{-# LANGUAGE Trustworthy #-} {-# LANGUAGE CPP, NoImplicitPrelude, ScopedTypeVariables #-} {-# LANGUAGE BangPatterns #-} {-# OPTIONS_GHC -Wno-incomplete-uni-patterns #-} ----------------------------------------------------------------------------- -- | -- Module : GHC.List -- Copyright : (c) The University of Glasgow 1994-2002 -- License : see libraries/base/LICENSE -- -- Maintainer : cvs-ghc@haskell.org -- Stability : internal -- Portability : non-portable (GHC Extensions) -- -- The List data type and its operations -- ----------------------------------------------------------------------------- module GHC.List ( -- The list data type List, -- List-monomorphic Foldable methods and misc functions foldr, foldr', foldr1, foldl, foldl', foldl1, null, length, elem, notElem, maximum, minimum, sum, product, and, or, any, all, -- Other functions foldl1', concat, concatMap, map, (++), filter, lookup, head, last, tail, init, uncons, unsnoc, (!?), (!!), scanl, scanl1, scanl', scanr, scanr1, iterate, iterate', repeat, replicate, cycle, take, drop, splitAt, takeWhile, dropWhile, span, break, reverse, zip, zip3, zipWith, zipWith3, unzip, unzip3, errorEmptyList, -- * GHC List fusion augment, build, ) where import Data.Maybe import GHC.Base import GHC.Num (Num(..)) import GHC.Num.Integer (Integer) import GHC.Stack.Types (HasCallStack) infixl 9 !?, !! infix 4 `elem`, `notElem` -- $setup -- >>> import GHC.Base -- >>> import Prelude (Num (..), Ord (..), Int, Double, odd, not, undefined) -- >>> import Control.DeepSeq (force) -- -- -- compiled versions are uninterruptible. -- https://gitlab.haskell.org/ghc/ghc/-/issues/367 -- -- >>> let or = foldr (||) False -- >>> let and = foldr (&&) True -------------------------------------------------------------- -- List-manipulation functions -------------------------------------------------------------- -- | \(\mathcal{O}(1)\). Extract the first element of a list, which must be non-empty. -- -- >>> head [1, 2, 3] -- 1 -- >>> head [1..] -- 1 -- >>> head [] -- *** Exception: Prelude.head: empty list -- -- WARNING: This function is partial. You can use case-matching, 'uncons' or -- 'listToMaybe' instead. head :: HasCallStack => [a] -> a head :: forall a. HasCallStack => [a] -> a head (a x:[a] _) = a x head [] = a forall a. HasCallStack => a badHead {-# NOINLINE [1] head #-} {-# WARNING in "x-partial" head "This is a partial function, it throws an error on empty lists. Use pattern matching or Data.List.uncons instead. Consider refactoring to use Data.List.NonEmpty." #-} badHead :: HasCallStack => a badHead :: forall a. HasCallStack => a badHead = String -> a forall a. HasCallStack => String -> a errorEmptyList String "head" -- This rule is useful in cases like -- head [y | (x,y) <- ps, x==t] {-# RULES "head/build" forall (g::forall b.(a->b->b)->b->b) . head (build g) = g (\x _ -> x) badHead "head/augment" forall xs (g::forall b. (a->b->b) -> b -> b) . head (augment g xs) = g (\x _ -> x) (head xs) #-} -- | \(\mathcal{O}(1)\). Decompose a list into its 'head' and 'tail'. -- -- * If the list is empty, returns 'Nothing'. -- * If the list is non-empty, returns @'Just' (x, xs)@, -- where @x@ is the 'head' of the list and @xs@ its 'tail'. -- -- @since 4.8.0.0 -- -- >>> uncons [] -- Nothing -- >>> uncons [1] -- Just (1,[]) -- >>> uncons [1, 2, 3] -- Just (1,[2,3]) uncons :: [a] -> Maybe (a, [a]) uncons :: forall a. [a] -> Maybe (a, [a]) uncons [] = Maybe (a, [a]) forall a. Maybe a Nothing uncons (a x:[a] xs) = (a, [a]) -> Maybe (a, [a]) forall a. a -> Maybe a Just (a x, [a] xs) -- | \(\mathcal{O}(n)\). Decompose a list into 'init' and 'last'. -- -- * If the list is empty, returns 'Nothing'. -- * If the list is non-empty, returns @'Just' (xs, x)@, -- where @xs@ is the 'init'ial part of the list and @x@ is its 'last' element. -- -- @since 4.19.0.0 -- -- >>> unsnoc [] -- Nothing -- >>> unsnoc [1] -- Just ([],1) -- >>> unsnoc [1, 2, 3] -- Just ([1,2],3) -- -- Laziness: -- -- >>> fst <$> unsnoc [undefined] -- Just [] -- >>> head . fst <$> unsnoc (1 : undefined) -- Just *** Exception: Prelude.undefined -- >>> head . fst <$> unsnoc (1 : 2 : undefined) -- Just 1 -- -- 'unsnoc' is dual to 'uncons': for a finite list @xs@ -- -- > unsnoc xs = (\(hd, tl) -> (reverse tl, hd)) <$> uncons (reverse xs) -- unsnoc :: [a] -> Maybe ([a], a) -- The lazy pattern ~(a, b) is important to be productive on infinite lists -- and not to be prone to stack overflows. -- Expressing the recursion via 'foldr' provides for list fusion. unsnoc :: forall a. [a] -> Maybe ([a], a) unsnoc = (a -> Maybe ([a], a) -> Maybe ([a], a)) -> Maybe ([a], a) -> [a] -> Maybe ([a], a) forall a b. (a -> b -> b) -> b -> [a] -> b foldr (\a x -> ([a], a) -> Maybe ([a], a) forall a. a -> Maybe a Just (([a], a) -> Maybe ([a], a)) -> (Maybe ([a], a) -> ([a], a)) -> Maybe ([a], a) -> Maybe ([a], a) forall b c a. (b -> c) -> (a -> b) -> a -> c . ([a], a) -> (([a], a) -> ([a], a)) -> Maybe ([a], a) -> ([a], a) forall b a. b -> (a -> b) -> Maybe a -> b maybe ([], a x) (\(~([a] a, a b)) -> (a x a -> [a] -> [a] forall a. a -> [a] -> [a] : [a] a, a b))) Maybe ([a], a) forall a. Maybe a Nothing {-# INLINABLE unsnoc #-} -- | \(\mathcal{O}(1)\). Extract the elements after the head of a list, which -- must be non-empty. -- -- >>> tail [1, 2, 3] -- [2,3] -- >>> tail [1] -- [] -- >>> tail [] -- *** Exception: Prelude.tail: empty list -- -- WARNING: This function is partial. You can use case-matching or 'uncons' -- instead. tail :: HasCallStack => [a] -> [a] tail :: forall a. HasCallStack => [a] -> [a] tail (a _:[a] xs) = [a] xs tail [] = String -> [a] forall a. HasCallStack => String -> a errorEmptyList String "tail" {-# WARNING in "x-partial" tail "This is a partial function, it throws an error on empty lists. Replace it with drop 1, or use pattern matching or Data.List.uncons instead. Consider refactoring to use Data.List.NonEmpty." #-} -- | \(\mathcal{O}(n)\). Extract the last element of a list, which must be -- finite and non-empty. -- -- >>> last [1, 2, 3] -- 3 -- >>> last [1..] -- * Hangs forever * -- >>> last [] -- *** Exception: Prelude.last: empty list -- -- WARNING: This function is partial. Consider using 'unsnoc' instead. last :: HasCallStack => [a] -> a #if defined(USE_REPORT_PRELUDE) last [x] = x last (_:xs) = last xs last [] = errorEmptyList "last" #else -- Use foldl to make last a good consumer. -- This will compile to good code for the actual GHC.List.last. -- (At least as long it is eta-expanded, otherwise it does not, #10260.) last :: forall a. HasCallStack => [a] -> a last [a] xs = (a -> a -> a) -> a -> [a] -> a forall a b. (b -> a -> b) -> b -> [a] -> b foldl (\a _ a x -> a x) a forall a. HasCallStack => a lastError [a] xs {-# INLINE last #-} -- The inline pragma is required to make GHC remember the implementation via -- foldl. lastError :: HasCallStack => a lastError :: forall a. HasCallStack => a lastError = String -> a forall a. HasCallStack => String -> a errorEmptyList String "last" #endif -- | \(\mathcal{O}(n)\). Return all the elements of a list except the last one. -- The list must be non-empty. -- -- >>> init [1, 2, 3] -- [1,2] -- >>> init [1] -- [] -- >>> init [] -- *** Exception: Prelude.init: empty list -- -- WARNING: This function is partial. Consider using 'unsnoc' instead. init :: HasCallStack => [a] -> [a] #if defined(USE_REPORT_PRELUDE) init [x] = [] init (x:xs) = x : init xs init [] = errorEmptyList "init" #else -- eliminate repeated cases init :: forall a. HasCallStack => [a] -> [a] init [] = String -> [a] forall a. HasCallStack => String -> a errorEmptyList String "init" init (a x:[a] xs) = a -> [a] -> [a] forall a. a -> [a] -> [a] init' a x [a] xs where init' :: t -> [t] -> [t] init' t _ [] = [] init' t y (t z:[t] zs) = t y t -> [t] -> [t] forall a. a -> [a] -> [a] : t -> [t] -> [t] init' t z [t] zs #endif -- | \(\mathcal{O}(1)\). Test whether a list is empty. -- -- >>> null [] -- True -- >>> null [1] -- False -- >>> null [1..] -- False null :: [a] -> Bool null :: forall a. [a] -> Bool null [] = Bool True null (a _:[a] _) = Bool False -- | \(\mathcal{O}(n)\). 'length' returns the length of a finite list as an -- 'Int'. It is an instance of the more general 'Data.List.genericLength', the -- result type of which may be any kind of number. -- -- >>> length [] -- 0 -- >>> length ['a', 'b', 'c'] -- 3 -- >>> length [1..] -- * Hangs forever * {-# NOINLINE [1] length #-} length :: [a] -> Int length :: forall a. [a] -> Int length [a] xs = [a] -> Int -> Int forall a. [a] -> Int -> Int lenAcc [a] xs Int 0 lenAcc :: [a] -> Int -> Int lenAcc :: forall a. [a] -> Int -> Int lenAcc [] Int n = Int n lenAcc (a _:[a] ys) Int n = [a] -> Int -> Int forall a. [a] -> Int -> Int lenAcc [a] ys (Int nInt -> Int -> Int forall a. Num a => a -> a -> a +Int 1) {-# RULES "length" [~1] forall xs . length xs = foldr lengthFB idLength xs 0 "lengthList" [1] foldr lengthFB idLength = lenAcc #-} -- The lambda form turns out to be necessary to make this inline -- when we need it to and give good performance. {-# INLINE [0] lengthFB #-} lengthFB :: x -> (Int -> Int) -> Int -> Int lengthFB :: forall x. x -> (Int -> Int) -> Int -> Int lengthFB x _ Int -> Int r = \ !Int a -> Int -> Int r (Int a Int -> Int -> Int forall a. Num a => a -> a -> a + Int 1) {-# INLINE [0] idLength #-} idLength :: Int -> Int idLength :: Int -> Int idLength = Int -> Int forall a. a -> a id -- | \(\mathcal{O}(n)\). 'filter', applied to a predicate and a list, returns -- the list of those elements that satisfy the predicate; i.e., -- -- > filter p xs = [ x | x <- xs, p x] -- -- >>> filter odd [1, 2, 3] -- [1,3] {-# NOINLINE [1] filter #-} filter :: (a -> Bool) -> [a] -> [a] filter :: forall a. (a -> Bool) -> [a] -> [a] filter a -> Bool _pred [] = [] filter a -> Bool pred (a x:[a] xs) | a -> Bool pred a x = a x a -> [a] -> [a] forall a. a -> [a] -> [a] : (a -> Bool) -> [a] -> [a] forall a. (a -> Bool) -> [a] -> [a] filter a -> Bool pred [a] xs | Bool otherwise = (a -> Bool) -> [a] -> [a] forall a. (a -> Bool) -> [a] -> [a] filter a -> Bool pred [a] xs {-# INLINE [0] filterFB #-} -- See Note [Inline FB functions] filterFB :: (a -> b -> b) -> (a -> Bool) -> a -> b -> b filterFB :: forall a b. (a -> b -> b) -> (a -> Bool) -> a -> b -> b filterFB a -> b -> b c a -> Bool p a x b r | a -> Bool p a x = a x a -> b -> b `c` b r | Bool otherwise = b r {-# RULES "filter" [~1] forall p xs. filter p xs = build (\c n -> foldr (filterFB c p) n xs) "filterList" [1] forall p. foldr (filterFB (:) p) [] = filter p "filterFB" forall c p q. filterFB (filterFB c p) q = filterFB c (\x -> q x && p x) #-} -- Note the filterFB rule, which has p and q the "wrong way round" in the RHS. -- filterFB (filterFB c p) q a b -- = if q a then filterFB c p a b else b -- = if q a then (if p a then c a b else b) else b -- = if q a && p a then c a b else b -- = filterFB c (\x -> q x && p x) a b -- I originally wrote (\x -> p x && q x), which is wrong, and actually -- gave rise to a live bug report. SLPJ. -- | 'foldl', applied to a binary operator, a starting value (typically -- the left-identity of the operator), and a list, reduces the list -- using the binary operator, from left to right: -- -- > foldl f z [x1, x2, ..., xn] == (...((z `f` x1) `f` x2) `f`...) `f` xn -- -- The list must be finite. -- -- >>> foldl (+) 0 [1..4] -- 10 -- >>> foldl (+) 42 [] -- 42 -- >>> foldl (-) 100 [1..4] -- 90 -- >>> foldl (\reversedString nextChar -> nextChar : reversedString) "foo" ['a', 'b', 'c', 'd'] -- "dcbafoo" -- >>> foldl (+) 0 [1..] -- * Hangs forever * foldl :: forall a b. (b -> a -> b) -> b -> [a] -> b {-# INLINE foldl #-} foldl :: forall a b. (b -> a -> b) -> b -> [a] -> b foldl b -> a -> b k b z0 [a] xs = (a -> (b -> b) -> b -> b) -> (b -> b) -> [a] -> b -> b forall a b. (a -> b -> b) -> b -> [a] -> b foldr (\(a v::a) (b -> b fn::b->b) -> (b -> b) -> b -> b forall a b. (a -> b) -> a -> b oneShot (\(b z::b) -> b -> b fn (b -> a -> b k b z a v))) (b -> b forall a. a -> a id :: b -> b) [a] xs b z0 -- See Note [Left folds via right fold] {- Note [Left folds via right fold] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Implementing foldl et. al. via foldr is only a good idea if the compiler can optimize the resulting code (eta-expand the recursive "go"). See #7994. We hope that one of the two measure kick in: * Call Arity (-fcall-arity, enabled by default) eta-expands it if it can see all calls and determine that the arity is large. * The oneShot annotation gives a hint to the regular arity analysis that it may assume that the lambda is called at most once. See [One-shot lambdas] in CoreArity and especially [Eta expanding thunks] in CoreArity. The oneShot annotations used in this module are correct, as we only use them in arguments to foldr, where we know how the arguments are called. Note [Inline FB functions] ~~~~~~~~~~~~~~~~~~~~~~~~~~ After fusion rules successfully fire, we are usually left with one or more calls to list-producing functions abstracted over cons and nil. Here we call them FB functions because their names usually end with 'FB'. It's a good idea to inline FB functions because: * They are higher-order functions and therefore benefit from inlining. * When the final consumer is a left fold, inlining the FB functions is the only way to make arity expansion happen. See Note [Left folds via right fold]. For this reason we mark all FB functions INLINE [0]. The [0] phase-specifier ensures that calls to FB functions can be written back to the original form when no fusion happens. Without these inline pragmas, the loop in perf/should_run/T13001 won't be allocation-free. Also see #13001. -} -- ---------------------------------------------------------------------------- -- | A strict version of 'foldl'. foldl' :: forall a b . (b -> a -> b) -> b -> [a] -> b {-# INLINE foldl' #-} foldl' :: forall a b. (b -> a -> b) -> b -> [a] -> b foldl' b -> a -> b k b z0 = \[a] xs -> (a -> (b -> b) -> b -> b) -> (b -> b) -> [a] -> b -> b forall a b. (a -> b -> b) -> b -> [a] -> b foldr (\(a v::a) (b -> b fn::b->b) -> (b -> b) -> b -> b forall a b. (a -> b) -> a -> b oneShot (\(b z::b) -> b z b -> b -> b forall a b. a -> b -> b `seq` b -> b fn (b -> a -> b k b z a v))) (b -> b forall a. a -> a id :: b -> b) [a] xs b z0 {- Note [Definition of foldl'] ~~~~~~~~~~~~~~~~~~~~~~~~~~~ We want foldl' to be a good consumer, so: * We define it (rather cunningly) with `foldr`. That way, the `fold/build` rule might fire. See Note [Left folds via right fold] * We give it an INLINE pragma, so that it'll inline at its call sites, again giving the `fold/build` rule a chance to fire. * We eta-reduce it so that it has arity 2, not 3. Reason: consider sumlen :: [Float] -> (Float, Int) sumlen = foldl' f (0, 0) where f (!s, !n) !x = (s + x, n + 1) The RHS of `sumlen` is a partial application of foldl', and is not eta-expanded (and it isn't, because we don't eta-expand PAPs. See Note [Do not eta-expand PAPs] in GHC.Core.Opt.Simplify.Utils) So foldl' is partially applied to two arguments, /and it won't inline/ if its defn is: {-# INLINE foldl' #-} foldl' k z xs = ... because INLINE functions only inline when saturated. Conclusion: move the `xs` parameter to the RHS, and define it thus fold' k z = \xs -> ... See !5259 for additional discussion. This may result in partial applications of 'foldl'' inlining in some functions where they previously did not. Absent an INLINE pragam for the calling function, it may become too expensive to automatically inline, resulting in a loss of previously accidental list fusion. Such call sites may now need explicit INLINE or INLINABLE pragmas to make the desired list fusion robust. -} -- | 'foldl1' is a variant of 'foldl' that has no starting value argument, -- and thus must be applied to non-empty lists. Note that unlike 'foldl', the accumulated value must be of the same type as the list elements. -- -- >>> foldl1 (+) [1..4] -- 10 -- >>> foldl1 (+) [] -- *** Exception: Prelude.foldl1: empty list -- >>> foldl1 (-) [1..4] -- -8 -- >>> foldl1 (&&) [True, False, True, True] -- False -- >>> foldl1 (||) [False, False, True, True] -- True -- >>> foldl1 (+) [1..] -- * Hangs forever * foldl1 :: HasCallStack => (a -> a -> a) -> [a] -> a foldl1 :: forall a. HasCallStack => (a -> a -> a) -> [a] -> a foldl1 a -> a -> a f (a x:[a] xs) = (a -> a -> a) -> a -> [a] -> a forall a b. (b -> a -> b) -> b -> [a] -> b foldl a -> a -> a f a x [a] xs foldl1 a -> a -> a _ [] = String -> a forall a. HasCallStack => String -> a errorEmptyList String "foldl1" -- | A strict version of 'foldl1'. foldl1' :: HasCallStack => (a -> a -> a) -> [a] -> a foldl1' :: forall a. HasCallStack => (a -> a -> a) -> [a] -> a foldl1' a -> a -> a f (a x:[a] xs) = (a -> a -> a) -> a -> [a] -> a forall a b. (b -> a -> b) -> b -> [a] -> b foldl' a -> a -> a f a x [a] xs foldl1' a -> a -> a _ [] = String -> a forall a. HasCallStack => String -> a errorEmptyList String "foldl1'" -- ----------------------------------------------------------------------------- -- List sum and product -- | The 'sum' function computes the sum of a finite list of numbers. -- -- >>> sum [] -- 0 -- >>> sum [42] -- 42 -- >>> sum [1..10] -- 55 -- >>> sum [4.1, 2.0, 1.7] -- 7.8 -- >>> sum [1..] -- * Hangs forever * sum :: (Num a) => [a] -> a {-# INLINE sum #-} sum :: forall a. Num a => [a] -> a sum = (a -> a -> a) -> a -> [a] -> a forall a b. (b -> a -> b) -> b -> [a] -> b foldl' a -> a -> a forall a. Num a => a -> a -> a (+) a 0 -- | The 'product' function computes the product of a finite list of numbers. -- -- >>> product [] -- 1 -- >>> product [42] -- 42 -- >>> product [1..10] -- 3628800 -- >>> product [4.1, 2.0, 1.7] -- 13.939999999999998 -- >>> product [1..] -- * Hangs forever * product :: (Num a) => [a] -> a {-# INLINE product #-} product :: forall a. Num a => [a] -> a product = (a -> a -> a) -> a -> [a] -> a forall a b. (b -> a -> b) -> b -> [a] -> b foldl' a -> a -> a forall a. Num a => a -> a -> a (*) a 1 -- | \(\mathcal{O}(n)\). 'scanl' is similar to 'foldl', but returns a list of -- successive reduced values from the left: -- -- > scanl f z [x1, x2, ...] == [z, z `f` x1, (z `f` x1) `f` x2, ...] -- -- Note that -- -- > last (scanl f z xs) == foldl f z xs -- -- >>> scanl (+) 0 [1..4] -- [0,1,3,6,10] -- >>> scanl (+) 42 [] -- [42] -- >>> scanl (-) 100 [1..4] -- [100,99,97,94,90] -- >>> scanl (\reversedString nextChar -> nextChar : reversedString) "foo" ['a', 'b', 'c', 'd'] -- ["foo","afoo","bafoo","cbafoo","dcbafoo"] -- >>> take 10 (scanl (+) 0 [1..]) -- [0,1,3,6,10,15,21,28,36,45] -- >>> take 1 (scanl undefined 'a' undefined) -- "a" -- This peculiar arrangement is necessary to prevent scanl being rewritten in -- its own right-hand side. {-# NOINLINE [1] scanl #-} scanl :: (b -> a -> b) -> b -> [a] -> [b] scanl :: forall b a. (b -> a -> b) -> b -> [a] -> [b] scanl = (b -> a -> b) -> b -> [a] -> [b] forall b a. (b -> a -> b) -> b -> [a] -> [b] scanlGo where scanlGo :: (b -> a -> b) -> b -> [a] -> [b] scanlGo :: forall b a. (b -> a -> b) -> b -> [a] -> [b] scanlGo b -> a -> b f b q [a] ls = b q b -> [b] -> [b] forall a. a -> [a] -> [a] : (case [a] ls of [] -> [] a x:[a] xs -> (b -> a -> b) -> b -> [a] -> [b] forall b a. (b -> a -> b) -> b -> [a] -> [b] scanlGo b -> a -> b f (b -> a -> b f b q a x) [a] xs) -- See Note [scanl rewrite rules] {-# RULES "scanl" [~1] forall f a bs . scanl f a bs = build (\c n -> a `c` foldr (scanlFB f c) (constScanl n) bs a) "scanlList" [1] forall f (a::a) bs . foldr (scanlFB f (:)) (constScanl []) bs a = tail (scanl f a bs) #-} {-# INLINE [0] scanlFB #-} -- See Note [Inline FB functions] scanlFB :: (b -> a -> b) -> (b -> c -> c) -> a -> (b -> c) -> b -> c scanlFB :: forall b a c. (b -> a -> b) -> (b -> c -> c) -> a -> (b -> c) -> b -> c scanlFB b -> a -> b f b -> c -> c c = \a b b -> c g -> (b -> c) -> b -> c forall a b. (a -> b) -> a -> b oneShot (\b x -> let b' :: b b' = b -> a -> b f b x a b in b b' b -> c -> c `c` b -> c g b b') -- See Note [Left folds via right fold] {-# INLINE [0] constScanl #-} constScanl :: a -> b -> a constScanl :: forall a b. a -> b -> a constScanl = a -> b -> a forall a b. a -> b -> a const -- | \(\mathcal{O}(n)\). 'scanl1' is a variant of 'scanl' that has no starting -- value argument: -- -- > scanl1 f [x1, x2, ...] == [x1, x1 `f` x2, ...] -- -- >>> scanl1 (+) [1..4] -- [1,3,6,10] -- >>> scanl1 (+) [] -- [] -- >>> scanl1 (-) [1..4] -- [1,-1,-4,-8] -- >>> scanl1 (&&) [True, False, True, True] -- [True,False,False,False] -- >>> scanl1 (||) [False, False, True, True] -- [False,False,True,True] -- >>> take 10 (scanl1 (+) [1..]) -- [1,3,6,10,15,21,28,36,45,55] -- >>> take 1 (scanl1 undefined ('a' : undefined)) -- "a" scanl1 :: (a -> a -> a) -> [a] -> [a] scanl1 :: forall a. (a -> a -> a) -> [a] -> [a] scanl1 a -> a -> a f (a x:[a] xs) = (a -> a -> a) -> a -> [a] -> [a] forall b a. (b -> a -> b) -> b -> [a] -> [b] scanl a -> a -> a f a x [a] xs scanl1 a -> a -> a _ [] = [] -- | \(\mathcal{O}(n)\). A strict version of 'scanl'. {-# NOINLINE [1] scanl' #-} scanl' :: (b -> a -> b) -> b -> [a] -> [b] -- This peculiar form is needed to prevent scanl' from being rewritten -- in its own right hand side. scanl' :: forall b a. (b -> a -> b) -> b -> [a] -> [b] scanl' = (b -> a -> b) -> b -> [a] -> [b] forall b a. (b -> a -> b) -> b -> [a] -> [b] scanlGo' where scanlGo' :: (b -> a -> b) -> b -> [a] -> [b] scanlGo' :: forall b a. (b -> a -> b) -> b -> [a] -> [b] scanlGo' b -> a -> b f !b q [a] ls = b q b -> [b] -> [b] forall a. a -> [a] -> [a] : (case [a] ls of [] -> [] a x:[a] xs -> (b -> a -> b) -> b -> [a] -> [b] forall b a. (b -> a -> b) -> b -> [a] -> [b] scanlGo' b -> a -> b f (b -> a -> b f b q a x) [a] xs) -- See Note [scanl rewrite rules] {-# RULES "scanl'" [~1] forall f a bs . scanl' f a bs = build (\c n -> a `c` foldr (scanlFB' f c) (flipSeq n) bs a) "scanlList'" [1] forall f a bs . foldr (scanlFB' f (:)) (flipSeq []) bs a = tail (scanl' f a bs) #-} {-# INLINE [0] scanlFB' #-} -- See Note [Inline FB functions] scanlFB' :: (b -> a -> b) -> (b -> c -> c) -> a -> (b -> c) -> b -> c scanlFB' :: forall b a c. (b -> a -> b) -> (b -> c -> c) -> a -> (b -> c) -> b -> c scanlFB' b -> a -> b f b -> c -> c c = \a b b -> c g -> (b -> c) -> b -> c forall a b. (a -> b) -> a -> b oneShot (\b x -> let !b' :: b b' = b -> a -> b f b x a b in b b' b -> c -> c `c` b -> c g b b') -- See Note [Left folds via right fold] {- Note [scanl rewrite rules] ~~~~~~~~~~~~~~~~~~~~~~~~~~ In most cases, when we rewrite a form to one that can fuse, we try to rewrite it back to the original form if it does not fuse. For scanl, we do something a little different. In particular, we rewrite scanl f a bs to build (\c n -> a `c` foldr (scanlFB f c) (constScanl n) bs a) When build is inlined, this becomes a : foldr (scanlFB f (:)) (constScanl []) bs a To rewrite this form back to scanl, we would need a rule that looked like forall f a bs. a : foldr (scanlFB f (:)) (constScanl []) bs a = scanl f a bs The problem with this rule is that it has (:) at its head. This would have the effect of changing the way the inliner looks at (:), not only here but everywhere. In most cases, this makes no difference, but in some cases it causes it to come to a different decision about whether to inline something. Based on nofib benchmarks, this is bad for performance. Therefore, we instead match on everything past the :, which is just the tail of scanl. -} -- foldr, foldr', foldr1, scanr, and scanr1 are the right-to-left duals of the -- above functions. -- | 'foldr'' is a variant of 'foldr' that begins list reduction from the last -- element and evaluates the accumulator strictly as it unwinds the stack back -- to the beginning of the list. The input list /must/ be finite, otherwise -- 'foldr'' runs out of space (/diverges/). -- -- Note that if the function that combines the accumulated value with each -- element is strict in the accumulator, other than a possible improvement -- in the constant factor, you get the same \(\mathcal{O}(n)\) space cost -- as with just 'foldr'. -- -- If you want a strict right fold in constant space, you need a structure -- that supports faster than \(\mathcal{O}(n)\) access to the right-most -- element, such as @Seq@ from the @containers@ package. -- -- Use of this function is a hint that the @[]@ structure may be a poor fit -- for the task at hand. If the order in which the elements are combined is -- not important, use 'foldl'' instead. -- -- >>> foldr' (+) [1..4] -- Use foldl' instead! -- 10 -- >>> foldr' (&&) [True, False, True, True] -- Use foldr instead! -- False -- >>> foldr' (||) [False, False, True, True] -- Use foldr instead! -- True foldr' :: (a -> b -> b) -> b -> [a] -> b foldr' :: forall a b. (a -> b -> b) -> b -> [a] -> b foldr' a -> b -> b f b z0 [a] xs = ((b -> b) -> a -> b -> b) -> (b -> b) -> [a] -> b -> b forall a b. (b -> a -> b) -> b -> [a] -> b foldl (b -> b) -> a -> b -> b forall {b}. (b -> b) -> a -> b -> b f' b -> b forall a. a -> a id [a] xs b z0 where f' :: (b -> b) -> a -> b -> b f' b -> b k a x b z = b -> b k (b -> b) -> b -> b forall a b. (a -> b) -> a -> b $! a -> b -> b f a x b z -- | 'foldr1' is a variant of 'foldr' that has no starting value argument, -- and thus must be applied to non-empty lists. Note that unlike 'foldr', the accumulated value must be of the same type as the list elements. -- -- >>> foldr1 (+) [1..4] -- 10 -- >>> foldr1 (+) [] -- *** Exception: Prelude.foldr1: empty list -- >>> foldr1 (-) [1..4] -- -2 -- >>> foldr1 (&&) [True, False, True, True] -- False -- >>> foldr1 (||) [False, False, True, True] -- True -- >>> force $ foldr1 (+) [1..] -- *** Exception: stack overflow foldr1 :: HasCallStack => (a -> a -> a) -> [a] -> a foldr1 :: forall a. HasCallStack => (a -> a -> a) -> [a] -> a foldr1 a -> a -> a f = [a] -> a go where go :: [a] -> a go [a x] = a x go (a x:[a] xs) = a -> a -> a f a x ([a] -> a go [a] xs) go [] = String -> a forall a. HasCallStack => String -> a errorEmptyList String "foldr1" {-# INLINE [0] foldr1 #-} -- | \(\mathcal{O}(n)\). 'scanr' is the right-to-left dual of 'scanl'. Note that the order of parameters on the accumulating function are reversed compared to 'scanl'. -- Also note that -- -- > head (scanr f z xs) == foldr f z xs. -- -- >>> scanr (+) 0 [1..4] -- [10,9,7,4,0] -- >>> scanr (+) 42 [] -- [42] -- >>> scanr (-) 100 [1..4] -- [98,-97,99,-96,100] -- >>> scanr (\nextChar reversedString -> nextChar : reversedString) "foo" ['a', 'b', 'c', 'd'] -- ["abcdfoo","bcdfoo","cdfoo","dfoo","foo"] -- >>> force $ scanr (+) 0 [1..] -- *** Exception: stack overflow {-# NOINLINE [1] scanr #-} scanr :: (a -> b -> b) -> b -> [a] -> [b] scanr :: forall a b. (a -> b -> b) -> b -> [a] -> [b] scanr a -> b -> b _ b q0 [] = [b q0] scanr a -> b -> b f b q0 (a x:[a] xs) = a -> b -> b f a x b q b -> [b] -> [b] forall a. a -> [a] -> [a] : [b] qs where qs :: [b] qs@(b q:[b] _) = (a -> b -> b) -> b -> [a] -> [b] forall a b. (a -> b -> b) -> b -> [a] -> [b] scanr a -> b -> b f b q0 [a] xs {-# INLINE [0] strictUncurryScanr #-} strictUncurryScanr :: (a -> b -> c) -> (a, b) -> c strictUncurryScanr :: forall a b c. (a -> b -> c) -> (a, b) -> c strictUncurryScanr a -> b -> c f (a, b) pair = case (a, b) pair of (a x, b y) -> a -> b -> c f a x b y {-# INLINE [0] scanrFB #-} -- See Note [Inline FB functions] scanrFB :: (a -> b -> b) -> (b -> c -> c) -> a -> (b, c) -> (b, c) scanrFB :: forall a b c. (a -> b -> b) -> (b -> c -> c) -> a -> (b, c) -> (b, c) scanrFB a -> b -> b f b -> c -> c c = \a x ~(b r, c est) -> (a -> b -> b f a x b r, b r b -> c -> c `c` c est) -- This lazy pattern match on the tuple is necessary to prevent -- an infinite loop when scanr receives a fusable infinite list, -- which was the reason for #16943. -- See Note [scanrFB and evaluation] below {-# RULES "scanr" [~1] forall f q0 ls . scanr f q0 ls = build (\c n -> strictUncurryScanr c (foldr (scanrFB f c) (q0,n) ls)) "scanrList" [1] forall f q0 ls . strictUncurryScanr (:) (foldr (scanrFB f (:)) (q0,[]) ls) = scanr f q0 ls #-} {- Note [scanrFB and evaluation] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ In a previous Version, the pattern match on the tuple in scanrFB used to be strict. If scanr is called with a build expression, the following would happen: The rule "scanr" would fire, and we obtain build (\c n -> strictUncurryScanr c (foldr (scanrFB f c) (q0,n) (build g)))) The rule "foldr/build" now fires, and the second argument of strictUncurryScanr will be the expression g (scanrFB f c) (q0,n) which will be evaluated, thanks to strictUncurryScanr. The type of (g :: (a -> b -> b) -> b -> b) allows us to apply parametricity: Either the tuple is returned (trivial), or scanrFB is called: g (scanrFB f c) (q0,n) = scanrFB ... (g' (scanrFB f c) (q0,n)) Notice that thanks to the strictness of scanrFB, the expression g' (scanrFB f c) (q0,n) gets evaluated as well. In particular, if g' is a recursive case of g, parametricity applies again and we will again have a possible call to scanrFB. In short, g (scanrFB f c) (q0,n) will end up being completely evaluated. This is resource consuming for large lists and if the recursion has no exit condition (and this will be the case in functions like repeat or cycle), the program will crash (see #16943). The solution: Don't make scanrFB strict in its last argument. Doing so will remove the cause for the chain of evaluations, and all is well. -} -- | \(\mathcal{O}(n)\). 'scanr1' is a variant of 'scanr' that has no starting -- value argument. -- -- >>> scanr1 (+) [1..4] -- [10,9,7,4] -- >>> scanr1 (+) [] -- [] -- >>> scanr1 (-) [1..4] -- [-2,3,-1,4] -- >>> scanr1 (&&) [True, False, True, True] -- [False,False,True,True] -- >>> scanr1 (||) [True, True, False, False] -- [True,True,False,False] -- >>> force $ scanr1 (+) [1..] -- *** Exception: stack overflow scanr1 :: (a -> a -> a) -> [a] -> [a] scanr1 :: forall a. (a -> a -> a) -> [a] -> [a] scanr1 a -> a -> a _ [] = [] scanr1 a -> a -> a _ [a x] = [a x] scanr1 a -> a -> a f (a x:[a] xs) = a -> a -> a f a x a q a -> [a] -> [a] forall a. a -> [a] -> [a] : [a] qs where qs :: [a] qs@(a q:[a] _) = (a -> a -> a) -> [a] -> [a] forall a. (a -> a -> a) -> [a] -> [a] scanr1 a -> a -> a f [a] xs -- | 'maximum' returns the maximum value from a list, -- which must be non-empty, finite, and of an ordered type. -- It is a special case of 'Data.List.maximumBy', which allows the -- programmer to supply their own comparison function. -- -- >>> maximum [] -- *** Exception: Prelude.maximum: empty list -- >>> maximum [42] -- 42 -- >>> maximum [55, -12, 7, 0, -89] -- 55 -- >>> maximum [1..] -- * Hangs forever * maximum :: (Ord a, HasCallStack) => [a] -> a {-# INLINABLE maximum #-} maximum :: forall a. (Ord a, HasCallStack) => [a] -> a maximum [] = String -> a forall a. HasCallStack => String -> a errorEmptyList String "maximum" maximum [a] xs = (a -> a -> a) -> [a] -> a forall a. HasCallStack => (a -> a -> a) -> [a] -> a foldl1' a -> a -> a forall a. Ord a => a -> a -> a max [a] xs -- We want this to be specialized so that with a strict max function, GHC -- produces good code. Note that to see if this is happening, one has to -- look at -ddump-prep, not -ddump-core! {-# SPECIALIZE maximum :: [Int] -> Int #-} {-# SPECIALIZE maximum :: [Integer] -> Integer #-} -- | 'minimum' returns the minimum value from a list, -- which must be non-empty, finite, and of an ordered type. -- It is a special case of 'Data.List.minimumBy', which allows the -- programmer to supply their own comparison function. -- -- >>> minimum [] -- *** Exception: Prelude.minimum: empty list -- >>> minimum [42] -- 42 -- >>> minimum [55, -12, 7, 0, -89] -- -89 -- >>> minimum [1..] -- * Hangs forever * minimum :: (Ord a, HasCallStack) => [a] -> a {-# INLINABLE minimum #-} minimum :: forall a. (Ord a, HasCallStack) => [a] -> a minimum [] = String -> a forall a. HasCallStack => String -> a errorEmptyList String "minimum" minimum [a] xs = (a -> a -> a) -> [a] -> a forall a. HasCallStack => (a -> a -> a) -> [a] -> a foldl1' a -> a -> a forall a. Ord a => a -> a -> a min [a] xs {-# SPECIALIZE minimum :: [Int] -> Int #-} {-# SPECIALIZE minimum :: [Integer] -> Integer #-} -- | 'iterate' @f x@ returns an infinite list of repeated applications -- of @f@ to @x@: -- -- > iterate f x == [x, f x, f (f x), ...] -- -- Note that 'iterate' is lazy, potentially leading to thunk build-up if -- the consumer doesn't force each iterate. See 'iterate'' for a strict -- variant of this function. -- -- >>> take 10 $ iterate not True -- [True,False,True,False,True,False,True,False,True,False] -- >>> take 10 $ iterate (+3) 42 -- [42,45,48,51,54,57,60,63,66,69] -- >>> take 1 $ iterate undefined 42 -- [42] -- {-# NOINLINE [1] iterate #-} iterate :: (a -> a) -> a -> [a] iterate :: forall a. (a -> a) -> a -> [a] iterate a -> a f a x = a x a -> [a] -> [a] forall a. a -> [a] -> [a] : (a -> a) -> a -> [a] forall a. (a -> a) -> a -> [a] iterate a -> a f (a -> a f a x) {-# INLINE [0] iterateFB #-} -- See Note [Inline FB functions] iterateFB :: (a -> b -> b) -> (a -> a) -> a -> b iterateFB :: forall a b. (a -> b -> b) -> (a -> a) -> a -> b iterateFB a -> b -> b c a -> a f a x0 = a -> b go a x0 where go :: a -> b go a x = a x a -> b -> b `c` a -> b go (a -> a f a x) {-# RULES "iterate" [~1] forall f x. iterate f x = build (\c _n -> iterateFB c f x) "iterateFB" [1] iterateFB (:) = iterate #-} -- | 'iterate'' is the strict version of 'iterate'. -- -- It forces the result of each application of the function to weak head normal -- form (WHNF) -- before proceeding. -- -- >>> take 1 $ iterate' undefined 42 -- *** Exception: Prelude.undefined -- {-# NOINLINE [1] iterate' #-} iterate' :: (a -> a) -> a -> [a] iterate' :: forall a. (a -> a) -> a -> [a] iterate' a -> a f a x = let x' :: a x' = a -> a f a x in a x' a -> [a] -> [a] forall a b. a -> b -> b `seq` (a x a -> [a] -> [a] forall a. a -> [a] -> [a] : (a -> a) -> a -> [a] forall a. (a -> a) -> a -> [a] iterate' a -> a f a x') {-# INLINE [0] iterate'FB #-} -- See Note [Inline FB functions] iterate'FB :: (a -> b -> b) -> (a -> a) -> a -> b iterate'FB :: forall a b. (a -> b -> b) -> (a -> a) -> a -> b iterate'FB a -> b -> b c a -> a f a x0 = a -> b go a x0 where go :: a -> b go a x = let x' :: a x' = a -> a f a x in a x' a -> b -> b forall a b. a -> b -> b `seq` (a x a -> b -> b `c` a -> b go a x') {-# RULES "iterate'" [~1] forall f x. iterate' f x = build (\c _n -> iterate'FB c f x) "iterate'FB" [1] iterate'FB (:) = iterate' #-} -- | 'repeat' @x@ is an infinite list, with @x@ the value of every element. -- -- >>> repeat 17 -- [17,17,17,17,17,17,17,17,17... repeat :: a -> [a] {-# INLINE [0] repeat #-} -- The pragma just gives the rules more chance to fire repeat :: forall a. a -> [a] repeat a x = [a] xs where xs :: [a] xs = a x a -> [a] -> [a] forall a. a -> [a] -> [a] : [a] xs {-# INLINE [0] repeatFB #-} -- ditto -- See Note [Inline FB functions] repeatFB :: (a -> b -> b) -> a -> b repeatFB :: forall a b. (a -> b -> b) -> a -> b repeatFB a -> b -> b c a x = b xs where xs :: b xs = a x a -> b -> b `c` b xs {-# RULES "repeat" [~1] forall x. repeat x = build (\c _n -> repeatFB c x) "repeatFB" [1] repeatFB (:) = repeat #-} -- | 'replicate' @n x@ is a list of length @n@ with @x@ the value of -- every element. -- It is an instance of the more general 'Data.List.genericReplicate', -- in which @n@ may be of any integral type. -- -- >>> replicate 0 True -- [] -- >>> replicate (-1) True -- [] -- >>> replicate 4 True -- [True,True,True,True] {-# INLINE replicate #-} replicate :: Int -> a -> [a] replicate :: forall a. Int -> a -> [a] replicate Int n a x = Int -> [a] -> [a] forall a. Int -> [a] -> [a] take Int n (a -> [a] forall a. a -> [a] repeat a x) -- | 'cycle' ties a finite list into a circular one, or equivalently, -- the infinite repetition of the original list. It is the identity -- on infinite lists. -- -- >>> cycle [] -- *** Exception: Prelude.cycle: empty list -- >>> take 10 (cycle [42]) -- [42,42,42,42,42,42,42,42,42,42] -- >>> take 10 (cycle [2, 5, 7]) -- [2,5,7,2,5,7,2,5,7,2] -- >>> take 1 (cycle (42 : undefined)) -- [42] -- cycle :: HasCallStack => [a] -> [a] cycle :: forall a. HasCallStack => [a] -> [a] cycle [] = String -> [a] forall a. HasCallStack => String -> a errorEmptyList String "cycle" cycle [a] xs = [a] xs' where xs' :: [a] xs' = [a] xs [a] -> [a] -> [a] forall a. [a] -> [a] -> [a] ++ [a] xs' -- | 'takeWhile', applied to a predicate @p@ and a list @xs@, returns the -- longest prefix (possibly empty) of @xs@ of elements that satisfy @p@. -- -- >>> takeWhile (< 3) [1,2,3,4,1,2,3,4] -- [1,2] -- >>> takeWhile (< 9) [1,2,3] -- [1,2,3] -- >>> takeWhile (< 0) [1,2,3] -- [] -- -- Laziness: -- -- >>> takeWhile (const False) undefined -- *** Exception: Prelude.undefined -- >>> takeWhile (const False) (undefined : undefined) -- [] -- >>> take 1 (takeWhile (const True) (1 : undefined)) -- [1] -- {-# NOINLINE [1] takeWhile #-} takeWhile :: (a -> Bool) -> [a] -> [a] takeWhile :: forall a. (a -> Bool) -> [a] -> [a] takeWhile a -> Bool _ [] = [] takeWhile a -> Bool p (a x:[a] xs) | a -> Bool p a x = a x a -> [a] -> [a] forall a. a -> [a] -> [a] : (a -> Bool) -> [a] -> [a] forall a. (a -> Bool) -> [a] -> [a] takeWhile a -> Bool p [a] xs | Bool otherwise = [] {-# INLINE [0] takeWhileFB #-} -- See Note [Inline FB functions] takeWhileFB :: (a -> Bool) -> (a -> b -> b) -> b -> a -> b -> b takeWhileFB :: forall a b. (a -> Bool) -> (a -> b -> b) -> b -> a -> b -> b takeWhileFB a -> Bool p a -> b -> b c b n = \a x b r -> if a -> Bool p a x then a x a -> b -> b `c` b r else b n -- The takeWhileFB rule is similar to the filterFB rule. It works like this: -- takeWhileFB q (takeWhileFB p c n) n = -- \x r -> if q x then (takeWhileFB p c n) x r else n = -- \x r -> if q x then (\x' r' -> if p x' then x' `c` r' else n) x r else n = -- \x r -> if q x then (if p x then x `c` r else n) else n = -- \x r -> if q x && p x then x `c` r else n = -- takeWhileFB (\x -> q x && p x) c n {-# RULES "takeWhile" [~1] forall p xs. takeWhile p xs = build (\c n -> foldr (takeWhileFB p c n) n xs) "takeWhileList" [1] forall p. foldr (takeWhileFB p (:) []) [] = takeWhile p "takeWhileFB" forall c n p q. takeWhileFB q (takeWhileFB p c n) n = takeWhileFB (\x -> q x && p x) c n #-} -- | 'dropWhile' @p xs@ returns the suffix remaining after 'takeWhile' @p xs@. -- -- >>> dropWhile (< 3) [1,2,3,4,5,1,2,3] -- [3,4,5,1,2,3] -- >>> dropWhile (< 9) [1,2,3] -- [] -- >>> dropWhile (< 0) [1,2,3] -- [1,2,3] dropWhile :: (a -> Bool) -> [a] -> [a] dropWhile :: forall a. (a -> Bool) -> [a] -> [a] dropWhile a -> Bool _ [] = [] dropWhile a -> Bool p xs :: [a] xs@(a x:[a] xs') | a -> Bool p a x = (a -> Bool) -> [a] -> [a] forall a. (a -> Bool) -> [a] -> [a] dropWhile a -> Bool p [a] xs' | Bool otherwise = [a] xs -- | 'take' @n@, applied to a list @xs@, returns the prefix of @xs@ -- of length @n@, or @xs@ itself if @n >= 'length' xs@. -- -- >>> take 5 "Hello World!" -- "Hello" -- >>> take 3 [1,2,3,4,5] -- [1,2,3] -- >>> take 3 [1,2] -- [1,2] -- >>> take 3 [] -- [] -- >>> take (-1) [1,2] -- [] -- >>> take 0 [1,2] -- [] -- -- Laziness: -- -- >>> take 0 undefined -- [] -- >>> take 1 (1 : undefined) -- [1] -- -- It is an instance of the more general 'Data.List.genericTake', -- in which @n@ may be of any integral type. take :: Int -> [a] -> [a] #if defined(USE_REPORT_PRELUDE) take n _ | n <= 0 = [] take _ [] = [] take n (x:xs) = x : take (n-1) xs #else {- We always want to inline this to take advantage of a known length argument sign. Note, however, that it's important for the RULES to grab take, rather than trying to INLINE take immediately and then letting the RULES grab unsafeTake. Presumably the latter approach doesn't grab it early enough; it led to an allocation regression in nofib/fft2. -} {-# INLINE [1] take #-} take :: forall a. Int -> [a] -> [a] take Int n [a] xs | Int 0 Int -> Int -> Bool forall a. Ord a => a -> a -> Bool < Int n = Int -> [a] -> [a] forall a. Int -> [a] -> [a] unsafeTake Int n [a] xs | Bool otherwise = [] -- A version of take that takes the whole list if it's given an argument less -- than 1. {-# NOINLINE [0] unsafeTake #-} -- See Note [Inline FB functions] unsafeTake :: Int -> [a] -> [a] unsafeTake :: forall a. Int -> [a] -> [a] unsafeTake !Int _ [] = [] unsafeTake Int 1 (a x: [a] _) = [a x] unsafeTake Int m (a x:[a] xs) = a x a -> [a] -> [a] forall a. a -> [a] -> [a] : Int -> [a] -> [a] forall a. Int -> [a] -> [a] unsafeTake (Int m Int -> Int -> Int forall a. Num a => a -> a -> a - Int 1) [a] xs {-# RULES "take" [~1] forall n xs . take n xs = build (\c nil -> if 0 < n then foldr (takeFB c nil) (flipSeq nil) xs n else nil) "unsafeTakeList" [1] forall n xs . foldr (takeFB (:) []) (flipSeq []) xs n = unsafeTake n xs #-} {-# INLINE [0] flipSeq #-} -- Just flip seq, but not inlined too early. -- It's important to force the argument here, even though it's not used. -- Otherwise, take n [] can't unbox n, leading to increased allocation in T7257. flipSeq :: a -> b -> a flipSeq :: forall a b. a -> b -> a flipSeq a x !b _n = a x {-# INLINE [0] takeFB #-} -- See Note [Inline FB functions] takeFB :: (a -> b -> b) -> b -> a -> (Int -> b) -> Int -> b -- The \m accounts for the fact that takeFB is used in a higher-order -- way by takeFoldr, so it's better to inline. A good example is -- take n (repeat x) -- for which we get excellent code... but only if we inline takeFB -- when given four arguments takeFB :: forall a b. (a -> b -> b) -> b -> a -> (Int -> b) -> Int -> b takeFB a -> b -> b c b n a x Int -> b xs = \ Int m -> case Int m of Int 1 -> a x a -> b -> b `c` b n Int _ -> a x a -> b -> b `c` Int -> b xs (Int m Int -> Int -> Int forall a. Num a => a -> a -> a - Int 1) #endif -- | 'drop' @n xs@ returns the suffix of @xs@ -- after the first @n@ elements, or @[]@ if @n >= 'length' xs@. -- -- >>> drop 6 "Hello World!" -- "World!" -- >>> drop 3 [1,2,3,4,5] -- [4,5] -- >>> drop 3 [1,2] -- [] -- >>> drop 3 [] -- [] -- >>> drop (-1) [1,2] -- [1,2] -- >>> drop 0 [1,2] -- [1,2] -- -- It is an instance of the more general 'Data.List.genericDrop', -- in which @n@ may be of any integral type. drop :: Int -> [a] -> [a] #if defined(USE_REPORT_PRELUDE) drop n xs | n <= 0 = xs drop _ [] = [] drop n (_:xs) = drop (n-1) xs #else /* hack away */ {-# INLINE drop #-} drop :: forall a. Int -> [a] -> [a] drop Int n [a] ls | Int n Int -> Int -> Bool forall a. Ord a => a -> a -> Bool <= Int 0 = [a] ls | Bool otherwise = Int -> [a] -> [a] forall a. Int -> [a] -> [a] unsafeDrop Int n [a] ls where -- A version of drop that drops the whole list if given an argument -- less than 1 unsafeDrop :: Int -> [a] -> [a] unsafeDrop :: forall a. Int -> [a] -> [a] unsafeDrop !Int _ [] = [] unsafeDrop Int 1 (a _:[a] xs) = [a] xs unsafeDrop Int m (a _:[a] xs) = Int -> [a] -> [a] forall a. Int -> [a] -> [a] unsafeDrop (Int m Int -> Int -> Int forall a. Num a => a -> a -> a - Int 1) [a] xs #endif -- | 'splitAt' @n xs@ returns a tuple where first element is @xs@ prefix of -- length @n@ and second element is the remainder of the list: -- -- >>> splitAt 6 "Hello World!" -- ("Hello ","World!") -- >>> splitAt 3 [1,2,3,4,5] -- ([1,2,3],[4,5]) -- >>> splitAt 1 [1,2,3] -- ([1],[2,3]) -- >>> splitAt 3 [1,2,3] -- ([1,2,3],[]) -- >>> splitAt 4 [1,2,3] -- ([1,2,3],[]) -- >>> splitAt 0 [1,2,3] -- ([],[1,2,3]) -- >>> splitAt (-1) [1,2,3] -- ([],[1,2,3]) -- -- It is equivalent to @('take' n xs, 'drop' n xs)@ -- unless @n@ is @_|_@: -- @splitAt _|_ xs = _|_@, not @(_|_, _|_)@). -- -- The first component of the tuple is produced lazily: -- -- >>> fst (splitAt 0 undefined) -- [] -- >>> take 1 (fst (splitAt 10 (1 : undefined))) -- [1] -- -- 'splitAt' is an instance of the more general 'Data.List.genericSplitAt', -- in which @n@ may be of any integral type. splitAt :: Int -> [a] -> ([a],[a]) #if defined(USE_REPORT_PRELUDE) splitAt n xs = (take n xs, drop n xs) #else splitAt :: forall a. Int -> [a] -> ([a], [a]) splitAt Int n [a] ls | Int n Int -> Int -> Bool forall a. Ord a => a -> a -> Bool <= Int 0 = ([], [a] ls) | Bool otherwise = Int -> [a] -> ([a], [a]) forall a. Int -> [a] -> ([a], [a]) splitAt' Int n [a] ls where splitAt' :: Int -> [a] -> ([a], [a]) splitAt' :: forall a. Int -> [a] -> ([a], [a]) splitAt' Int _ [] = ([], []) splitAt' Int 1 (a x:[a] xs) = ([a x], [a] xs) splitAt' Int m (a x:[a] xs) = (a xa -> [a] -> [a] forall a. a -> [a] -> [a] :[a] xs', [a] xs'') where ([a] xs', [a] xs'') = Int -> [a] -> ([a], [a]) forall a. Int -> [a] -> ([a], [a]) splitAt' (Int m Int -> Int -> Int forall a. Num a => a -> a -> a - Int 1) [a] xs #endif /* USE_REPORT_PRELUDE */ -- | 'span', applied to a predicate @p@ and a list @xs@, returns a tuple where -- first element is the longest prefix (possibly empty) of @xs@ of elements that -- satisfy @p@ and second element is the remainder of the list: -- -- >>> span (< 3) [1,2,3,4,1,2,3,4] -- ([1,2],[3,4,1,2,3,4]) -- >>> span (< 9) [1,2,3] -- ([1,2,3],[]) -- >>> span (< 0) [1,2,3] -- ([],[1,2,3]) -- -- 'span' @p xs@ is equivalent to @('takeWhile' p xs, 'dropWhile' p xs)@, even if @p@ is @_|_@. -- -- Laziness: -- -- >>> span undefined [] -- ([],[]) -- >>> fst (span (const False) undefined) -- *** Exception: Prelude.undefined -- >>> fst (span (const False) (undefined : undefined)) -- [] -- >>> take 1 (fst (span (const True) (1 : undefined))) -- [1] -- -- 'span' produces the first component of the tuple lazily: -- -- >>> take 10 (fst (span (const True) [1..])) -- [1,2,3,4,5,6,7,8,9,10] -- span :: (a -> Bool) -> [a] -> ([a],[a]) span :: forall a. (a -> Bool) -> [a] -> ([a], [a]) span a -> Bool _ xs :: [a] xs@[] = ([a] xs, [a] xs) span a -> Bool p xs :: [a] xs@(a x:[a] xs') | a -> Bool p a x = let ([a] ys,[a] zs) = (a -> Bool) -> [a] -> ([a], [a]) forall a. (a -> Bool) -> [a] -> ([a], [a]) span a -> Bool p [a] xs' in (a xa -> [a] -> [a] forall a. a -> [a] -> [a] :[a] ys,[a] zs) | Bool otherwise = ([],[a] xs) -- | 'break', applied to a predicate @p@ and a list @xs@, returns a tuple where -- first element is longest prefix (possibly empty) of @xs@ of elements that -- /do not satisfy/ @p@ and second element is the remainder of the list: -- -- >>> break (> 3) [1,2,3,4,1,2,3,4] -- ([1,2,3],[4,1,2,3,4]) -- >>> break (< 9) [1,2,3] -- ([],[1,2,3]) -- >>> break (> 9) [1,2,3] -- ([1,2,3],[]) -- -- 'break' @p@ is equivalent to @'span' ('not' . p)@ -- and consequently to @('takeWhile' ('not' . p) xs, 'dropWhile' ('not' . p) xs)@, -- even if @p@ is @_|_@. -- -- Laziness: -- -- >>> break undefined [] -- ([],[]) -- >>> fst (break (const True) undefined) -- *** Exception: Prelude.undefined -- >>> fst (break (const True) (undefined : undefined)) -- [] -- >>> take 1 (fst (break (const False) (1 : undefined))) -- [1] -- -- 'break' produces the first component of the tuple lazily: -- -- >>> take 10 (fst (break (const False) [1..])) -- [1,2,3,4,5,6,7,8,9,10] -- break :: (a -> Bool) -> [a] -> ([a],[a]) #if defined(USE_REPORT_PRELUDE) break p = span (not . p) #else -- HBC version (stolen) break :: forall a. (a -> Bool) -> [a] -> ([a], [a]) break a -> Bool _ xs :: [a] xs@[] = ([a] xs, [a] xs) break a -> Bool p xs :: [a] xs@(a x:[a] xs') | a -> Bool p a x = ([],[a] xs) | Bool otherwise = let ([a] ys,[a] zs) = (a -> Bool) -> [a] -> ([a], [a]) forall a. (a -> Bool) -> [a] -> ([a], [a]) break a -> Bool p [a] xs' in (a xa -> [a] -> [a] forall a. a -> [a] -> [a] :[a] ys,[a] zs) #endif -- | 'reverse' @xs@ returns the elements of @xs@ in reverse order. -- @xs@ must be finite. -- -- >>> reverse [] -- [] -- >>> reverse [42] -- [42] -- >>> reverse [2,5,7] -- [7,5,2] -- >>> reverse [1..] -- * Hangs forever * reverse :: [a] -> [a] #if defined(USE_REPORT_PRELUDE) reverse = foldl (flip (:)) [] #else reverse :: forall a. [a] -> [a] reverse [a] l = [a] -> [a] -> [a] forall a. [a] -> [a] -> [a] rev [a] l [] where rev :: [a] -> [a] -> [a] rev [] [a] a = [a] a rev (a x:[a] xs) [a] a = [a] -> [a] -> [a] rev [a] xs (a xa -> [a] -> [a] forall a. a -> [a] -> [a] :[a] a) #endif -- | 'and' returns the conjunction of a Boolean list. For the result to be -- 'True', the list must be finite; 'False', however, results from a 'False' -- value at a finite index of a finite or infinite list. -- -- >>> and [] -- True -- >>> and [True] -- True -- >>> and [False] -- False -- >>> and [True, True, False] -- False -- >>> and (False : repeat True) -- Infinite list [False,True,True,True,True,True,True... -- False -- >>> and (repeat True) -- * Hangs forever * and :: [Bool] -> Bool #if defined(USE_REPORT_PRELUDE) and = foldr (&&) True #else and :: [Bool] -> Bool and [] = Bool True and (Bool x:[Bool] xs) = Bool x Bool -> Bool -> Bool && [Bool] -> Bool and [Bool] xs {-# NOINLINE [1] and #-} {-# RULES "and/build" forall (g::forall b.(Bool->b->b)->b->b) . and (build g) = g (&&) True #-} #endif -- | 'or' returns the disjunction of a Boolean list. For the result to be -- 'False', the list must be finite; 'True', however, results from a 'True' -- value at a finite index of a finite or infinite list. -- -- >>> or [] -- False -- >>> or [True] -- True -- >>> or [False] -- False -- >>> or [True, True, False] -- True -- >>> or (True : repeat False) -- Infinite list [True,False,False,False,False,False,False... -- True -- >>> or (repeat False) -- * Hangs forever * or :: [Bool] -> Bool #if defined(USE_REPORT_PRELUDE) or = foldr (||) False #else or :: [Bool] -> Bool or [] = Bool False or (Bool x:[Bool] xs) = Bool x Bool -> Bool -> Bool || [Bool] -> Bool or [Bool] xs {-# NOINLINE [1] or #-} {-# RULES "or/build" forall (g::forall b.(Bool->b->b)->b->b) . or (build g) = g (||) False #-} #endif -- | Applied to a predicate and a list, 'any' determines if any element -- of the list satisfies the predicate. For the result to be -- 'False', the list must be finite; 'True', however, results from a 'True' -- value for the predicate applied to an element at a finite index of a finite -- or infinite list. -- -- >>> any (> 3) [] -- False -- >>> any (> 3) [1,2] -- False -- >>> any (> 3) [1,2,3,4,5] -- True -- >>> any (> 3) [1..] -- True -- >>> any (> 3) [0, -1..] -- * Hangs forever * any :: (a -> Bool) -> [a] -> Bool #if defined(USE_REPORT_PRELUDE) any p = or . map p #else any :: forall a. (a -> Bool) -> [a] -> Bool any a -> Bool _ [] = Bool False any a -> Bool p (a x:[a] xs) = a -> Bool p a x Bool -> Bool -> Bool || (a -> Bool) -> [a] -> Bool forall a. (a -> Bool) -> [a] -> Bool any a -> Bool p [a] xs {-# NOINLINE [1] any #-} {-# RULES "any/build" forall p (g::forall b.(a->b->b)->b->b) . any p (build g) = g ((||) . p) False #-} #endif -- | Applied to a predicate and a list, 'all' determines if all elements -- of the list satisfy the predicate. For the result to be -- 'True', the list must be finite; 'False', however, results from a 'False' -- value for the predicate applied to an element at a finite index of a finite -- or infinite list. -- -- >>> all (> 3) [] -- True -- >>> all (> 3) [1,2] -- False -- >>> all (> 3) [1,2,3,4,5] -- False -- >>> all (> 3) [1..] -- False -- >>> all (> 3) [4..] -- * Hangs forever * all :: (a -> Bool) -> [a] -> Bool #if defined(USE_REPORT_PRELUDE) all p = and . map p #else all :: forall a. (a -> Bool) -> [a] -> Bool all a -> Bool _ [] = Bool True all a -> Bool p (a x:[a] xs) = a -> Bool p a x Bool -> Bool -> Bool && (a -> Bool) -> [a] -> Bool forall a. (a -> Bool) -> [a] -> Bool all a -> Bool p [a] xs {-# NOINLINE [1] all #-} {-# RULES "all/build" forall p (g::forall b.(a->b->b)->b->b) . all p (build g) = g ((&&) . p) True #-} #endif -- | 'elem' is the list membership predicate, usually written in infix form, -- e.g., @x \`elem\` xs@. For the result to be -- 'False', the list must be finite; 'True', however, results from an element -- equal to @x@ found at a finite index of a finite or infinite list. -- -- >>> 3 `elem` [] -- False -- >>> 3 `elem` [1,2] -- False -- >>> 3 `elem` [1,2,3,4,5] -- True -- >>> 3 `elem` [1..] -- True -- >>> 3 `elem` [4..] -- * Hangs forever * elem :: (Eq a) => a -> [a] -> Bool #if defined(USE_REPORT_PRELUDE) elem x = any (== x) #else elem :: forall a. Eq a => a -> [a] -> Bool elem a _ [] = Bool False elem a x (a y:[a] ys) = a xa -> a -> Bool forall a. Eq a => a -> a -> Bool ==a y Bool -> Bool -> Bool || a -> [a] -> Bool forall a. Eq a => a -> [a] -> Bool elem a x [a] ys {-# NOINLINE [1] elem #-} {-# RULES "elem/build" forall x (g :: forall b . (a -> b -> b) -> b -> b) . elem x (build g) = g (\ y r -> (x == y) || r) False #-} #endif -- | 'notElem' is the negation of 'elem'. -- -- >>> 3 `notElem` [] -- True -- >>> 3 `notElem` [1,2] -- True -- >>> 3 `notElem` [1,2,3,4,5] -- False -- >>> 3 `notElem` [1..] -- False -- >>> 3 `notElem` [4..] -- * Hangs forever * notElem :: (Eq a) => a -> [a] -> Bool #if defined(USE_REPORT_PRELUDE) notElem x = all (/= x) #else notElem :: forall a. Eq a => a -> [a] -> Bool notElem a _ [] = Bool True notElem a x (a y:[a] ys)= a x a -> a -> Bool forall a. Eq a => a -> a -> Bool /= a y Bool -> Bool -> Bool && a -> [a] -> Bool forall a. Eq a => a -> [a] -> Bool notElem a x [a] ys {-# NOINLINE [1] notElem #-} {-# RULES "notElem/build" forall x (g :: forall b . (a -> b -> b) -> b -> b) . notElem x (build g) = g (\ y r -> (x /= y) && r) True #-} #endif -- | \(\mathcal{O}(n)\). 'lookup' @key assocs@ looks up a key in an association -- list. -- For the result to be 'Nothing', the list must be finite. -- -- >>> lookup 2 [] -- Nothing -- >>> lookup 2 [(1, "first")] -- Nothing -- >>> lookup 2 [(1, "first"), (2, "second"), (3, "third")] -- Just "second" -- lookup :: (Eq a) => a -> [(a,b)] -> Maybe b lookup :: forall a b. Eq a => a -> [(a, b)] -> Maybe b lookup a _key [] = Maybe b forall a. Maybe a Nothing lookup a key ((a x,b y):[(a, b)] xys) | a key a -> a -> Bool forall a. Eq a => a -> a -> Bool == a x = b -> Maybe b forall a. a -> Maybe a Just b y | Bool otherwise = a -> [(a, b)] -> Maybe b forall a b. Eq a => a -> [(a, b)] -> Maybe b lookup a key [(a, b)] xys -- | Map a function returning a list over a list and concatenate the results. -- 'concatMap' can be seen as the composition of 'concat' and 'map'. -- -- > concatMap f xs == (concat . map f) xs -- -- >>> concatMap (\i -> [-i,i]) [] -- [] -- >>> concatMap (\i -> [-i,i]) [1,2,3] -- [-1,1,-2,2,-3,3] concatMap :: (a -> [b]) -> [a] -> [b] concatMap :: forall a b. (a -> [b]) -> [a] -> [b] concatMap a -> [b] f = (a -> [b] -> [b]) -> [b] -> [a] -> [b] forall a b. (a -> b -> b) -> b -> [a] -> b foldr ([b] -> [b] -> [b] forall a. [a] -> [a] -> [a] (++) ([b] -> [b] -> [b]) -> (a -> [b]) -> a -> [b] -> [b] forall b c a. (b -> c) -> (a -> b) -> a -> c . a -> [b] f) [] {-# NOINLINE [1] concatMap #-} {-# RULES "concatMap" forall f xs . concatMap f xs = build (\c n -> foldr (\x b -> foldr c b (f x)) n xs) #-} -- | Concatenate a list of lists. -- -- >>> concat [] -- [] -- >>> concat [[42]] -- [42] -- >>> concat [[1,2,3], [4,5], [6], []] -- [1,2,3,4,5,6] concat :: [[a]] -> [a] concat :: forall a. [[a]] -> [a] concat = ([a] -> [a] -> [a]) -> [a] -> [[a]] -> [a] forall a b. (a -> b -> b) -> b -> [a] -> b foldr [a] -> [a] -> [a] forall a. [a] -> [a] -> [a] (++) [] {-# NOINLINE [1] concat #-} {-# RULES "concat" forall xs. concat xs = build (\c n -> foldr (\x y -> foldr c y x) n xs) -- We don't bother to turn non-fusible applications of concat back into concat #-} -- | List index (subscript) operator, starting from 0. -- It is an instance of the more general 'Data.List.genericIndex', -- which takes an index of any integral type. -- -- >>> ['a', 'b', 'c'] !! 0 -- 'a' -- >>> ['a', 'b', 'c'] !! 2 -- 'c' -- >>> ['a', 'b', 'c'] !! 3 -- *** Exception: Prelude.!!: index too large -- >>> ['a', 'b', 'c'] !! (-1) -- *** Exception: Prelude.!!: negative index -- -- WARNING: This function is partial, and should only be used if you are -- sure that the indexing will not fail. Otherwise, use 'Data.List.!?'. -- -- WARNING: This function takes linear time in the index. #if defined(USE_REPORT_PRELUDE) (!!) :: [a] -> Int -> a xs !! n | n < 0 = errorWithoutStackTrace "Prelude.!!: negative index" [] !! _ = errorWithoutStackTrace "Prelude.!!: index too large" (x:_) !! 0 = x (_:xs) !! n = xs !! (n-1) -- Prelude version is without HasCallStack to avoid building linear one #else (!!) :: HasCallStack => [a] -> Int -> a -- We don't really want the errors to inline with (!!). -- We may want to fuss around a bit with NOINLINE, and -- if so we should be careful not to trip up known-bottom -- optimizations. tooLarge :: HasCallStack => Int -> a tooLarge :: forall a. HasCallStack => Int -> a tooLarge Int _ = String -> a forall a. HasCallStack => String -> a error (String prel_list_str String -> String -> String forall a. [a] -> [a] -> [a] ++ String "!!: index too large") negIndex :: HasCallStack => a negIndex :: forall a. HasCallStack => a negIndex = String -> a forall a. HasCallStack => String -> a error (String -> a) -> String -> a forall a b. (a -> b) -> a -> b $ String prel_list_str String -> String -> String forall a. [a] -> [a] -> [a] ++ String "!!: negative index" {-# INLINABLE (!!) #-} [a] xs !! :: forall a. HasCallStack => [a] -> Int -> a !! Int n | Int n Int -> Int -> Bool forall a. Ord a => a -> a -> Bool < Int 0 = a forall a. HasCallStack => a negIndex | Bool otherwise = (a -> (Int -> a) -> Int -> a) -> (Int -> a) -> [a] -> Int -> a forall a b. (a -> b -> b) -> b -> [a] -> b foldr (\a x Int -> a r Int k -> case Int k of Int 0 -> a x Int _ -> Int -> a r (Int kInt -> Int -> Int forall a. Num a => a -> a -> a -Int 1)) Int -> a forall a. HasCallStack => Int -> a tooLarge [a] xs Int n #endif -- | List index (subscript) operator, starting from 0. Returns 'Nothing' -- if the index is out of bounds -- -- >>> ['a', 'b', 'c'] !? 0 -- Just 'a' -- >>> ['a', 'b', 'c'] !? 2 -- Just 'c' -- >>> ['a', 'b', 'c'] !? 3 -- Nothing -- >>> ['a', 'b', 'c'] !? (-1) -- Nothing -- -- This is the total variant of the partial '!!' operator. -- -- WARNING: This function takes linear time in the index. (!?) :: [a] -> Int -> Maybe a {-# INLINABLE (!?) #-} [a] xs !? :: forall a. [a] -> Int -> Maybe a !? Int n | Int n Int -> Int -> Bool forall a. Ord a => a -> a -> Bool < Int 0 = Maybe a forall a. Maybe a Nothing | Bool otherwise = (a -> (Int -> Maybe a) -> Int -> Maybe a) -> (Int -> Maybe a) -> [a] -> Int -> Maybe a forall a b. (a -> b -> b) -> b -> [a] -> b foldr (\a x Int -> Maybe a r Int k -> case Int k of Int 0 -> a -> Maybe a forall a. a -> Maybe a Just a x Int _ -> Int -> Maybe a r (Int kInt -> Int -> Int forall a. Num a => a -> a -> a -Int 1)) (Maybe a -> Int -> Maybe a forall a b. a -> b -> a const Maybe a forall a. Maybe a Nothing) [a] xs Int n -------------------------------------------------------------- -- The zip family -------------------------------------------------------------- foldr2 :: (a -> b -> c -> c) -> c -> [a] -> [b] -> c foldr2 :: forall a b c. (a -> b -> c -> c) -> c -> [a] -> [b] -> c foldr2 a -> b -> c -> c k c z = [a] -> [b] -> c go where go :: [a] -> [b] -> c go [] [b] _ys = c z go [a] _xs [] = c z go (a x:[a] xs) (b y:[b] ys) = a -> b -> c -> c k a x b y ([a] -> [b] -> c go [a] xs [b] ys) {-# INLINE [0] foldr2 #-} -- See Note [Fusion for foldrN] foldr2_left :: (a -> b -> c -> d) -> d -> a -> ([b] -> c) -> [b] -> d foldr2_left :: forall a b c d. (a -> b -> c -> d) -> d -> a -> ([b] -> c) -> [b] -> d foldr2_left a -> b -> c -> d _k d z a _x [b] -> c _r [] = d z foldr2_left a -> b -> c -> d k d _z a x [b] -> c r (b y:[b] ys) = a -> b -> c -> d k a x b y ([b] -> c r [b] ys) -- foldr2 k z xs ys = foldr (foldr2_left k z) (\_ -> z) xs ys {-# RULES -- See Note [Fusion for foldrN] "foldr2/left" forall k z ys (g::forall b.(a->b->b)->b->b) . foldr2 k z (build g) ys = g (foldr2_left k z) (\_ -> z) ys #-} foldr3 :: (a -> b -> c -> d -> d) -> d -> [a] -> [b] -> [c] -> d foldr3 :: forall a b c d. (a -> b -> c -> d -> d) -> d -> [a] -> [b] -> [c] -> d foldr3 a -> b -> c -> d -> d k d z = [a] -> [b] -> [c] -> d go where go :: [a] -> [b] -> [c] -> d go [] [b] _ [c] _ = d z go [a] _ [] [c] _ = d z go [a] _ [b] _ [] = d z go (a a:[a] as) (b b:[b] bs) (c c:[c] cs) = a -> b -> c -> d -> d k a a b b c c ([a] -> [b] -> [c] -> d go [a] as [b] bs [c] cs) {-# INLINE [0] foldr3 #-} -- See Note [Fusion for foldrN] foldr3_left :: (a -> b -> c -> d -> e) -> e -> a -> ([b] -> [c] -> d) -> [b] -> [c] -> e foldr3_left :: forall a b c d e. (a -> b -> c -> d -> e) -> e -> a -> ([b] -> [c] -> d) -> [b] -> [c] -> e foldr3_left a -> b -> c -> d -> e k e _z a a [b] -> [c] -> d r (b b:[b] bs) (c c:[c] cs) = a -> b -> c -> d -> e k a a b b c c ([b] -> [c] -> d r [b] bs [c] cs) foldr3_left a -> b -> c -> d -> e _ e z a _ [b] -> [c] -> d _ [b] _ [c] _ = e z -- foldr3 k n xs ys zs = foldr (foldr3_left k n) (\_ _ -> n) xs ys zs {-# RULES -- See Note [Fusion for foldrN] "foldr3/left" forall k z (g::forall b.(a->b->b)->b->b). foldr3 k z (build g) = g (foldr3_left k z) (\_ _ -> z) #-} {- Note [Fusion for foldrN] ~~~~~~~~~~~~~~~~~~~~~~~~ We arrange that foldr2, foldr3, etc is a good consumer for its first (left) list argument. Here's how. See below for the second, third etc list arguments * The rule "foldr2/left" (active only before phase 1) does this: foldr2 k z (build g) ys = g (foldr2_left k z) (\_ -> z) ys thereby fusing away the 'build' on the left argument * To ensure this rule has a chance to fire, foldr2 has a NOINLINE[1] pragma There used to be a "foldr2/right" rule, allowing foldr2 to fuse with a build form on the right. However, this causes trouble if the right list ends in a bottom that is only avoided by the left list ending at that spot. That is, foldr2 f z [a,b,c] (d:e:f:_|_), where the right list is produced by a build form, would cause the foldr2/right rule to introduce bottom. Example: zip [1,2,3,4] (unfoldr (\s -> if s > 4 then undefined else Just (s,s+1)) 1) should produce [(1,1),(2,2),(3,3),(4,4)] but with the foldr2/right rule it would instead produce (1,1):(2,2):(3,3):(4,4):_|_ Note [Fusion for zipN/zipWithN] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ We arrange that zip, zip3, etc, and zipWith, zipWit3 etc, are all good consumers for their first (left) argument, and good producers. Here's how. See Note [Fusion for foldrN] for why it can't fuse its second (right) list argument. NB: Zips for larger tuples are in the List module. * Rule "zip" (active only before phase 1) rewrites zip xs ys = build (\c n -> foldr2 (zipFB c) n xs ys) See also Note [Inline FB functions] Ditto rule "zipWith". * To give this rule a chance to fire, we give zip a NOLINLINE[1] pragma (although since zip is recursive it might not need it) * Now the rules for foldr2 (see Note [Fusion for foldrN]) may fire, or rules that fuse the build-produced output of zip. * If none of these fire, rule "zipList" (active only in phase 1) rewrites the foldr2 call back to zip foldr2 (zipFB (:)) [] = zip This rule will only fire when build has inlined, which also happens in phase 1. Ditto rule "zipWithList". -} ---------------------------------------------- -- | \(\mathcal{O}(\min(m,n))\). 'zip' takes two lists and returns a list of -- corresponding pairs. -- -- >>> zip [1, 2] ['a', 'b'] -- [(1,'a'),(2,'b')] -- -- If one input list is shorter than the other, excess elements of the longer -- list are discarded, even if one of the lists is infinite: -- -- >>> zip [1] ['a', 'b'] -- [(1,'a')] -- >>> zip [1, 2] ['a'] -- [(1,'a')] -- >>> zip [] [1..] -- [] -- >>> zip [1..] [] -- [] -- -- 'zip' is right-lazy: -- -- >>> zip [] undefined -- [] -- >>> zip undefined [] -- *** Exception: Prelude.undefined -- ... -- -- 'zip' is capable of list fusion, but it is restricted to its -- first list argument and its resulting list. {-# NOINLINE [1] zip #-} -- See Note [Fusion for zipN/zipWithN] zip :: [a] -> [b] -> [(a,b)] zip :: forall a b. [a] -> [b] -> [(a, b)] zip [] [b] _bs = [] zip [a] _as [] = [] zip (a a:[a] as) (b b:[b] bs) = (a a,b b) (a, b) -> [(a, b)] -> [(a, b)] forall a. a -> [a] -> [a] : [a] -> [b] -> [(a, b)] forall a b. [a] -> [b] -> [(a, b)] zip [a] as [b] bs {-# INLINE [0] zipFB #-} -- See Note [Inline FB functions] zipFB :: ((a, b) -> c -> d) -> a -> b -> c -> d zipFB :: forall a b c d. ((a, b) -> c -> d) -> a -> b -> c -> d zipFB (a, b) -> c -> d c = \a x b y c r -> (a x,b y) (a, b) -> c -> d `c` c r {-# RULES -- See Note [Fusion for zipN/zipWithN] "zip" [~1] forall xs ys. zip xs ys = build (\c n -> foldr2 (zipFB c) n xs ys) "zipList" [1] foldr2 (zipFB (:)) [] = zip #-} ---------------------------------------------- -- | 'zip3' takes three lists and returns a list of triples, analogous to -- 'zip'. -- It is capable of list fusion, but it is restricted to its -- first list argument and its resulting list. {-# NOINLINE [1] zip3 #-} zip3 :: [a] -> [b] -> [c] -> [(a,b,c)] -- Specification -- zip3 = zipWith3 (,,) zip3 :: forall a b c. [a] -> [b] -> [c] -> [(a, b, c)] zip3 (a a:[a] as) (b b:[b] bs) (c c:[c] cs) = (a a,b b,c c) (a, b, c) -> [(a, b, c)] -> [(a, b, c)] forall a. a -> [a] -> [a] : [a] -> [b] -> [c] -> [(a, b, c)] forall a b c. [a] -> [b] -> [c] -> [(a, b, c)] zip3 [a] as [b] bs [c] cs zip3 [a] _ [b] _ [c] _ = [] {-# INLINE [0] zip3FB #-} -- See Note [Inline FB functions] zip3FB :: ((a,b,c) -> xs -> xs') -> a -> b -> c -> xs -> xs' zip3FB :: forall a b c xs xs'. ((a, b, c) -> xs -> xs') -> a -> b -> c -> xs -> xs' zip3FB (a, b, c) -> xs -> xs' cons = \a a b b c c xs r -> (a a,b b,c c) (a, b, c) -> xs -> xs' `cons` xs r {-# RULES -- See Note [Fusion for zipN/zipWithN] "zip3" [~1] forall as bs cs. zip3 as bs cs = build (\c n -> foldr3 (zip3FB c) n as bs cs) "zip3List" [1] foldr3 (zip3FB (:)) [] = zip3 #-} -- The zipWith family generalises the zip family by zipping with the -- function given as the first argument, instead of a tupling function. ---------------------------------------------- -- | \(\mathcal{O}(\min(m,n))\). 'zipWith' generalises 'zip' by zipping with the -- function given as the first argument, instead of a tupling function. -- -- > zipWith (,) xs ys == zip xs ys -- > zipWith f [x1,x2,x3..] [y1,y2,y3..] == [f x1 y1, f x2 y2, f x3 y3..] -- -- For example, @'zipWith' (+)@ is applied to two lists to produce the list of -- corresponding sums: -- -- >>> zipWith (+) [1, 2, 3] [4, 5, 6] -- [5,7,9] -- -- 'zipWith' is right-lazy: -- -- >>> let f = undefined -- >>> zipWith f [] undefined -- [] -- -- 'zipWith' is capable of list fusion, but it is restricted to its -- first list argument and its resulting list. {-# NOINLINE [1] zipWith #-} -- See Note [Fusion for zipN/zipWithN] zipWith :: (a->b->c) -> [a]->[b]->[c] zipWith :: forall a b c. (a -> b -> c) -> [a] -> [b] -> [c] zipWith a -> b -> c f = [a] -> [b] -> [c] go where go :: [a] -> [b] -> [c] go [] [b] _ = [] go [a] _ [] = [] go (a x:[a] xs) (b y:[b] ys) = a -> b -> c f a x b y c -> [c] -> [c] forall a. a -> [a] -> [a] : [a] -> [b] -> [c] go [a] xs [b] ys -- zipWithFB must have arity 2 since it gets two arguments in the "zipWith" -- rule; it might not get inlined otherwise {-# INLINE [0] zipWithFB #-} -- See Note [Inline FB functions] zipWithFB :: (a -> b -> c) -> (d -> e -> a) -> d -> e -> b -> c zipWithFB :: forall a b c d e. (a -> b -> c) -> (d -> e -> a) -> d -> e -> b -> c zipWithFB a -> b -> c c d -> e -> a f = \d x e y b r -> (d x d -> e -> a `f` e y) a -> b -> c `c` b r {-# RULES -- See Note [Fusion for zipN/zipWithN] "zipWith" [~1] forall f xs ys. zipWith f xs ys = build (\c n -> foldr2 (zipWithFB c f) n xs ys) "zipWithList" [1] forall f. foldr2 (zipWithFB (:) f) [] = zipWith f #-} -- | The 'zipWith3' function takes a function which combines three -- elements, as well as three lists and returns a list of the function applied -- to corresponding elements, analogous to 'zipWith'. -- It is capable of list fusion, but it is restricted to its -- first list argument and its resulting list. -- -- > zipWith3 (,,) xs ys zs == zip3 xs ys zs -- > zipWith3 f [x1,x2,x3..] [y1,y2,y3..] [z1,z2,z3..] == [f x1 y1 z1, f x2 y2 z2, f x3 y3 z3..] {-# NOINLINE [1] zipWith3 #-} zipWith3 :: (a->b->c->d) -> [a]->[b]->[c]->[d] zipWith3 :: forall a b c d. (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d] zipWith3 a -> b -> c -> d z = [a] -> [b] -> [c] -> [d] go where go :: [a] -> [b] -> [c] -> [d] go (a a:[a] as) (b b:[b] bs) (c c:[c] cs) = a -> b -> c -> d z a a b b c c d -> [d] -> [d] forall a. a -> [a] -> [a] : [a] -> [b] -> [c] -> [d] go [a] as [b] bs [c] cs go [a] _ [b] _ [c] _ = [] {-# INLINE [0] zipWith3FB #-} -- See Note [Inline FB functions] zipWith3FB :: (d -> xs -> xs') -> (a -> b -> c -> d) -> a -> b -> c -> xs -> xs' zipWith3FB :: forall d xs xs' a b c. (d -> xs -> xs') -> (a -> b -> c -> d) -> a -> b -> c -> xs -> xs' zipWith3FB d -> xs -> xs' cons a -> b -> c -> d func = \a a b b c c xs r -> (a -> b -> c -> d func a a b b c c) d -> xs -> xs' `cons` xs r {-# RULES "zipWith3" [~1] forall f as bs cs. zipWith3 f as bs cs = build (\c n -> foldr3 (zipWith3FB c f) n as bs cs) "zipWith3List" [1] forall f. foldr3 (zipWith3FB (:) f) [] = zipWith3 f #-} -- | 'unzip' transforms a list of pairs into a list of first components -- and a list of second components. -- -- >>> unzip [] -- ([],[]) -- >>> unzip [(1, 'a'), (2, 'b')] -- ([1,2],"ab") unzip :: [(a,b)] -> ([a],[b]) {-# INLINE unzip #-} -- Inline so that fusion `foldr` has an opportunity to fire. -- See Note [Inline @unzipN@ functions] in GHC/OldList.hs. unzip :: forall a b. [(a, b)] -> ([a], [b]) unzip = ((a, b) -> ([a], [b]) -> ([a], [b])) -> ([a], [b]) -> [(a, b)] -> ([a], [b]) forall a b. (a -> b -> b) -> b -> [a] -> b foldr (\(a a,b b) ~([a] as,[b] bs) -> (a aa -> [a] -> [a] forall a. a -> [a] -> [a] :[a] as,b bb -> [b] -> [b] forall a. a -> [a] -> [a] :[b] bs)) ([],[]) -- | The 'unzip3' function takes a list of triples and returns three -- lists, analogous to 'unzip'. -- -- >>> unzip3 [] -- ([],[],[]) -- >>> unzip3 [(1, 'a', True), (2, 'b', False)] -- ([1,2],"ab",[True,False]) unzip3 :: [(a,b,c)] -> ([a],[b],[c]) {-# INLINE unzip3 #-} -- Inline so that fusion `foldr` has an opportunity to fire. -- See Note [Inline @unzipN@ functions] in GHC/OldList.hs. unzip3 :: forall a b c. [(a, b, c)] -> ([a], [b], [c]) unzip3 = ((a, b, c) -> ([a], [b], [c]) -> ([a], [b], [c])) -> ([a], [b], [c]) -> [(a, b, c)] -> ([a], [b], [c]) forall a b. (a -> b -> b) -> b -> [a] -> b foldr (\(a a,b b,c c) ~([a] as,[b] bs,[c] cs) -> (a aa -> [a] -> [a] forall a. a -> [a] -> [a] :[a] as,b bb -> [b] -> [b] forall a. a -> [a] -> [a] :[b] bs,c cc -> [c] -> [c] forall a. a -> [a] -> [a] :[c] cs)) ([],[],[]) -------------------------------------------------------------- -- Error code -------------------------------------------------------------- -- Common up near identical calls to `error' to reduce the number -- constant strings created when compiled: errorEmptyList :: HasCallStack => String -> a errorEmptyList :: forall a. HasCallStack => String -> a errorEmptyList String fun = String -> a forall a. HasCallStack => String -> a error (String prel_list_str String -> String -> String forall a. [a] -> [a] -> [a] ++ String fun String -> String -> String forall a. [a] -> [a] -> [a] ++ String ": empty list") prel_list_str :: String prel_list_str :: String prel_list_str = String "Prelude."