9 표준 프렐류드
9 표준 프렐류드 (Standard Prelude)
하스켈로 프로그램을 짜기 시작하면 가장 먼저 만나는 것이 바로 프렐류드예요. import 한 줄 없이 바로 쓸 수 있는 모든 함수와 타입, 타입클래스가 여기 모여 있죠. 그런데 이번 장은 프렐류드를 설명하는 장이 아니라, 프렐류드의 명세 그 자체를 통째로 담은 문서예요. 즉 평소에 자연스럽게 써 온 map, foldr, (++) 같은 함수들이 실제로 어떻게 정의되어 있는지를 한눈에 볼 수 있는 곳이랍니다. 코드를 천천히 읽다 보면 「아, 이게 그 의미였구나」 하는 순간이 꽤 많아질 거예요. 특히 이 정의들이 효율보다 명확성을 우선해서 쓰여 있다는 점만 기억해 두면 독해가 훨씬 수월해져요.
출처: https://www.haskell.org/onlinereport/haskell2010/haskellch9.html
본문
이 장에서는 하스켈 프렐류드(Prelude) 전체를 싣고 있어요. 그리고 이 코드 자체가 곧 프렐류드에 대한 명세(specification)가 됩니다. 정의 중 상당수가 효율보다는 명확성에 초점을 맞춰 작성됐기 때문에, 「이대로 구현해야 한다」고 생각할 필요는 없어요. 각 함수가 어떤 의미로 동작한다는 기준점을 보여 주는 문서라고 보면 돼요.
클래스 선언에 함께 따라오는 기본 메서드(default method) 정의는 말 그대로 기본값에 대한 명세일 뿐이에요. 모든 인스턴스에서 그 메서드의 의미를 구속하는 건 아니죠. 좋은 예가 하나 있어요. Enum 클래스의 enumFrom 기본 메서드는, 타입의 값 범위가 Int를 넘어가는 경우 제대로 동작하지 않아요. fromEnum이 그 타입의 모든 값을 서로 다른 Int 값으로 대응시킬 수 없기 때문이에요.
여기 실린 프렐류드는 루트 모듈인 Prelude와, 그 아래 세 개의 하위 모듈 PreludeList, PreludeText, PreludeIO로 나뉘어 있어요. 다만 이 구조는 순전히 보여 주기 위한 것뿐이에요. 구현체가 프렐류드를 꼭 이런 식으로 구성해야 하는 것도 아니고, 이 세 모듈을 따로 import 할 수 있는 것도 아니에요. 실제로 의미가 있는 건 오직 module Prelude가 내보내는 것(export)뿐이에요.
이 모듈 중 일부는 Data.Char, Control.Monad, System.IO, Numeric 같은 라이브러리 모듈을 import 해요. 이 모듈들은 이 보고서의 Part II에서 자세히 다루는데, 그런 import는 당연히 프렐류드 명세의 일부가 아니에요. 구현체가 라이브러리 모듈을 얼마든지 더 가져오거나 덜 가져와도 된다는 뜻이에요.
하스켈로는 정의할 수 없는 프리미티브, 즉 이름이 prim으로 시작하는 것들은 시스템에 의존적인 방식으로 module PreludeBuiltin에 정의돼 있고, 여기서는 보여 주지 않아요. 프리미티브를 클래스 메서드에 그냥 묶어 놓은 인스턴스 선언도 생략했고, 너무 장황하면서 동작이 뻔히 보이는 인스턴스 몇 개도 간결함을 위해 빼뒀어요.
Integer나 () 같은 특별한 타입의 선언도 완결성을 위해 프렐류드에 넣었지만, 그 선언 자체는 불완전하거나 문법적으로 유효하지 않을 수 있어요. 하스켈로는 표현할 수 없는 나머지 정의가 들어갈 자리에는 생략 부호 ...가 자주 쓰여요.
뜻밖의 모호성(ambiguity) 오류를 줄이고 효율을 높이기 위해, 자주 쓰이는 리스트 함수 몇몇은 Integral a나 Num a 같은 일반적인 숫자 타입 대신 Int 타입을 사용해요. 그 함수들은 take, drop, !!, length, splitAt, replicate이에요. 더 일반화된 버전은 Data.List 라이브러리에 generic이라는 접두어를 붙여서 있어요. 예를 들어 genericLength처럼요.
module Prelude (
module PreludeList, module PreludeText, module PreludeIO,
Bool(False, True),
Maybe(Nothing, Just),
Either(Left, Right),
Ordering(LT, EQ, GT),
Char, String, Int, Integer, Float, Double, Rational, IO,
-- These built-in types are defined in the Prelude, but
-- are denoted by built-in syntax, and cannot legally
-- appear in an export list.
-- List type: []((:), [])
-- Tuple types: (,)((,)), (,,)((,,)), etc.
-- Trivial type: ()(())
-- Functions: (->)
Eq((==), (/=)),
Ord(compare, (<), (<=), (>=), (>), max, min),
Enum(succ, pred, toEnum, fromEnum, enumFrom, enumFromThen,
enumFromTo, enumFromThenTo),
Bounded(minBound, maxBound),
Num((+), (-), (⋆), negate, abs, signum, fromInteger),
Real(toRational),
Integral(quot, rem, div, mod, quotRem, divMod, toInteger),
Fractional((/), recip, fromRational),
Floating(pi, exp, log, sqrt, (⋆⋆), logBase, sin, cos, tan,
asin, acos, atan, sinh, cosh, tanh, asinh, acosh, atanh),
RealFrac(properFraction, truncate, round, ceiling, floor),
RealFloat(floatRadix, floatDigits, floatRange, decodeFloat,
encodeFloat, exponent, significand, scaleFloat, isNaN,
isInfinite, isDenormalized, isIEEE, isNegativeZero, atan2),
Monad((>>=), (>>), return, fail),
Functor(fmap),
mapM, mapM_, sequence, sequence_, (=<<),
maybe, either,
(&&), (||), not, otherwise,
subtract, even, odd, gcd, lcm, (^), (^^),
fromIntegral, realToFrac,
fst, snd, curry, uncurry, id, const, (.), flip, ($), until,
asTypeOf, error, undefined,
seq, ($!)
) where
import PreludeBuiltin -- Contains all ‘prim' values
import UnicodePrims( primUnicodeMaxChar ) -- Unicode primitives
import PreludeList
import PreludeText
import PreludeIO
import Data.Ratio( Rational )
infixr 9 .
infixr 8 ^, ^^, ⋆⋆
infixl 7 ⋆, /, ‘quot‘, ‘rem‘, ‘div‘, ‘mod‘
infixl 6 +, -
-- The (:) operator is built-in syntax, and cannot legally be given
-- a fixity declaration; but its fixity is given by:
-- infixr 5 :
infix 4 ==, /=, <, <=, >=, >
infixr 3 &&
infixr 2 ||
infixl 1 >>, >>=
infixr 1 =<<
infixr 0 $, $!, ‘seq‘
-- Standard types, classes, instances and related functions
-- Equality and Ordered classes
class Eq a where
(==), (/=) :: a -> a -> Bool
-- Minimal complete definition:
-- (==) or (/=)
x /= y = not (x == y)
x == y = not (x /= y)
class (Eq a) => Ord a where
compare :: a -> a -> Ordering
(<), (<=), (>=), (>) :: a -> a -> Bool
max, min :: a -> a -> a
-- Minimal complete definition:
-- (<=) or compare
-- Using compare can be more efficient for complex types.
compare x y
| x == y = EQ
| x <= y = LT
| otherwise = GT
x <= y = compare x y /= GT
x < y = compare x y == LT
x >= y = compare x y /= LT
x > y = compare x y == GT
-- note that (min x y, max x y) = (x,y) or (y,x)
max x y
| x <= y = y
| otherwise = x
min x y
| x <= y = x
| otherwise = y
-- Enumeration and Bounded classes
class Enum a where
succ, pred :: a -> a
toEnum :: Int -> a
fromEnum :: a -> Int
enumFrom :: a -> [a] -- [n..]
enumFromThen :: a -> a -> [a] -- [n,n'..]
enumFromTo :: a -> a -> [a] -- [n..m]
enumFromThenTo :: a -> a -> a -> [a] -- [n,n'..m]
-- Minimal complete definition:
-- toEnum, fromEnum
--
-- NOTE: these default methods only make sense for types
-- that map injectively into Int using fromEnum
-- and toEnum.
succ = toEnum . (+1) . fromEnum
pred = toEnum . (subtract 1) . fromEnum
enumFrom x = map toEnum [fromEnum x ..]
enumFromTo x y = map toEnum [fromEnum x .. fromEnum y]
enumFromThen x y = map toEnum [fromEnum x, fromEnum y ..]
enumFromThenTo x y z =
map toEnum [fromEnum x, fromEnum y .. fromEnum z]
class Bounded a where
minBound :: a
maxBound :: a
-- Numeric classes
class (Eq a, Show a) => Num a where
(+), (-), (⋆) :: a -> a -> a
negate :: a -> a
abs, signum :: a -> a
fromInteger :: Integer -> a
-- Minimal complete definition:
-- All, except negate or (-)
x - y = x + negate y
negate x = 0 - x
class (Num a, Ord a) => Real a where
toRational :: a -> Rational
class (Real a, Enum a) => Integral a where
quot, rem :: a -> a -> a
div, mod :: a -> a -> a
quotRem, divMod :: a -> a -> (a,a)
toInteger :: a -> Integer
-- Minimal complete definition:
-- quotRem, toInteger
n ‘quot‘ d = q where (q,r) = quotRem n d
n ‘rem‘ d = r where (q,r) = quotRem n d
n ‘div‘ d = q where (q,r) = divMod n d
n ‘mod‘ d = r where (q,r) = divMod n d
divMod n d = if signum r == - signum d then (q-1, r+d) else qr
where qr@(q,r) = quotRem n d
class (Num a) => Fractional a where
(/) :: a -> a -> a
recip :: a -> a
fromRational :: Rational -> a
-- Minimal complete definition:
-- fromRational and (recip or (/))
recip x = 1 / x
x / y = x ⋆ recip y
class (Fractional a) => Floating a where
pi :: a
exp, log, sqrt :: a -> a
(⋆⋆), logBase :: a -> a -> a
sin, cos, tan :: a -> a
asin, acos, atan :: a -> a
sinh, cosh, tanh :: a -> a
asinh, acosh, atanh :: a -> a
-- Minimal complete definition:
-- pi, exp, log, sin, cos, sinh, cosh
-- asin, acos, atan
-- asinh, acosh, atanh
x ⋆⋆ y = exp (log x ⋆ y)
logBase x y = log y / log x
sqrt x = x ⋆⋆ 0.5
tan x = sin x / cos x
tanh x = sinh x / cosh x
class (Real a, Fractional a) => RealFrac a where
properFraction :: (Integral b) => a -> (b,a)
truncate, round :: (Integral b) => a -> b
ceiling, floor :: (Integral b) => a -> b
-- Minimal complete definition:
-- properFraction
truncate x = m where (m,_) = properFraction x
round x = let (n,r) = properFraction x
m = if r < 0 then n - 1 else n + 1
in case signum (abs r - 0.5) of
-1 -> n
0 -> if even n then n else m
1 -> m
ceiling x = if r > 0 then n + 1 else n
where (n,r) = properFraction x
floor x = if r < 0 then n - 1 else n
where (n,r) = properFraction x
class (RealFrac a, Floating a) => RealFloat a where
floatRadix :: a -> Integer
floatDigits :: a -> Int
floatRange :: a -> (Int,Int)
decodeFloat :: a -> (Integer,Int)
encodeFloat :: Integer -> Int -> a
exponent :: a -> Int
significand :: a -> a
scaleFloat :: Int -> a -> a
isNaN, isInfinite, isDenormalized, isNegativeZero, isIEEE
:: a -> Bool
atan2 :: a -> a -> a
-- Minimal complete definition:
-- All except exponent, significand,
-- scaleFloat, atan2
exponent x = if m == 0 then 0 else n + floatDigits x
where (m,n) = decodeFloat x
significand x = encodeFloat m (- floatDigits x)
where (m,_) = decodeFloat x
scaleFloat k x = encodeFloat m (n+k)
where (m,n) = decodeFloat x
atan2 y x
| x>0 = atan (y/x)
| x==0 && y>0 = pi/2
| x<0 && y>0 = pi + atan (y/x)
|(x<=0 && y<0) ||
(x<0 && isNegativeZero y) ||
(isNegativeZero x && isNegativeZero y)
= -atan2 (-y) x
| y==0 && (x<0 || isNegativeZero x)
= pi -- must be after the previous test on zero y
| x==0 && y==0 = y -- must be after the other double zero tests
| otherwise = x + y -- x or y is a NaN, return a NaN (via +)
-- Numeric functions
subtract :: (Num a) => a -> a -> a
subtract = flip (-)
even, odd :: (Integral a) => a -> Bool
even n = n ‘rem‘ 2 == 0
odd = not . even
gcd :: (Integral a) => a -> a -> a
gcd 0 0 = error "Prelude.gcd: gcd 0 0 is undefined"
gcd x y = gcd' (abs x) (abs y)
where gcd' x 0 = x
gcd' x y = gcd' y (x ‘rem‘ y)
lcm :: (Integral a) => a -> a -> a
lcm _ 0 = 0
lcm 0 _ = 0
lcm x y = abs ((x ‘quot‘ (gcd x y)) ⋆ y)
(^) :: (Num a, Integral b) => a -> b -> a
x ^ 0 = 1
x ^ n | n > 0 = f x (n-1) x
where f _ 0 y = y
f x n y = g x n where
g x n | even n = g (x⋆x) (n ‘quot‘ 2)
| otherwise = f x (n-1) (x⋆y)
_ ^ _ = error "Prelude.^: negative exponent"
(^^) :: (Fractional a, Integral b) => a -> b -> a
x ^^ n = if n >= 0 then x^n else recip (x^(-n))
fromIntegral :: (Integral a, Num b) => a -> b
fromIntegral = fromInteger . toInteger
realToFrac :: (Real a, Fractional b) => a -> b
realToFrac = fromRational . toRational
-- Monadic classes
class Functor f where
fmap :: (a -> b) -> f a -> f b
class Monad m where
(>>=) :: m a -> (a -> m b) -> m b
(>>) :: m a -> m b -> m b
return :: a -> m a
fail :: String -> m a
-- Minimal complete definition:
-- (>>=), return
m >> k = m >>= \_ -> k
fail s = error s
sequence :: Monad m => [m a] -> m [a]
sequence = foldr mcons (return [])
where mcons p q = p >>= \x -> q >>= \y -> return (x:y)
sequence_ :: Monad m => [m a] -> m ()
sequence_ = foldr (>>) (return ())
-- The xxxM functions take list arguments, but lift the function or
-- list element to a monad type
mapM :: Monad m => (a -> m b) -> [a] -> m [b]
mapM f as = sequence (map f as)
mapM_ :: Monad m => (a -> m b) -> [a] -> m ()
mapM_ f as = sequence_ (map f as)
(=<<) :: Monad m => (a -> m b) -> m a -> m b
f =<< x = x >>= f
-- Trivial type
data () = () deriving (Eq, Ord, Enum, Bounded)
-- Not legal Haskell; for illustration only
-- Function type
-- identity function
id :: a -> a
id x = x
-- constant function
const :: a -> b -> a
const x _ = x
-- function composition
(.) :: (b -> c) -> (a -> b) -> a -> c
f . g = \ x -> f (g x)
-- flip f takes its (first) two arguments in the reverse order of f.
flip :: (a -> b -> c) -> b -> a -> c
flip f x y = f y x
seq :: a -> b -> b
seq = ... -- Primitive
-- right-associating infix application operators
-- (useful in continuation-passing style)
($), ($!) :: (a -> b) -> a -> b
f $ x = f x
f $! x = x ‘seq‘ f x
-- Boolean type
data Bool = False | True deriving (Eq, Ord, Enum, Read, Show, Bounded)
-- Boolean functions
(&&), (||) :: Bool -> Bool -> Bool
True && x = x
False && _ = False
True || _ = True
False || x = x
not :: Bool -> Bool
not True = False
not False = True
otherwise :: Bool
otherwise = True
-- Character type
data Char = ... 'a' | 'b' ... -- Unicode values
instance Eq Char where
c == c' = fromEnum c == fromEnum c'
instance Ord Char where
c <= c' = fromEnum c <= fromEnum c'
instance Enum Char where
toEnum = primIntToChar
fromEnum = primCharToInt
enumFrom c = map toEnum [fromEnum c .. fromEnum (maxBound::Char)]
enumFromThen c c' = map toEnum [fromEnum c, fromEnum c' .. fromEnum lastChar]
where lastChar :: Char
lastChar | c' < c = minBound
| otherwise = maxBound
instance Bounded Char where
minBound = '\0'
maxBound = primUnicodeMaxChar
type String = [Char]
-- Maybe type
data Maybe a = Nothing | Just a deriving (Eq, Ord, Read, Show)
maybe :: b -> (a -> b) -> Maybe a -> b
maybe n f Nothing = n
maybe n f (Just x) = f x
instance Functor Maybe where
fmap f Nothing = Nothing
fmap f (Just x) = Just (f x)
instance Monad Maybe where
(Just x) >>= k = k x
Nothing >>= k = Nothing
return = Just
fail s = Nothing
-- Either type
data Either a b = Left a | Right b deriving (Eq, Ord, Read, Show)
either :: (a -> c) -> (b -> c) -> Either a b -> c
either f g (Left x) = f x
either f g (Right y) = g y
-- IO type
data IO a = ... -- abstract
instance Functor IO where
fmap f x = x >>= (return . f)
instance Monad IO where
(>>=) = ...
return = ...
fail s = ioError (userError s)
-- Ordering type
data Ordering = LT | EQ | GT
deriving (Eq, Ord, Enum, Read, Show, Bounded)
-- Standard numeric types. The data declarations for these types cannot
-- be expressed directly in Haskell since the constructor lists would be
-- far too large.
data Int = minBound ... -1 | 0 | 1 ... maxBound
instance Eq Int where ...
instance Ord Int where ...
instance Num Int where ...
instance Real Int where ...
instance Integral Int where ...
instance Enum Int where ...
instance Bounded Int where ...
data Integer = ... -1 | 0 | 1 ...
instance Eq Integer where ...
instance Ord Integer where ...
instance Num Integer where ...
instance Real Integer where ...
instance Integral Integer where ...
instance Enum Integer where ...
data Float
instance Eq Float where ...
instance Ord Float where ...
instance Num Float where ...
instance Real Float where ...
instance Fractional Float where ...
instance Floating Float where ...
instance RealFrac Float where ...
instance RealFloat Float where ...
data Double
instance Eq Double where ...
instance Ord Double where ...
instance Num Double where ...
instance Real Double where ...
instance Fractional Double where ...
instance Floating Double where ...
instance RealFrac Double where ...
instance RealFloat Double where ...
-- The Enum instances for Floats and Doubles are slightly unusual.
-- The ‘toEnum' function truncates numbers to Int. The definitions
-- of enumFrom and enumFromThen allow floats to be used in arithmetic
-- series: [0,0.1 .. 0.95]. However, roundoff errors make these somewhat
-- dubious. This example may have either 10 or 11 elements, depending on
-- how 0.1 is represented.
instance Enum Float where
succ x = x+1
pred x = x-1
toEnum = fromIntegral
fromEnum = fromInteger . truncate -- may overflow
enumFrom = numericEnumFrom
enumFromThen = numericEnumFromThen
enumFromTo = numericEnumFromTo
enumFromThenTo = numericEnumFromThenTo
instance Enum Double where
succ x = x+1
pred x = x-1
toEnum = fromIntegral
fromEnum = fromInteger . truncate -- may overflow
enumFrom = numericEnumFrom
enumFromThen = numericEnumFromThen
enumFromTo = numericEnumFromTo
enumFromThenTo = numericEnumFromThenTo
numericEnumFrom :: (Fractional a) => a -> [a]
numericEnumFromThen :: (Fractional a) => a -> a -> [a]
numericEnumFromTo :: (Fractional a, Ord a) => a -> a -> [a]
numericEnumFromThenTo :: (Fractional a, Ord a) => a -> a -> a -> [a]
numericEnumFrom = iterate (+1)
numericEnumFromThen n m = iterate (+(m-n)) n
numericEnumFromTo n m = takeWhile (<= m+1/2) (numericEnumFrom n)
numericEnumFromThenTo n n' m = takeWhile p (numericEnumFromThen n n')
where
p | n' >= n = (<= m + (n'-n)/2)
| otherwise = (>= m + (n'-n)/2)
-- Lists
data [a] = [] | a : [a] deriving (Eq, Ord)
-- Not legal Haskell; for illustration only
instance Functor [] where
fmap = map
instance Monad [] where
m >>= k = concat (map k m)
return x = [x]
fail s = []
-- Tuples
data (a,b) = (a,b) deriving (Eq, Ord, Bounded)
data (a,b,c) = (a,b,c) deriving (Eq, Ord, Bounded)
-- Not legal Haskell; for illustration only
-- component projections for pairs:
-- (NB: not provided for triples, quadruples, etc.)
fst :: (a,b) -> a
fst (x,y) = x
snd :: (a,b) -> b
snd (x,y) = y
-- curry converts an uncurried function to a curried function;
-- uncurry converts a curried function to a function on pairs.
curry :: ((a, b) -> c) -> a -> b -> c
curry f x y = f (x, y)
uncurry :: (a -> b -> c) -> ((a, b) -> c)
uncurry f p = f (fst p) (snd p)
-- Misc functions
-- until p f yields the result of applying f until p holds.
until :: (a -> Bool) -> (a -> a) -> a -> a
until p f x
| p x = x
| otherwise = until p f (f x)
-- asTypeOf is a type-restricted version of const. It is usually used
-- as an infix operator, and its typing forces its first argument
-- (which is usually overloaded) to have the same type as the second.
asTypeOf :: a -> a -> a
asTypeOf = const
-- error stops execution and displays an error message
error :: String -> a
error = primError
-- It is expected that compilers will recognize this and insert error
-- messages that are more appropriate to the context in which undefined
-- appears.
undefined :: a
undefined = error "Prelude.undefined"
9.1 Prelude — PreludeList (리스트 모듈)
이 모듈은 리스트를 다루는 표준 함수들을 모아 둔 곳이에요. 여기 있는 map, filter, foldl, zip 같은 함수는 이미 자주 써 왔을 것들이죠. Prelude가 이 모듈을 다시 내보내기 때문에 이 함수들을 따로 import 할 필요가 없다는 점이 포인트예요.
-- Standard list functions
module PreludeList (
map, (++), filter, concat, concatMap,
head, last, tail, init, null, length, (!!),
foldl, foldl1, scanl, scanl1, foldr, foldr1, scanr, scanr1,
iterate, repeat, replicate, cycle,
take, drop, splitAt, takeWhile, dropWhile, span, break,
lines, words, unlines, unwords, reverse, and, or,
any, all, elem, notElem, lookup,
sum, product, maximum, minimum,
zip, zip3, zipWith, zipWith3, unzip, unzip3)
where
import qualified Data.Char(isSpace)
infixl 9 !!
infixr 5 ++
infix 4 ‘elem‘, ‘notElem‘
-- Map and append
map :: (a -> b) -> [a] -> [b]
map f [] = []
map f (x:xs) = f x : map f xs
(++) :: [a] -> [a] -> [a]
[] ++ ys = ys
(x:xs) ++ ys = x : (xs ++ ys)
filter :: (a -> Bool) -> [a] -> [a]
filter p [] = []
filter p (x:xs) | p x = x : filter p xs
| otherwise = filter p xs
concat :: [[a]] -> [a]
concat xss = foldr (++) [] xss
concatMap :: (a -> [b]) -> [a] -> [b]
concatMap f = concat . map f
-- head and tail extract the first element and remaining elements,
-- respectively, of a list, which must be non-empty. last and init
-- are the dual functions working from the end of a finite list,
-- rather than the beginning.
head :: [a] -> a
head (x:_) = x
head [] = error "Prelude.head: empty list"
tail :: [a] -> [a]
tail (_:xs) = xs
tail [] = error "Prelude.tail: empty list"
last :: [a] -> a
last [x] = x
last (_:xs) = last xs
last [] = error "Prelude.last: empty list"
init :: [a] -> [a]
init [x] = []
init (x:xs) = x : init xs
init [] = error "Prelude.init: empty list"
null :: [a] -> Bool
null [] = True
null (_:_) = False
-- length returns the length of a finite list as an Int.
length :: [a] -> Int
length [] = 0
length (_:l) = 1 + length l
-- List index (subscript) operator, 0-origin
(!!) :: [a] -> Int -> a
xs !! n | n < 0 = error "Prelude.!!: negative index"
[] !! _ = error "Prelude.!!: index too large"
(x:_) !! 0 = x
(_:xs) !! n = xs !! (n-1)
-- 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
-- foldl1 is a variant that has no starting value argument, and thus must
-- be applied to non-empty lists. 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.
-- scanl1 is similar, again without the starting element:
-- scanl1 f [x1, x2, ...] == [x1, x1 ‘f‘ x2, ...]
foldl :: (a -> b -> a) -> a -> [b] -> a
foldl f z [] = z
foldl f z (x:xs) = foldl f (f z x) xs
foldl1 :: (a -> a -> a) -> [a] -> a
foldl1 f (x:xs) = foldl f x xs
foldl1 _ [] = error "Prelude.foldl1: empty list"
scanl :: (a -> b -> a) -> a -> [b] -> [a]
scanl f q xs = q : (case xs of
[] -> []
x:xs -> scanl f (f q x) xs)
scanl1 :: (a -> a -> a) -> [a] -> [a]
scanl1 f (x:xs) = scanl f x xs
scanl1 _ [] = []
-- foldr, foldr1, scanr, and scanr1 are the right-to-left duals of the
-- above functions.
foldr :: (a -> b -> b) -> b -> [a] -> b
foldr f z [] = z
foldr f z (x:xs) = f x (foldr f z xs)
foldr1 :: (a -> a -> a) -> [a] -> a
foldr1 f [x] = x
foldr1 f (x:xs) = f x (foldr1 f xs)
foldr1 _ [] = error "Prelude.foldr1: empty list"
scanr :: (a -> b -> b) -> b -> [a] -> [b]
scanr f q0 [] = [q0]
scanr f q0 (x:xs) = f x q : qs
where qs@(q:_) = scanr f q0 xs
scanr1 :: (a -> a -> a) -> [a] -> [a]
scanr1 f [] = []
scanr1 f [x] = [x]
scanr1 f (x:xs) = f x q : qs
where qs@(q:_) = scanr1 f xs
-- 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)
-- repeat x is an infinite list, with x the value of every element.
repeat :: a -> [a]
repeat x = xs where xs = x:xs
-- replicate n x is a list of length n with x the value of every element
replicate :: Int -> a -> [a]
replicate n x = take n (repeat 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 :: [a] -> [a]
cycle [] = error "Prelude.cycle: empty list"
cycle xs = xs' where xs' = xs ++ xs'
-- take n, applied to a list xs, returns the prefix of xs of length n,
-- or xs itself if n > length xs. drop n xs returns the suffix of xs
-- after the first n elements, or [] if n > length xs. splitAt n xs
-- is equivalent to (take n xs, drop n xs).
take :: Int -> [a] -> [a]
take n _ | n <= 0 = []
take _ [] = []
take n (x:xs) = x : take (n-1) xs
drop :: Int -> [a] -> [a]
drop n xs | n <= 0 = xs
drop _ [] = []
drop n (_:xs) = drop (n-1) xs
splitAt :: Int -> [a] -> ([a],[a])
splitAt n xs = (take n xs, drop n xs)
-- takeWhile, applied to a predicate p and a list xs, returns the longest
-- prefix (possibly empty) of xs of elements that satisfy p. dropWhile p xs
-- returns the remaining suffix. span p xs is equivalent to
-- (takeWhile p xs, dropWhile p xs), while break p uses the negation of p.
takeWhile :: (a -> Bool) -> [a] -> [a]
takeWhile p [] = []
takeWhile p (x:xs)
| p x = x : takeWhile p xs
| otherwise = []
dropWhile :: (a -> Bool) -> [a] -> [a]
dropWhile p [] = []
dropWhile p xs@(x:xs')
| p x = dropWhile p xs'
| otherwise = xs
span, break :: (a -> Bool) -> [a] -> ([a],[a])
span p [] = ([],[])
span p xs@(x:xs')
| p x = (x:ys,zs)
| otherwise = ([],xs)
where (ys,zs) = span p xs'
break p = span (not . p)
-- lines breaks a string up into a list of strings at newline characters.
-- The resulting strings do not contain newlines. Similary, words
-- breaks a string up into a list of words, which were delimited by
-- white space. unlines and unwords are the inverse operations.
-- unlines joins lines with terminating newlines, and unwords joins
-- words with separating spaces.
lines :: String -> [String]
lines "" = []
lines s = let (l, s') = break (== '\n') s
in l : case s' of
[] -> []
(_:s'') -> lines s''
words :: String -> [String]
words s = case dropWhile Char.isSpace s of
"" -> []
s' -> w : words s''
where (w, s'') = break Char.isSpace s'
unlines :: [String] -> String
unlines = concatMap (++ "\n")
unwords :: [String] -> String
unwords [] = ""
unwords ws = foldr1 (\w s -> w ++ ' ':s) ws
-- reverse xs returns the elements of xs in reverse order. xs must be finite.
reverse :: [a] -> [a]
reverse = foldl (flip (:)) []
-- 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. or is the
-- disjunctive dual of and.
and, or :: [Bool] -> Bool
and = foldr (&&) True
or = foldr (||) False
-- Applied to a predicate and a list, any determines if any element
-- of the list satisfies the predicate. Similarly, for all.
any, all :: (a -> Bool) -> [a] -> Bool
any p = or . map p
all p = and . map p
-- elem is the list membership predicate, usually written in infix form,
-- e.g., x ‘elem‘ xs. notElem is the negation.
elem, notElem :: (Eq a) => a -> [a] -> Bool
elem x = any (== x)
notElem x = all (/= x)
-- lookup key assocs looks up a key in an association list.
lookup :: (Eq a) => a -> [(a,b)] -> Maybe b
lookup key [] = Nothing
lookup key ((x,y):xys)
| key == x = Just y
| otherwise = lookup key xys
-- sum and product compute the sum or product of a finite list of numbers.
sum, product :: (Num a) => [a] -> a
sum = foldl (+) 0
product = foldl (⋆) 1
-- maximum and minimum return the maximum or minimum value from a list,
-- which must be non-empty, finite, and of an ordered type.
maximum, minimum :: (Ord a) => [a] -> a
maximum [] = error "Prelude.maximum: empty list"
maximum xs = foldl1 max xs
minimum [] = error "Prelude.minimum: empty list"
minimum xs = foldl1 min xs
-- 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.
-- zip3 takes three lists and returns a list of triples. Zips for larger
-- tuples are in the List library
zip :: [a] -> [b] -> [(a,b)]
zip = zipWith (,)
zip3 :: [a] -> [b] -> [c] -> [(a,b,c)]
zip3 = zipWith3 (,,)
-- The zipWith family generalises the zip family 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.
zipWith :: (a->b->c) -> [a]->[b]->[c]
zipWith z (a:as) (b:bs)
= z a b : zipWith z as bs
zipWith _ _ _ = []
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 _ _ _ _ = []
-- unzip transforms a list of pairs into a pair of lists.
unzip :: [(a,b)] -> ([a],[b])
unzip = foldr (\(a,b) ~(as,bs) -> (a:as,b:bs)) ([],[])
unzip3 :: [(a,b,c)] -> ([a],[b],[c])
unzip3 = foldr (\(a,b,c) ~(as,bs,cs) -> (a:as,b:bs,c:cs))
([],[],[])
9.2 Prelude — PreludeText (텍스트·읽기/보여주기 모듈)
여기서는 값을 문자열로 보여 주는 Show와, 문자열에서 값을 다시 읽어 들이는 Read, 그리고 그 바탕이 되는 ShowS, ReadS, lex 같은 저수준 도구들을 다뤄요. 기본 타입들은 deriving 절로 처리되거나 아래처럼 명시적인 인스턴스로 정의되어 있어요.
module PreludeText (
ReadS, ShowS,
Read(readsPrec, readList),
Show(showsPrec, show, showList),
reads, shows, read, lex,
showChar, showString, readParen, showParen ) where
-- The instances of Read and Show for
-- Bool, Maybe, Either, Ordering
-- are done via "deriving" clauses in Prelude.hs
import Data.Char(isSpace, isAlpha, isDigit, isAlphaNum,
showLitChar, readLitChar, lexLitChar)
import Numeric(showSigned, showInt, readSigned, readDec, showFloat,
readFloat, lexDigits)
type ReadS a = String -> [(a,String)]
type ShowS = String -> String
class Read a where
readsPrec :: Int -> ReadS a
readList :: ReadS [a]
-- Minimal complete definition:
-- readsPrec
readList = readParen False (\r -> [pr | ("[",s) <- lex r,
pr <- readl s])
where readl s = [([],t) | ("]",t) <- lex s] ++
[(x:xs,u) | (x,t) <- reads s,
(xs,u) <- readl' t]
readl' s = [([],t) | ("]",t) <- lex s] ++
[(x:xs,v) | (",",t) <- lex s,
(x,u) <- reads t,
(xs,v) <- readl' u]
class Show a where
showsPrec :: Int -> a -> ShowS
show :: a -> String
showList :: [a] -> ShowS
-- Mimimal complete definition:
-- show or showsPrec
showsPrec _ x s = show x ++ s
show x = showsPrec 0 x ""
showList [] = showString "[]"
showList (x:xs) = showChar '[' . shows x . showl xs
where showl [] = showChar ']'
showl (x:xs) = showChar ',' . shows x .
showl xs
reads :: (Read a) => ReadS a
reads = readsPrec 0
shows :: (Show a) => a -> ShowS
shows = showsPrec 0
read :: (Read a) => String -> a
read s = case [x | (x,t) <- reads s, ("","") <- lex t] of
[x] -> x
[] -> error "Prelude.read: no parse"
_ -> error "Prelude.read: ambiguous parse"
showChar :: Char -> ShowS
showChar = (:)
showString :: String -> ShowS
showString = (++)
showParen :: Bool -> ShowS -> ShowS
showParen b p = if b then showChar '(' . p . showChar ')' else p
readParen :: Bool -> ReadS a -> ReadS a
readParen b g = if b then mandatory else optional
where optional r = g r ++ mandatory r
mandatory r = [(x,u) | ("(",s) <- lex r,
(x,t) <- optional s,
(")",u) <- lex t ]
-- This lexer is not completely faithful to the Haskell lexical syntax.
-- Current limitations:
-- Qualified names are not handled properly
-- Octal and hexidecimal numerics are not recognized as a single token
-- Comments are not treated properly
lex :: ReadS String
lex "" = [("","")]
lex (c:s)
| isSpace c = lex (dropWhile isSpace s)
lex ('\'':s) = [('\'':ch++"'", t) | (ch,'\'':t) <- lexLitChar s,
ch /= "'" ]
lex ('"':s) = [('"':str, t) | (str,t) <- lexString s]
where
lexString ('"':s) = [("\"",s)]
lexString s = [(ch++str, u)
| (ch,t) <- lexStrItem s,
(str,u) <- lexString t ]
lexStrItem ('\\':'&':s) = [("\\&",s)]
lexStrItem ('\\':c:s) | isSpace c
= [("\\&",t) |
'\\':t <-
[dropWhile isSpace s]]
lexStrItem s = lexLitChar s
lex (c:s) | isSingle c = [([c],s)]
| isSym c = [(c:sym,t) | (sym,t) <- [span isSym s]]
| isAlpha c = [(c:nam,t) | (nam,t) <- [span isIdChar s]]
| isDigit c = [(c:ds++fe,t) | (ds,s) <- [span isDigit s],
(fe,t) <- lexFracExp s ]
| otherwise = [] -- bad character
where
isSingle c = c ‘elem‘ ",;()[]{}_‘"
isSym c = c ‘elem‘ "!@#$%&⋆+./<=>?\\^|:-~"
isIdChar c = isAlphaNum c || c ‘elem‘ "_'"
lexFracExp ('.':c:cs) | isDigit c
= [('.':ds++e,u) | (ds,t) <- lexDigits (c:cs),
(e,u) <- lexExp t]
lexFracExp s = lexExp s
lexExp (e:s) | e ‘elem‘ "eE"
= [(e:c:ds,u) | (c:t) <- [s], c ‘elem‘ "+-",
(ds,u) <- lexDigits t] ++
[(e:ds,t) | (ds,t) <- lexDigits s]
lexExp s = [("",s)]
instance Show Int where
showsPrec n = showsPrec n . toInteger
-- Converting to Integer avoids
-- possible difficulty with minInt
instance Read Int where
readsPrec p r = [(fromInteger i, t) | (i,t) <- readsPrec p r]
-- Reading at the Integer type avoids
-- possible difficulty with minInt
instance Show Integer where
showsPrec = showSigned showInt
instance Read Integer where
readsPrec p = readSigned readDec
instance Show Float where
showsPrec p = showFloat
instance Read Float where
readsPrec p = readSigned readFloat
instance Show Double where
showsPrec p = showFloat
instance Read Double where
readsPrec p = readSigned readFloat
instance Show () where
showsPrec p () = showString "()"
instance Read () where
readsPrec p = readParen False
(\r -> [((),t) | ("(",s) <- lex r,
(")",t) <- lex s ] )
instance Show Char where
showsPrec p '\'' = showString "'\\''"
showsPrec p c = showChar '\'' . showLitChar c . showChar '\''
showList cs = showChar '"' . showl cs
where showl "" = showChar '"'
showl ('"':cs) = showString "\\\"" . showl cs
showl (c:cs) = showLitChar c . showl cs
instance Read Char where
readsPrec p = readParen False
(\r -> [(c,t) | ('\'':s,t)<- lex r,
(c,"\'") <- readLitChar s])
readList = readParen False (\r -> [(l,t) | ('"':s, t) <- lex r,
(l,_) <- readl s ])
where readl ('"':s) = [("",s)]
readl ('\\':'&':s) = readl s
readl s = [(c:cs,u) | (c ,t) <- readLitChar s,
(cs,u) <- readl t ]
instance (Show a) => Show [a] where
showsPrec p = showList
instance (Read a) => Read [a] where
readsPrec p = readList
-- Tuples
instance (Show a, Show b) => Show (a,b) where
showsPrec p (x,y) = showChar '(' . shows x . showChar ',' .
shows y . showChar ')'
instance (Read a, Read b) => Read (a,b) where
readsPrec p = readParen False
(\r -> [((x,y), w) | ("(",s) <- lex r,
(x,t) <- reads s,
(",",u) <- lex t,
(y,v) <- reads u,
(")",w) <- lex v ] )
-- Other tuples have similar Read and Show instances
9.3 Prelude — PreludeIO (입출력 모듈)
입출력은 순수한 함수형 언어에서 특히 까다로운 부분이죠. 이 모듈은 IO 타입과 함께, 화면에 쓰고(putStr, print) 읽는(getLine, readLn) 기본 함수들, 그리고 파일 입출력(readFile, writeFile)까지 제공해요. 대부분의 함수가 시스템 프리미티브(prim...)에 그대로 연결되어 있다는 걸 보면, 입출력 동작 하나하나가 사실상 컴파일러에 맡겨져 있음을 알 수 있어요.
module PreludeIO (
FilePath, IOError, ioError, userError, catch,
putChar, putStr, putStrLn, print,
getChar, getLine, getContents, interact,
readFile, writeFile, appendFile, readIO, readLn
) where
import PreludeBuiltin
type FilePath = String
data IOError -- The internals of this type are system dependent
instance Show IOError where ...
instance Eq IOError where ...
ioError :: IOError -> IO a
ioError = primIOError
userError :: String -> IOError
userError = primUserError
catch :: IO a -> (IOError -> IO a) -> IO a
catch = primCatch
putChar :: Char -> IO ()
putChar = primPutChar
putStr :: String -> IO ()
putStr s = mapM_ putChar s
putStrLn :: String -> IO ()
putStrLn s = do putStr s
putStr "\n"
print :: Show a => a -> IO ()
print x = putStrLn (show x)
getChar :: IO Char
getChar = primGetChar
getLine :: IO String
getLine = do c <- getChar
if c == '\n' then return "" else
do s <- getLine
return (c:s)
getContents :: IO String
getContents = primGetContents
interact :: (String -> String) -> IO ()
-- The hSetBuffering ensures the expected interactive behaviour
interact f = do hSetBuffering stdin NoBuffering
hSetBuffering stdout NoBuffering
s <- getContents
putStr (f s)
readFile :: FilePath -> IO String
readFile = primReadFile
writeFile :: FilePath -> String -> IO ()
writeFile = primWriteFile
appendFile :: FilePath -> String -> IO ()
appendFile = primAppendFile
-- raises an exception instead of an error
readIO :: Read a => String -> IO a
readIO s = case [x | (x,t) <- reads s, ("","") <- lex t] of
[x] -> return x
[] -> ioError (userError "Prelude.readIO: no parse")
_ -> ioError (userError "Prelude.readIO: ambiguous parse")
readLn :: Read a => IO a
readLn = do l <- getLine
r <- readIO l
return r
더 알아보기 (Learn more)
- 전체 보고서 보기 — Haskell 2010 Language Report의 다른 챕터도 온라인판에서 함께 읽을 수 있어요: https://www.haskell.org/onlinereport/haskell2010/
- 실제 컴파일러의 프렐류드 — 여기 명세보다 훨씬 상세하고, 성능을 고려한 구현은 GHC의
Prelude(GHC.Base,Data.List,GHC.Show등) 소스를 참고하면 좋아요. - 이어서 읽기 — 프렐류드가 사용하는 라이브러리 모듈(
Data.Char,Control.Monad,System.IO,Numeric)의 자세한 설명은 이 보고서의 Part II에 있어요.