{-# LANGUAGE BangPatterns #-} {-# LANGUAGE MagicHash #-} -- | -- Module : Data.List.Stream -- Copyright : (c) Duncan Coutts 2007 -- (c) Don Stewart 2007-2013 -- License : BSD-style -- Maintainer : dons00@gmail.com -- Stability : experimental -- Portability : portable -- -- A reimplementation of the standard Haskell list library to take advantage of -- stream fusion, and new GHC optimisations. The fusion mechanism is -- based on stream fusion for sequences. Described in: -- -- * /Stream Fusion: From Lists to Streams to Nothing at All/, by -- Duncan Coutts, Roman Leshchinskiy and Don Stwwart, ICFP 2007. -- <http://www.cse.unsw.edu.au/~dons/papers/CLS07.html> -- -- * /Rewriting Haskell Strings/, by Duncan Coutts, Don Stewart and -- Roman Leshchinskiy, Practical Aspects of Declarative Languages -- 8th International Symposium, PADL 2007, 2007. -- <http://www.cse.unsw.edu.au/~dons/papers/CSL06.html> -- -- See the source for the complete story: -- -- * <http://www.cse.unsw.edu.au/~dons/code/streams/list/Data/Stream.hs> -- -- This library is a drop in replacement for "Data.List". -- module Data.List.Stream ( -- $fusion_intro -- * Basic interface (++), -- :: [a] -> [a] -> [a] head, -- :: [a] -> a last, -- :: [a] -> a tail, -- :: [a] -> [a] init, -- :: [a] -> [a] null, -- :: [a] -> Bool length, -- :: [a] -> Int -- * List transformations map, -- :: (a -> b) -> [a] -> [b] reverse, -- :: [a] -> [a] intersperse, -- :: a -> [a] -> [a] intercalate, -- :: [a] -> [[a]] -> [a] transpose, -- :: [[a]] -> [[a]] -- * Reducing lists (folds) foldl, -- :: (a -> b -> a) -> a -> [b] -> a foldl', -- :: (a -> b -> a) -> a -> [b] -> a foldl1, -- :: (a -> a -> a) -> [a] -> a foldl1', -- :: (a -> a -> a) -> [a] -> a foldr, -- :: (a -> b -> b) -> b -> [a] -> b foldr1, -- :: (a -> a -> a) -> [a] -> a -- ** Special folds concat, -- :: [[a]] -> [a] concatMap, -- :: (a -> [b]) -> [a] -> [b] and, -- :: [Bool] -> Bool or, -- :: [Bool] -> Bool any, -- :: (a -> Bool) -> [a] -> Bool all, -- :: (a -> Bool) -> [a] -> Bool sum, -- :: Num a => [a] -> a product, -- :: Num a => [a] -> a maximum, -- :: Ord a => [a] -> a minimum, -- :: Ord a => [a] -> a -- * Building lists -- ** Scans scanl, -- :: (a -> b -> a) -> a -> [b] -> [a] scanl1, -- :: (a -> a -> a) -> [a] -> [a] scanr, -- :: (a -> b -> b) -> b -> [a] -> [b] scanr1, -- :: (a -> a -> a) -> [a] -> [a] -- ** Accumulating maps mapAccumL, -- :: (acc -> x -> (acc, y)) -> acc -> [x] -> (acc, [y]) mapAccumR, -- :: (acc -> x -> (acc, y)) -> acc -> [x] -> (acc, [y]) -- ** Infinite lists iterate, -- :: (a -> a) -> a -> [a] repeat, -- :: a -> [a] replicate, -- :: Int -> a -> [a] cycle, -- :: [a] -> [a] -- ** Unfolding unfoldr, -- :: (b -> Maybe (a, b)) -> b -> [a] -- * Sublists -- ** Extracting sublists take, -- :: Int -> [a] -> [a] drop, -- :: Int -> [a] -> [a] splitAt, -- :: Int -> [a] -> ([a], [a]) takeWhile, -- :: (a -> Bool) -> [a] -> [a] dropWhile, -- :: (a -> Bool) -> [a] -> [a] span, -- :: (a -> Bool) -> [a] -> ([a], [a]) break, -- :: (a -> Bool) -> [a] -> ([a], [a]) group, -- :: Eq a => [a] -> [[a]] inits, -- :: [a] -> [[a]] tails, -- :: [a] -> [[a]] -- * Predicates isPrefixOf, -- :: Eq a => [a] -> [a] -> Bool isSuffixOf, -- :: Eq a => [a] -> [a] -> Bool isInfixOf, -- :: Eq a => [a] -> [a] -> Bool -- * Searching lists -- ** Searching by equality elem, -- :: Eq a => a -> [a] -> Bool notElem, -- :: Eq a => a -> [a] -> Bool lookup, -- :: Eq a => a -> [(a, b)] -> Maybe b -- ** Searching with a predicate find, -- :: (a -> Bool) -> [a] -> Maybe a filter, -- :: (a -> Bool) -> [a] -> [a] partition, -- :: (a -> Bool) -> [a] -> ([a], [a]) -- * Indexing lists -- | These functions treat a list @xs@ as a indexed collection, -- with indices ranging from 0 to @'length' xs - 1@. (!!), -- :: [a] -> Int -> a elemIndex, -- :: Eq a => a -> [a] -> Maybe Int elemIndices, -- :: Eq a => a -> [a] -> [Int] findIndex, -- :: (a -> Bool) -> [a] -> Maybe Int findIndices, -- :: (a -> Bool) -> [a] -> [Int] -- * Zipping and unzipping lists zip, -- :: [a] -> [b] -> [(a, b)] zip3, -- :: [a] -> [b] -> [c] -> [(a, b, c)] zip4, zip5, zip6, zip7, -- | The zipWith family generalises the zip family by zipping with the -- function given as the first argument, instead of a tupling function. zipWith, -- :: (a -> b -> c) -> [a] -> [b] -> [c] zipWith3, -- :: (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d] zipWith4, zipWith5, zipWith6, zipWith7, unzip, -- :: [(a, b)] -> ([a], [b]) unzip3, -- :: [(a, b, c)] -> ([a], [b], [c]) unzip4, unzip5, unzip6, unzip7, -- * Special lists -- ** Functions on strings lines, -- :: String -> [String] words, -- :: String -> [String] unlines, -- :: [String] -> String unwords, -- :: [String] -> String -- ** \"Set\" operations nub, -- :: Eq a => [a] -> [a] delete, -- :: Eq a => a -> [a] -> [a] (\\), -- :: Eq a => [a] -> [a] -> [a] union, -- :: Eq a => [a] -> [a] -> [a] intersect, -- :: Eq a => [a] -> [a] -> [a] -- ** Ordered lists sort, -- :: Ord a => [a] -> [a] insert, -- :: Ord a => a -> [a] -> [a] -- * Generalized functions -- ** The \"By\" operations -- | By convention, overloaded functions have a non-overloaded -- counterpart whose name is suffixed with \`@By@\'. -- -- It is often convenient to use these functions together with -- 'Data.Function.on', for instance @'sortBy' ('compare' -- \`on\` 'fst')@. -- *** User-supplied equality (replacing an Eq context) -- | The predicate is assumed to define an equivalence. nubBy, -- :: (a -> a -> Bool) -> [a] -> [a] deleteBy, -- :: (a -> a -> Bool) -> a -> [a] -> [a] deleteFirstsBy, -- :: (a -> a -> Bool) -> [a] -> [a] -> [a] unionBy, -- :: (a -> a -> Bool) -> [a] -> [a] -> [a] intersectBy, -- :: (a -> a -> Bool) -> [a] -> [a] -> [a] groupBy, -- :: (a -> a -> Bool) -> [a] -> [[a]] -- *** User-supplied comparison (replacing an Ord context) sortBy, -- :: (a -> a -> Ordering) -> [a] -> [a] insertBy, -- :: (a -> a -> Ordering) -> a -> [a] -> [a] maximumBy, -- :: (a -> a -> Ordering) -> [a] -> a minimumBy, -- :: (a -> a -> Ordering) -> [a] -> a -- * The \"generic\" operations -- | The prefix \`@generic@\' indicates an overloaded function that -- is a generalized version of a "Prelude" function. genericLength, -- :: Num i => [b] -> i genericTake, -- :: Integral i => i -> [a] -> [a] genericDrop, -- :: Integral i => i -> [a] -> [a] genericSplitAt, -- :: Integral i => i -> [a] -> ([a], [a]) genericIndex, -- :: Integral a => [b] -> a -> b genericReplicate, -- :: Integral i => i -> a -> [a] -- helper for GHC.List errorEmptyList -- :: String -> a ) where #ifndef EXTERNAL_PACKAGE import {-# SOURCE #-} GHC.Err ( error ) import {-# SOURCE #-} GHC.Real (Integral) import {-# SOURCE #-} GHC.Num (Num(..)) import {-# SOURCE #-} GHC.Unicode (isSpace) import GHC.Base (Int, Eq(..), Ord(..), Ordering(..), Bool(..), not, Ordering(..), seq, otherwise, flip, Monad(..), Char, String, Int(I#), Int#, (+#), -- we just reuse these: foldr, (++), map ) import Data.Maybe (Maybe(..)) #else import GHC.Exts (Int(I#), Int#, (+#)) import Prelude (Int, Integral, Num(..), Eq(..), Ord(..), Ordering(..), Bool(..), not, Maybe(..), Char, String, error, seq, otherwise, flip) import Data.Char (isSpace) #endif import qualified Data.Stream as Stream import Data.Stream (stream ,unstream) -- ----------------------------------------------------------------------------- #ifdef EXTERNAL_PACKAGE infixr 5 ++ #endif infix 5 \\ -- comment to fool cpp infixl 9 !! infix 4 `elem`, `notElem` -- ----------------------------------------------------------------------------- -- $fusion_intro -- -- The functions in this library marked with /fusion/ are -- (transparently) rewritten by the compiler to stream functions, using -- the fusion framework described in /Rewriting Haskell Strings/. -- -- For example: -- -- > map f xs -- -- is transformed via rewrite rules to: -- -- > (unstream . mapS f . stream) xs -- -- The 'unstream' and 'stream' functions identify the allocation points -- for each function. -- -- When two or more fusible functions are in close proximity (i.e. -- directly composed, or with only intermediate lets and cases), the -- fusion rule will fire, removing the intermediate structures. -- -- Consider: -- -- > map f . map g -- -- The rewrite engine will transform this code to: -- -- > unstream . mapS f . stream . unstream . mapS g . stream -- -- The fusion rule will then fire: -- -- > unstream . mapS f . mapS g . stream -- -- Removing the intermeidate list that is allocated. The compiler then -- optimises the result. -- -- Functions that fail to fuse are not left in stream form. In the final -- simplifier phase any remaining unfused functions of the form: -- -- > unstream . g . stream -- -- Will be transformed back to their original list implementation. -- -- -- Notes on simplifer phasing -- -- * api functions should be rewritten to fusible forms as soon as possble -- * This implies a NOINLINE [1] on the top level functions, so if ghc wants -- to inline them they'll only have their bodies inlined at the end. -- * These rewrite rules can then fire in any but the last phase: -- "++ -> fusible" [~1] forall xs ys. -- * Finally, if we reach the final phase, rewrite back to best effort [a] forms: -- "++ -> unfused" [1] forall xs ys. -- * And then inline the result. -- -- If fusion occurs though, hang on to those 'stream' and 'unstream' pairs: -- {-# INLINE [0] unstream #-} -- hmm? -- -- Todo: notes on the phasing of Streams -- -- ----------------------------------------------------------------------------- -- Fusion for the constructors: -- -- We do not enable fusion for (:), as it leads to a massive massive -- slow down in compilation time. -- {- RULES "(:) -> fusible" [~1] forall x xs. x : xs = unstream (Stream.cons x (stream xs)) "(:) -> unfused" [1] forall x xs. unstream (Stream.cons x (stream xs)) = x : xs -} -- ----------------------------------------------------------------------------- -- Basic interface -- | /O(n)/, /fusion/. 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. -- The spine of the first list argument must be copied. #ifdef EXTERNAL_PACKAGE (++) :: [a] -> [a] -> [a] (++) [] ys = ys (++) (x:xs) ys = x : xs ++ ys {-# NOINLINE [1] (++) #-} #endif -- NOTE: This is quite subtle as we do not want to copy the last list in -- -- xs1 ++ xs2 ++ ... ++ xsn -- -- Indeed, we don't really want to fuse the above at all unless at least -- one of the arguments has the form (unstream s) or the result of the -- concatenation is streamed. The rules below do precisely that. Note they -- really fuse instead of just rewriting things into a fusible form so there -- is no need to rewrite back. {-# RULES "++ -> fused on 1st arg" [~1] forall xs ys. unstream xs ++ ys = Stream.append1 xs ys "++ -> fused on 2nd arg" [~1] forall xs ys. Stream.append1 xs (unstream ys) = unstream (Stream.append xs ys) "++ -> fused (1)" [~1] forall xs ys. stream (xs ++ ys) = Stream.append (stream xs) (stream ys) "++ -> fused (2)" [~1] forall xs ys. stream (Stream.append1 xs ys) = Stream.append xs (stream ys) "++ -> 1st arg empty" forall xs. [] ++ xs = xs "++ -> 2nd arg empty" forall xs. xs ++ [] = xs "++ / :" forall x xs ys. (x:xs) ++ ys = x : (xs ++ ys) #-} -- | /O(1)/, /fusion/. Extract the first element of a list, which must be -- non-empty. head :: [a] -> a head (x:_) = x head [] = errorEmptyList "head" {-# NOINLINE [1] head #-} {-# RULES "head -> fusible" [~1] forall xs. head xs = Stream.head (stream xs) --"head -> unfused" [1] forall xs. -- Stream.head (stream xs) = head xs #-} -- | /O(n)/, /fusion/. Extract the last element of a list, which must be finite -- and non-empty. last :: [a] -> a last [] = errorEmptyList "last" last (x:xs) = last' x xs where last' y [] = y last' _ (y:ys) = last' y ys {-# NOINLINE [1] last #-} {-# RULES "last -> fusible" [~1] forall xs. last xs = Stream.last (stream xs) --"last -> unfused" [1] forall xs. -- Stream.last (stream xs) = last xs #-} -- | /O(1)/, /fusion/. Extract the elements after the head of a list, which -- must be non-empty. tail :: [a] -> [a] tail (_:xs) = xs tail [] = errorEmptyList "tail" {-# NOINLINE [1] tail #-} {-# RULES "tail -> fusible" [~1] forall xs. tail xs = unstream (Stream.tail (stream xs)) --"tail -> unfused" [1] forall xs. -- unstream (Stream.tail (stream xs)) = tail xs #-} -- | /O(n)/, /fusion/. Return all the elements of a list except the last one. -- The list must be finite and non-empty. init :: [a] -> [a] init [] = errorEmptyList "init" init (x:xs) = init' x xs where init' _ [] = [] init' y (z:zs) = y : init' z zs {-# NOINLINE [1] init #-} {-# RULES "init -> fusible" [~1] forall xs. init xs = unstream (Stream.init (stream xs)) --"init -> unfused" [1] forall xs. -- unstream (Stream.init (stream xs)) = init xs #-} -- | /O(1)/, /fusion/. Test whether a list is empty. null :: [a] -> Bool null [] = True null (_:_) = False {-# NOINLINE [1] null #-} {-# RULES "null -> fusible" [~1] forall xs. null xs = Stream.null (stream xs) --"null -> unfused" [1] forall xs. -- Stream.null (stream xs) = null xs #-} -- | /O(n)/, /fusion/. '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 :: [a] -> Int length xs0 = len xs0 0# #ifndef __HADDOCK__ where len :: [a] -> Int# -> Int len [] a# = I# a# len (_:xs) a# = len xs (a# +# 1#) #endif {-# NOINLINE [1] length #-} {-# RULES "length -> fusible" [~1] forall xs. length xs = Stream.length (stream xs) --"length -> unfused" [1] forall xs. -- Stream.length (stream xs) = length xs #-} -- --------------------------------------------------------------------- -- List transformations -- | /O(n)/, /fusion/. '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, ...] -- -- Properties: -- -- > map f . map g = map (f . g) -- > map f (repeat x) = repeat (f x) -- > map f (replicate n x) = replicate n (f x) #ifdef EXTERNAL_PACKAGE map :: (a -> b) -> [a] -> [b] map _ [] = [] map f (x:xs) = f x : map f xs {-# NOINLINE [1] map #-} #endif {-# RULES "map -> fusible" [~1] forall f xs. map f xs = unstream (Stream.map f (stream xs)) --"map -> unfused" [1] forall f xs. -- unstream (Stream.map f (stream xs)) = map f xs #-} -- | /O(n)/, /fusion/. 'reverse' @xs@ returns the elements of @xs@ in reverse order. -- @xs@ must be finite. Will fuse as a consumer only. reverse :: [a] -> [a] reverse = foldl' (flip (:)) [] {-# INLINE reverse #-} {- reverse l = rev l [] where rev [] a = a rev (x:xs) a = rev xs (x:a) -} {- --TODO: I'm sure there are some cunning things we can do with optimising -- reverse. Of course if we try and fuse we may need to still force the -- sping of the list: eg reverse . reverse = forceSpine forceSpine :: [a] -> [a] forceSpine xs = forceSpine' xs `seq` xs {-# INLINE forceSpine #-} -- The idea of this slightly odd construction is that we inline the above form -- and in the context we may then be able to use xs directly and just keep -- around the fact that xs must be forced at some point. Remember, seq does not -- imply any evaluation order. forceSpine' :: [a] -> () forceSpine' [] = () forceSpine' (_:xs') = forceSpine' xs' {-# NOINLINE forceSpine' #-} -} -- | /O(n)/, /fusion/. The 'intersperse' function takes an element and a list and -- \`intersperses\' that element between the elements of the list. -- For example, -- -- > intersperse ',' "abcde" == "a,b,c,d,e" -- intersperse :: a -> [a] -> [a] intersperse _ [] = [] intersperse sep (x0:xs0) = x0 : go xs0 where go [] = [] go (x:xs) = sep : x : go xs {-# NOINLINE [1] intersperse #-} {- RULES "intersperse -> fusible" [~1] forall x xs. intersperse x xs = unstream (Stream.intersperse x (stream xs)) "intersperse -> unfused" [1] forall x xs. unstream (Stream.intersperse x (stream xs)) = intersperse x xs -} -- | /O(n)/, /fusion/. 'intercalate' @xs xss@ is equivalent to @('concat' ('intersperse' xs xss))@. -- It inserts the list @xs@ in between the lists in @xss@ and concatenates the -- result. -- -- > intercalate = concat . intersperse -- intercalate :: [a] -> [[a]] -> [a] intercalate sep xss = go (intersperse sep xss) where go [] = [] go (y:ys) = y ++ go ys {-# NOINLINE [1] intercalate #-} {- intercalate _ [] = [] intercalate sep (xs0:xss0) = go xs0 xss0 where go [] xss = to xss go (x:xs) xss = x : go xs xss to [] = [] to (xs:xss) = go' sep xs xss go' [] xs xss = go xs xss go' (s:ss) xs xss = s : go' ss xs xss {-# NOINLINE [1] intercalate #-} -} -- fusion rule based on: -- intercalate = concat . intersperse -- {- RULES "intercalate -> fusible" [~1] forall x xs. intercalate x xs = Stream.concat (Stream.intersperse x (stream xs)) "intercalate -> unfused" [1] forall x xs. Stream.concat (Stream.intersperse x (stream xs)) = intercalate x xs -} -- | The 'transpose' function transposes the rows and columns of its argument. -- For example, -- -- > transpose [[1,2,3],[4,5,6]] == [[1,4],[2,5],[3,6]] -- transpose :: [[a]] -> [[a]] transpose [] = [] transpose ([] : xss) = transpose xss transpose ((x:xs) : xss) = (x : [h | (h:_t) <- xss]) : transpose (xs : [ t | (_h:t) <- xss]) -- TODO fuse -- --------------------------------------------------------------------- -- Reducing lists (folds) -- | /O(n)/, /fusion/. '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 :: (a -> b -> a) -> a -> [b] -> a foldl f z0 xs0 = go z0 xs0 where go z [] = z go z (x:xs) = go (f z x) xs {-# INLINE [1] foldl #-} {-# RULES "foldl -> fusible" [~1] forall f z xs. foldl f z xs = Stream.foldl f z (stream xs) --"foldl -> unfused" [1] forall f z xs. -- Stream.foldl f z (stream xs) = foldl f z xs #-} -- | /O(n)/, /fusion/. A strict version of 'foldl'. foldl' :: (a -> b -> a) -> a -> [b] -> a foldl' f z0 xs0 = go z0 xs0 #ifndef __HADDOCK__ where go !z [] = z go !z (x:xs) = go (f z x) xs #endif {-# INLINE [1] foldl' #-} {-# RULES "foldl' -> fusible" [~1] forall f z xs. foldl' f z xs = Stream.foldl' f z (stream xs) --"foldl' -> unfused" [1] forall f z xs. -- Stream.foldl' f z (stream xs) = foldl' f z xs #-} -- | /O(n)/, /fusion/. 'foldl1' is a variant of 'foldl' that has no starting value argument, -- and thus must be applied to non-empty lists. foldl1 :: (a -> a -> a) -> [a] -> a foldl1 _ [] = errorEmptyList "foldl1" foldl1 f (x0:xs0) = go x0 xs0 where go z [] = z go z (x:xs) = go (f z x) xs {-# INLINE [1] foldl1 #-} {-# RULES "foldl1 -> fusible" [~1] forall f xs. foldl1 f xs = Stream.foldl1 f (stream xs) --"foldl1 -> unfused" [1] forall f xs. -- Stream.foldl1 f (stream xs) = foldl1 f xs #-} -- | /O(n)/, /fusion/. A strict version of 'foldl1' foldl1' :: (a -> a -> a) -> [a] -> a foldl1' _ [] = errorEmptyList "foldl1'" foldl1' f (x0:xs0) = go x0 xs0 #ifndef __HADDOCK__ where go !z [] = z go !z (x:xs) = go (f z x) xs #endif {-# INLINE [1] foldl1' #-} {-# RULES "foldl1' -> fusible" [~1] forall f xs. foldl1' f xs = Stream.foldl1' f (stream xs) --"foldl1 -> unfused" [1] forall f xs. -- Stream.foldl1' f (stream xs) = foldl1' f xs #-} -- | /O(n)/, /fusion/. '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)...) #ifdef EXTERNAL_PACKAGE foldr :: (a -> b -> b) -> b -> [a] -> b foldr k z xs = go xs where go [] = z go (y:ys) = y `k` go ys {-# INLINE [0] foldr #-} #endif {-# RULES "foldr -> fusible" [~1] forall f z xs. foldr f z xs = Stream.foldr f z (stream xs) --"foldr -> unfused" [1] forall f z xs. -- Stream.foldr f z (stream xs) = foldr f z xs #-} -- | /O(n)/, /fusion/. 'foldr1' is a variant of 'foldr' that has no starting value argument, -- and thus must be applied to non-empty lists. foldr1 :: (a -> a -> a) -> [a] -> a foldr1 _ [] = errorEmptyList "foldr1" foldr1 k (x0:xs0) = go x0 xs0 where go x [] = x go x (x':xs) = k x (go x' xs) {-# INLINE [1] foldr1 #-} {-# RULES "foldr1 -> fusible" [~1] forall f xs. foldr1 f xs = Stream.foldr1 f (stream xs) --"foldr1 -> unfused" [1] forall f xs. -- Stream.foldr1 f (stream xs) = foldr1 f xs #-} -- --------------------------------------------------------------------- -- Special folds -- | /O(n)/, /fusion/. Concatenate a list of lists. concat :: [[a]] -> [a] concat xss0 = to xss0 where go [] xss = to xss go (x:xs) xss = x : go xs xss to [] = [] to (xs:xss) = go xs xss -- hmm, this is slower than the old concat? {-# NOINLINE [1] concat #-} -- -- fuse via concatMap, as the Stream (Stream a) is too hard to construct -- -- or via foldr (++) ? -- {-# RULES "concat -> fused" [~1] forall xs. concat xs = Stream.concat (stream xs) --"concat -> unfused" [1] forall xs. -- Stream.concat (stream xs) = concat xs #-} -- | /O(n)/, /fusion/. Map a function over a list and concatenate the results. concatMap :: (a -> [b]) -> [a] -> [b] concatMap f = foldr (\x y -> f x ++ y) [] -- at least it will fuse. {-# INLINE concatMap #-} {- concatMap f as0 = to as0 where go [] as = to as go (b:bs) as = b : go bs as to [] = [] to (a:as) = go (f a) as {-# NOINLINE [1] concatMap #-} -} {- RULES "concatMap -> fusible" [~1] forall f xs. concatMap f xs = Stream.concatMap f (stream xs) "concatMap -> unfused" [1] forall f xs. Stream.concatMap f (stream xs) = concatMap f xs -} -- | /O(n)/, /fusion/. '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 :: [Bool] -> Bool and [] = True and (False:_ ) = False and (_ :xs) = and xs {-# NOINLINE [1] and #-} {-# RULES "and -> fused" [~1] forall xs. and xs = Stream.and (stream xs) --"and -> unfused" [1] forall xs. -- Stream.and (stream xs) = and xs #-} -- | /O(n)/, /fusion/. '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 :: [Bool] -> Bool or [] = False or (True:_ ) = True or (_ :xs) = or xs {-# NOINLINE [1] or #-} {-# RULES "or -> fused" [~1] forall xs. or xs = Stream.or (stream xs) --"or -> unfused" [1] forall xs. -- Stream.or (stream xs) = or xs #-} -- | /O(n)/, /fusion/. Applied to a predicate and a list, 'any' determines if any element -- of the list satisfies the predicate. any :: (a -> Bool) -> [a] -> Bool any p xs0 = go xs0 where go [] = False go (x:xs) = case p x of True -> True False -> go xs {-# NOINLINE [1] any #-} --TODO: check if being lazy in p is a cost, -- should we do [] as a special case and then strictly evaluate p? {-# RULES "any -> fusible" [~1] forall f xs. any f xs = Stream.any f (stream xs) --"any -> unfused" [1] forall f xs. -- Stream.any f (stream xs) = any f xs #-} -- | Applied to a predicate and a list, 'all' determines if all elements -- of the list satisfy the predicate. all :: (a -> Bool) -> [a] -> Bool all p xs0 = go xs0 where go [] = True go (x:xs) = case p x of True -> go xs False -> False {-# NOINLINE [1] all #-} {-# RULES "all -> fusible" [~1] forall f xs. all f xs = Stream.all f (stream xs) --"all -> unfused" [1] forall f xs. -- Stream.all f (stream xs) = all f xs #-} -- | /O(n)/, /fusion/. The 'sum' function computes the sum of a finite list of numbers. sum :: Num a => [a] -> a sum l = sum' l 0 #ifndef __HADDOCK__ where sum' [] a = a sum' (x:xs) a = sum' xs (a+x) #endif {-# NOINLINE [1] sum #-} sumInt :: [Int] -> Int sumInt l = sum' l 0 #ifndef __HADDOCK__ where sum' [] a = a sum' (x:xs) !a = sum' xs (a+x) #endif {-# NOINLINE [1] sumInt #-} {-# RULES "sum spec Int" sum = sumInt :: [Int] -> Int #-} {-# RULES "sum -> fusible" [~1] forall xs. sum xs = Stream.sum (stream xs) --"sum -> unfused" [1] forall xs. -- Stream.sum (stream xs) = sum xs #-} {-# RULES "sumInt -> fusible" [~1] forall (xs :: [Int]). sumInt xs = Stream.sum (stream xs) --"sumInt -> unfused" [1] forall (xs :: [Int]). -- Stream.sum (stream xs) = sumInt xs #-} -- | /O(n)/,/fusion/. The 'product' function computes the product of a finite list of numbers. product :: Num a => [a] -> a product l = prod l 1 #ifndef __HADDOCK__ where prod [] a = a prod (x:xs) a = prod xs (a*x) #endif {-# NOINLINE [1] product #-} productInt :: [Int] -> Int productInt l = product' l 0 #ifndef __HADDOCK__ where product' [] a = a product' (x:xs) !a = product' xs (a*x) #endif {-# NOINLINE [1] productInt #-} {-# RULES "product spec Int" product = productInt :: [Int] -> Int #-} {-# RULES "product -> fused" [~1] forall xs. product xs = Stream.product (stream xs) --"product -> unfused" [1] forall xs. -- Stream.product (stream xs) = product xs #-} {-# RULES "productInt -> fusible" [~1] forall (xs :: [Int]). productInt xs = Stream.product (stream xs) --"productInt -> unfused" [1] forall (xs :: [Int]). -- Stream.product (stream xs) = productInt xs #-} -- | /O(n)/,/fusion/. '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 :: Ord a => [a] -> a maximum [] = errorEmptyList "maximum" maximum xs = foldl1 max xs {-# NOINLINE [1] maximum #-} {-# RULES "maximum -> fused" [~1] forall xs. maximum xs = Stream.maximum (stream xs) --"maximum -> unfused" [1] forall xs. -- Stream.maximum (stream xs) = maximum xs #-} -- We can't make the overloaded version of maximum strict without -- changing its semantics (max might not be strict), but we can for -- the version specialised to 'Int'. {-# RULES "maximumInt" maximum = (strictMaximum :: [Int] -> Int); "maximumChar" maximum = (strictMaximum :: [Char] -> Char) #-} strictMaximum :: (Ord a) => [a] -> a strictMaximum [] = errorEmptyList "maximum" strictMaximum xs = foldl1' max xs {-# NOINLINE [1] strictMaximum #-} {-# RULES "strictMaximum -> fused" [~1] forall xs. strictMaximum xs = Stream.strictMaximum (stream xs) --"strictMaximum -> unfused" [1] forall xs. -- Stream.strictMaximum (stream xs) = strictMaximum xs #-} -- | /O(n)/,/fusion/. '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 :: Ord a => [a] -> a minimum [] = errorEmptyList "minimum" minimum xs = foldl1 min xs {-# NOINLINE [1] minimum #-} {-# RULES "minimum -> fused" [~1] forall xs. minimum xs = Stream.minimum (stream xs) --"minimum -> unfused" [1] forall xs. -- Stream.minimum (stream xs) = minimum xs #-} {-# RULES "minimumInt" minimum = (strictMinimum :: [Int] -> Int); "minimumChar" minimum = (strictMinimum :: [Char] -> Char) #-} strictMinimum :: (Ord a) => [a] -> a strictMinimum [] = errorEmptyList "maximum" strictMinimum xs = foldl1' min xs {-# NOINLINE [1] strictMinimum #-} {-# RULES "strictMinimum -> fused" [~1] forall xs. strictMinimum xs = Stream.strictMinimum (stream xs) --"strictMinimum -> unfused" [1] forall xs. -- Stream.strictMinimum (stream xs) = strictMinimum xs #-} -- --------------------------------------------------------------------- -- * Building lists -- ** Scans -- | /O(n)/, /fusion/. '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, ...] -- -- Properties: -- -- > last (scanl f z xs) == foldl f z x -- scanl :: (a -> b -> a) -> a -> [b] -> [a] scanl f q ls = q : case ls of [] -> [] x:xs -> scanl f (f q x) xs {-# INLINE [1] scanl #-} {- or perhaps: scanl f q xs0 = q : go q xs0 where go q [] = [] go q (x:xs) = let q' = f q x in q' : go q' xs -} -- -- note: Haskell's 'scan' is a bit weird, as it always puts the initial -- state as a prefix. this complicates the rules. -- {-# RULES "scanl -> fusible" [~1] forall f z xs. scanl f z xs = unstream (Stream.scanl f z (Stream.snoc (stream xs) bottom)) --"scanl -> unfused" [1] forall f z xs. -- unstream (Stream.scanl f z (Stream.snoc (stream xs) bottom)) = scanl f z xs #-} -- | /O(n)/,/fusion/. 'scanl1' is a variant of 'scanl' that has no starting value argument: -- -- > scanl1 f [x1, x2, ...] == [x1, x1 `f` x2, ...] -- scanl1 :: (a -> a -> a) -> [a] -> [a] scanl1 f (x:xs) = scanl f x xs scanl1 _ [] = [] {-# INLINE [1] scanl1 #-} {-# RULES "scanl1 -> fusible" [~1] forall f xs. scanl1 f xs = unstream (Stream.scanl1 f (Stream.snoc (stream xs) bottom)) --"scanl1 -> unfused" [1] forall f xs. -- unstream (Stream.scanl1 f (Stream.snoc (stream xs) bottom)) = scanl1 f xs #-} -- | /O(n)/. 'scanr' is the right-to-left dual of 'scanl'. -- Properties: -- -- > head (scanr f z xs) == foldr f z xs -- scanr :: (a -> b -> b) -> b -> [a] -> [b] scanr _ q0 [] = [q0] scanr f q0 (x:xs) = f x q : qs where qs@(q:_) = scanr f q0 xs {-# INLINE [1] scanr #-} {- RULES "scanr -> fusible" [~1] forall f z xs. scanr f z xs = unstream (Stream.scanr f z (Stream.cons bottom (stream xs))) "scanr -> unfused" [1] forall f z xs. unstream (Stream.scanr f z (Stream.cons bottom (stream xs))) = scanr f z xs -} -- | 'scanr1' is a variant of 'scanr' that has no starting value argument. scanr1 :: (a -> a -> a) -> [a] -> [a] scanr1 _ [] = [] scanr1 _ [x] = [x] scanr1 f (x:xs) = f x q : qs where qs@(q:_) = scanr1 f xs -- TODO fuse -- --------------------------------------------------------------------- -- ** Accumulating maps -- | The 'mapAccumL' function behaves like a combination of 'map' and -- 'foldl'; it applies a function to each element of a list, passing -- an accumulating parameter from left to right, and returning a final -- value of this accumulator together with the new list. -- mapAccumL :: (acc -> x -> (acc, y)) -> acc -> [x] -> (acc, [y]) mapAccumL _ s [] = (s, []) mapAccumL f s (x:xs) = (s'',y:ys) where (s', y ) = f s x (s'',ys) = mapAccumL f s' xs -- TODO fuse -- | The 'mapAccumR' function behaves like a combination of 'map' and -- 'foldr'; it applies a function to each element of a list, passing -- an accumulating parameter from right to left, and returning a final -- value of this accumulator together with the new list. -- mapAccumR :: (acc -> x -> (acc, y)) -> acc -> [x] -> (acc, [y]) mapAccumR _ s [] = (s, []) mapAccumR f s (x:xs) = (s'', y:ys) where (s'',y ) = f s' x (s', ys) = mapAccumR f s xs -- TODO fuse ------------------------------------------------------------------------ -- ** Infinite lists -- | /fusion/. 'iterate' @f x@ returns an infinite list of repeated applications -- of @f@ to @x@: -- -- > iterate f x == [x, f x, f (f x), ...] iterate :: (a -> a) -> a -> [a] iterate f x = x : iterate f (f x) {-# NOINLINE [1] iterate #-} {-# RULES "iterate -> fusible" [~1] forall f x. iterate f x = unstream (Stream.iterate f x) --"iterate -> unfused" [1] forall f x. -- unstream (Stream.iterate f x) = iterate f x #-} -- | /fusion/. 'repeat' @x@ is an infinite list, with @x@ the value of every element. repeat :: a -> [a] repeat x = xs where xs = x : xs {-# INLINE [1] repeat #-} {-# RULES "repeat -> fusible" [~1] forall x. repeat x = unstream (Stream.repeat x) --"repeat -> unfused" [1] forall x. -- unstream (Stream.repeat x) = repeat x #-} -- | /O(n)/, /fusion/. '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 :: Int -> a -> [a] replicate n0 _ | n0 <= 0 = [] replicate n0 x = go n0 where go 0 = [] go n = x : go (n-1) {-# NOINLINE [1] replicate #-} {-# RULES "replicate -> fusible" [~1] replicate = \n x -> unstream (Stream.replicate n x) --"replicate -> unfused" [1] forall n x. -- unstream (Stream.replicate n x) = replicate n x #-} -- | /fusion/. '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 :: [a] -> [a] cycle [] = error "Prelude.cycle: empty list" cycle xs0 = go xs0 where go [] = go xs0 go (x:xs) = x : go xs {-# NOINLINE [1] cycle #-} {-# RULES "cycle -> fusible" [~1] forall xs. cycle xs = unstream (Stream.cycle (stream xs)) --"cycle -> unfused" [1] forall xs. -- unstream (Stream.cycle (stream xs)) = cycle xs #-} -- --------------------------------------------------------------------- -- ** Unfolding -- | /fusion/. The 'unfoldr' function is a \`dual\' to 'foldr': while 'foldr' -- reduces a list to a summary value, 'unfoldr' builds a list from -- a seed value. The function takes the element and returns 'Nothing' -- if it is done producing the list or returns 'Just' @(a,b)@, in which -- case, @a@ is a prepended to the list and @b@ is used as the next -- element in a recursive call. For example, -- -- > iterate f == unfoldr (\x -> Just (x, f x)) -- -- In some cases, 'unfoldr' can undo a 'foldr' operation: -- -- > unfoldr f' (foldr f z xs) == xs -- -- if the following holds: -- -- > f' (f x y) = Just (x,y) -- > f' z = Nothing -- -- A simple use of unfoldr: -- -- > unfoldr (\b -> if b == 0 then Nothing else Just (b, b-1)) 10 -- > [10,9,8,7,6,5,4,3,2,1] -- unfoldr :: (b -> Maybe (a, b)) -> b -> [a] unfoldr f b0 = unfold b0 where unfold b = case f b of Just (a,b') -> a : unfold b' Nothing -> [] {-# INLINE [1] unfoldr #-} {-# RULES "unfoldr -> fusible" [~1] forall f x. unfoldr f x = unstream (Stream.unfoldr f x) --"unfoldr -> unfused" [1] forall f x. -- unstream (Stream.unfoldr f x) = unfoldr f x #-} ------------------------------------------------------------------------ -- * Sublists -- ** Extracting sublists -- | /O(n)/,/fusion/. '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] == [] -- -- It is an instance of the more general 'Data.List.genericTake', -- in which @n@ may be of any integral type. -- take :: Int -> [a] -> [a] take i _ | i <= 0 = [] take i ls = take' i ls where take' :: Int -> [a] -> [a] take' 0 _ = [] take' _ [] = [] take' n (x:xs) = x : take' (n-1) xs {-# NOINLINE [1] take #-} {-# RULES "take -> fusible" [~1] forall n x. take n x = unstream (Stream.take n (stream x)) --"take -> unfused" [1] forall n x. -- unstream (Stream.take n (stream x)) = take n x #-} {- take :: Int -> [a] -> [a] take (I# n#) xs = takeUInt n# xs takeUInt :: Int# -> [b] -> [b] takeUInt n xs | n >=# 0# = take_unsafe_UInt n xs | otherwise = [] take_unsafe_UInt :: Int# -> [b] -> [b] take_unsafe_UInt 0# _ = [] take_unsafe_UInt m ls = case ls of [] -> [] (x:xs) -> x : take_unsafe_UInt (m -# 1#) xs -} -- | /O(n)/,/fusion/. '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] drop n ls | n < 0 = ls | otherwise = drop' n ls where drop' :: Int -> [a] -> [a] drop' 0 xs = xs drop' _ xs@[] = xs drop' m (_:xs) = drop' (m-1) xs {-# NOINLINE [1] drop #-} {-# RULES "drop -> fusible" [~1] forall n x. drop n x = unstream (Stream.drop n (stream x)) --"drop -> unfused" [1] forall n x. -- unstream (Stream.drop n (stream x)) = drop n x #-} -- | '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)@. -- '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]) splitAt n ls | n < 0 = ([], ls) | otherwise = splitAt' n ls where splitAt' :: Int -> [a] -> ([a], [a]) splitAt' 0 xs = ([], xs) splitAt' _ xs@[] = (xs, xs) splitAt' m (x:xs) = (x:xs', xs'') where (xs', xs'') = splitAt' (m-1) xs {-# NOINLINE [1] splitAt #-} {- splitAt n xs | n <= 0 = ([], xs) splitAt _ [] = ([], []) splitAt n (x:xs) = (x:xs', xs'') where (xs', xs'') = splitAt (n-1) xs -} {-# RULES "splitAt -> fusible" [~1] forall n xs. splitAt n xs = Stream.splitAt n (stream xs) --"splitAt -> unfused" [1] forall n xs. -- Stream.splitAt n (stream xs) = splitAt n xs #-} -- | /O(n)/,/fusion/. '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] == [] -- takeWhile :: (a -> Bool) -> [a] -> [a] takeWhile _ [] = [] takeWhile p xs0 = go xs0 where go [] = [] go (x:xs) | p x = x : go xs | otherwise = [] {-# NOINLINE [1] takeWhile #-} {-# RULES "takeWhile -> fusible" [~1] forall f xs. takeWhile f xs = unstream (Stream.takeWhile f (stream xs)) --"takeWhile -> unfused" [1] forall f xs. -- unstream (Stream.takeWhile f (stream xs)) = takeWhile f xs #-} -- | /O(n)/,/fusion/. '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 _ [] = [] dropWhile p xs0 = go xs0 where go [] = [] go xs@(x:xs') | p x = go xs' | otherwise = xs {-# NOINLINE [1] dropWhile #-} {-# RULES "dropWhile -> fusible" [~1] forall f xs. dropWhile f xs = unstream (Stream.dropWhile f (stream xs)) --"dropWhile -> unfused" [1] forall f xs. -- unstream (Stream.dropWhile f (stream xs)) = dropWhile f xs #-} -- | 'span', 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 -- 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)@ span :: (a -> Bool) -> [a] -> ([a], [a]) span _ [] = ([], []) span p xs0 = go xs0 where go [] = ([], []) go xs@(x:xs') | p x = let (ys,zs) = go xs' in (x:ys,zs) | otherwise = ([],xs) -- TODO fuse -- Hmm, these do a lot of sharing, but is it worth it? -- | '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)@. -- break :: (a -> Bool) -> [a] -> ([a], [a]) break _ [] = ([], []) break p xs0 = go xs0 where go [] = ([], []) go xs@(x:xs') | p x = ([],xs) | otherwise = let (ys,zs) = go xs' in (x:ys,zs) -- TODO fuse -- | The 'group' function takes a list and returns a list of lists such -- that the concatenation of the result is equal to the argument. Moreover, -- each sublist in the result contains only equal elements. For example, -- -- > group "Mississippi" = ["M","i","ss","i","ss","i","pp","i"] -- -- It is a special case of 'groupBy', which allows the programmer to supply -- their own equality test. group :: Eq a => [a] -> [[a]] group [] = [] group (x:xs) = (x:ys) : group zs where (ys,zs) = span (x ==) xs -- TODO fuse -- | The 'inits' function returns all initial segments of the argument, -- shortest first. For example, -- -- > inits "abc" == ["","a","ab","abc"] -- inits :: [a] -> [[a]] inits [] = [] : [] inits (x:xs) = [] : map (x:) (inits xs) -- TODO fuse -- | The 'tails' function returns all final segments of the argument, -- longest first. For example, -- -- > tails "abc" == ["abc", "bc", "c",""] -- tails :: [a] -> [[a]] tails [] = [] : [] tails xxs@(_:xs) = xxs : tails xs -- TODO fuse ------------------------------------------------------------------------ -- * Predicates -- | /O(n)/,/fusion/. The 'isPrefixOf' function takes two lists and -- returns 'True' iff the first list is a prefix of the second. -- isPrefixOf :: Eq a => [a] -> [a] -> Bool isPrefixOf [] _ = True isPrefixOf _ [] = False isPrefixOf (x:xs) (y:ys) | x == y = isPrefixOf xs ys | otherwise = False {-# NOINLINE [1] isPrefixOf #-} {-# RULES "isPrefixOf -> fusible" [~1] forall xs ys. isPrefixOf xs ys = Stream.isPrefixOf (stream xs) (stream ys) --"isPrefixOf -> unfused" [1] forall xs ys. -- Stream.isPrefixOf (stream xs) (stream ys) = isPrefixOf xs ys #-} -- | The 'isSuffixOf' function takes two lists and returns 'True' -- iff the first list is a suffix of the second. -- Both lists must be finite. isSuffixOf :: Eq a => [a] -> [a] -> Bool isSuffixOf x y = reverse x `isPrefixOf` reverse y -- TODO fuse -- | The 'isInfixOf' function takes two lists and returns 'True' -- iff the first list is contained, wholly and intact, -- anywhere within the second. -- -- Example: -- -- > isInfixOf "Haskell" "I really like Haskell." -> True -- > isInfixOf "Ial" "I really like Haskell." -> False -- isInfixOf :: Eq a => [a] -> [a] -> Bool isInfixOf needle haystack = any (isPrefixOf needle) (tails haystack) -- TODO fuse -- --------------------------------------------------------------------- -- * Searching lists -- ** Searching by equality -- | /O(n)/, /fusion/. 'elem' is the list membership predicate, usually written -- in infix form, e.g., @x `elem` xs@. -- elem :: Eq a => a -> [a] -> Bool elem _ [] = False elem x (y:ys) | x == y = True | otherwise = elem x ys {-# NOINLINE [1] elem #-} {-# RULES "elem -> fusible" [~1] forall x xs. elem x xs = Stream.elem x (stream xs) --"elem -> unfused" [1] forall x xs. -- Stream.elem x (stream xs) = elem x xs #-} -- | /O(n)/, /fusion/. 'notElem' is the negation of 'elem'. notElem :: Eq a => a -> [a] -> Bool notElem x xs = not (elem x xs) {-# INLINE notElem #-} {- RULES -- We don't provide an expicilty fusible version, since not . elem is -- just as good. "notElem -> fusible" [~1] forall x xs. notElem x xs = Stream.notElem x (stream xs) "notElem -> unfused" [1] forall x xs. Stream.notElem x (stream xs) = notElem x xs -} -- | /O(n)/,/fusion/. 'lookup' @key assocs@ looks up a key in an association list. lookup :: Eq a => a -> [(a, b)] -> Maybe b lookup _ [] = Nothing lookup key xys0 = go xys0 where go [] = Nothing go ((x,y):xys) | key == x = Just y | otherwise = lookup key xys {-# NOINLINE [1] lookup #-} {-# RULES "lookup -> fusible" [~1] forall x xs. lookup x xs = Stream.lookup x (stream xs) --"lookup -> unfused" [1] forall x xs. -- Stream.lookup x (stream xs) = lookup x xs #-} -- | /O(n)/,/fusion/. '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] -- -- Properties: -- -- > filter p (filter q s) = filter (\x -> q x && p x) s -- filter :: (a -> Bool) -> [a] -> [a] filter _ [] = [] filter p xs0 = go xs0 where go [] = [] go (x:xs) | p x = x : go xs | otherwise = go xs {-# NOINLINE [1] filter #-} {-# RULES "filter -> fusible" [~1] forall f xs. filter f xs = unstream (Stream.filter f (stream xs)) --"filter -> unfused" [1] forall f xs. -- unstream (Stream.filter f (stream xs)) = filter f xs #-} ------------------------------------------------------------------------ -- ** Searching with a predicate -- | /O(n)/,/fusion/. The 'find' function takes a predicate and a list and returns the -- first element in the list matching the predicate, or 'Nothing' if -- there is no such element. find :: (a -> Bool) -> [a] -> Maybe a find _ [] = Nothing find p xs0 = go xs0 where go [] = Nothing go (x:xs) | p x = Just x | otherwise = go xs {-# NOINLINE [1] find #-} {-# RULES "find -> fusible" [~1] forall f xs. find f xs = Stream.find f (stream xs) --"find -> unfused" [1] forall f xs. -- Stream.find f (stream xs) = find f xs #-} -- | The 'partition' function takes a predicate a list and returns -- the pair of lists of elements which do and do not satisfy the -- predicate, respectively; i.e., -- -- > partition p xs == (filter p xs, filter (not . p) xs) partition :: (a -> Bool) -> [a] -> ([a], [a]) partition p xs = foldr (select p) ([],[]) xs {-# INLINE partition #-} -- TODO fuse select :: (a -> Bool) -> a -> ([a], [a]) -> ([a], [a]) select p x ~(ts,fs) | p x = (x:ts,fs) | otherwise = (ts, x:fs) ------------------------------------------------------------------------ -- * Indexing lists -- | /O(n)/,/fusion/. 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] -> Int -> a xs0 !! n0 | n0 < 0 = error "Prelude.(!!): negative index" | otherwise = index xs0 n0 #ifndef __HADDOCK__ where index [] _ = error "Prelude.(!!): index too large" index (y:ys) n = if n == 0 then y else index ys (n-1) #endif {-# NOINLINE [1] (!!) #-} {-# RULES "!! -> fusible" [~1] forall xs n. xs !! n = Stream.index (stream xs) n -- "!! -> unfused" [1] forall xs n. -- Stream.index (stream xs) n = xs !! n #-} -- | The 'elemIndex' function returns the index of the first element -- in the given list which is equal (by '==') to the query element, -- or 'Nothing' if there is no such element. -- -- Properties: -- -- > elemIndex x xs = listToMaybe [ n | (n,a) <- zip [0..] xs, a == x ] -- > elemIndex x xs = findIndex (x==) xs -- elemIndex :: Eq a => a -> [a] -> Maybe Int elemIndex x = findIndex (x==) {-# INLINE elemIndex #-} {- elemIndex :: Eq a => a -> [a] -> Maybe Int elemIndex y xs0 = loop_elemIndex xs0 0 #ifndef __HADDOCK__ where loop_elemIndex [] !_ = Nothing loop_elemIndex (x:xs) !n | p x = Just n | otherwise = loop_elemIndex xs (n + 1) p = (y ==) #endif {-# NOINLINE [1] elemIndex #-} -} {- RULES "elemIndex -> fusible" [~1] forall x xs. elemIndex x xs = Stream.elemIndex x (stream xs) "elemIndex -> unfused" [1] forall x xs. Stream.elemIndex x (stream xs) = elemIndex x xs -} -- | /O(n)/,/fusion/. The 'elemIndices' function extends 'elemIndex', by -- returning the indices of all elements equal to the query element, in -- ascending order. -- -- Properties: -- -- > length (filter (==a) xs) = length (elemIndices a xs) -- elemIndices :: Eq a => a -> [a] -> [Int] elemIndices x = findIndices (x==) {-# INLINE elemIndices #-} {- elemIndices :: Eq a => a -> [a] -> [Int] elemIndices y xs0 = loop_elemIndices xs0 0 #ifndef __HADDOCK__ where loop_elemIndices [] !_ = [] loop_elemIndices (x:xs) !n | p x = n : loop_elemIndices xs (n + 1) | otherwise = loop_elemIndices xs (n + 1) p = (y ==) #endif {-# NOINLINE [1] elemIndices #-} -} {- RULES "elemIndices -> fusible" [~1] forall x xs. elemIndices x xs = unstream (Stream.elemIndices x (stream xs)) "elemIndices -> unfused" [1] forall x xs. unstream (Stream.elemIndices x (stream xs)) = elemIndices x xs -} -- | The 'findIndex' function takes a predicate and a list and returns -- the index of the first element in the list satisfying the predicate, -- or 'Nothing' if there is no such element. -- -- Properties: -- -- > findIndex p xs = listToMaybe [ n | (n,x) <- zip [0..] xs, p x ] -- findIndex :: (a -> Bool) -> [a] -> Maybe Int findIndex p ls = loop_findIndex ls 0# where loop_findIndex [] _ = Nothing loop_findIndex (x:xs) n | p x = Just (I# n) | otherwise = loop_findIndex xs (n +# 1#) {-# NOINLINE [1] findIndex #-} {-# RULES "findIndex -> fusible" [~1] forall f xs. findIndex f xs = Stream.findIndex f (stream xs) -- "findIndex -> unfused" [1] forall f xs. -- Stream.findIndex f (stream xs) = findIndex f xs #-} -- | /O(n)/,/fusion/. The 'findIndices' function extends 'findIndex', by -- returning the indices of all elements satisfying the predicate, in -- ascending order. -- -- Properties: -- -- > length (filter p xs) = length (findIndices p xs) -- findIndices :: (a -> Bool) -> [a] -> [Int] findIndices p ls = loop_findIndices ls 0# where loop_findIndices [] _ = [] loop_findIndices (x:xs) n | p x = I# n : loop_findIndices xs (n +# 1#) | otherwise = loop_findIndices xs (n +# 1#) {-# NOINLINE [1] findIndices #-} {-# RULES "findIndices -> fusible" [~1] forall p xs. findIndices p xs = unstream (Stream.findIndices p (stream xs)) -- "findIndices -> unfused" [1] forall p xs. -- unstream (Stream.findIndices p (stream xs)) = findIndices p xs #-} ------------------------------------------------------------------------ -- * Zipping and unzipping lists -- | /O(n)/,/fusion/. 'zip' takes two lists and returns a list of -- corresponding pairs. If one input list is short, excess elements of -- the longer list are discarded. -- -- Properties: -- -- > zip a b = zipWith (,) a b -- zip :: [a] -> [b] -> [(a, b)] zip (a:as) (b:bs) = (a,b) : zip as bs zip _ _ = [] {-# NOINLINE [1] zip #-} {-# RULES "zip -> fusible" [~1] forall xs ys. zip xs ys = unstream (Stream.zip (stream xs) (stream ys)) -- "zip -> unfused" [1] forall xs ys. -- unstream (Stream.zip (stream xs) (stream ys)) = zip xs ys #-} -- | /O(n)/,/fusion/. 'zip3' takes three lists and returns a list of -- triples, analogous to 'zip'. -- -- Properties: -- -- > zip3 a b c = zipWith (,,) a b c -- zip3 :: [a] -> [b] -> [c] -> [(a, b, c)] zip3 (a:as) (b:bs) (c:cs) = (a,b,c) : zip3 as bs cs zip3 _ _ _ = [] {-# NOINLINE [1] zip3 #-} {-# RULES "zip3 -> fusible" [~1] forall xs ys zs. zip3 xs ys zs = unstream (Stream.zipWith3 (,,) (stream xs) (stream ys) (stream zs)) -- "zip3 -> unfused" [1] forall xs ys zs. -- unstream (Stream.zipWith3 (,,) (stream xs) (stream ys) (stream zs)) = zip3 xs ys zs #-} -- | /O(n)/,/fusion/. The 'zip4' function takes four lists and returns a list of -- quadruples, analogous to 'zip'. zip4 :: [a] -> [b] -> [c] -> [d] -> [(a, b, c, d)] zip4 = zipWith4 (,,,) {-# INLINE zip4 #-} -- | The 'zip5' function takes five lists and returns a list of -- five-tuples, analogous to 'zip'. zip5 :: [a] -> [b] -> [c] -> [d] -> [e] -> [(a, b, c, d, e)] zip5 = zipWith5 (,,,,) -- | The 'zip6' function takes six lists and returns a list of six-tuples, -- analogous to 'zip'. zip6 :: [a] -> [b] -> [c] -> [d] -> [e] -> [f] -> [(a, b, c, d, e, f)] zip6 = zipWith6 (,,,,,) -- | The 'zip7' function takes seven lists and returns a list of -- seven-tuples, analogous to 'zip'. zip7 :: [a] -> [b] -> [c] -> [d] -> [e] -> [f] -> [g] -> [(a, b, c, d, e, f, g)] zip7 = zipWith7 (,,,,,,) -- | /O(n)/,/fusion/. 'zipWith' generalises 'zip' by zipping with the -- function given as the first argument, instead of a tupling function. -- For example, @'zipWith' (+)@ is applied to two lists to produce the -- list of corresponding sums. -- Properties: -- -- > zipWith (,) = zip -- zipWith :: (a -> b -> c) -> [a] -> [b] -> [c] zipWith f (a:as) (b:bs) = f a b : zipWith f as bs zipWith _ _ _ = [] {-# INLINE [1] zipWith #-} --FIXME: If we change the above INLINE to NOINLINE then ghc goes into -- a loop, why? Do we have some dodgy recursive rules somewhere? {-# RULES "zipWith -> fusible" [~1] forall f xs ys. zipWith f xs ys = unstream (Stream.zipWith f (stream xs) (stream ys)) -- "zipWith -> unfused" [1] forall f xs ys. -- unstream (Stream.zipWith f (stream xs) (stream ys)) = zipWith f xs ys #-} -- | /O(n)/,/fusion/. The 'zipWith3' function takes a function which -- combines three elements, as well as three lists and returns a list of -- their point-wise combination, analogous to 'zipWith'. -- -- Properties: -- -- > zipWith3 (,,) = zip3 -- zipWith3 :: (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d] zipWith3 z (a:as) (b:bs) (c:cs) = z a b c : zipWith3 z as bs cs zipWith3 _ _ _ _ = [] {-# NOINLINE [1] zipWith3 #-} {-# RULES "zipWith3 -> fusible" [~1] forall f xs ys zs. zipWith3 f xs ys zs = unstream (Stream.zipWith3 f (stream xs) (stream ys) (stream zs)) -- "zipWith3 -> unfused" [1] forall f xs ys zs. -- unstream (Stream.zipWith3 f (stream xs) (stream ys) (stream zs)) = zipWith3 f xs ys zs #-} -- | /O(n)/,/fusion/. The 'zipWith4' function takes a function which combines four -- elements, as well as four lists and returns a list of their point-wise -- combination, analogous to 'zipWith'. zipWith4 :: (a -> b -> c -> d -> e) -> [a] -> [b] -> [c] -> [d] -> [e] zipWith4 z (a:as) (b:bs) (c:cs) (d:ds) = z a b c d : zipWith4 z as bs cs ds zipWith4 _ _ _ _ _ = [] {-# NOINLINE [1] zipWith4 #-} {-# RULES "zipWith4 -> fusible" [~1] forall f ws xs ys zs. zipWith4 f ws xs ys zs = unstream (Stream.zipWith4 f (stream ws) (stream xs) (stream ys) (stream zs)) -- "zipWith4 -> unfused" [1] forall f ws xs ys zs. -- unstream (Stream.zipWith4 f (stream ws) (stream xs) (stream ys) (stream zs)) = zipWith4 f ws xs ys zs #-} -- | The 'zipWith5' function takes a function which combines five -- elements, as well as five lists and returns a list of their point-wise -- combination, analogous to 'zipWith'. zipWith5 :: (a -> b -> c -> d -> e -> f) -> [a] -> [b] -> [c] -> [d] -> [e] -> [f] zipWith5 z (a:as) (b:bs) (c:cs) (d:ds) (e:es) = z a b c d e : zipWith5 z as bs cs ds es zipWith5 _ _ _ _ _ _ = [] -- TODO fuse -- | The 'zipWith6' function takes a function which combines six -- elements, as well as six lists and returns a list of their point-wise -- combination, analogous to 'zipWith'. zipWith6 :: (a -> b -> c -> d -> e -> f -> g) -> [a] -> [b] -> [c] -> [d] -> [e] -> [f] -> [g] zipWith6 z (a:as) (b:bs) (c:cs) (d:ds) (e:es) (f:fs) = z a b c d e f : zipWith6 z as bs cs ds es fs zipWith6 _ _ _ _ _ _ _ = [] -- TODO fuse -- | The 'zipWith7' function takes a function which combines seven -- elements, as well as seven lists and returns a list of their point-wise -- combination, analogous to 'zipWith'. zipWith7 :: (a -> b -> c -> d -> e -> f -> g -> h) -> [a] -> [b] -> [c] -> [d] -> [e] -> [f] -> [g] -> [h] zipWith7 z (a:as) (b:bs) (c:cs) (d:ds) (e:es) (f:fs) (g:gs) = z a b c d e f g : zipWith7 z as bs cs ds es fs gs zipWith7 _ _ _ _ _ _ _ _ = [] -- TODO fuse ------------------------------------------------------------------------ -- unzips -- | 'unzip' transforms a list of pairs into a list of first components -- and a list of second components. unzip :: [(a, b)] -> ([a], [b]) unzip = foldr (\(a,b) ~(as,bs) -> (a:as,b:bs)) ([],[]) -- TODO fuse -- | The 'unzip3' function takes a list of triples and returns three -- lists, analogous to 'unzip'. unzip3 :: [(a, b, c)] -> ([a], [b], [c]) unzip3 = foldr (\(a,b,c) ~(as,bs,cs) -> (a:as,b:bs,c:cs)) ([],[],[]) -- TODO fuse -- | The 'unzip4' function takes a list of quadruples and returns four -- lists, analogous to 'unzip'. unzip4 :: [(a, b, c, d)] -> ([a], [b], [c], [d]) unzip4 = foldr (\(a,b,c,d) ~(as,bs,cs,ds) -> (a:as,b:bs,c:cs,d:ds)) ([],[],[],[]) -- TODO fuse -- | The 'unzip5' function takes a list of five-tuples and returns five -- lists, analogous to 'unzip'. unzip5 :: [(a, b, c, d, e)] -> ([a], [b], [c], [d], [e]) unzip5 = foldr (\(a,b,c,d,e) ~(as,bs,cs,ds,es) -> (a:as,b:bs,c:cs,d:ds,e:es)) ([],[],[],[],[]) -- TODO fuse -- | The 'unzip6' function takes a list of six-tuples and returns six -- lists, analogous to 'unzip'. unzip6 :: [(a, b, c, d, e, f)] -> ([a], [b], [c], [d], [e], [f]) unzip6 = foldr (\(a,b,c,d,e,f) ~(as,bs,cs,ds,es,fs) -> (a:as,b:bs,c:cs,d:ds,e:es,f:fs)) ([],[],[],[],[],[]) -- TODO fuse -- | The 'unzip7' function takes a list of seven-tuples and returns -- seven lists, analogous to 'unzip'. unzip7 :: [(a, b, c, d, e, f, g)] -> ([a], [b], [c], [d], [e], [f], [g]) unzip7 = foldr (\(a,b,c,d,e,f,g) ~(as,bs,cs,ds,es,fs,gs) -> (a:as,b:bs,c:cs,d:ds,e:es,f:fs,g:gs)) ([],[],[],[],[],[],[]) -- TODO fuse ------------------------------------------------------------------------ -- * Special lists -- ** Functions on strings -- | /O(O)/,/fusion/. 'lines' breaks a string up into a list of strings -- at newline characters. The resulting strings do not contain -- newlines. lines :: String -> [String] lines [] = [] lines s = let (l, s') = break (== '\n') s in l : case s' of [] -> [] (_:s'') -> lines s'' --TODO: can we do better than this and preserve the same strictness? {- -- This implementation is fast but too strict :-( -- it doesn't yield each line until it has seen the ending '\n' lines :: String -> [String] lines [] = [] lines cs0 = go [] cs0 where go l [] = reverse l : [] go l ('\n':cs) = reverse l : case cs of [] -> [] _ -> go [] cs go l ( c :cs) = go (c:l) cs -} {-# INLINE [1] lines #-} {- RULES "lines -> fusible" [~1] forall xs. lines xs = unstream (Stream.lines (stream xs)) "lines -> unfused" [1] forall xs. unstream (Stream.lines (stream xs)) = lines xs -} -- | 'words' breaks a string up into a list of words, which were delimited -- by white space. words :: String -> [String] words s = case dropWhile isSpace s of "" -> [] s' -> w : words s'' where (w, s'') = break isSpace s' -- TODO fuse --TODO: can we do better than this and preserve the same strictness? {- -- This implementation is fast but too strict :-( -- it doesn't yield each word until it has seen the ending space words cs0 = dropSpaces cs0 where dropSpaces :: String -> [String] dropSpaces [] = [] dropSpaces (c:cs) | isSpace c = dropSpaces cs | otherwise = munchWord [c] cs munchWord :: String -> String -> [String] munchWord w [] = reverse w : [] munchWord w (c:cs) | isSpace c = reverse w : dropSpaces cs | otherwise = munchWord (c:w) cs -} -- | /O(n)/,/fusion/. 'unlines' is an inverse operation to 'lines'. -- It joins lines, after appending a terminating newline to each. -- -- > unlines xs = concatMap (++"\n") -- unlines :: [String] -> String unlines css0 = to css0 where go [] css = '\n' : to css go (c:cs) css = c : go cs css to [] = [] to (cs:css) = go cs css {-# NOINLINE [1] unlines #-} -- -- fuse via: -- unlines xs = concatMap (snoc xs '\n') -- {- RULES "unlines -> fusible" [~1] forall xs. unlines xs = unstream (Stream.concatMap (\x -> Stream.snoc (stream x) '\n') (stream xs)) "unlines -> unfused" [1] forall xs. unstream (Stream.concatMap (\x -> Stream.snoc (stream x) '\n') (stream xs)) = unlines xs -} -- | 'unwords' is an inverse operation to 'words'. -- It joins words with separating spaces. unwords :: [String] -> String unwords [] = [] unwords (cs0:css0) = go cs0 css0 where go [] css = to css go (c:cs) css = c : go cs css to [] = [] to (cs:ccs) = ' ' : go cs ccs -- TODO fuse ------------------------------------------------------------------------ -- ** \"Set\" operations -- | The 'nub' function removes duplicate elements from a list. -- In particular, it keeps only the first occurrence of each element. -- (The name 'nub' means \`essence\'.) -- It is a special case of 'nubBy', which allows the programmer to supply -- their own equality test. -- nub :: Eq a => [a] -> [a] nub l = nub' l [] where nub' [] _ = [] nub' (x:xs) ls | x `elem` ls = nub' xs ls | otherwise = x : nub' xs (x:ls) {- RULES -- ndm's optimisation "sort/nub" forall xs. sort (nub xs) = map head (group (sort xs)) -} -- TODO fuse -- | 'delete' @x@ removes the first occurrence of @x@ from its list argument. -- For example, -- -- > delete 'a' "banana" == "bnana" -- -- It is a special case of 'deleteBy', which allows the programmer to -- supply their own equality test. -- delete :: Eq a => a -> [a] -> [a] delete = deleteBy (==) -- TODO fuse -- | The '\\' function is list difference ((non-associative). -- In the result of @xs@ '\\' @ys@, the first occurrence of each element of -- @ys@ in turn (if any) has been removed from @xs@. Thus -- -- > (xs ++ ys) \\ xs == ys. -- -- It is a special case of 'deleteFirstsBy', which allows the programmer -- to supply their own equality test. (\\) :: Eq a => [a] -> [a] -> [a] (\\) = foldl (flip delete) -- | The 'union' function returns the list union of the two lists. -- For example, -- -- > "dog" `union` "cow" == "dogcw" -- -- Duplicates, and elements of the first list, are removed from the -- the second list, but if the first list contains duplicates, so will -- the result. -- It is a special case of 'unionBy', which allows the programmer to supply -- their own equality test. -- union :: Eq a => [a] -> [a] -> [a] union = unionBy (==) -- TODO fuse -- | The 'intersect' function takes the list intersection of two lists. -- For example, -- -- > [1,2,3,4] `intersect` [2,4,6,8] == [2,4] -- -- If the first list contains duplicates, so will the result. -- It is a special case of 'intersectBy', which allows the programmer to -- supply their own equality test. -- intersect :: Eq a => [a] -> [a] -> [a] intersect = intersectBy (==) -- TODO fuse ------------------------------------------------------------------------ -- ** Ordered lists -- TODO stuff in Ord can use Map/IntMap -- TODO Hooray, an Ord constraint! we could use a better structure. -- | The 'sort' function implements a stable sorting algorithm. -- It is a special case of 'sortBy', which allows the programmer to supply -- their own comparison function. -- -- Properties: -- -- > not (null x) ==> (head . sort) x = minimum x -- > not (null x) ==> (last . sort) x = maximum x -- sort :: Ord a => [a] -> [a] sort l = mergesort compare l -- TODO fuse, we have an Ord constraint! -- | /O(n)/,/fusion/. The 'insert' function takes an element and a list and inserts the -- element into the list at the last position where it is still less -- than or equal to the next element. In particular, if the list -- is sorted before the call, the result will also be sorted. -- It is a special case of 'insertBy', which allows the programmer to -- supply their own comparison function. -- insert :: Ord a => a -> [a] -> [a] insert e ls = insertBy (compare) e ls {-# INLINE insert #-} ------------------------------------------------------------------------ -- * Generalized functions -- ** The \"By\" operations -- *** User-supplied equality (replacing an Eq context) -- | The 'nubBy' function behaves just like 'nub', except it uses a -- user-supplied equality predicate instead of the overloaded '==' -- function. nubBy :: (a -> a -> Bool) -> [a] -> [a] nubBy eq l = nubBy' l [] where nubBy' [] _ = [] nubBy' (y:ys) xs | elem_by eq y xs = nubBy' ys xs | otherwise = y : nubBy' ys (y:xs) -- TODO fuse -- Not exported: -- Note that we keep the call to `eq` with arguments in the -- same order as in the reference implementation -- 'xs' is the list of things we've seen so far, -- 'y' is the potential new element -- elem_by :: (a -> a -> Bool) -> a -> [a] -> Bool elem_by _ _ [] = False elem_by eq y (x:xs) = if x `eq` y then True else elem_by eq y xs -- | The 'deleteBy' function behaves like 'delete', but takes a -- user-supplied equality predicate. deleteBy :: (a -> a -> Bool) -> a -> [a] -> [a] deleteBy _ _ [] = [] deleteBy eq x (y:ys) = if x `eq` y then ys else y : deleteBy eq x ys -- TODO fuse deleteFirstsBy :: (a -> a -> Bool) -> [a] -> [a] -> [a] deleteFirstsBy eq = foldl (flip (deleteBy eq)) -- | The 'unionBy' function is the non-overloaded version of 'union'. unionBy :: (a -> a -> Bool) -> [a] -> [a] -> [a] unionBy eq xs ys = xs ++ foldl (flip (deleteBy eq)) (nubBy eq ys) xs -- TODO fuse -- | The 'intersectBy' function is the non-overloaded version of 'intersect'. intersectBy :: (a -> a -> Bool) -> [a] -> [a] -> [a] intersectBy eq xs ys = [x | x <- xs, any (eq x) ys] -- TODO fuse -- | The 'groupBy' function is the non-overloaded version of 'group'. groupBy :: (a -> a -> Bool) -> [a] -> [[a]] groupBy _ [] = [] groupBy eq (x:xs) = (x:ys) : groupBy eq zs where (ys,zs) = span (eq x) xs -- TODO fuse ------------------------------------------------------------------------ -- *** User-supplied comparison (replacing an Ord context) -- | The 'sortBy' function is the non-overloaded version of 'sort'. sortBy :: (a -> a -> Ordering) -> [a] -> [a] sortBy cmp l = mergesort cmp l -- TODO fuse mergesort :: (a -> a -> Ordering) -> [a] -> [a] mergesort cmp xs = mergesort' cmp (map wrap xs) mergesort' :: (a -> a -> Ordering) -> [[a]] -> [a] mergesort' _ [] = [] mergesort' _ [xs] = xs mergesort' cmp xss = mergesort' cmp (merge_pairs cmp xss) merge_pairs :: (a -> a -> Ordering) -> [[a]] -> [[a]] merge_pairs _ [] = [] merge_pairs _ [xs] = [xs] merge_pairs cmp (xs:ys:xss) = merge cmp xs ys : merge_pairs cmp xss merge :: (a -> a -> Ordering) -> [a] -> [a] -> [a] merge _ xs [] = xs merge _ [] ys = ys merge cmp (x:xs) (y:ys) = case x `cmp` y of GT -> y : merge cmp (x:xs) ys _ -> x : merge cmp xs (y:ys) wrap :: a -> [a] wrap x = [x] -- | /O(n)/,/fusion/. The non-overloaded version of 'insert'. insertBy :: (a -> a -> Ordering) -> a -> [a] -> [a] insertBy _ x [] = [x] insertBy cmp x ys@(y:ys') = case cmp x y of GT -> y : insertBy cmp x ys' _ -> x : ys {-# NOINLINE [1] insertBy #-} {-# RULES "insertBy -> fusible" [~1] forall f x xs. insertBy f x xs = unstream (Stream.insertBy f x (stream xs)) -- "insertBy -> unfused" [1] forall f x xs. -- unstream (Stream.insertBy f x (stream xs)) = insertBy f x xs #-} -- | /O(n)/,/fusion/. The 'maximumBy' function takes a comparison function and a list -- and returns the greatest element of the list by the comparison function. -- The list must be finite and non-empty. -- maximumBy :: (a -> a -> Ordering) -> [a] -> a maximumBy _ [] = error "List.maximumBy: empty list" maximumBy cmp xs = foldl1 max' xs where max' x y = case cmp x y of GT -> x _ -> y {-# NOINLINE [1] maximumBy #-} {-# RULES "maximumBy -> fused" [~1] forall p xs. maximumBy p xs = Stream.maximumBy p (stream xs) -- "maximumBy -> unfused" [1] forall p xs. -- Stream.maximumBy p (stream xs) = maximumBy p xs #-} -- | /O(n)/,/fusion/. The 'minimumBy' function takes a comparison function and a list -- and returns the least element of the list by the comparison function. -- The list must be finite and non-empty. minimumBy :: (a -> a -> Ordering) -> [a] -> a minimumBy _ [] = error "List.minimumBy: empty list" minimumBy cmp xs = foldl1 min' xs where min' x y = case cmp x y of GT -> y _ -> x {-# NOINLINE [1] minimumBy #-} {-# RULES "minimumBy -> fused" [~1] forall p xs. minimumBy p xs = Stream.minimumBy p (stream xs) -- "minimumBy -> unfused" [1] forall p xs. -- Stream.minimumBy p (stream xs) = minimumBy p xs #-} ------------------------------------------------------------------------ -- * The \"generic\" operations -- | The 'genericLength' function is an overloaded version of 'length'. In -- particular, instead of returning an 'Int', it returns any type which is -- an instance of 'Num'. It is, however, less efficient than 'length'. -- genericLength :: Num i => [b] -> i genericLength [] = 0 genericLength (_:l) = 1 + genericLength l {-# NOINLINE [1] genericLength #-} {-# RULES "genericLength -> fusible" [~1] forall xs. genericLength xs = Stream.genericLength (stream xs) -- "genericLength -> unfused" [1] forall xs. -- Stream.genericLength (stream xs) = genericLength xs #-} {-# RULES "genericLength -> length/Int" genericLength = length :: [a] -> Int #-} -- | /O(n)/,/fusion/. The 'genericTake' function is an overloaded version of 'take', which -- accepts any 'Integral' value as the number of elements to take. genericTake :: Integral i => i -> [a] -> [a] genericTake 0 _ = [] genericTake _ [] = [] genericTake n (x:xs) | n > 0 = x : genericTake (n-1) xs | otherwise = error "List.genericTake: negative argument" {-# NOINLINE [1] genericTake #-} {-# RULES "genericTake -> fusible" [~1] forall xs n. genericTake n xs = unstream (Stream.genericTake n (stream xs)) -- "genericTake -> unfused" [1] forall xs n. -- unstream (Stream.genericTake n (stream xs)) = genericTake n xs #-} {-# RULES "genericTake -> take/Int" genericTake = take :: Int -> [a] -> [a] #-} -- | /O(n)/,/fusion/. The 'genericDrop' function is an overloaded version of 'drop', which -- accepts any 'Integral' value as the number of elements to drop. genericDrop :: Integral i => i -> [a] -> [a] genericDrop 0 xs = xs genericDrop _ [] = [] genericDrop n (_:xs) | n > 0 = genericDrop (n-1) xs genericDrop _ _ = error "List.genericDrop: negative argument" {-# NOINLINE [1] genericDrop #-} {-# RULES "genericDrop -> fusible" [~1] forall xs n. genericDrop n xs = unstream (Stream.genericDrop n (stream xs)) -- "genericDrop -> unfused" [1] forall xs n. -- unstream (Stream.genericDrop n (stream xs)) = genericDrop n xs #-} {-# RULES "genericDrop -> drop/Int" genericDrop = drop :: Int -> [a] -> [a] #-} -- | /O(n)/,/fusion/. The 'genericIndex' function is an overloaded version of '!!', which -- accepts any 'Integral' value as the index. genericIndex :: Integral a => [b] -> a -> b genericIndex (x:_) 0 = x genericIndex (_:xs) n | n > 0 = genericIndex xs (n-1) | otherwise = error "List.genericIndex: negative argument." genericIndex _ _ = error "List.genericIndex: index too large." {-# NOINLINE [1] genericIndex #-} -- can we pull the n > 0 test out and do it just once? -- probably not since we don't know what n-1 does!! -- can only specialise it for sane Integral instances :-( {-# RULES "genericIndex -> fusible" [~1] forall xs n. genericIndex xs n = Stream.genericIndex (stream xs) n -- "genericIndex -> unfused" [1] forall xs n. -- Stream.genericIndex (stream xs) n = genericIndex n xs #-} {-# RULES "genericIndex -> index/Int" genericIndex = (!!) :: [a] -> Int -> a #-} -- | /O(n)/,/fusion/. The 'genericSplitAt' function is an overloaded -- version of 'splitAt', which accepts any 'Integral' value as the -- position at which to split. -- genericSplitAt :: Integral i => i -> [a] -> ([a], [a]) genericSplitAt 0 xs = ([],xs) genericSplitAt _ [] = ([],[]) genericSplitAt n (x:xs) | n > 0 = (x:xs',xs'') where (xs',xs'') = genericSplitAt (n-1) xs genericSplitAt _ _ = error "List.genericSplitAt: negative argument" {-# RULES "genericSplitAt -> fusible" [~1] forall xs n. genericSplitAt n xs = Stream.genericSplitAt n (stream xs) -- "genericSplitAt -> unfused" [1] forall xs n. -- Stream.genericSplitAt n (stream xs) = genericSplitAt n xs #-} {-# RULES "genericSplitAt -> splitAt/Int" genericSplitAt = splitAt :: Int -> [a] -> ([a], [a]) #-} -- | /O(n)/,/fusion/. The 'genericReplicate' function is an overloaded version of 'replicate', -- which accepts any 'Integral' value as the number of repetitions to make. -- genericReplicate :: Integral i => i -> a -> [a] genericReplicate n x = genericTake n (repeat x) {-# INLINE genericReplicate #-} {-# RULES "genericReplicate -> replicate/Int" genericReplicate = replicate :: Int -> a -> [a] #-} -- --------------------------------------------------------------------- -- Internal utilities -- Common up near identical calls to `error' to reduce the number -- constant strings created when compiled: errorEmptyList :: String -> a errorEmptyList fun = moduleError fun "empty list" {-# NOINLINE errorEmptyList #-} moduleError :: String -> String -> a moduleError fun msg = error ("Data.List." ++ fun ++ ':':' ':msg) {-# NOINLINE moduleError #-} bottom :: a bottom = error "Data.List.Stream: bottom" {-# NOINLINE bottom #-}