section 6.5: -- http://research.microsoft.com/en-us/um/people/simonpj/papers/ext-f/coercible.pdf {-# RULES "map/coerce" [1] map coerce = coerce #-} ---------------------------------------------- -- append ---------------------------------------------- -- | Append two lists, i.e., -- -- > [x1, ..., xm] ++ [y1, ..., yn] == [x1, ..., xm, y1, ..., yn] -- > [x1, ..., xm] ++ [y1, ...] == [x1, ..., xm, y1, ...] -- -- If the first list is not finite, the result is the first list. (++) :: [a] -> [a] -> [a] {-# NOINLINE [1] (++) #-} -- We want the RULE to fire first. -- It's recursive, so won't inline anyway, -- but saying so is more explicit (++) [] ys = ys (++) (x:xs) ys = x : xs ++ ys {-# RULES "++" [~1] forall xs ys. xs ++ ys = augment (\c n -> foldr c n xs) ys #-} -- |'otherwise' is defined as the value 'True'. It helps to make -- guards more readable. eg. -- -- > f x | x < 0 = ... -- > | otherwise = ... otherwise :: Bool otherwise = True ---------------------------------------------- -- Type Char and String ---------------------------------------------- -- | A 'String' is a list of characters. String constants in Haskell are values -- of type 'String'. -- type String = [Char] unsafeChr :: Int -> Char unsafeChr (I# i#) = C# (chr# i#) -- | The 'Prelude.fromEnum' method restricted to the type 'Data.Char.Char'. ord :: Char -> Int ord (C# c#) = I# (ord# c#) -- | This 'String' equality predicate is used when desugaring -- pattern-matches against strings. eqString :: String -> String -> Bool eqString [] [] = True eqString (c1:cs1) (c2:cs2) = c1 == c2 && cs1 `eqString` cs2 eqString _ _ = False {-# RULES "eqString" (==) = eqString #-} -- eqString also has a BuiltInRule in PrelRules.hs: -- eqString (unpackCString# (Lit s1)) (unpackCString# (Lit s2)) = s1==s2 ---------------------------------------------- -- 'Int' related definitions ---------------------------------------------- maxInt, minInt :: Int {- Seems clumsy. Should perhaps put minInt and MaxInt directly into MachDeps.h -} #if WORD_SIZE_IN_BITS == 31 minInt = I# (-0x40000000#) maxInt = I# 0x3FFFFFFF# #elif WORD_SIZE_IN_BITS == 32 minInt = I# (-0x80000000#) maxInt = I# 0x7FFFFFFF# #else minInt = I# (-0x8000000000000000#) maxInt = I# 0x7FFFFFFFFFFFFFFF# #endif ---------------------------------------------- -- The function type ---------------------------------------------- -- | Identity function. -- -- > id x = x id :: a -> a id x = x -- Assertion function. This simply ignores its boolean argument. -- The compiler may rewrite it to @('assertError' line)@. -- | If the first argument evaluates to 'True', then the result is the -- second argument. Otherwise an 'Control.Exception.AssertionFailed' exception -- is raised, containing a 'String' with the source file and line number of the -- call to 'assert'. -- -- Assertions can normally be turned on or off with a compiler flag -- (for GHC, assertions are normally on unless optimisation is turned on -- with @-O@ or the @-fignore-asserts@ -- option is given). When assertions are turned off, the first -- argument to 'assert' is ignored, and the second argument is -- returned as the result. -- SLPJ: in 5.04 etc 'assert' is in GHC.Prim, -- but from Template Haskell onwards it's simply -- defined here in Base.hs assert :: Bool -> a -> a assert _pred r = r breakpoint :: a -> a breakpoint r = r breakpointCond :: Bool -> a -> a breakpointCond _ r = r data Opaque = forall a. O a -- | @const x@ is a unary function which evaluates to @x@ for all inputs. -- -- >>> const 42 "hello" -- 42 -- -- >>> map (const 42) [0..3] -- [42,42,42,42] const :: a -> b -> a const x _ = x -- | Function composition. {-# INLINE (.) #-} -- Make sure it has TWO args only on the left, so that it inlines -- when applied to two functions, even if there is no final argument (.) :: (b -> c) -> (a -> b) -> a -> c (.) f g = \x -> f (g x) -- | @'flip' f@ takes its (first) two arguments in the reverse order of @f@. -- -- >>> flip (++) "hello" "world" -- "worldhello" flip :: (a -> b -> c) -> b -> a -> c flip f x y = f y x -- | Application operator. This operator is redundant, since ordinary -- application @(f x)@ means the same as @(f '$' x)@. However, '$' has -- low, right-associative binding precedence, so it sometimes allows -- parentheses to be omitted; for example: -- -- > f $ g $ h x = f (g (h x)) -- -- It is also useful in higher-order situations, such as @'map' ('$' 0) xs@, -- or @'Data.List.zipWith' ('$') fs xs@. -- -- Note that @('$')@ is levity-polymorphic in its result type, so that -- @foo '$' True@ where @foo :: Bool -> Int#@ is well-typed. {-# INLINE ($) #-} ($) :: forall r a (b :: TYPE r). (a -> b) -> a -> b f $ x = f x -- | Strict (call-by-value) application operator. It takes a function and an -- argument, evaluates the argument to weak head normal form (WHNF), then calls -- the function with that value. ($!) :: forall r a (b :: TYPE r). (a -> b) -> a -> b f $! x = let !vx = x in f vx -- see #2273 -- | @'until' p f@ yields the result of applying @f@ until @p@ holds. until :: (a -> Bool) -> (a -> a) -> a -> a until p f = go where go x | p x = x | otherwise = go (f x) -- | 'asTypeOf' is a type-restricted version of 'const'. It is usually -- used as an infix operator, and its typing forces its first argument -- (which is usually overloaded) to have the same type as the second. asTypeOf :: a -> a -> a asTypeOf = const ---------------------------------------------- -- Functor/Applicative/Monad instances for IO ---------------------------------------------- -- | @since 2.01 instance Functor IO where fmap f x = x >>= (pure . f) -- | @since 2.01 instance Applicative IO where {-# INLINE pure #-} {-# INLINE (*>) #-} {-# INLINE liftA2 #-} pure = returnIO (*>) = thenIO (<*>) = ap liftA2 = liftM2 -- | @since 2.01 instance Monad IO where {-# INLINE (>>) #-} {-# INLINE (>>=) #-} (>>) = (*>) (>>=) = bindIO -- | @since 4.9.0.0 instance Alternative IO where empty = failIO "mzero" (<|>) = mplusIO -- | @since 4.9.0.0 instance MonadPlus IO returnIO :: a -> IO a returnIO x = IO (\ s -> (# s, x #)) bindIO :: IO a -> (a -> IO b) -> IO b bindIO (IO m) k = IO (\ s -> case m s of (# new_s, a #) -> unIO (k a) new_s) thenIO :: IO a -> IO b -> IO b thenIO (IO m) k = IO (\ s -> case m s of (# new_s, _ #) -> unIO k new_s) unIO :: IO a -> (State# RealWorld -> (# State# RealWorld, a #)) unIO (IO a) = a {- | Returns the tag of a constructor application; this function is used by the deriving code for Eq, Ord and Enum. -} {-# INLINE getTag #-} getTag :: a -> Int# getTag x = dataToTag# x ---------------------------------------------- -- Numeric primops ---------------------------------------------- -- Definitions of the boxed PrimOps; these will be -- used in the case of partial applications, etc. {-# INLINE quotInt #-} {-# INLINE remInt #-} quotInt, remInt, divInt, modInt :: Int -> Int -> Int (I# x) `quotInt` (I# y) = I# (x `quotInt#` y) (I# x) `remInt` (I# y) = I# (x `remInt#` y) (I# x) `divInt` (I# y) = I# (x `divInt#` y) (I# x) `modInt` (I# y) = I# (x `modInt#` y) quotRemInt :: Int -> Int -> (Int, Int) (I# x) `quotRemInt` (I# y) = case x `quotRemInt#` y of (# q, r #) -> (I# q, I# r) divModInt :: Int -> Int -> (Int, Int) (I# x) `divModInt` (I# y) = case x `divModInt#` y of (# q, r #) -> (I# q, I# r) divModInt# :: Int# -> Int# -> (# Int#, Int# #) x# `divModInt#` y# | isTrue# (x# ># 0#) && isTrue# (y# <# 0#) = case (x# -# 1#) `quotRemInt#` y# of (# q, r #) -> (# q -# 1#, r +# y# +# 1# #) | isTrue# (x# <# 0#) && isTrue# (y# ># 0#) = case (x# +# 1#) `quotRemInt#` y# of (# q, r #) -> (# q -# 1#, r +# y# -# 1# #) | otherwise = x# `quotRemInt#` y# -- Wrappers for the shift operations. The uncheckedShift# family are -- undefined when the amount being shifted by is greater than the size -- in bits of Int#, so these wrappers perform a check and return -- either zero or -1 appropriately. -- -- Note that these wrappers still produce undefined results when the -- second argument (the shift amount) is negative. -- | Shift the argument left by the specified number of bits -- (which must be non-negative). shiftL# :: Word# -> Int# -> Word# a `shiftL#` b | isTrue# (b >=# WORD_SIZE_IN_BITS#) = 0## | otherwise = a `uncheckedShiftL#` b -- | Shift the argument right by the specified number of bits -- (which must be non-negative). -- The "RL" means "right, logical" (as opposed to RA for arithmetic) -- (although an arithmetic right shift wouldn't make sense for Word#) shiftRL# :: Word# -> Int# -> Word# a `shiftRL#` b | isTrue# (b >=# WORD_SIZE_IN_BITS#) = 0## | otherwise = a `uncheckedShiftRL#` b -- | Shift the argument left by the specified number of bits -- (which must be non-negative). iShiftL# :: Int# -> Int# -> Int# a `iShiftL#` b | isTrue# (b >=# WORD_SIZE_IN_BITS#) = 0# | otherwise = a `uncheckedIShiftL#` b -- | Shift the argument right (signed) by the specified number of bits -- (which must be non-negative). -- The "RA" means "right, arithmetic" (as opposed to RL for logical) iShiftRA# :: Int# -> Int# -> Int# a `iShiftRA#` b | isTrue# (b >=# WORD_SIZE_IN_BITS#) = if isTrue# (a <# 0#) then (-1#) else 0# | otherwise = a `uncheckedIShiftRA#` b -- | Shift the argument right (unsigned) by the specified number of bits -- (which must be non-negative). -- The "RL" means "right, logical" (as opposed to RA for arithmetic) iShiftRL# :: Int# -> Int# -> Int# a `iShiftRL#` b | isTrue# (b >=# WORD_SIZE_IN_BITS#) = 0# | otherwise = a `uncheckedIShiftRL#` b -- Rules for C strings (the functions themselves are now in GHC.CString) {-# RULES "unpack" [~1] forall a . unpackCString# a = build (unpackFoldrCString# a) "unpack-list" [1] forall a . unpackFoldrCString# a (:) [] = unpackCString# a "unpack-append" forall a n . unpackFoldrCString# a (:) n = unpackAppendCString# a n -- There's a built-in rule (in PrelRules.hs) for -- unpackFoldr "foo" c (unpackFoldr "baz" c n) = unpackFoldr "foobaz" c n #-}