-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/
-- | A compatibility layer for base
--
@package base-compat
@version 0.8.1
module Text.Read.Compat
-- | Parsing of Strings, producing values.
--
-- Minimal complete definition: readsPrec (or, for GHC only,
-- readPrec)
--
-- Derived instances of Read make the following assumptions, which
-- derived instances of Show obey:
--
--
-- - If the constructor is defined to be an infix operator, then the
-- derived Read instance will parse only infix applications of the
-- constructor (not the prefix form).
-- - Associativity is not used to reduce the occurrence of parentheses,
-- although precedence may be.
-- - If the constructor is defined using record syntax, the derived
-- Read will parse only the record-syntax form, and furthermore,
-- the fields must be given in the same order as the original
-- declaration.
-- - The derived Read instance allows arbitrary Haskell
-- whitespace between tokens of the input string. Extra parentheses are
-- also allowed.
--
--
-- For example, given the declarations
--
--
-- infixr 5 :^:
-- data Tree a = Leaf a | Tree a :^: Tree a
--
--
-- the derived instance of Read in Haskell 2010 is equivalent to
--
--
-- instance (Read a) => Read (Tree a) where
--
-- readsPrec d r = readParen (d > app_prec)
-- (\r -> [(Leaf m,t) |
-- ("Leaf",s) <- lex r,
-- (m,t) <- readsPrec (app_prec+1) s]) r
--
-- ++ readParen (d > up_prec)
-- (\r -> [(u:^:v,w) |
-- (u,s) <- readsPrec (up_prec+1) r,
-- (":^:",t) <- lex s,
-- (v,w) <- readsPrec (up_prec+1) t]) r
--
-- where app_prec = 10
-- up_prec = 5
--
--
-- Note that right-associativity of :^: is unused.
--
-- The derived instance in GHC is equivalent to
--
--
-- instance (Read a) => Read (Tree a) where
--
-- readPrec = parens $ (prec app_prec $ do
-- Ident "Leaf" <- lexP
-- m <- step readPrec
-- return (Leaf m))
--
-- +++ (prec up_prec $ do
-- u <- step readPrec
-- Symbol ":^:" <- lexP
-- v <- step readPrec
-- return (u :^: v))
--
-- where app_prec = 10
-- up_prec = 5
--
-- readListPrec = readListPrecDefault
--
class Read a
readsPrec :: Read a => Int -> ReadS a
readList :: Read a => ReadS [a]
readPrec :: Read a => ReadPrec a
readListPrec :: Read a => ReadPrec [a]
-- | A parser for a type a, represented as a function that takes a
-- String and returns a list of possible parses as
-- (a,String) pairs.
--
-- Note that this kind of backtracking parser is very inefficient;
-- reading a large structure may be quite slow (cf ReadP).
type ReadS a = String -> [(a, String)]
-- | equivalent to readsPrec with a precedence of 0.
reads :: Read a => ReadS a
-- | The read function reads input from a string, which must be
-- completely consumed by the input process.
read :: Read a => String -> a
-- | readParen True p parses what p parses,
-- but surrounded with parentheses.
--
-- readParen False p parses what p
-- parses, but optionally surrounded with parentheses.
readParen :: Bool -> ReadS a -> ReadS a
-- | The lex function reads a single lexeme from the input,
-- discarding initial white space, and returning the characters that
-- constitute the lexeme. If the input string contains only white space,
-- lex returns a single successful `lexeme' consisting of the
-- empty string. (Thus lex "" = [("","")].) If there is
-- no legal lexeme at the beginning of the input string, lex fails
-- (i.e. returns []).
--
-- This lexer is not completely faithful to the Haskell lexical syntax in
-- the following respects:
--
--
-- - Qualified names are not handled properly
-- - Octal and hexadecimal numerics are not recognized as a single
-- token
-- - Comments are not treated properly
--
lex :: ReadS String
-- | Haskell lexemes.
data Lexeme :: *
-- | Character literal
Char :: Char -> Lexeme
-- | String literal, with escapes interpreted
String :: String -> Lexeme
-- | Punctuation or reserved symbol, e.g. (, ::
Punc :: String -> Lexeme
-- | Haskell identifier, e.g. foo, Baz
Ident :: String -> Lexeme
-- | Haskell symbol, e.g. >>, :%
Symbol :: String -> Lexeme
-- | Since: 4.6.0.0
Number :: Number -> Lexeme
EOF :: Lexeme
-- | Parse a single lexeme
lexP :: ReadPrec Lexeme
-- | (parens p) parses "P", "(P0)", "((P0))", etc, where
-- p parses "P" in the current precedence context and parses
-- "P0" in precedence context zero
parens :: ReadPrec a -> ReadPrec a
-- | A possible replacement definition for the readList method (GHC
-- only). This is only needed for GHC, and even then only for Read
-- instances where readListPrec isn't defined as
-- readListPrecDefault.
readListDefault :: Read a => ReadS [a]
-- | A possible replacement definition for the readListPrec method,
-- defined using readPrec (GHC only).
readListPrecDefault :: Read a => ReadPrec [a]
-- | Parse a string using the Read instance. Succeeds if there is
-- exactly one valid result. A Left value indicates a parse error.
--
-- Since: 4.6.0.0
readEither :: Read a => String -> Either String a
-- | Parse a string using the Read instance. Succeeds if there is
-- exactly one valid result.
--
-- Since: 4.6.0.0
readMaybe :: Read a => String -> Maybe a
-- | Miscellaneous information about the system environment.
module System.Environment.Compat
-- | Computation getArgs returns a list of the program's command
-- line arguments (not including the program name).
getArgs :: IO [String]
-- | Computation getProgName returns the name of the program as it
-- was invoked.
--
-- However, this is hard-to-impossible to implement on some non-Unix
-- OSes, so instead, for maximum portability, we just return the leafname
-- of the program as invoked. Even then there are some differences
-- between platforms: on Windows, for example, a program invoked as foo
-- is probably really FOO.EXE, and that is what
-- getProgName will return.
getProgName :: IO String
-- | Computation getEnv var returns the value of the
-- environment variable var. For the inverse, POSIX users can
-- use putEnv.
--
-- This computation may fail with:
--
--
getEnv :: String -> IO String
-- | Return the value of the environment variable var, or
-- Nothing if there is no such value.
--
-- For POSIX users, this is equivalent to getEnv.
--
-- Since: 4.6.0.0
lookupEnv :: String -> IO (Maybe String)
-- | setEnv name value sets the specified environment variable to
-- value.
--
-- On Windows setting an environment variable to the empty string
-- removes that environment variable from the environment. For the sake
-- of compatibility we adopt that behavior. In particular
--
--
-- setEnv name ""
--
--
-- has the same effect as
--
--
-- unsetEnv name
--
--
-- If you don't care about Windows support and want to set an environment
-- variable to the empty string use System.Posix.Env.setEnv from
-- the unix package instead.
--
-- Throws IOException if name is the empty string or
-- contains an equals sign.
--
-- Since: 4.7.0.0
setEnv :: String -> String -> IO ()
-- | unSet name removes the specified environment variable from
-- the environment of the current process.
--
-- Throws IOException if name is the empty string or
-- contains an equals sign.
--
-- Since: 4.7.0.0
unsetEnv :: String -> IO ()
-- | withArgs args act - while executing action
-- act, have getArgs return args.
withArgs :: [String] -> IO a -> IO a
-- | withProgName name act - while executing action
-- act, have getProgName return name.
withProgName :: String -> IO a -> IO a
-- | getEnvironment retrieves the entire environment as a list of
-- (key,value) pairs.
--
-- If an environment entry does not contain an '=' character,
-- the key is the whole entry and the value is the
-- empty string.
getEnvironment :: IO [(String, String)]
module Debug.Trace.Compat
-- | Like trace but returns the message instead of a third value.
--
-- Since: 4.7.0.0
traceId :: String -> String
-- | Like traceShow but returns the shown value instead of a third
-- value.
--
-- Since: 4.7.0.0
traceShowId :: Show a => a -> a
-- | Like trace but returning unit in an arbitrary monad. Allows for
-- convenient use in do-notation. Note that the application of
-- trace is not an action in the monad, as traceIO is in
-- the IO monad.
--
--
-- ... = do
-- x <- ...
-- traceM $ "x: " ++ show x
-- y <- ...
-- traceM $ "y: " ++ show y
--
--
-- Since: 4.7.0.0
traceM :: Monad m => String -> m ()
-- | Like traceM, but uses show on the argument to convert it
-- to a String.
--
--
-- ... = do
-- x <- ...
-- traceMShow $ x
-- y <- ...
-- traceMShow $ x + y
--
--
-- Since: 4.7.0.0
traceShowM :: (Show a, Monad m) => a -> m ()
module Data.Monoid.Compat
-- | An infix synonym for mappend.
--
-- Since: 4.5.0.0
(<>) :: Monoid m => m -> m -> m
module Data.Functor.Compat
-- | The Functor class is used for types that can be mapped over.
-- Instances of Functor should satisfy the following laws:
--
--
-- fmap id == id
-- fmap (f . g) == fmap f . fmap g
--
--
-- The instances of Functor for lists, Maybe and IO
-- satisfy these laws.
class Functor (f :: * -> *)
fmap :: Functor f => (a -> b) -> f a -> f b
(<$) :: Functor f => a -> f b -> f a
-- | Flipped version of <$.
--
-- Since: 4.7.0.0
($>) :: Functor f => f a -> b -> f b
-- | void value discards or ignores the result of
-- evaluation, such as the return value of an IO action.
void :: Functor f => f a -> f ()
module Data.Function.Compat
-- | & is a reverse application operator. This provides
-- notational convenience. Its precedence is one higher than that of the
-- forward application operator $, which allows & to be
-- nested in $.
--
-- Since: 4.8.0.0
(&) :: a -> (a -> b) -> b
module Data.Either.Compat
-- | Return True if the given value is a Left-value,
-- False otherwise.
--
-- Since: 4.7.0.0
isLeft :: Either a b -> Bool
-- | Return True if the given value is a Right-value,
-- False otherwise.
--
-- Since: 4.7.0.0
isRight :: Either a b -> Bool
module Data.Bool.Compat
-- | Case analysis for the Bool type. bool a b p evaluates
-- to a when p is False, and evaluates to
-- b when p is True.
--
-- Since: 4.7.0.0
bool :: a -> a -> Bool -> a
module Data.Foldable.Compat
-- | Returns the size/length of a finite structure as an Int. The
-- default implementation is optimized for structures that are similar to
-- cons-lists, because there is no general way to do better.
length :: Foldable t => t a -> Int
-- | Test whether the structure is empty. The default implementation is
-- optimized for structures that are similar to cons-lists, because there
-- is no general way to do better.
null :: Foldable t => t a -> Bool
module Prelude.Compat
-- | Case analysis for the Either type. If the value is
-- Left a, apply the first function to a; if it
-- is Right b, apply the second function to b.
either :: (a -> c) -> (b -> c) -> Either a b -> c
-- | Determines whether all elements of the structure satisfy the
-- predicate.
all :: Foldable t => (a -> Bool) -> t a -> Bool
-- | and returns the conjunction of a container of Bools. For the
-- result to be True, the container must be finite; False,
-- however, results from a False value finitely far from the left
-- end.
and :: Foldable t => t Bool -> Bool
-- | Determines whether any element of the structure satisfies the
-- predicate.
any :: Foldable t => (a -> Bool) -> t a -> Bool
-- | The concatenation of all the elements of a container of lists.
concat :: Foldable t => t [a] -> [a]
-- | Map a function over all the elements of a container and concatenate
-- the resulting lists.
concatMap :: Foldable t => (a -> [b]) -> t a -> [b]
-- | Map each element of a structure to a monadic action, evaluate these
-- actions from left to right, and ignore the results.
mapM_ :: (Foldable t, Monad m) => (a -> m b) -> t a -> m ()
-- | notElem is the negation of elem.
notElem :: (Foldable t, Eq a) => a -> t a -> Bool
-- | or returns the disjunction of a container of Bools. For the
-- result to be False, the container must be finite; True,
-- however, results from a True value finitely far from the left
-- end.
or :: Foldable t => t Bool -> Bool
-- | Evaluate each monadic action in the structure from left to right, and
-- ignore the results.
sequence_ :: (Foldable t, Monad m) => t (m a) -> m ()
-- | An infix synonym for fmap.
(<$>) :: Functor f => (a -> b) -> f a -> f b
-- | The maybe function takes a default value, a function, and a
-- Maybe value. If the Maybe value is Nothing, the
-- function returns the default value. Otherwise, it applies the function
-- to the value inside the Just and returns the result.
maybe :: b -> (a -> b) -> Maybe a -> b
-- | lines breaks a string up into a list of strings at newline
-- characters. The resulting strings do not contain newlines.
lines :: String -> [String]
-- | unlines is an inverse operation to lines. It joins
-- lines, after appending a terminating newline to each.
unlines :: [String] -> String
-- | unwords is an inverse operation to words. It joins words
-- with separating spaces.
unwords :: [String] -> String
-- | words breaks a string up into a list of words, which were
-- delimited by white space.
words :: String -> [String]
-- | curry converts an uncurried function to a curried function.
curry :: ((a, b) -> c) -> a -> b -> c
-- | Extract the first component of a pair.
fst :: (a, b) -> a
-- | Extract the second component of a pair.
snd :: (a, b) -> b
-- | uncurry converts a curried function to a function on pairs.
uncurry :: (a -> b -> c) -> (a, b) -> c
-- | Strict (call-by-value) application, defined in terms of seq.
($!) :: (a -> b) -> a -> b
-- | Append two lists, i.e.,
--
--
-- [x1, ..., xm] ++ [y1, ..., yn] == [x1, ..., xm, y1, ..., yn]
-- [x1, ..., xm] ++ [y1, ...] == [x1, ..., xm, y1, ...]
--
--
-- If the first list is not finite, the result is the first list.
(++) :: [a] -> [a] -> [a]
-- | Function composition.
(.) :: (b -> c) -> (a -> b) -> a -> c
-- | Same as >>=, but with the arguments interchanged.
(=<<) :: Monad m => (a -> m b) -> m a -> m b
-- | 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
-- | Constant function.
const :: a -> b -> a
-- | flip f takes its (first) two arguments in the reverse
-- order of f.
flip :: (a -> b -> c) -> b -> a -> c
-- | Identity function.
id :: a -> a
-- | map f xs is the list obtained by applying f
-- to each element of xs, i.e.,
--
--
-- map f [x1, x2, ..., xn] == [f x1, f x2, ..., f xn]
-- map f [x1, x2, ...] == [f x1, f x2, ...]
--
map :: (a -> b) -> [a] -> [b]
-- | otherwise is defined as the value True. It helps to make
-- guards more readable. eg.
--
--
-- f x | x < 0 = ...
-- | otherwise = ...
--
otherwise :: Bool
-- | until p f yields the result of applying f
-- until p holds.
until :: (a -> Bool) -> (a -> a) -> a -> a
-- | Raise an IOError in the IO monad.
ioError :: IOError -> IO a
-- | Construct an IOError value with a string describing the error.
-- The fail method of the IO instance of the Monad
-- class raises a userError, thus:
--
--
-- instance Monad IO where
-- ...
-- fail s = ioError (userError s)
--
userError :: String -> IOError
-- | List index (subscript) operator, starting from 0. It is an instance of
-- the more general genericIndex, which takes an index of any
-- integral type.
(!!) :: [a] -> Int -> a
-- | 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])
-- | 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]
-- | 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 genericDrop, in which
-- n may be of any integral type.
drop :: Int -> [a] -> [a]
-- | 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]
-- | filter, applied to a predicate and a list, returns the list of
-- those elements that satisfy the predicate; i.e.,
--
--
-- filter p xs = [ x | x <- xs, p x]
--
filter :: (a -> Bool) -> [a] -> [a]
-- | Extract the first element of a list, which must be non-empty.
head :: [a] -> a
-- | Return all the elements of a list except the last one. The list must
-- be non-empty.
init :: [a] -> [a]
-- | 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]
-- | Extract the last element of a list, which must be finite and
-- non-empty.
last :: [a] -> a
-- | lookup key assocs looks up a key in an association
-- list.
lookup :: Eq a => a -> [(a, b)] -> Maybe b
-- | repeat x is an infinite list, with x the
-- value of every element.
repeat :: a -> [a]
-- | replicate n x is a list of length n with
-- x the value of every element. It is an instance of the more
-- general genericReplicate, in which n may be of any
-- integral type.
replicate :: Int -> a -> [a]
-- | reverse xs returns the elements of xs in
-- reverse order. xs must be finite.
reverse :: [a] -> [a]
-- | scanl is similar to foldl, but returns a list of
-- successive reduced values from the left:
--
--
-- scanl f z [x1, x2, ...] == [z, z `f` x1, (z `f` x1) `f` x2, ...]
--
--
-- Note that
--
--
-- last (scanl f z xs) == foldl f z xs.
--
scanl :: (b -> a -> b) -> b -> [a] -> [b]
-- | 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]
-- | scanr is the right-to-left dual of scanl. Note that
--
--
-- head (scanr f z xs) == foldr f z xs.
--
scanr :: (a -> b -> b) -> b -> [a] -> [b]
-- | scanr1 is a variant of scanr that has no starting value
-- argument.
scanr1 :: (a -> a -> a) -> [a] -> [a]
-- | 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])
-- | 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) when
-- n is not _|_ (splitAt _|_ xs = _|_).
-- splitAt is an instance of the more general
-- genericSplitAt, in which n may be of any integral
-- type.
splitAt :: Int -> [a] -> ([a], [a])
-- | Extract the elements after the head of a list, which must be
-- non-empty.
tail :: [a] -> [a]
-- | 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 genericTake, in which
-- n may be of any integral type.
take :: Int -> [a] -> [a]
-- | 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]
-- | unzip transforms a list of pairs into a list of first
-- components and a list of second components.
unzip :: [(a, b)] -> ([a], [b])
-- | The unzip3 function takes a list of triples and returns three
-- lists, analogous to unzip.
unzip3 :: [(a, b, c)] -> ([a], [b], [c])
-- | 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.
zip :: [a] -> [b] -> [(a, b)]
-- | zip3 takes three lists and returns a list of triples, analogous
-- to zip.
zip3 :: [a] -> [b] -> [c] -> [(a, b, c)]
-- | 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.
zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
-- | 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.
zipWith3 :: (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d]
-- | the same as flip (-).
--
-- Because - is treated specially in the Haskell grammar,
-- (- e) is not a section, but an application of
-- prefix negation. However, (subtract
-- exp) is equivalent to the disallowed section.
subtract :: Num a => a -> a -> a
-- | The lex function reads a single lexeme from the input,
-- discarding initial white space, and returning the characters that
-- constitute the lexeme. If the input string contains only white space,
-- lex returns a single successful `lexeme' consisting of the
-- empty string. (Thus lex "" = [("","")].) If there is
-- no legal lexeme at the beginning of the input string, lex fails
-- (i.e. returns []).
--
-- This lexer is not completely faithful to the Haskell lexical syntax in
-- the following respects:
--
--
-- - Qualified names are not handled properly
-- - Octal and hexadecimal numerics are not recognized as a single
-- token
-- - Comments are not treated properly
--
lex :: ReadS String
-- | readParen True p parses what p parses,
-- but surrounded with parentheses.
--
-- readParen False p parses what p
-- parses, but optionally surrounded with parentheses.
readParen :: Bool -> ReadS a -> ReadS a
-- | raise a number to a non-negative integral power
(^) :: (Num a, Integral b) => a -> b -> a
-- | raise a number to an integral power
(^^) :: (Fractional a, Integral b) => a -> b -> a
even :: Integral a => a -> Bool
-- | general coercion from integral types
fromIntegral :: (Integral a, Num b) => a -> b
-- | gcd x y is the non-negative factor of both x
-- and y of which every common factor of x and
-- y is also a factor; for example gcd 4 2 = 2,
-- gcd (-4) 6 = 2, gcd 0 4 = 4.
-- gcd 0 0 = 0. (That is, the common divisor
-- that is "greatest" in the divisibility preordering.)
--
-- Note: Since for signed fixed-width integer types, abs
-- minBound < 0, the result may be negative if one of the
-- arguments is minBound (and necessarily is if the other
-- is 0 or minBound) for such types.
gcd :: Integral a => a -> a -> a
-- | lcm x y is the smallest positive integer that both
-- x and y divide.
lcm :: Integral a => a -> a -> a
odd :: Integral a => a -> Bool
-- | general coercion to fractional types
realToFrac :: (Real a, Fractional b) => a -> b
-- | utility function converting a Char to a show function that
-- simply prepends the character unchanged.
showChar :: Char -> ShowS
-- | utility function that surrounds the inner show function with
-- parentheses when the Bool parameter is True.
showParen :: Bool -> ShowS -> ShowS
-- | utility function converting a String to a show function that
-- simply prepends the string unchanged.
showString :: String -> ShowS
-- | equivalent to showsPrec with a precedence of 0.
shows :: Show a => a -> ShowS
-- | The computation appendFile file str function appends
-- the string str, to the file file.
--
-- Note that writeFile and appendFile write a literal
-- string to a file. To write a value of any printable type, as with
-- print, use the show function to convert the value to a
-- string first.
--
--
-- main = appendFile "squares" (show [(x,x*x) | x <- [0,0.1..2]])
--
appendFile :: FilePath -> String -> IO ()
-- | Read a character from the standard input device (same as
-- hGetChar stdin).
getChar :: IO Char
-- | The getContents operation returns all user input as a single
-- string, which is read lazily as it is needed (same as
-- hGetContents stdin).
getContents :: IO String
-- | Read a line from the standard input device (same as hGetLine
-- stdin).
getLine :: IO String
-- | The interact function takes a function of type
-- String->String as its argument. The entire input from the
-- standard input device is passed to this function as its argument, and
-- the resulting string is output on the standard output device.
interact :: (String -> String) -> IO ()
-- | The print function outputs a value of any printable type to the
-- standard output device. Printable types are those that are instances
-- of class Show; print converts values to strings for
-- output using the show operation and adds a newline.
--
-- For example, a program to print the first 20 integers and their powers
-- of 2 could be written as:
--
--
-- main = print ([(n, 2^n) | n <- [0..19]])
--
print :: Show a => a -> IO ()
-- | Write a character to the standard output device (same as
-- hPutChar stdout).
putChar :: Char -> IO ()
-- | Write a string to the standard output device (same as hPutStr
-- stdout).
putStr :: String -> IO ()
-- | The same as putStr, but adds a newline character.
putStrLn :: String -> IO ()
-- | The readFile function reads a file and returns the contents of
-- the file as a string. The file is read lazily, on demand, as with
-- getContents.
readFile :: FilePath -> IO String
-- | The readIO function is similar to read except that it
-- signals parse failure to the IO monad instead of terminating
-- the program.
readIO :: Read a => String -> IO a
-- | The readLn function combines getLine and readIO.
readLn :: Read a => IO a
-- | The computation writeFile file str function writes the
-- string str, to the file file.
writeFile :: FilePath -> String -> IO ()
-- | The read function reads input from a string, which must be
-- completely consumed by the input process.
read :: Read a => String -> a
-- | equivalent to readsPrec with a precedence of 0.
reads :: Read a => ReadS a
-- | Boolean "and"
(&&) :: Bool -> Bool -> Bool
-- | Boolean "not"
not :: Bool -> Bool
-- | Boolean "or"
(||) :: Bool -> Bool -> Bool
-- | Application operator. This operator is redundant, since ordinary
-- application (f x) means the same as (f $ x).
-- However, $ has low, right-associative binding precedence, so it
-- sometimes allows parentheses to be omitted; for example:
--
--
-- f $ g $ h x = f (g (h x))
--
--
-- It is also useful in higher-order situations, such as map
-- ($ 0) xs, or zipWith ($) fs xs.
($) :: (a -> b) -> a -> b
-- | error stops execution and displays an error message.
error :: [Char] -> a
-- | A special case of error. It is expected that compilers will
-- recognize this and insert error messages which are more appropriate to
-- the context in which undefined appears.
undefined :: a
-- | Evaluates its first argument to head normal form, and then returns its
-- second argument as the result.
seq :: a -> b -> b
-- | Does the element occur in the structure?
elem :: (Foldable t, Eq a) => a -> t a -> Bool
-- | Map each element of the structure to a monoid, and combine the
-- results.
foldMap :: Foldable t => forall a m. Monoid m => (a -> m) -> t a -> m
-- | Left-associative fold of a structure.
--
--
-- foldl f z = foldl f z . toList
--
foldl :: Foldable t => forall b a. (b -> a -> b) -> b -> t a -> b
-- | A variant of foldl that has no base case, and thus may only be
-- applied to non-empty structures.
--
--
-- foldl1 f = foldl1 f . toList
--
foldl1 :: Foldable t => forall a. (a -> a -> a) -> t a -> a
-- | Right-associative fold of a structure.
--
--
-- foldr f z = foldr f z . toList
--
foldr :: Foldable t => forall a b. (a -> b -> b) -> b -> t a -> b
-- | A variant of foldr that has no base case, and thus may only be
-- applied to non-empty structures.
--
--
-- foldr1 f = foldr1 f . toList
--
foldr1 :: Foldable t => forall a. (a -> a -> a) -> t a -> a
-- | Returns the size/length of a finite structure as an Int. The
-- default implementation is optimized for structures that are similar to
-- cons-lists, because there is no general way to do better.
length :: Foldable t => t a -> Int
-- | The largest element of a non-empty structure.
maximum :: (Foldable t, Ord a) => t a -> a
-- | The least element of a non-empty structure.
minimum :: (Foldable t, Ord a) => t a -> a
-- | Test whether the structure is empty. The default implementation is
-- optimized for structures that are similar to cons-lists, because there
-- is no general way to do better.
null :: Foldable t => t a -> Bool
-- | The product function computes the product of the numbers of a
-- structure.
product :: (Foldable t, Num a) => t a -> a
-- | The sum function computes the sum of the numbers of a
-- structure.
sum :: (Foldable t, Num a) => t a -> a
-- | Map each element of a structure to a monadic action, evaluate these
-- actions from left to right, and collect the results.
mapM :: Traversable t => forall a (m :: * -> *) b. Monad m => (a -> m b) -> t a -> m (t b)
-- | Evaluate each monadic action in the structure from left to right, and
-- collect the results.
sequence :: Traversable t => forall (m :: * -> *) a. Monad m => t (m a) -> m (t a)
-- | Evaluate each action in the structure from left to right, and collect
-- the results.
sequenceA :: Traversable t => forall (f :: * -> *) a. Applicative f => t (f a) -> f (t a)
-- | Map each element of a structure to an action, evaluate these actions
-- from left to right, and collect the results.
traverse :: Traversable t => forall a (f :: * -> *) b. Applicative f => (a -> f b) -> t a -> f (t b)
-- | Sequence actions, discarding the value of the first argument.
(*>) :: Applicative f => forall a b. f a -> f b -> f b
-- | Sequence actions, discarding the value of the second argument.
(<*) :: Applicative f => forall a b. f a -> f b -> f a
-- | Sequential application.
(<*>) :: Applicative f => forall a b. f (a -> b) -> f a -> f b
-- | Lift a value.
pure :: Applicative f => forall a. a -> f a
-- | Replace all locations in the input with the same value. The default
-- definition is fmap . const, but this may be
-- overridden with a more efficient version.
(<$) :: Functor f => forall a b. a -> f b -> f a
fmap :: Functor f => forall a b. (a -> b) -> f a -> f b
-- | Sequentially compose two actions, discarding any value produced by the
-- first, like sequencing operators (such as the semicolon) in imperative
-- languages.
(>>) :: Monad m => forall a b. m a -> m b -> m b
-- | Sequentially compose two actions, passing any value produced by the
-- first as an argument to the second.
(>>=) :: Monad m => forall a b. m a -> (a -> m b) -> m b
-- | Fail with a message. This operation is not part of the mathematical
-- definition of a monad, but is invoked on pattern-match failure in a
-- do expression.
fail :: Monad m => forall a. String -> m a
-- | Inject a value into the monadic type.
return :: Monad m => forall a. a -> m a
-- | An associative operation
mappend :: Monoid a => a -> a -> a
-- | Fold a list using the monoid. For most types, the default definition
-- for mconcat will be used, but the function is included in the
-- class definition so that an optimized version can be provided for
-- specific types.
mconcat :: Monoid a => [a] -> a
-- | Identity of mappend
mempty :: Monoid a => a
maxBound :: Bounded a => a
minBound :: Bounded a => a
-- | Used in Haskell's translation of [n..].
enumFrom :: Enum a => a -> [a]
-- | Used in Haskell's translation of [n,n'..].
enumFromThen :: Enum a => a -> a -> [a]
-- | Used in Haskell's translation of [n,n'..m].
enumFromThenTo :: Enum a => a -> a -> a -> [a]
-- | Used in Haskell's translation of [n..m].
enumFromTo :: Enum a => a -> a -> [a]
-- | Convert to an Int. It is implementation-dependent what
-- fromEnum returns when applied to a value that is too large to
-- fit in an Int.
fromEnum :: Enum a => a -> Int
-- | the predecessor of a value. For numeric types, pred subtracts
-- 1.
pred :: Enum a => a -> a
-- | the successor of a value. For numeric types, succ adds 1.
succ :: Enum a => a -> a
-- | Convert from an Int.
toEnum :: Enum a => Int -> a
(**) :: Floating a => a -> a -> a
acos :: Floating a => a -> a
acosh :: Floating a => a -> a
asin :: Floating a => a -> a
asinh :: Floating a => a -> a
atan :: Floating a => a -> a
atanh :: Floating a => a -> a
cos :: Floating a => a -> a
cosh :: Floating a => a -> a
exp :: Floating a => a -> a
log :: Floating a => a -> a
logBase :: Floating a => a -> a -> a
pi :: Floating a => a
sin :: Floating a => a -> a
sinh :: Floating a => a -> a
sqrt :: Floating a => a -> a
tan :: Floating a => a -> a
tanh :: Floating a => a -> a
-- | a version of arctangent taking two real floating-point arguments. For
-- real floating x and y, atan2 y x
-- computes the angle (from the positive x-axis) of the vector from the
-- origin to the point (x,y). atan2 y x returns
-- a value in the range [-pi, pi]. It follows the
-- Common Lisp semantics for the origin when signed zeroes are supported.
-- atan2 y 1, with y in a type that is
-- RealFloat, should return the same value as atan
-- y. A default definition of atan2 is provided, but
-- implementors can provide a more accurate implementation.
atan2 :: RealFloat a => a -> a -> a
-- | The function decodeFloat applied to a real floating-point
-- number returns the significand expressed as an Integer and an
-- appropriately scaled exponent (an Int). If
-- decodeFloat x yields (m,n), then x
-- is equal in value to m*b^^n, where b is the
-- floating-point radix, and furthermore, either m and
-- n are both zero or else b^(d-1) <= abs m <
-- b^d, where d is the value of floatDigits
-- x. In particular, decodeFloat 0 = (0,0). If the
-- type contains a negative zero, also decodeFloat (-0.0) =
-- (0,0). The result of decodeFloat x is
-- unspecified if either of isNaN x or
-- isInfinite x is True.
decodeFloat :: RealFloat a => a -> (Integer, Int)
-- | encodeFloat performs the inverse of decodeFloat in the
-- sense that for finite x with the exception of -0.0,
-- uncurry encodeFloat (decodeFloat x) =
-- x. encodeFloat m n is one of the two closest
-- representable floating-point numbers to m*b^^n (or
-- ±Infinity if overflow occurs); usually the closer, but if
-- m contains too many bits, the result may be rounded in the
-- wrong direction.
encodeFloat :: RealFloat a => Integer -> Int -> a
-- | exponent corresponds to the second component of
-- decodeFloat. exponent 0 = 0 and for finite
-- nonzero x, exponent x = snd (decodeFloat x)
-- + floatDigits x. If x is a finite floating-point
-- number, it is equal in value to significand x * b ^^
-- exponent x, where b is the floating-point radix.
-- The behaviour is unspecified on infinite or NaN values.
exponent :: RealFloat a => a -> Int
-- | a constant function, returning the number of digits of
-- floatRadix in the significand
floatDigits :: RealFloat a => a -> Int
-- | a constant function, returning the radix of the representation (often
-- 2)
floatRadix :: RealFloat a => a -> Integer
-- | a constant function, returning the lowest and highest values the
-- exponent may assume
floatRange :: RealFloat a => a -> (Int, Int)
-- | True if the argument is too small to be represented in
-- normalized format
isDenormalized :: RealFloat a => a -> Bool
-- | True if the argument is an IEEE floating point number
isIEEE :: RealFloat a => a -> Bool
-- | True if the argument is an IEEE infinity or negative infinity
isInfinite :: RealFloat a => a -> Bool
-- | True if the argument is an IEEE "not-a-number" (NaN) value
isNaN :: RealFloat a => a -> Bool
-- | True if the argument is an IEEE negative zero
isNegativeZero :: RealFloat a => a -> Bool
-- | multiplies a floating-point number by an integer power of the radix
scaleFloat :: RealFloat a => Int -> a -> a
-- | The first component of decodeFloat, scaled to lie in the open
-- interval (-1,1), either 0.0 or of absolute
-- value >= 1/b, where b is the floating-point
-- radix. The behaviour is unspecified on infinite or NaN
-- values.
significand :: RealFloat a => a -> a
(*) :: Num a => a -> a -> a
(+) :: Num a => a -> a -> a
(-) :: Num a => a -> a -> a
-- | Absolute value.
abs :: Num a => a -> a
-- | Unary negation.
negate :: Num a => a -> a
-- | Sign of a number. The functions abs and signum should
-- satisfy the law:
--
--
-- abs x * signum x == x
--
--
-- For real numbers, the signum is either -1 (negative),
-- 0 (zero) or 1 (positive).
signum :: Num a => a -> a
-- | The method readList is provided to allow the programmer to give
-- a specialised way of parsing lists of values. For example, this is
-- used by the predefined Read instance of the Char type,
-- where values of type String should be are expected to use
-- double quotes, rather than square brackets.
readList :: Read a => ReadS [a]
-- | attempts to parse a value from the front of the string, returning a
-- list of (parsed value, remaining string) pairs. If there is no
-- successful parse, the returned list is empty.
--
-- Derived instances of Read and Show satisfy the
-- following:
--
--
--
-- That is, readsPrec parses the string produced by
-- showsPrec, and delivers the value that showsPrec started
-- with.
readsPrec :: Read a => Int -> ReadS a
-- | fractional division
(/) :: Fractional a => a -> a -> a
-- | Conversion from a Rational (that is Ratio
-- Integer). A floating literal stands for an application of
-- fromRational to a value of type Rational, so such
-- literals have type (Fractional a) => a.
fromRational :: Fractional a => Rational -> a
-- | reciprocal fraction
recip :: Fractional a => a -> a
-- | integer division truncated toward negative infinity
div :: Integral a => a -> a -> a
-- | simultaneous div and mod
divMod :: Integral a => a -> a -> (a, a)
-- | integer modulus, satisfying
--
--
-- (x `div` y)*y + (x `mod` y) == x
--
mod :: Integral a => a -> a -> a
-- | integer division truncated toward zero
quot :: Integral a => a -> a -> a
-- | simultaneous quot and rem
quotRem :: Integral a => a -> a -> (a, a)
-- | integer remainder, satisfying
--
--
-- (x `quot` y)*y + (x `rem` y) == x
--
rem :: Integral a => a -> a -> a
-- | conversion to Integer
toInteger :: Integral a => a -> Integer
-- | the rational equivalent of its real argument with full precision
toRational :: Real a => a -> Rational
-- | ceiling x returns the least integer not less than
-- x
ceiling :: RealFrac a => forall b. Integral b => a -> b
-- | floor x returns the greatest integer not greater than
-- x
floor :: RealFrac a => forall b. Integral b => a -> b
-- | The function properFraction takes a real fractional number
-- x and returns a pair (n,f) such that x =
-- n+f, and:
--
--
-- - n is an integral number with the same sign as x;
-- and
-- - f is a fraction with the same type and sign as
-- x, and with absolute value less than 1.
--
--
-- The default definitions of the ceiling, floor,
-- truncate and round functions are in terms of
-- properFraction.
properFraction :: RealFrac a => forall b. Integral b => a -> (b, a)
-- | round x returns the nearest integer to x; the
-- even integer if x is equidistant between two integers
round :: RealFrac a => forall b. Integral b => a -> b
-- | truncate x returns the integer nearest x
-- between zero and x
truncate :: RealFrac a => forall b. Integral b => a -> b
-- | A specialised variant of showsPrec, using precedence context
-- zero, and returning an ordinary String.
show :: Show a => a -> String
-- | The method showList is provided to allow the programmer to give
-- a specialised way of showing lists of values. For example, this is
-- used by the predefined Show instance of the Char type,
-- where values of type String should be shown in double quotes,
-- rather than between square brackets.
showList :: Show a => [a] -> ShowS
-- | Convert a value to a readable String.
--
-- showsPrec should satisfy the law
--
--
-- showsPrec d x r ++ s == showsPrec d x (r ++ s)
--
--
-- Derived instances of Read and Show satisfy the
-- following:
--
--
--
-- That is, readsPrec parses the string produced by
-- showsPrec, and delivers the value that showsPrec started
-- with.
showsPrec :: Show a => Int -> a -> ShowS
(/=) :: Eq a => a -> a -> Bool
(==) :: Eq a => a -> a -> Bool
(<) :: Ord a => a -> a -> Bool
(<=) :: Ord a => a -> a -> Bool
(>) :: Ord a => a -> a -> Bool
(>=) :: Ord a => a -> a -> Bool
compare :: Ord a => a -> a -> Ordering
max :: Ord a => a -> a -> a
min :: Ord a => a -> a -> a
-- | A functor with application, providing operations to
--
--
-- - embed pure expressions (pure), and
-- - sequence computations and combine their results
-- (<*>).
--
--
-- A minimal complete definition must include implementations of these
-- functions satisfying the following laws:
--
--
--
-- The other methods have the following default definitions, which may be
-- overridden with equivalent specialized implementations:
--
--
--
-- As a consequence of these laws, the Functor instance for
-- f will satisfy
--
--
--
-- If f is also a Monad, it should satisfy
--
--
--
-- (which implies that pure and <*> satisfy the
-- applicative functor laws).
class Functor f => Applicative (f :: * -> *)
pure :: Applicative f => a -> f a
(<*>) :: Applicative f => f (a -> b) -> f a -> f b
(*>) :: Applicative f => f a -> f b -> f b
(<*) :: Applicative f => f a -> f b -> f a
-- | The Bounded class is used to name the upper and lower limits of
-- a type. Ord is not a superclass of Bounded since types
-- that are not totally ordered may also have upper and lower bounds.
--
-- The Bounded class may be derived for any enumeration type;
-- minBound is the first constructor listed in the data
-- declaration and maxBound is the last. Bounded may also
-- be derived for single-constructor datatypes whose constituent types
-- are in Bounded.
class Bounded a
minBound :: Bounded a => a
maxBound :: Bounded a => a
-- | Class Enum defines operations on sequentially ordered types.
--
-- The enumFrom... methods are used in Haskell's translation of
-- arithmetic sequences.
--
-- Instances of Enum may be derived for any enumeration type
-- (types whose constructors have no fields). The nullary constructors
-- are assumed to be numbered left-to-right by fromEnum from
-- 0 through n-1. See Chapter 10 of the Haskell
-- Report for more details.
--
-- For any type that is an instance of class Bounded as well as
-- Enum, the following should hold:
--
--
--
--
-- enumFrom x = enumFromTo x maxBound
-- enumFromThen x y = enumFromThenTo x y bound
-- where
-- bound | fromEnum y >= fromEnum x = maxBound
-- | otherwise = minBound
--
class Enum a
succ :: Enum a => a -> a
pred :: Enum a => a -> a
toEnum :: Enum a => Int -> a
fromEnum :: Enum a => a -> Int
enumFrom :: Enum a => a -> [a]
enumFromThen :: Enum a => a -> a -> [a]
enumFromTo :: Enum a => a -> a -> [a]
enumFromThenTo :: Enum a => a -> a -> a -> [a]
-- | The Eq class defines equality (==) and inequality
-- (/=). All the basic datatypes exported by the Prelude
-- are instances of Eq, and Eq may be derived for any
-- datatype whose constituents are also instances of Eq.
--
-- Minimal complete definition: either == or /=.
class Eq a
(==) :: Eq a => a -> a -> Bool
(/=) :: Eq a => a -> a -> Bool
-- | Trigonometric and hyperbolic functions and related functions.
--
-- Minimal complete definition: pi, exp, log,
-- sin, cos, sinh, cosh, asin,
-- acos, atan, asinh, acosh and atanh
class Fractional a => Floating a
pi :: Floating a => a
exp :: Floating a => a -> a
sqrt :: Floating a => a -> a
log :: Floating a => a -> a
(**) :: Floating a => a -> a -> a
logBase :: Floating a => a -> a -> a
sin :: Floating a => a -> a
tan :: Floating a => a -> a
cos :: Floating a => a -> a
asin :: Floating a => a -> a
atan :: Floating a => a -> a
acos :: Floating a => a -> a
sinh :: Floating a => a -> a
tanh :: Floating a => a -> a
cosh :: Floating a => a -> a
asinh :: Floating a => a -> a
atanh :: Floating a => a -> a
acosh :: Floating a => a -> a
-- | Data structures that can be folded.
--
-- Minimal complete definition: foldMap or foldr.
--
-- For example, given a data type
--
--
-- data Tree a = Empty | Leaf a | Node (Tree a) a (Tree a)
--
--
-- a suitable instance would be
--
--
-- instance Foldable Tree where
-- foldMap f Empty = mempty
-- foldMap f (Leaf x) = f x
-- foldMap f (Node l k r) = foldMap f l `mappend` f k `mappend` foldMap f r
--
--
-- This is suitable even for abstract types, as the monoid is assumed to
-- satisfy the monoid laws. Alternatively, one could define
-- foldr:
--
--
-- instance Foldable Tree where
-- foldr f z Empty = z
-- foldr f z (Leaf x) = f x z
-- foldr f z (Node l k r) = foldr f (f k (foldr f z r)) l
--
class Foldable (t :: * -> *)
foldMap :: (Foldable t, Monoid m) => (a -> m) -> t a -> m
foldr :: Foldable t => (a -> b -> b) -> b -> t a -> b
foldl :: Foldable t => (b -> a -> b) -> b -> t a -> b
foldr1 :: Foldable t => (a -> a -> a) -> t a -> a
foldl1 :: Foldable t => (a -> a -> a) -> t a -> a
-- | Fractional numbers, supporting real division.
--
-- Minimal complete definition: fromRational and (recip or
-- (/))
class Num a => Fractional a
(/) :: Fractional a => a -> a -> a
recip :: Fractional a => a -> a
fromRational :: Fractional a => Rational -> a
-- | The Functor class is used for types that can be mapped over.
-- Instances of Functor should satisfy the following laws:
--
--
-- fmap id == id
-- fmap (f . g) == fmap f . fmap g
--
--
-- The instances of Functor for lists, Maybe and IO
-- satisfy these laws.
class Functor (f :: * -> *)
fmap :: Functor f => (a -> b) -> f a -> f b
(<$) :: Functor f => a -> f b -> f a
-- | Integral numbers, supporting integer division.
--
-- Minimal complete definition: quotRem and toInteger
class (Real a, Enum a) => Integral a
quot :: Integral a => a -> a -> a
rem :: Integral a => a -> a -> a
div :: Integral a => a -> a -> a
mod :: Integral a => a -> a -> a
quotRem :: Integral a => a -> a -> (a, a)
divMod :: Integral a => a -> a -> (a, a)
toInteger :: Integral a => a -> Integer
-- | The Monad class defines the basic operations over a
-- monad, a concept from a branch of mathematics known as
-- category theory. From the perspective of a Haskell programmer,
-- however, it is best to think of a monad as an abstract datatype
-- of actions. Haskell's do expressions provide a convenient
-- syntax for writing monadic expressions.
--
-- Minimal complete definition: >>= and return.
--
-- Instances of Monad should satisfy the following laws:
--
--
-- return a >>= k == k a
-- m >>= return == m
-- m >>= (\x -> k x >>= h) == (m >>= k) >>= h
--
--
-- Instances of both Monad and Functor should additionally
-- satisfy the law:
--
--
-- fmap f xs == xs >>= return . f
--
--
-- The instances of Monad for lists, Maybe and IO
-- defined in the Prelude satisfy these laws.
class Monad (m :: * -> *)
(>>=) :: Monad m => m a -> (a -> m b) -> m b
(>>) :: Monad m => m a -> m b -> m b
return :: Monad m => a -> m a
fail :: Monad m => String -> m a
-- | The class of monoids (types with an associative binary operation that
-- has an identity). Instances should satisfy the following laws:
--
--
--
-- The method names refer to the monoid of lists under concatenation, but
-- there are many other instances.
--
-- Minimal complete definition: mempty and mappend.
--
-- Some types can be viewed as a monoid in more than one way, e.g. both
-- addition and multiplication on numbers. In such cases we often define
-- newtypes and make those instances of Monoid, e.g.
-- Sum and Product.
class Monoid a
mempty :: Monoid a => a
mappend :: Monoid a => a -> a -> a
mconcat :: Monoid a => [a] -> a
-- | Basic numeric class.
--
-- Minimal complete definition: all except negate or (-)
class Num a
(+) :: Num a => a -> a -> a
(*) :: Num a => a -> a -> a
(-) :: Num a => a -> a -> a
negate :: Num a => a -> a
abs :: Num a => a -> a
signum :: Num a => a -> a
fromInteger :: Num a => Integer -> a
-- | The Ord class is used for totally ordered datatypes.
--
-- Instances of Ord can be derived for any user-defined datatype
-- whose constituent types are in Ord. The declared order of the
-- constructors in the data declaration determines the ordering in
-- derived Ord instances. The Ordering datatype allows a
-- single comparison to determine the precise ordering of two objects.
--
-- Minimal complete definition: either compare or <=.
-- Using compare can be more efficient for complex types.
class Eq a => Ord a
compare :: Ord a => a -> a -> Ordering
(<) :: Ord a => a -> a -> Bool
(>=) :: Ord a => a -> a -> Bool
(>) :: Ord a => a -> a -> Bool
(<=) :: Ord a => a -> a -> Bool
max :: Ord a => a -> a -> a
min :: Ord a => a -> a -> a
-- | Parsing of Strings, producing values.
--
-- Minimal complete definition: readsPrec (or, for GHC only,
-- readPrec)
--
-- Derived instances of Read make the following assumptions, which
-- derived instances of Show obey:
--
--
-- - If the constructor is defined to be an infix operator, then the
-- derived Read instance will parse only infix applications of the
-- constructor (not the prefix form).
-- - Associativity is not used to reduce the occurrence of parentheses,
-- although precedence may be.
-- - If the constructor is defined using record syntax, the derived
-- Read will parse only the record-syntax form, and furthermore,
-- the fields must be given in the same order as the original
-- declaration.
-- - The derived Read instance allows arbitrary Haskell
-- whitespace between tokens of the input string. Extra parentheses are
-- also allowed.
--
--
-- For example, given the declarations
--
--
-- infixr 5 :^:
-- data Tree a = Leaf a | Tree a :^: Tree a
--
--
-- the derived instance of Read in Haskell 2010 is equivalent to
--
--
-- instance (Read a) => Read (Tree a) where
--
-- readsPrec d r = readParen (d > app_prec)
-- (\r -> [(Leaf m,t) |
-- ("Leaf",s) <- lex r,
-- (m,t) <- readsPrec (app_prec+1) s]) r
--
-- ++ readParen (d > up_prec)
-- (\r -> [(u:^:v,w) |
-- (u,s) <- readsPrec (up_prec+1) r,
-- (":^:",t) <- lex s,
-- (v,w) <- readsPrec (up_prec+1) t]) r
--
-- where app_prec = 10
-- up_prec = 5
--
--
-- Note that right-associativity of :^: is unused.
--
-- The derived instance in GHC is equivalent to
--
--
-- instance (Read a) => Read (Tree a) where
--
-- readPrec = parens $ (prec app_prec $ do
-- Ident "Leaf" <- lexP
-- m <- step readPrec
-- return (Leaf m))
--
-- +++ (prec up_prec $ do
-- u <- step readPrec
-- Symbol ":^:" <- lexP
-- v <- step readPrec
-- return (u :^: v))
--
-- where app_prec = 10
-- up_prec = 5
--
-- readListPrec = readListPrecDefault
--
class Read a
readsPrec :: Read a => Int -> ReadS a
readList :: Read a => ReadS [a]
class (Num a, Ord a) => Real a
toRational :: Real a => a -> Rational
-- | Efficient, machine-independent access to the components of a
-- floating-point number.
--
-- Minimal complete definition: all except exponent,
-- significand, scaleFloat and atan2
class (RealFrac a, Floating a) => RealFloat a
floatRadix :: RealFloat a => a -> Integer
floatDigits :: RealFloat a => a -> Int
floatRange :: RealFloat a => a -> (Int, Int)
decodeFloat :: RealFloat a => a -> (Integer, Int)
encodeFloat :: RealFloat a => Integer -> Int -> a
exponent :: RealFloat a => a -> Int
significand :: RealFloat a => a -> a
scaleFloat :: RealFloat a => Int -> a -> a
isNaN :: RealFloat a => a -> Bool
isInfinite :: RealFloat a => a -> Bool
isDenormalized :: RealFloat a => a -> Bool
isNegativeZero :: RealFloat a => a -> Bool
isIEEE :: RealFloat a => a -> Bool
atan2 :: RealFloat a => a -> a -> a
-- | Extracting components of fractions.
--
-- Minimal complete definition: properFraction
class (Real a, Fractional a) => RealFrac a
properFraction :: (RealFrac a, Integral b) => a -> (b, a)
truncate :: (RealFrac a, Integral b) => a -> b
round :: (RealFrac a, Integral b) => a -> b
ceiling :: (RealFrac a, Integral b) => a -> b
floor :: (RealFrac a, Integral b) => a -> b
-- | Conversion of values to readable Strings.
--
-- Minimal complete definition: showsPrec or show.
--
-- Derived instances of Show have the following properties, which
-- are compatible with derived instances of Read:
--
--
-- - The result of show is a syntactically correct Haskell
-- expression containing only constants, given the fixity declarations in
-- force at the point where the type is declared. It contains only the
-- constructor names defined in the data type, parentheses, and spaces.
-- When labelled constructor fields are used, braces, commas, field
-- names, and equal signs are also used.
-- - If the constructor is defined to be an infix operator, then
-- showsPrec will produce infix applications of the
-- constructor.
-- - the representation will be enclosed in parentheses if the
-- precedence of the top-level constructor in x is less than
-- d (associativity is ignored). Thus, if d is
-- 0 then the result is never surrounded in parentheses; if
-- d is 11 it is always surrounded in parentheses,
-- unless it is an atomic expression.
-- - If the constructor is defined using record syntax, then
-- show will produce the record-syntax form, with the fields given
-- in the same order as the original declaration.
--
--
-- For example, given the declarations
--
--
-- infixr 5 :^:
-- data Tree a = Leaf a | Tree a :^: Tree a
--
--
-- the derived instance of Show is equivalent to
--
--
-- instance (Show a) => Show (Tree a) where
--
-- showsPrec d (Leaf m) = showParen (d > app_prec) $
-- showString "Leaf " . showsPrec (app_prec+1) m
-- where app_prec = 10
--
-- showsPrec d (u :^: v) = showParen (d > up_prec) $
-- showsPrec (up_prec+1) u .
-- showString " :^: " .
-- showsPrec (up_prec+1) v
-- where up_prec = 5
--
--
-- Note that right-associativity of :^: is ignored. For example,
--
--
-- - show (Leaf 1 :^: Leaf 2 :^: Leaf 3) produces the
-- string "Leaf 1 :^: (Leaf 2 :^: Leaf 3)".
--
class Show a
showsPrec :: Show a => Int -> a -> ShowS
show :: Show a => a -> String
showList :: Show a => [a] -> ShowS
-- | Functors representing data structures that can be traversed from left
-- to right.
--
-- Minimal complete definition: traverse or sequenceA.
--
-- A definition of traverse must satisfy the following laws:
--
--
--
-- A definition of sequenceA must satisfy the following laws:
--
--
--
-- where an applicative transformation is a function
--
--
-- t :: (Applicative f, Applicative g) => f a -> g a
--
--
-- preserving the Applicative operations, i.e.
--
--
--
-- and the identity functor Identity and composition of functors
-- Compose are defined as
--
--
-- newtype Identity a = Identity a
--
-- instance Functor Identity where
-- fmap f (Identity x) = Identity (f x)
--
-- instance Applicative Indentity where
-- pure x = Identity x
-- Identity f <*> Identity x = Identity (f x)
--
-- newtype Compose f g a = Compose (f (g a))
--
-- instance (Functor f, Functor g) => Functor (Compose f g) where
-- fmap f (Compose x) = Compose (fmap (fmap f) x)
--
-- instance (Applicative f, Applicative g) => Applicative (Compose f g) where
-- pure x = Compose (pure (pure x))
-- Compose f <*> Compose x = Compose ((<*>) <$> f <*> x)
--
--
-- (The naturality law is implied by parametricity.)
--
-- Instances are similar to Functor, e.g. given a data type
--
--
-- data Tree a = Empty | Leaf a | Node (Tree a) a (Tree a)
--
--
-- a suitable instance would be
--
--
-- instance Traversable Tree where
-- traverse f Empty = pure Empty
-- traverse f (Leaf x) = Leaf <$> f x
-- traverse f (Node l k r) = Node <$> traverse f l <*> f k <*> traverse f r
--
--
-- This is suitable even for abstract types, as the laws for
-- <*> imply a form of associativity.
--
-- The superclass instances should satisfy the following:
--
--
-- - In the Functor instance, fmap should be equivalent
-- to traversal with the identity applicative functor
-- (fmapDefault).
-- - In the Foldable instance, foldMap should be
-- equivalent to traversal with a constant applicative functor
-- (foldMapDefault).
--
class (Functor t, Foldable t) => Traversable (t :: * -> *)
traverse :: (Traversable t, Applicative f) => (a -> f b) -> t a -> f (t b)
sequenceA :: (Traversable t, Applicative f) => t (f a) -> f (t a)
mapM :: (Traversable t, Monad m) => (a -> m b) -> t a -> m (t b)
sequence :: (Traversable t, Monad m) => t (m a) -> m (t a)
-- | A value of type IO a is a computation which, when
-- performed, does some I/O before returning a value of type a.
--
-- There is really only one way to "perform" an I/O action: bind it to
-- Main.main in your program. When your program is run, the I/O
-- will be performed. It isn't possible to perform I/O from an arbitrary
-- function, unless that function is itself in the IO monad and
-- called at some point, directly or indirectly, from Main.main.
--
-- IO is a monad, so IO actions can be combined using
-- either the do-notation or the >> and >>=
-- operations from the Monad class.
data IO a :: * -> *
-- | The character type Char is an enumeration whose values
-- represent Unicode (or equivalently ISO/IEC 10646) characters (see
-- http://www.unicode.org/ for details). This set extends the ISO
-- 8859-1 (Latin-1) character set (the first 256 characters), which is
-- itself an extension of the ASCII character set (the first 128
-- characters). A character literal in Haskell has type Char.
--
-- To convert a Char to or from the corresponding Int value
-- defined by Unicode, use toEnum and fromEnum from the
-- Enum class respectively (or equivalently ord and
-- chr).
data Char :: *
-- | Double-precision floating point numbers. It is desirable that this
-- type be at least equal in range and precision to the IEEE
-- double-precision type.
data Double :: *
-- | Single-precision floating point numbers. It is desirable that this
-- type be at least equal in range and precision to the IEEE
-- single-precision type.
data Float :: *
-- | A fixed-precision integer type with at least the range [-2^29 ..
-- 2^29-1]. The exact range for a given implementation can be
-- determined by using minBound and maxBound from the
-- Bounded class.
data Int :: *
-- | Arbitrary-precision integers.
data Integer :: *
-- | A Word is an unsigned integral type, with the same size as
-- Int.
data Word :: *
data Bool :: *
False :: Bool
True :: Bool
-- | The Either type represents values with two possibilities: a
-- value of type Either a b is either Left
-- a or Right b.
--
-- The Either type is sometimes used to represent a value which is
-- either correct or an error; by convention, the Left constructor
-- is used to hold an error value and the Right constructor is
-- used to hold a correct value (mnemonic: "right" also means "correct").
data Either a b :: * -> * -> *
Left :: a -> Either a b
Right :: b -> Either a b
-- | The Maybe type encapsulates an optional value. A value of type
-- Maybe a either contains a value of type a
-- (represented as Just a), or it is empty (represented
-- as Nothing). Using Maybe is a good way to deal with
-- errors or exceptional cases without resorting to drastic measures such
-- as error.
--
-- The Maybe type is also a monad. It is a simple kind of error
-- monad, where all errors are represented by Nothing. A richer
-- error monad can be built using the Either type.
data Maybe a :: * -> *
Nothing :: Maybe a
Just :: a -> Maybe a
data Ordering :: *
LT :: Ordering
EQ :: Ordering
GT :: Ordering
-- | File and directory names are values of type String, whose
-- precise meaning is operating system dependent. Files can be opened,
-- yielding a handle which can then be used to operate on the contents of
-- that file.
type FilePath = String
-- | The Haskell 2010 type for exceptions in the IO monad. Any I/O
-- operation may raise an IOError instead of returning a result.
-- For a more general type of exception, including also those that arise
-- in pure code, see Control.Exception.Exception.
--
-- In Haskell 2010, this is an opaque type.
type IOError = IOException
-- | Arbitrary-precision rational numbers, represented as a ratio of two
-- Integer values. A rational number may be constructed using the
-- % operator.
type Rational = Ratio Integer
-- | A parser for a type a, represented as a function that takes a
-- String and returns a list of possible parses as
-- (a,String) pairs.
--
-- Note that this kind of backtracking parser is very inefficient;
-- reading a large structure may be quite slow (cf ReadP).
type ReadS a = String -> [(a, String)]
-- | The shows functions return a function that prepends the
-- output String to an existing String. This allows
-- constant-time concatenation of results using function composition.
type ShowS = String -> String
-- | A String is a list of characters. String constants in Haskell
-- are values of type String.
type String = [Char]
module Data.Version.Compat
-- | Construct tag-less Version
--
-- Since: 4.8.0.0
makeVersion :: [Int] -> Version
module Foreign.Marshal.Alloc.Compat
-- | Like malloc but memory is filled with bytes of value zero.
calloc :: Storable a => IO (Ptr a)
-- | Llike mallocBytes but memory is filled with bytes of value
-- zero.
callocBytes :: Int -> IO (Ptr a)
module Foreign.Marshal.Array.Compat
-- | Like mallocArray, but allocated memory is filled with bytes of
-- value zero.
callocArray :: Storable a => Int -> IO (Ptr a)
-- | Like callocArray0, but allocated memory is filled with bytes of
-- value zero.
callocArray0 :: Storable a => Int -> IO (Ptr a)
module Foreign.Marshal.Compat
module Foreign.Compat
module System.Exit.Compat
-- | Write given error message to stderr and terminate with
-- exitFailure.
--
-- @since 4.8.0.0
die :: String -> IO a
module Data.List.Compat
-- | Determines whether all elements of the structure satisfy the
-- predicate.
all :: Foldable t => (a -> Bool) -> t a -> Bool
-- | and returns the conjunction of a container of Bools. For the
-- result to be True, the container must be finite; False,
-- however, results from a False value finitely far from the left
-- end.
and :: Foldable t => t Bool -> Bool
-- | Determines whether any element of the structure satisfies the
-- predicate.
any :: Foldable t => (a -> Bool) -> t a -> Bool
-- | The concatenation of all the elements of a container of lists.
concat :: Foldable t => t [a] -> [a]
-- | Map a function over all the elements of a container and concatenate
-- the resulting lists.
concatMap :: Foldable t => (a -> [b]) -> t a -> [b]
-- | Does the element occur in the structure?
elem :: (Foldable t, Eq a) => a -> t a -> Bool
-- | The find function takes a predicate and a structure and returns
-- the leftmost element of the structure matching the predicate, or
-- Nothing if there is no such element.
find :: Foldable t => (a -> Bool) -> t a -> Maybe a
-- | Left-associative fold of a structure.
--
--
-- foldl f z = foldl f z . toList
--
foldl :: Foldable t => forall b a. (b -> a -> b) -> b -> t a -> b
-- | Left-associative fold of a structure. but with strict application of
-- the operator.
--
--
-- foldl f z = foldl' f z . toList
--
foldl' :: Foldable t => forall b a. (b -> a -> b) -> b -> t a -> b
-- | A variant of foldl that has no base case, and thus may only be
-- applied to non-empty structures.
--
--
-- foldl1 f = foldl1 f . toList
--
foldl1 :: Foldable t => forall a. (a -> a -> a) -> t a -> a
-- | Right-associative fold of a structure.
--
--
-- foldr f z = foldr f z . toList
--
foldr :: Foldable t => forall a b. (a -> b -> b) -> b -> t a -> b
-- | A variant of foldr that has no base case, and thus may only be
-- applied to non-empty structures.
--
--
-- foldr1 f = foldr1 f . toList
--
foldr1 :: Foldable t => forall a. (a -> a -> a) -> t a -> a
-- | Returns the size/length of a finite structure as an Int. The
-- default implementation is optimized for structures that are similar to
-- cons-lists, because there is no general way to do better.
length :: Foldable t => t a -> Int
-- | The largest element of a non-empty structure.
maximum :: (Foldable t, Ord a) => t a -> a
-- | The largest element of a non-empty structure with respect to the given
-- comparison function.
maximumBy :: Foldable t => (a -> a -> Ordering) -> t a -> a
-- | The least element of a non-empty structure.
minimum :: (Foldable t, Ord a) => t a -> a
-- | The least element of a non-empty structure with respect to the given
-- comparison function.
minimumBy :: Foldable t => (a -> a -> Ordering) -> t a -> a
-- | notElem is the negation of elem.
notElem :: (Foldable t, Eq a) => a -> t a -> Bool
-- | Test whether the structure is empty. The default implementation is
-- optimized for structures that are similar to cons-lists, because there
-- is no general way to do better.
null :: Foldable t => t a -> Bool
-- | or returns the disjunction of a container of Bools. For the
-- result to be False, the container must be finite; True,
-- however, results from a True value finitely far from the left
-- end.
or :: Foldable t => t Bool -> Bool
-- | The product function computes the product of the numbers of a
-- structure.
product :: (Foldable t, Num a) => t a -> a
-- | The sum function computes the sum of the numbers of a
-- structure.
sum :: (Foldable t, Num a) => t a -> a
-- | The mapAccumL function behaves like a combination of
-- fmap and foldl; it applies a function to each element of
-- a structure, passing an accumulating parameter from left to right, and
-- returning a final value of this accumulator together with the new
-- structure.
mapAccumL :: Traversable t => (a -> b -> (a, c)) -> a -> t b -> (a, t c)
-- | The mapAccumR function behaves like a combination of
-- fmap and foldr; it applies a function to each element
-- of a structure, passing an accumulating parameter from right to left,
-- and returning a final value of this accumulator together with the new
-- structure.
mapAccumR :: Traversable t => (a -> b -> (a, c)) -> a -> t b -> (a, t c)
-- | The isSubsequenceOf function takes two lists and returns
-- True if the first list is a subsequence of the second list.
--
-- isSubsequenceOf x y is equivalent to elem x
-- (subsequences y).
--
-- Since: 4.8.0.0
--
-- Examples
--
--
-- >>> isSubsequenceOf "GHC" "The Glorious Haskell Compiler"
-- True
--
-- >>> isSubsequenceOf ['a','d'..'z'] ['a'..'z']
-- True
--
-- >>> isSubsequenceOf [1..10] [10,9..0]
-- False
--
isSubsequenceOf :: Eq a => [a] -> [a] -> Bool
-- | Sort a list by comparing the results of a key function applied to each
-- element. sortOn f is equivalent to sortBy . comparing
-- f, but has the performance advantage of only evaluating
-- f once for each element in the input list. This is called the
-- decorate-sort-undecorate paradigm, or Schwartzian transform.
--
-- Since: 4.8.0.0
sortOn :: Ord b => (a -> b) -> [a] -> [a]
-- | Decompose a list into its head and tail. If the list is empty, returns
-- Nothing. If the list is non-empty, returns Just (x,
-- xs), where x is the head of the list and xs its
-- tail.
--
-- Since: 4.8.0.0
uncons :: [a] -> Maybe (a, [a])
-- | A strictly accumulating version of scanl
scanl' :: (b -> a -> b) -> b -> [a] -> [b]
module Control.Monad.Compat
-- | The Monad class defines the basic operations over a
-- monad, a concept from a branch of mathematics known as
-- category theory. From the perspective of a Haskell programmer,
-- however, it is best to think of a monad as an abstract datatype
-- of actions. Haskell's do expressions provide a convenient
-- syntax for writing monadic expressions.
--
-- Minimal complete definition: >>= and return.
--
-- Instances of Monad should satisfy the following laws:
--
--
-- return a >>= k == k a
-- m >>= return == m
-- m >>= (\x -> k x >>= h) == (m >>= k) >>= h
--
--
-- Instances of both Monad and Functor should additionally
-- satisfy the law:
--
--
-- fmap f xs == xs >>= return . f
--
--
-- The instances of Monad for lists, Maybe and IO
-- defined in the Prelude satisfy these laws.
class Monad (m :: * -> *)
(>>=) :: Monad m => m a -> (a -> m b) -> m b
(>>) :: Monad m => m a -> m b -> m b
return :: Monad m => a -> m a
fail :: Monad m => String -> m a
-- | Monads that also support choice and failure.
class Monad m => MonadPlus (m :: * -> *)
mzero :: MonadPlus m => m a
mplus :: MonadPlus m => m a -> m a -> m a
-- | The foldM function is analogous to foldl, except that
-- its result is encapsulated in a monad. Note that foldM works
-- from left-to-right over the list arguments. This could be an issue
-- where (>>) and the `folded function' are not
-- commutative.
--
--
-- foldM f a1 [x1, x2, ..., xm]
--
--
-- ==
--
--
-- do
-- a2 <- f a1 x1
-- a3 <- f a2 x2
-- ...
-- f am xm
--
--
-- If right-to-left evaluation is required, the input list should be
-- reversed.
--
-- Note: foldM is the same as foldlM
foldM :: (Foldable t, Monad m) => (b -> a -> m b) -> b -> t a -> m b
-- | Like foldM, but discards the result.
foldM_ :: (Foldable t, Monad m) => (b -> a -> m b) -> b -> t a -> m ()
-- | forM is mapM with its arguments flipped.
forM :: (Traversable t, Monad m) => t a -> (a -> m b) -> m (t b)
-- | forM_ is mapM_ with its arguments flipped.
forM_ :: (Foldable t, Monad m) => t a -> (a -> m b) -> m ()
-- | guard b is pure () if b is
-- True, and empty if b is False.
guard :: Alternative f => Bool -> f ()
-- | Map each element of a structure to a monadic action, evaluate these
-- actions from left to right, and collect the results.
mapM :: Traversable t => forall a (m :: * -> *) b. Monad m => (a -> m b) -> t a -> m (t b)
-- | Map each element of a structure to a monadic action, evaluate these
-- actions from left to right, and ignore the results.
mapM_ :: (Foldable t, Monad m) => (a -> m b) -> t a -> m ()
-- | The sum of a collection of actions, generalizing concat.
msum :: (Foldable t, MonadPlus m) => t (m a) -> m a
-- | Evaluate each monadic action in the structure from left to right, and
-- collect the results.
sequence :: Traversable t => forall (m :: * -> *) a. Monad m => t (m a) -> m (t a)
-- | Evaluate each monadic action in the structure from left to right, and
-- ignore the results.
sequence_ :: (Foldable t, Monad m) => t (m a) -> m ()
-- | The reverse of when.
unless :: Applicative f => Bool -> f () -> f ()
-- | Conditional execution of Applicative expressions. For example,
--
--
-- when debug (putStrLn "Debugging")
--
--
-- will output the string Debugging if the Boolean value
-- debug is True, and otherwise do nothing.
when :: Applicative f => Bool -> f () -> f ()
-- | Strict version of <$>.
--
-- Since: 4.8.0.0
(<$!>) :: Monad m => (a -> b) -> m a -> m b
module Control.Concurrent.MVar.Compat
-- | Like withMVar, but the IO action in the second
-- argument is executed with asynchronous exceptions masked.
--
-- Since: 4.7.0.0
withMVarMasked :: MVar a -> (a -> IO b) -> IO b