-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/
-- | A lexer generator
--
-- Tlex is haskell libraries and toolchains for generating lexical
-- analyzer. See also: https://github.com/mizunashi-mana/tlex
@package tlex-core
@version 0.4.0.0
module Language.Lexer.Tlex.Data.SymEnumSet
data SymEnumSet a
empty :: Enum a => SymEnumSet a
full :: Enum a => SymEnumSet a
complement :: Enum a => SymEnumSet a -> SymEnumSet a
singleton :: Enum a => a -> SymEnumSet a
member :: Enum a => a -> SymEnumSet a -> Bool
union :: Enum a => SymEnumSet a -> SymEnumSet a -> SymEnumSet a
intersection :: Enum a => SymEnumSet a -> SymEnumSet a -> SymEnumSet a
difference :: Enum a => SymEnumSet a -> SymEnumSet a -> SymEnumSet a
fromEnumSet :: Enum a => Bool -> EnumSet a -> SymEnumSet a
toEnumSet :: Enum a => SymEnumSet a -> (Bool, EnumSet a)
instance (GHC.Enum.Enum a, GHC.Show.Show a) => GHC.Show.Show (Language.Lexer.Tlex.Data.SymEnumSet.SymEnumSet a)
instance GHC.Classes.Eq (Language.Lexer.Tlex.Data.SymEnumSet.SymEnumSet a)
instance GHC.Enum.Enum a => GHC.Base.Semigroup (Language.Lexer.Tlex.Data.SymEnumSet.SymEnumSet a)
instance GHC.Enum.Enum a => GHC.Base.Monoid (Language.Lexer.Tlex.Data.SymEnumSet.SymEnumSet a)
module Language.Lexer.Tlex.Prelude
-- | 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]
infixr 5 ++
-- | The value of seq a b is bottom if a is bottom, and
-- otherwise equal to b. In other words, it evaluates the first
-- argument a to weak head normal form (WHNF). seq is
-- usually introduced to improve performance by avoiding unneeded
-- laziness.
--
-- A note on evaluation order: the expression seq a b does
-- not guarantee that a will be evaluated before
-- b. The only guarantee given by seq is that the both
-- a and b will be evaluated before seq
-- returns a value. In particular, this means that b may be
-- evaluated before a. If you need to guarantee a specific order
-- of evaluation, you must use the function pseq from the
-- "parallel" package.
seq :: forall {r :: RuntimeRep} a (b :: TYPE r). a -> b -> b
infixr 0 `seq`
-- | <math>. filter, applied to a predicate and a list,
-- returns the list of those elements that satisfy the predicate; i.e.,
--
--
-- filter p xs = [ x | x <- xs, p x]
--
--
--
-- >>> filter odd [1, 2, 3]
-- [1,3]
--
filter :: (a -> Bool) -> [a] -> [a]
-- | <math>. zip takes two lists and returns a list of
-- corresponding pairs.
--
--
-- >>> zip [1, 2] ['a', 'b']
-- [(1,'a'),(2,'b')]
--
--
-- If one input list is shorter than the other, excess elements of the
-- longer list are discarded, even if one of the lists is infinite:
--
--
-- >>> zip [1] ['a', 'b']
-- [(1,'a')]
--
-- >>> zip [1, 2] ['a']
-- [(1,'a')]
--
-- >>> zip [] [1..]
-- []
--
-- >>> zip [1..] []
-- []
--
--
-- zip is right-lazy:
--
--
-- >>> zip [] undefined
-- []
--
-- >>> zip undefined []
-- *** Exception: Prelude.undefined
-- ...
--
--
-- zip is capable of list fusion, but it is restricted to its
-- first list argument and its resulting list.
zip :: [a] -> [b] -> [(a, b)]
-- | 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 ()
-- | Extract the first component of a pair.
fst :: (a, b) -> a
-- | Extract the second component of a pair.
snd :: (a, b) -> b
-- | otherwise is defined as the value True. It helps to make
-- guards more readable. eg.
--
--
-- f x | x < 0 = ...
-- | otherwise = ...
--
otherwise :: Bool
-- | <math>. map f xs is the list obtained by
-- applying f to each element of xs, i.e.,
--
--
-- map f [x1, x2, ..., xn] == [f x1, f x2, ..., f xn]
-- map f [x1, x2, ...] == [f x1, f x2, ...]
--
--
--
-- >>> map (+1) [1, 2, 3]
-- [2,3,4]
--
map :: (a -> b) -> [a] -> [b]
-- | general coercion from integral types
fromIntegral :: (Integral a, Num b) => a -> b
-- | general coercion to fractional types
realToFrac :: (Real a, Fractional b) => a -> b
-- | 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
-- | the successor of a value. For numeric types, succ adds 1.
succ :: Enum a => a -> a
-- | the predecessor of a value. For numeric types, pred subtracts
-- 1.
pred :: Enum a => a -> a
-- | Convert from an Int.
toEnum :: Enum a => Int -> 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
-- | Used in Haskell's translation of [n..] with [n..] =
-- enumFrom n, a possible implementation being enumFrom n = n :
-- enumFrom (succ n). For example:
--
--
-- enumFrom 4 :: [Integer] = [4,5,6,7,...]
enumFrom 6 :: [Int] = [6,7,8,9,...,maxBound ::
-- Int]
enumFrom :: Enum a => a -> [a]
-- | Used in Haskell's translation of [n,n'..] with [n,n'..] =
-- enumFromThen n n', a possible implementation being
-- enumFromThen n n' = n : n' : worker (f x) (f x n'),
-- worker s v = v : worker s (s v), x = fromEnum n' -
-- fromEnum n and f n y | n > 0 = f (n - 1) (succ y) | n <
-- 0 = f (n + 1) (pred y) | otherwise = y For example:
--
--
-- enumFromThen 4 6 :: [Integer] = [4,6,8,10...]
enumFromThen 6 2 :: [Int] = [6,2,-2,-6,...,minBound ::
-- Int]
enumFromThen :: Enum a => a -> a -> [a]
-- | Used in Haskell's translation of [n..m] with [n..m] =
-- enumFromTo n m, a possible implementation being enumFromTo n
-- m | n <= m = n : enumFromTo (succ n) m | otherwise = []. For
-- example:
--
--
-- enumFromTo 6 10 :: [Int] = [6,7,8,9,10]
enumFromTo 42 1 :: [Integer] = []
enumFromTo :: Enum a => a -> a -> [a]
-- | Used in Haskell's translation of [n,n'..m] with [n,n'..m]
-- = enumFromThenTo n n' m, a possible implementation being
-- enumFromThenTo n n' m = worker (f x) (c x) n m, x =
-- fromEnum n' - fromEnum n, c x = bool (>=) ((x
-- 0) f n y | n > 0 = f (n - 1) (succ y) | n < 0 = f (n +
-- 1) (pred y) | otherwise = y and worker s c v m | c v m = v :
-- worker s c (s v) m | otherwise = [] For example:
--
--
-- enumFromThenTo 4 2 -6 :: [Integer] =
-- [4,2,0,-2,-4,-6]
enumFromThenTo 6 8 2 :: [Int] = []
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.
--
-- The Haskell Report defines no laws for Eq. However, instances
-- are encouraged to follow these properties:
--
--
-- - Reflexivity x == x = True
-- - Symmetry x == y = y == x
-- - Transitivity if x == y && y == z =
-- True, then x == z = True
-- - Extensionality if x == y = True and
-- f is a function whose return type is an instance of
-- Eq, then f x == f y = True
-- - Negation x /= y = not (x ==
-- y)
--
--
-- Minimal complete definition: either == or /=.
class Eq a
(==) :: Eq a => a -> a -> Bool
(/=) :: Eq a => a -> a -> Bool
infix 4 ==
infix 4 /=
-- | Trigonometric and hyperbolic functions and related functions.
--
-- The Haskell Report defines no laws for Floating. However,
-- (+), (*) and exp are
-- customarily expected to define an exponential field and have the
-- following properties:
--
--
-- - exp (a + b) = exp a * exp b
-- - exp (fromInteger 0) = fromInteger 1
--
class Fractional a => Floating a
exp :: Floating a => a -> a
log :: Floating a => a -> a
sqrt :: Floating a => a -> a
(**) :: Floating a => a -> a -> a
logBase :: Floating a => a -> a -> a
sin :: Floating a => a -> a
cos :: Floating a => a -> a
tan :: Floating a => a -> a
asin :: Floating a => a -> a
acos :: Floating a => a -> a
atan :: Floating a => a -> a
sinh :: Floating a => a -> a
cosh :: Floating a => a -> a
tanh :: Floating a => a -> a
asinh :: Floating a => a -> a
acosh :: Floating a => a -> a
atanh :: Floating a => a -> a
infixr 8 **
-- | Fractional numbers, supporting real division.
--
-- The Haskell Report defines no laws for Fractional. However,
-- (+) and (*) are customarily expected
-- to define a division ring and have the following properties:
--
--
-- - recip gives the multiplicative inverse x
-- * recip x = recip x * x = fromInteger 1
--
--
-- Note that it isn't customarily expected that a type instance of
-- Fractional implement a field. However, all instances in
-- base do.
class Num a => Fractional a
-- | Fractional division.
(/) :: Fractional a => a -> a -> a
-- | Reciprocal fraction.
recip :: Fractional 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
infixl 7 /
-- | Integral numbers, supporting integer division.
--
-- The Haskell Report defines no laws for Integral. However,
-- Integral instances are customarily expected to define a
-- Euclidean domain and have the following properties for the
-- div/mod and quot/rem pairs, given suitable
-- Euclidean functions f and g:
--
--
-- - x = y * quot x y + rem x y with rem x y
-- = fromInteger 0 or g (rem x y) < g
-- y
-- - x = y * div x y + mod x y with mod x y
-- = fromInteger 0 or f (mod x y) < f
-- y
--
--
-- An example of a suitable Euclidean function, for Integer's
-- instance, is abs.
class (Real a, Enum a) => Integral a
-- | integer division truncated toward zero
quot :: Integral a => a -> a -> a
-- | integer remainder, satisfying
--
--
-- (x `quot` y)*y + (x `rem` y) == x
--
rem :: Integral a => a -> a -> a
-- | integer division truncated toward negative infinity
div :: Integral a => a -> a -> a
-- | integer modulus, satisfying
--
--
-- (x `div` y)*y + (x `mod` y) == x
--
mod :: Integral a => a -> a -> a
-- | simultaneous quot and rem
quotRem :: Integral a => a -> a -> (a, a)
-- | simultaneous div and mod
divMod :: Integral a => a -> a -> (a, a)
-- | conversion to Integer
toInteger :: Integral a => a -> Integer
infixl 7 `rem`
infixl 7 `quot`
infixl 7 `mod`
infixl 7 `div`
-- | The Monad class defines the basic operations over a
-- monad, a concept from a branch of mathematics known as
-- category theory. From the perspective of a Haskell programmer,
-- however, it is best to think of a monad as an abstract datatype
-- of actions. Haskell's do expressions provide a convenient
-- syntax for writing monadic expressions.
--
-- Instances of Monad should satisfy the following:
--
--
--
-- Furthermore, the Monad and Applicative operations should
-- relate as follows:
--
--
--
-- The above laws imply:
--
--
--
-- and that pure and (<*>) satisfy the applicative
-- functor laws.
--
-- The instances of Monad for lists, Maybe and IO
-- defined in the Prelude satisfy these laws.
class Applicative m => Monad (m :: Type -> Type)
-- | Sequentially compose two actions, passing any value produced by the
-- first as an argument to the second.
--
-- 'as >>= bs' can be understood as the do
-- expression
--
--
-- do a <- as
-- bs a
--
(>>=) :: Monad m => m a -> (a -> m b) -> m b
-- | Sequentially compose two actions, discarding any value produced by the
-- first, like sequencing operators (such as the semicolon) in imperative
-- languages.
--
-- 'as >> bs' can be understood as the do
-- expression
--
--
-- do as
-- bs
--
(>>) :: Monad m => m a -> m b -> m b
-- | Inject a value into the monadic type.
return :: Monad m => a -> m a
infixl 1 >>=
infixl 1 >>
-- | A type f is a Functor if it provides a function fmap
-- which, given any types a and b lets you apply any
-- function from (a -> b) to turn an f a into an
-- f b, preserving the structure of f. Furthermore
-- f needs to adhere to the following:
--
--
--
-- Note, that the second law follows from the free theorem of the type
-- fmap and the first law, so you need only check that the former
-- condition holds.
class Functor (f :: Type -> Type)
-- | fmap is used to apply a function of type (a -> b)
-- to a value of type f a, where f is a functor, to produce a
-- value of type f b. Note that for any type constructor with
-- more than one parameter (e.g., Either), only the last type
-- parameter can be modified with fmap (e.g., b in
-- `Either a b`).
--
-- Some type constructors with two parameters or more have a
-- Bifunctor instance that allows both the last and the
-- penultimate parameters to be mapped over.
--
-- Examples
--
-- Convert from a Maybe Int to a Maybe String
-- using show:
--
--
-- >>> fmap show Nothing
-- Nothing
--
-- >>> fmap show (Just 3)
-- Just "3"
--
--
-- Convert from an Either Int Int to an Either Int
-- String using show:
--
--
-- >>> fmap show (Left 17)
-- Left 17
--
-- >>> fmap show (Right 17)
-- Right "17"
--
--
-- Double each element of a list:
--
--
-- >>> fmap (*2) [1,2,3]
-- [2,4,6]
--
--
-- Apply even to the second element of a pair:
--
--
-- >>> fmap even (2,2)
-- (2,True)
--
--
-- It may seem surprising that the function is only applied to the last
-- element of the tuple compared to the list example above which applies
-- it to every element in the list. To understand, remember that tuples
-- are type constructors with multiple type parameters: a tuple of 3
-- elements (a,b,c) can also be written (,,) a b c and
-- its Functor instance is defined for Functor ((,,) a
-- b) (i.e., only the third parameter is free to be mapped over with
-- fmap).
--
-- It explains why fmap can be used with tuples containing
-- values of different types as in the following example:
--
--
-- >>> fmap even ("hello", 1.0, 4)
-- ("hello",1.0,True)
--
fmap :: Functor f => (a -> b) -> f a -> f b
-- | Replace all locations in the input with the same value. The default
-- definition is fmap . const, but this may be
-- overridden with a more efficient version.
(<$) :: Functor f => a -> f b -> f a
infixl 4 <$
-- | Basic numeric class.
--
-- The Haskell Report defines no laws for Num. However,
-- (+) and (*) are customarily expected
-- to define a ring and have the following properties:
--
--
-- - Associativity of (+) (x + y) +
-- z = x + (y + z)
-- - Commutativity of (+) x + y
-- = y + x
-- - fromInteger 0 is the additive
-- identity x + fromInteger 0 = x
-- - negate gives the additive inverse x +
-- negate x = fromInteger 0
-- - Associativity of (*) (x * y) *
-- z = x * (y * z)
-- - fromInteger 1 is the multiplicative
-- identity x * fromInteger 1 = x and
-- fromInteger 1 * x = x
-- - Distributivity of (*) with respect to
-- (+) a * (b + c) = (a * b) + (a *
-- c) and (b + c) * a = (b * a) + (c * a)
--
--
-- Note that it isn't customarily expected that a type instance of
-- both Num and Ord implement an ordered ring. Indeed, in
-- base only Integer and Rational do.
class Num a
(+) :: Num a => a -> a -> a
(-) :: Num a => a -> a -> a
(*) :: Num a => a -> a -> a
-- | Unary negation.
negate :: Num a => a -> a
-- | Absolute value.
abs :: 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
-- | Conversion from an Integer. An integer literal represents the
-- application of the function fromInteger to the appropriate
-- value of type Integer, so such literals have type
-- (Num a) => a.
fromInteger :: Num a => Integer -> a
infixl 7 *
infixl 6 +
infixl 6 -
-- | 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.
--
-- Ord, as defined by the Haskell report, implements a total order
-- and has the following properties:
--
--
-- - Comparability x <= y || y <= x =
-- True
-- - Transitivity if x <= y && y <=
-- z = True, then x <= z = True
-- - Reflexivity x <= x = True
-- - Antisymmetry if x <= y && y <=
-- x = True, then x == y = True
--
--
-- The following operator interactions are expected to hold:
--
--
-- - x >= y = y <= x
-- - x < y = x <= y && x /= y
-- - x > y = y < x
-- - x < y = compare x y == LT
-- - x > y = compare x y == GT
-- - x == y = compare x y == EQ
-- - min x y == if x <= y then x else y = True
-- - max x y == if x >= y then x else y = True
--
--
-- Note that (7.) and (8.) do not require min and
-- max to return either of their arguments. The result is merely
-- required to equal one of the arguments in terms of (==).
--
-- 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
infix 4 <
infix 4 <=
infix 4 >
infix 4 >=
-- | Parsing of Strings, producing values.
--
-- 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
--
--
-- Why do both readsPrec and readPrec exist, and why does
-- GHC opt to implement readPrec in derived Read instances
-- instead of readsPrec? The reason is that readsPrec is
-- based on the ReadS type, and although ReadS is mentioned
-- in the Haskell 2010 Report, it is not a very efficient parser data
-- structure.
--
-- readPrec, on the other hand, is based on a much more efficient
-- ReadPrec datatype (a.k.a "new-style parsers"), but its
-- definition relies on the use of the RankNTypes language
-- extension. Therefore, readPrec (and its cousin,
-- readListPrec) are marked as GHC-only. Nevertheless, it is
-- recommended to use readPrec instead of readsPrec
-- whenever possible for the efficiency improvements it brings.
--
-- As mentioned above, derived Read instances in GHC will
-- implement readPrec instead of readsPrec. The default
-- implementations of readsPrec (and its cousin, readList)
-- will simply use readPrec under the hood. If you are writing a
-- Read instance by hand, it is recommended to write it like so:
--
--
-- instance Read T where
-- readPrec = ...
-- readListPrec = readListPrecDefault
--
class Read 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
-- | 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]
class (Num a, Ord a) => Real a
-- | the rational equivalent of its real argument with full precision
toRational :: Real a => a -> Rational
-- | Efficient, machine-independent access to the components of a
-- floating-point number.
class (RealFrac a, Floating a) => RealFloat a
-- | a constant function, returning the radix of the representation (often
-- 2)
floatRadix :: RealFloat a => a -> Integer
-- | a constant function, returning the number of digits of
-- floatRadix in the significand
floatDigits :: RealFloat a => a -> Int
-- | a constant function, returning the lowest and highest values the
-- exponent may assume
floatRange :: RealFloat a => a -> (Int, Int)
-- | 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
-- | 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
-- | multiplies a floating-point number by an integer power of the radix
scaleFloat :: RealFloat a => Int -> a -> a
-- | True if the argument is an IEEE "not-a-number" (NaN) value
isNaN :: 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 too small to be represented in
-- normalized format
isDenormalized :: RealFloat a => a -> Bool
-- | True if the argument is an IEEE negative zero
isNegativeZero :: RealFloat a => a -> Bool
-- | True if the argument is an IEEE floating point number
isIEEE :: RealFloat a => a -> Bool
-- | 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
-- | Extracting components of fractions.
class (Real a, Fractional a) => RealFrac a
-- | 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, Integral b) => a -> (b, a)
-- | truncate x returns the integer nearest x
-- between zero and x
truncate :: (RealFrac a, Integral b) => a -> b
-- | round x returns the nearest integer to x; the
-- even integer if x is equidistant between two integers
round :: (RealFrac a, Integral b) => a -> b
-- | ceiling x returns the least integer not less than
-- x
ceiling :: (RealFrac a, Integral b) => a -> b
-- | floor x returns the greatest integer not greater than
-- x
floor :: (RealFrac a, Integral b) => a -> b
-- | Conversion of values to readable Strings.
--
-- 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
-- | 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
-- | 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
-- | When a value is bound in do-notation, the pattern on the left
-- hand side of <- might not match. In this case, this class
-- provides a function to recover.
--
-- A Monad without a MonadFail instance may only be used in
-- conjunction with pattern that always match, such as newtypes, tuples,
-- data types with only a single data constructor, and irrefutable
-- patterns (~pat).
--
-- Instances of MonadFail should satisfy the following law:
-- fail s should be a left zero for >>=,
--
--
-- fail s >>= f = fail s
--
--
-- If your Monad is also MonadPlus, a popular definition is
--
--
-- fail _ = mzero
--
class Monad m => MonadFail (m :: Type -> Type)
fail :: MonadFail m => String -> m a
-- | A functor with application, providing operations to
--
--
-- - embed pure expressions (pure), and
-- - sequence computations and combine their results (<*>
-- and liftA2).
--
--
-- A minimal complete definition must include implementations of
-- pure and of either <*> or liftA2. If it
-- defines both, then they must behave the same as their default
-- definitions:
--
--
-- (<*>) = liftA2 id
--
--
--
-- liftA2 f x y = f <$> x <*> y
--
--
-- Further, any definition must satisfy the following:
--
--
--
-- The other methods have the following default definitions, which may be
-- overridden with equivalent specialized implementations:
--
--
--
-- As a consequence of these laws, the Functor instance for
-- f will satisfy
--
--
--
-- It may be useful to note that supposing
--
--
-- forall x y. p (q x y) = f x . g y
--
--
-- it follows from the above that
--
--
-- liftA2 p (liftA2 q u v) = liftA2 f u . liftA2 g v
--
--
-- If f is also a Monad, it should satisfy
--
--
--
-- (which implies that pure and <*> satisfy the
-- applicative functor laws).
class Functor f => Applicative (f :: Type -> Type)
-- | Lift a value.
pure :: Applicative f => a -> f a
-- | Sequential application.
--
-- A few functors support an implementation of <*> that is
-- more efficient than the default one.
--
-- Example
--
-- Used in combination with (<$>),
-- (<*>) can be used to build a record.
--
--
-- >>> data MyState = MyState {arg1 :: Foo, arg2 :: Bar, arg3 :: Baz}
--
--
--
-- >>> produceFoo :: Applicative f => f Foo
--
--
--
-- >>> produceBar :: Applicative f => f Bar
--
-- >>> produceBaz :: Applicative f => f Baz
--
--
--
-- >>> mkState :: Applicative f => f MyState
--
-- >>> mkState = MyState <$> produceFoo <*> produceBar <*> produceBaz
--
(<*>) :: Applicative f => f (a -> b) -> f a -> f b
-- | Sequence actions, discarding the value of the first argument.
--
-- Examples
--
-- If used in conjunction with the Applicative instance for Maybe,
-- you can chain Maybe computations, with a possible "early return" in
-- case of Nothing.
--
--
-- >>> Just 2 *> Just 3
-- Just 3
--
--
--
-- >>> Nothing *> Just 3
-- Nothing
--
--
-- Of course a more interesting use case would be to have effectful
-- computations instead of just returning pure values.
--
--
-- >>> import Data.Char
--
-- >>> import Text.ParserCombinators.ReadP
--
-- >>> let p = string "my name is " *> munch1 isAlpha <* eof
--
-- >>> readP_to_S p "my name is Simon"
-- [("Simon","")]
--
(*>) :: Applicative f => f a -> f b -> f b
-- | Sequence actions, discarding the value of the second argument.
(<*) :: Applicative f => f a -> f b -> f a
infixl 4 <*
infixl 4 *>
infixl 4 <*>
-- | The Foldable class represents data structures that can be reduced to a
-- summary value one element at a time. Strict left-associative folds are
-- a good fit for space-efficient reduction, while lazy right-associative
-- folds are a good fit for corecursive iteration, or for folds that
-- short-circuit after processing an initial subsequence of the
-- structure's elements.
--
-- Instances can be derived automatically by enabling the
-- DeriveFoldable extension. For example, a derived instance for
-- a binary tree might be:
--
--
-- {-# LANGUAGE DeriveFoldable #-}
-- data Tree a = Empty
-- | Leaf a
-- | Node (Tree a) a (Tree a)
-- deriving Foldable
--
--
-- A more detailed description can be found in the Overview
-- section of Data.Foldable#overview.
--
-- For the class laws see the Laws section of
-- Data.Foldable#laws.
class Foldable (t :: TYPE LiftedRep -> Type)
-- | Map each element of the structure into a monoid, and combine the
-- results with (<>). This fold is
-- right-associative and lazy in the accumulator. For strict
-- left-associative folds consider foldMap' instead.
--
-- Examples
--
-- Basic usage:
--
--
-- >>> foldMap Sum [1, 3, 5]
-- Sum {getSum = 9}
--
--
--
-- >>> foldMap Product [1, 3, 5]
-- Product {getProduct = 15}
--
--
--
-- >>> foldMap (replicate 3) [1, 2, 3]
-- [1,1,1,2,2,2,3,3,3]
--
--
-- When a Monoid's (<>) is lazy in its second
-- argument, foldMap can return a result even from an unbounded
-- structure. For example, lazy accumulation enables
-- Data.ByteString.Builder to efficiently serialise large data
-- structures and produce the output incrementally:
--
--
-- >>> import qualified Data.ByteString.Lazy as L
--
-- >>> import qualified Data.ByteString.Builder as B
--
-- >>> let bld :: Int -> B.Builder; bld i = B.intDec i <> B.word8 0x20
--
-- >>> let lbs = B.toLazyByteString $ foldMap bld [0..]
--
-- >>> L.take 64 lbs
-- "0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24"
--
foldMap :: (Foldable t, Monoid m) => (a -> m) -> t a -> m
-- | A variant of foldr that has no base case, and thus may only be
-- applied to non-empty structures.
--
-- This function is non-total and will raise a runtime exception if the
-- structure happens to be empty.
--
-- Examples
--
-- Basic usage:
--
--
-- >>> foldr1 (+) [1..4]
-- 10
--
--
--
-- >>> foldr1 (+) []
-- Exception: Prelude.foldr1: empty list
--
--
--
-- >>> foldr1 (+) Nothing
-- *** Exception: foldr1: empty structure
--
--
--
-- >>> foldr1 (-) [1..4]
-- -2
--
--
--
-- >>> foldr1 (&&) [True, False, True, True]
-- False
--
--
--
-- >>> foldr1 (||) [False, False, True, True]
-- True
--
--
--
-- >>> foldr1 (+) [1..]
-- * Hangs forever *
--
foldr1 :: Foldable t => (a -> a -> a) -> t a -> a
-- | A variant of foldl that has no base case, and thus may only be
-- applied to non-empty structures.
--
-- This function is non-total and will raise a runtime exception if the
-- structure happens to be empty.
--
--
-- foldl1 f = foldl1 f . toList
--
--
-- Examples
--
-- Basic usage:
--
--
-- >>> foldl1 (+) [1..4]
-- 10
--
--
--
-- >>> foldl1 (+) []
-- *** Exception: Prelude.foldl1: empty list
--
--
--
-- >>> foldl1 (+) Nothing
-- *** Exception: foldl1: empty structure
--
--
--
-- >>> foldl1 (-) [1..4]
-- -8
--
--
--
-- >>> foldl1 (&&) [True, False, True, True]
-- False
--
--
--
-- >>> foldl1 (||) [False, False, True, True]
-- True
--
--
--
-- >>> foldl1 (+) [1..]
-- * Hangs forever *
--
foldl1 :: Foldable t => (a -> a -> a) -> t a -> a
-- | Test whether the structure is empty. The default implementation is
-- Left-associative and lazy in both the initial element and the
-- accumulator. Thus optimised for structures where the first element can
-- be accessed in constant time. Structures where this is not the case
-- should have a non-default implementation.
--
-- Examples
--
-- Basic usage:
--
--
-- >>> null []
-- True
--
--
--
-- >>> null [1]
-- False
--
--
-- null is expected to terminate even for infinite structures. The
-- default implementation terminates provided the structure is bounded on
-- the left (there is a leftmost element).
--
--
-- >>> null [1..]
-- False
--
null :: Foldable t => t a -> Bool
-- | Returns the size/length of a finite structure as an Int. The
-- default implementation just counts elements starting with the
-- leftmost. Instances for structures that can compute the element count
-- faster than via element-by-element counting, should provide a
-- specialised implementation.
--
-- Examples
--
-- Basic usage:
--
--
-- >>> length []
-- 0
--
--
--
-- >>> length ['a', 'b', 'c']
-- 3
--
-- >>> length [1..]
-- * Hangs forever *
--
length :: Foldable t => t a -> Int
-- | Does the element occur in the structure?
--
-- Note: elem is often used in infix form.
--
-- Examples
--
-- Basic usage:
--
--
-- >>> 3 `elem` []
-- False
--
--
--
-- >>> 3 `elem` [1,2]
-- False
--
--
--
-- >>> 3 `elem` [1,2,3,4,5]
-- True
--
--
-- For infinite structures, the default implementation of elem
-- terminates if the sought-after value exists at a finite distance from
-- the left side of the structure:
--
--
-- >>> 3 `elem` [1..]
-- True
--
--
--
-- >>> 3 `elem` ([4..] ++ [3])
-- * Hangs forever *
--
elem :: (Foldable t, Eq a) => a -> t a -> Bool
-- | The largest element of a non-empty structure.
--
-- This function is non-total and will raise a runtime exception if the
-- structure happens to be empty. A structure that supports random access
-- and maintains its elements in order should provide a specialised
-- implementation to return the maximum in faster than linear time.
--
-- Examples
--
-- Basic usage:
--
--
-- >>> maximum [1..10]
-- 10
--
--
--
-- >>> maximum []
-- *** Exception: Prelude.maximum: empty list
--
--
--
-- >>> maximum Nothing
-- *** Exception: maximum: empty structure
--
--
-- WARNING: This function is partial for possibly-empty structures like
-- lists.
maximum :: (Foldable t, Ord a) => t a -> a
-- | The least element of a non-empty structure.
--
-- This function is non-total and will raise a runtime exception if the
-- structure happens to be empty. A structure that supports random access
-- and maintains its elements in order should provide a specialised
-- implementation to return the minimum in faster than linear time.
--
-- Examples
--
-- Basic usage:
--
--
-- >>> minimum [1..10]
-- 1
--
--
--
-- >>> minimum []
-- *** Exception: Prelude.minimum: empty list
--
--
--
-- >>> minimum Nothing
-- *** Exception: minimum: empty structure
--
--
-- WARNING: This function is partial for possibly-empty structures like
-- lists.
minimum :: (Foldable t, Ord a) => t a -> a
-- | The sum function computes the sum of the numbers of a
-- structure.
--
-- Examples
--
-- Basic usage:
--
--
-- >>> sum []
-- 0
--
--
--
-- >>> sum [42]
-- 42
--
--
--
-- >>> sum [1..10]
-- 55
--
--
--
-- >>> sum [4.1, 2.0, 1.7]
-- 7.8
--
--
--
-- >>> sum [1..]
-- * Hangs forever *
--
sum :: (Foldable t, Num a) => t a -> a
-- | The product function computes the product of the numbers of a
-- structure.
--
-- Examples
--
-- Basic usage:
--
--
-- >>> product []
-- 1
--
--
--
-- >>> product [42]
-- 42
--
--
--
-- >>> product [1..10]
-- 3628800
--
--
--
-- >>> product [4.1, 2.0, 1.7]
-- 13.939999999999998
--
--
--
-- >>> product [1..]
-- * Hangs forever *
--
product :: (Foldable t, Num a) => t a -> a
infix 4 `elem`
-- | Functors representing data structures that can be transformed to
-- structures of the same shape by performing an
-- Applicative (or, therefore, Monad) action on each
-- element from left to right.
--
-- A more detailed description of what same shape means, the
-- various methods, how traversals are constructed, and example advanced
-- use-cases can be found in the Overview section of
-- Data.Traversable#overview.
--
-- For the class laws see the Laws section of
-- Data.Traversable#laws.
class (Functor t, Foldable t) => Traversable (t :: Type -> Type)
-- | Map each element of a structure to an action, evaluate these actions
-- from left to right, and collect the results. For a version that
-- ignores the results see traverse_.
--
-- Examples
--
-- Basic usage:
--
-- In the first two examples we show each evaluated action mapping to the
-- output structure.
--
--
-- >>> traverse Just [1,2,3,4]
-- Just [1,2,3,4]
--
--
--
-- >>> traverse id [Right 1, Right 2, Right 3, Right 4]
-- Right [1,2,3,4]
--
--
-- In the next examples, we show that Nothing and Left
-- values short circuit the created structure.
--
--
-- >>> traverse (const Nothing) [1,2,3,4]
-- Nothing
--
--
--
-- >>> traverse (\x -> if odd x then Just x else Nothing) [1,2,3,4]
-- Nothing
--
--
--
-- >>> traverse id [Right 1, Right 2, Right 3, Right 4, Left 0]
-- Left 0
--
traverse :: (Traversable t, Applicative f) => (a -> f b) -> t a -> f (t b)
-- | Evaluate each action in the structure from left to right, and collect
-- the results. For a version that ignores the results see
-- sequenceA_.
--
-- Examples
--
-- Basic usage:
--
-- For the first two examples we show sequenceA fully evaluating a a
-- structure and collecting the results.
--
--
-- >>> sequenceA [Just 1, Just 2, Just 3]
-- Just [1,2,3]
--
--
--
-- >>> sequenceA [Right 1, Right 2, Right 3]
-- Right [1,2,3]
--
--
-- The next two example show Nothing and Just will short
-- circuit the resulting structure if present in the input. For more
-- context, check the Traversable instances for Either and
-- Maybe.
--
--
-- >>> sequenceA [Just 1, Just 2, Just 3, Nothing]
-- Nothing
--
--
--
-- >>> sequenceA [Right 1, Right 2, Right 3, Left 4]
-- Left 4
--
sequenceA :: (Traversable t, Applicative f) => t (f a) -> f (t a)
-- | Map each element of a structure to a monadic action, evaluate these
-- actions from left to right, and collect the results. For a version
-- that ignores the results see mapM_.
--
-- Examples
--
-- mapM is literally a traverse with a type signature
-- restricted to Monad. Its implementation may be more efficient
-- due to additional power of Monad.
mapM :: (Traversable t, 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. For a version that ignores the results see
-- sequence_.
--
-- Examples
--
-- Basic usage:
--
-- The first two examples are instances where the input and and output of
-- sequence are isomorphic.
--
--
-- >>> sequence $ Right [1,2,3,4]
-- [Right 1,Right 2,Right 3,Right 4]
--
--
--
-- >>> sequence $ [Right 1,Right 2,Right 3,Right 4]
-- Right [1,2,3,4]
--
--
-- The following examples demonstrate short circuit behavior for
-- sequence.
--
--
-- >>> sequence $ Left [1,2,3,4]
-- Left [1,2,3,4]
--
--
--
-- >>> sequence $ [Left 0, Right 1,Right 2,Right 3,Right 4]
-- Left 0
--
sequence :: (Traversable t, Monad m) => t (m a) -> m (t a)
-- | The class of semigroups (types with an associative binary operation).
--
-- Instances should satisfy the following:
--
--
-- - Associativity x <> (y <> z) =
-- (x <> y) <> z
--
class Semigroup a
-- | An associative operation.
--
--
-- >>> [1,2,3] <> [4,5,6]
-- [1,2,3,4,5,6]
--
(<>) :: Semigroup a => a -> a -> a
infixr 6 <>
-- | The class of monoids (types with an associative binary operation that
-- has an identity). Instances should satisfy the following:
--
--
--
-- The method names refer to the monoid of lists under concatenation, but
-- there are many other instances.
--
-- Some types can be viewed as a monoid in more than one way, e.g. both
-- addition and multiplication on numbers. In such cases we often define
-- newtypes and make those instances of Monoid, e.g.
-- Sum and Product.
--
-- NOTE: Semigroup is a superclass of Monoid since
-- base-4.11.0.0.
class Semigroup a => Monoid a
-- | Identity of mappend
--
--
-- >>> "Hello world" <> mempty
-- "Hello world"
--
mempty :: Monoid a => a
-- | An associative operation
--
-- NOTE: This method is redundant and has the default
-- implementation mappend = (<>) since
-- base-4.11.0.0. Should it be implemented manually, since
-- mappend is a synonym for (<>), it is expected that
-- the two functions are defined the same way. In a future GHC release
-- mappend will be removed from Monoid.
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 ["Hello", " ", "Haskell", "!"]
-- "Hello Haskell!"
--
mconcat :: Monoid a => [a] -> a
data Bool
False :: Bool
True :: Bool
-- | The character type Char is an enumeration whose values
-- represent Unicode (or equivalently ISO/IEC 10646) code points (i.e.
-- 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. In contrast with fixed-size integral
-- types such as Int, the Integer type represents the
-- entire infinite range of integers.
--
-- Integers are stored in a kind of sign-magnitude form, hence do not
-- expect two's complement form when using bit operations.
--
-- If the value is small (fit into an Int), IS constructor
-- is used. Otherwise Integer and IN constructors are used
-- to store a BigNat representing respectively the positive or the
-- negative value magnitude.
--
-- Invariant: Integer and IN are used iff value doesn't fit
-- in IS
data Integer
-- | 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
-- | 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 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
-- | A Word is an unsigned integral type, with the same size as
-- Int.
data Word
-- | 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").
--
-- Examples
--
-- The type Either String Int is the type
-- of values which can be either a String or an Int. The
-- Left constructor can be used only on Strings, and the
-- Right constructor can be used only on Ints:
--
--
-- >>> let s = Left "foo" :: Either String Int
--
-- >>> s
-- Left "foo"
--
-- >>> let n = Right 3 :: Either String Int
--
-- >>> n
-- Right 3
--
-- >>> :type s
-- s :: Either String Int
--
-- >>> :type n
-- n :: Either String Int
--
--
-- The fmap from our Functor instance will ignore
-- Left values, but will apply the supplied function to values
-- contained in a Right:
--
--
-- >>> let s = Left "foo" :: Either String Int
--
-- >>> let n = Right 3 :: Either String Int
--
-- >>> fmap (*2) s
-- Left "foo"
--
-- >>> fmap (*2) n
-- Right 6
--
--
-- The Monad instance for Either allows us to chain
-- together multiple actions which may fail, and fail overall if any of
-- the individual steps failed. First we'll write a function that can
-- either parse an Int from a Char, or fail.
--
--
-- >>> import Data.Char ( digitToInt, isDigit )
--
-- >>> :{
-- let parseEither :: Char -> Either String Int
-- parseEither c
-- | isDigit c = Right (digitToInt c)
-- | otherwise = Left "parse error"
--
-- >>> :}
--
--
-- The following should work, since both '1' and '2'
-- can be parsed as Ints.
--
--
-- >>> :{
-- let parseMultiple :: Either String Int
-- parseMultiple = do
-- x <- parseEither '1'
-- y <- parseEither '2'
-- return (x + y)
--
-- >>> :}
--
--
--
-- >>> parseMultiple
-- Right 3
--
--
-- But the following should fail overall, since the first operation where
-- we attempt to parse 'm' as an Int will fail:
--
--
-- >>> :{
-- let parseMultiple :: Either String Int
-- parseMultiple = do
-- x <- parseEither 'm'
-- y <- parseEither '2'
-- return (x + y)
--
-- >>> :}
--
--
--
-- >>> parseMultiple
-- Left "parse error"
--
data Either a b
Left :: a -> Either a b
Right :: b -> Either a b
-- | An infix synonym for fmap.
--
-- The name of this operator is an allusion to $. Note the
-- similarities between their types:
--
--
-- ($) :: (a -> b) -> a -> b
-- (<$>) :: Functor f => (a -> b) -> f a -> f b
--
--
-- Whereas $ is function application, <$> is function
-- application lifted over a Functor.
--
-- Examples
--
-- Convert from a Maybe Int to a Maybe
-- String using show:
--
--
-- >>> show <$> Nothing
-- Nothing
--
-- >>> show <$> Just 3
-- Just "3"
--
--
-- Convert from an Either Int Int to an
-- Either Int String using show:
--
--
-- >>> show <$> Left 17
-- Left 17
--
-- >>> show <$> Right 17
-- Right "17"
--
--
-- Double each element of a list:
--
--
-- >>> (*2) <$> [1,2,3]
-- [2,4,6]
--
--
-- Apply even to the second element of a pair:
--
--
-- >>> even <$> (2,2)
-- (2,True)
--
(<$>) :: Functor f => (a -> b) -> f a -> f b
infixl 4 <$>
-- | const x is a unary function which evaluates to x for
-- all inputs.
--
--
-- >>> const 42 "hello"
-- 42
--
--
--
-- >>> map (const 42) [0..3]
-- [42,42,42,42]
--
const :: a -> b -> a
-- | Function composition.
(.) :: (b -> c) -> (a -> b) -> a -> c
infixr 9 .
-- | Identity function.
--
--
-- id x = x
--
id :: a -> a
-- | The read function reads input from a string, which must be
-- completely consumed by the input process. read fails with an
-- error if the parse is unsuccessful, and it is therefore
-- discouraged from being used in real applications. Use readMaybe
-- or readEither for safe alternatives.
--
--
-- >>> read "123" :: Int
-- 123
--
--
--
-- >>> read "hello" :: Int
-- *** Exception: Prelude.read: no parse
--
read :: Read a => String -> a
-- | The computation writeFile file str function writes the
-- string str, to the file file.
writeFile :: FilePath -> String -> IO ()
-- | The readLn function combines getLine and readIO.
readLn :: Read a => IO a
-- | 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 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 same as putStr, but adds a newline character.
putStrLn :: String -> IO ()
-- | Write a string to the standard output device (same as hPutStr
-- stdout).
putStr :: String -> IO ()
-- | Write a character to the standard output device (same as
-- hPutChar stdout).
putChar :: Char -> IO ()
-- | 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 ()
-- | Read a line from the standard input device (same as hGetLine
-- stdin).
getLine :: IO String
-- | 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 character from the standard input device (same as
-- hGetChar stdin).
getChar :: IO Char
-- | 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 ()
-- | Raise an IOException in the IO monad.
ioError :: IOError -> IO a
-- | 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 IOException instead of returning a
-- result. For a more general type of exception, including also those
-- that arise in pure code, see Exception.
--
-- In Haskell 2010, this is an opaque type.
type IOError = IOException
-- | Construct an IOException 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
-- | Evaluate each monadic action in the structure from left to right, and
-- ignore the results. For a version that doesn't ignore the results see
-- sequence.
--
-- sequence_ is just like sequenceA_, but specialised to
-- monadic actions.
sequence_ :: (Foldable t, Monad m) => t (m a) -> m ()
-- | 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.
--
-- Examples
--
-- Basic usage:
--
--
-- >>> or []
-- False
--
--
--
-- >>> or [True]
-- True
--
--
--
-- >>> or [False]
-- False
--
--
--
-- >>> or [True, True, False]
-- True
--
--
--
-- >>> or (True : repeat False) -- Infinite list [True,False,False,False,...
-- True
--
--
--
-- >>> or (repeat False)
-- * Hangs forever *
--
or :: Foldable t => t Bool -> Bool
-- | notElem is the negation of elem.
--
-- Examples
--
-- Basic usage:
--
--
-- >>> 3 `notElem` []
-- True
--
--
--
-- >>> 3 `notElem` [1,2]
-- True
--
--
--
-- >>> 3 `notElem` [1,2,3,4,5]
-- False
--
--
-- For infinite structures, notElem terminates if the value exists
-- at a finite distance from the left side of the structure:
--
--
-- >>> 3 `notElem` [1..]
-- False
--
--
--
-- >>> 3 `notElem` ([4..] ++ [3])
-- * Hangs forever *
--
notElem :: (Foldable t, Eq a) => a -> t a -> Bool
infix 4 `notElem`
-- | Map each element of a structure to a monadic action, evaluate these
-- actions from left to right, and ignore the results. For a version that
-- doesn't ignore the results see mapM.
--
-- mapM_ is just like traverse_, but specialised to monadic
-- actions.
mapM_ :: (Foldable t, Monad m) => (a -> m b) -> t a -> m ()
-- | Map a function over all the elements of a container and concatenate
-- the resulting lists.
--
-- Examples
--
-- Basic usage:
--
--
-- >>> concatMap (take 3) [[1..], [10..], [100..], [1000..]]
-- [1,2,3,10,11,12,100,101,102,1000,1001,1002]
--
--
--
-- >>> concatMap (take 3) (Just [1..])
-- [1,2,3]
--
concatMap :: Foldable t => (a -> [b]) -> t a -> [b]
-- | The concatenation of all the elements of a container of lists.
--
-- Examples
--
-- Basic usage:
--
--
-- >>> concat (Just [1, 2, 3])
-- [1,2,3]
--
--
--
-- >>> concat (Left 42)
-- []
--
--
--
-- >>> concat [[1, 2, 3], [4, 5], [6], []]
-- [1,2,3,4,5,6]
--
concat :: Foldable t => t [a] -> [a]
-- | Determines whether any element of the structure satisfies the
-- predicate.
--
-- Examples
--
-- Basic usage:
--
--
-- >>> any (> 3) []
-- False
--
--
--
-- >>> any (> 3) [1,2]
-- False
--
--
--
-- >>> any (> 3) [1,2,3,4,5]
-- True
--
--
--
-- >>> any (> 3) [1..]
-- True
--
--
--
-- >>> any (> 3) [0, -1..]
-- * Hangs forever *
--
any :: 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.
--
-- Examples
--
-- Basic usage:
--
--
-- >>> and []
-- True
--
--
--
-- >>> and [True]
-- True
--
--
--
-- >>> and [False]
-- False
--
--
--
-- >>> and [True, True, False]
-- False
--
--
--
-- >>> and (False : repeat True) -- Infinite list [False,True,True,True,...
-- False
--
--
--
-- >>> and (repeat True)
-- * Hangs forever *
--
and :: Foldable t => t Bool -> Bool
-- | Determines whether all elements of the structure satisfy the
-- predicate.
--
-- Examples
--
-- Basic usage:
--
--
-- >>> all (> 3) []
-- True
--
--
--
-- >>> all (> 3) [1,2]
-- False
--
--
--
-- >>> all (> 3) [1,2,3,4,5]
-- False
--
--
--
-- >>> all (> 3) [1..]
-- False
--
--
--
-- >>> all (> 3) [4..]
-- * Hangs forever *
--
all :: Foldable t => (a -> Bool) -> t a -> Bool
-- | words breaks a string up into a list of words, which were
-- delimited by white space.
--
--
-- >>> words "Lorem ipsum\ndolor"
-- ["Lorem","ipsum","dolor"]
--
words :: String -> [String]
-- | unwords is an inverse operation to words. It joins words
-- with separating spaces.
--
--
-- >>> unwords ["Lorem", "ipsum", "dolor"]
-- "Lorem ipsum dolor"
--
unwords :: [String] -> String
-- | unlines is an inverse operation to lines. It joins
-- lines, after appending a terminating newline to each.
--
--
-- >>> unlines ["Hello", "World", "!"]
-- "Hello\nWorld\n!\n"
--
unlines :: [String] -> String
-- | lines breaks a string up into a list of strings at newline
-- characters. The resulting strings do not contain newlines.
--
-- Note that after splitting the string at newline characters, the last
-- part of the string is considered a line even if it doesn't end with a
-- newline. For example,
--
--
-- >>> lines ""
-- []
--
--
--
-- >>> lines "\n"
-- [""]
--
--
--
-- >>> lines "one"
-- ["one"]
--
--
--
-- >>> lines "one\n"
-- ["one"]
--
--
--
-- >>> lines "one\n\n"
-- ["one",""]
--
--
--
-- >>> lines "one\ntwo"
-- ["one","two"]
--
--
--
-- >>> lines "one\ntwo\n"
-- ["one","two"]
--
--
-- Thus lines s contains at least as many elements as
-- newlines in s.
lines :: String -> [String]
-- | equivalent to readsPrec with a precedence of 0.
reads :: Read a => ReadS a
-- | 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.
--
-- Examples
--
-- We create two values of type Either String
-- Int, one using the Left constructor and another
-- using the Right constructor. Then we apply "either" the
-- length function (if we have a String) or the "times-two"
-- function (if we have an Int):
--
--
-- >>> let s = Left "foo" :: Either String Int
--
-- >>> let n = Right 3 :: Either String Int
--
-- >>> either length (*2) s
-- 3
--
-- >>> either length (*2) n
-- 6
--
either :: (a -> c) -> (b -> c) -> Either a b -> c
-- | 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
-- | 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)]
odd :: Integral a => a -> Bool
-- | lcm x y is the smallest positive integer that both
-- x and y divide.
lcm :: Integral a => a -> a -> a
-- | 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
even :: Integral a => a -> Bool
-- | raise a number to an integral power
(^^) :: (Fractional a, Integral b) => a -> b -> a
infixr 8 ^^
-- | raise a number to a non-negative integral power
(^) :: (Num a, Integral b) => a -> b -> a
infixr 8 ^
-- | 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
-- | equivalent to showsPrec with a precedence of 0.
shows :: Show a => a -> ShowS
-- | utility function converting a String to a show function that
-- simply prepends the string unchanged.
showString :: String -> 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 Char to a show function that
-- simply prepends the character unchanged.
showChar :: Char -> ShowS
-- | The zipWith3 function takes a function which combines three
-- elements, as well as three lists and returns a list of the function
-- applied to corresponding elements, analogous to zipWith. It is
-- capable of list fusion, but it is restricted to its first list
-- argument and its resulting list.
--
--
-- zipWith3 (,,) xs ys zs == zip3 xs ys zs
-- zipWith3 f [x1,x2,x3..] [y1,y2,y3..] [z1,z2,z3..] == [f x1 y1 z1, f x2 y2 z2, f x3 y3 z3..]
--
zipWith3 :: (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d]
-- | <math>. zipWith generalises zip by zipping with
-- the function given as the first argument, instead of a tupling
-- function.
--
--
-- zipWith (,) xs ys == zip xs ys
-- zipWith f [x1,x2,x3..] [y1,y2,y3..] == [f x1 y1, f x2 y2, f x3 y3..]
--
--
-- For example, zipWith (+) is applied to two lists to
-- produce the list of corresponding sums:
--
--
-- >>> zipWith (+) [1, 2, 3] [4, 5, 6]
-- [5,7,9]
--
--
-- zipWith is right-lazy:
--
--
-- >>> let f = undefined
--
-- >>> zipWith f [] undefined
-- []
--
--
-- zipWith is capable of list fusion, but it is restricted to its
-- first list argument and its resulting list.
zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
-- | zip3 takes three lists and returns a list of triples, analogous
-- to zip. It is capable of list fusion, but it is restricted to
-- its first list argument and its resulting list.
zip3 :: [a] -> [b] -> [c] -> [(a, b, c)]
-- | The unzip3 function takes a list of triples and returns three
-- lists, analogous to unzip.
--
--
-- >>> unzip3 []
-- ([],[],[])
--
-- >>> unzip3 [(1, 'a', True), (2, 'b', False)]
-- ([1,2],"ab",[True,False])
--
unzip3 :: [(a, b, c)] -> ([a], [b], [c])
-- | unzip transforms a list of pairs into a list of first
-- components and a list of second components.
--
--
-- >>> unzip []
-- ([],[])
--
-- >>> unzip [(1, 'a'), (2, 'b')]
-- ([1,2],"ab")
--
unzip :: [(a, b)] -> ([a], [b])
-- | 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]
-- | 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]
-- | 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])
-- | 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])
-- | <math>. scanr1 is a variant of scanr that has no
-- starting value argument.
--
--
-- >>> scanr1 (+) [1..4]
-- [10,9,7,4]
--
-- >>> scanr1 (+) []
-- []
--
-- >>> scanr1 (-) [1..4]
-- [-2,3,-1,4]
--
-- >>> scanr1 (&&) [True, False, True, True]
-- [False,False,True,True]
--
-- >>> scanr1 (||) [True, True, False, False]
-- [True,True,False,False]
--
-- >>> force $ scanr1 (+) [1..]
-- *** Exception: stack overflow
--
scanr1 :: (a -> a -> a) -> [a] -> [a]
-- | <math>. scanr is the right-to-left dual of scanl.
-- Note that the order of parameters on the accumulating function are
-- reversed compared to scanl. Also note that
--
--
-- head (scanr f z xs) == foldr f z xs.
--
--
--
-- >>> scanr (+) 0 [1..4]
-- [10,9,7,4,0]
--
-- >>> scanr (+) 42 []
-- [42]
--
-- >>> scanr (-) 100 [1..4]
-- [98,-97,99,-96,100]
--
-- >>> scanr (\nextChar reversedString -> nextChar : reversedString) "foo" ['a', 'b', 'c', 'd']
-- ["abcdfoo","bcdfoo","cdfoo","dfoo","foo"]
--
-- >>> force $ scanr (+) 0 [1..]
-- *** Exception: stack overflow
--
scanr :: (a -> b -> b) -> b -> [a] -> [b]
-- | <math>. scanl1 is a variant of scanl that has no
-- starting value argument:
--
--
-- scanl1 f [x1, x2, ...] == [x1, x1 `f` x2, ...]
--
--
--
-- >>> scanl1 (+) [1..4]
-- [1,3,6,10]
--
-- >>> scanl1 (+) []
-- []
--
-- >>> scanl1 (-) [1..4]
-- [1,-1,-4,-8]
--
-- >>> scanl1 (&&) [True, False, True, True]
-- [True,False,False,False]
--
-- >>> scanl1 (||) [False, False, True, True]
-- [False,False,True,True]
--
-- >>> scanl1 (+) [1..]
-- * Hangs forever *
--
scanl1 :: (a -> a -> a) -> [a] -> [a]
-- | <math>. scanl is similar to foldl, but returns a
-- list of successive reduced values from the left:
--
--
-- scanl f z [x1, x2, ...] == [z, z `f` x1, (z `f` x1) `f` x2, ...]
--
--
-- Note that
--
--
-- last (scanl f z xs) == foldl f z xs
--
--
--
-- >>> scanl (+) 0 [1..4]
-- [0,1,3,6,10]
--
-- >>> scanl (+) 42 []
-- [42]
--
-- >>> scanl (-) 100 [1..4]
-- [100,99,97,94,90]
--
-- >>> scanl (\reversedString nextChar -> nextChar : reversedString) "foo" ['a', 'b', 'c', 'd']
-- ["foo","afoo","bafoo","cbafoo","dcbafoo"]
--
-- >>> scanl (+) 0 [1..]
-- * Hangs forever *
--
scanl :: (b -> a -> b) -> b -> [a] -> [b]
-- | reverse xs returns the elements of xs in
-- reverse order. xs must be finite.
--
--
-- >>> reverse []
-- []
--
-- >>> reverse [42]
-- [42]
--
-- >>> reverse [2,5,7]
-- [7,5,2]
--
-- >>> reverse [1..]
-- * Hangs forever *
--
reverse :: [a] -> [a]
-- | 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 0 True
-- []
--
-- >>> replicate (-1) True
-- []
--
-- >>> replicate 4 True
-- [True,True,True,True]
--
replicate :: Int -> a -> [a]
-- | repeat x is an infinite list, with x the
-- value of every element.
--
--
-- >>> take 20 $ repeat 17
-- [17,17,17,17,17,17,17,17,17...
--
repeat :: a -> [a]
-- | <math>. lookup key assocs looks up a key in an
-- association list.
--
--
-- >>> lookup 2 []
-- Nothing
--
-- >>> lookup 2 [(1, "first")]
-- Nothing
--
-- >>> lookup 2 [(1, "first"), (2, "second"), (3, "third")]
-- Just "second"
--
lookup :: Eq a => a -> [(a, b)] -> Maybe b
-- | <math>. Extract the last element of a list, which must be finite
-- and non-empty.
--
--
-- >>> last [1, 2, 3]
-- 3
--
-- >>> last [1..]
-- * Hangs forever *
--
-- >>> last []
-- *** Exception: Prelude.last: empty list
--
last :: [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), ...]
--
--
-- Note that iterate is lazy, potentially leading to thunk
-- build-up if the consumer doesn't force each iterate. See
-- iterate' for a strict variant of this function.
--
--
-- >>> take 10 $ iterate not True
-- [True,False,True,False...
--
-- >>> take 10 $ iterate (+3) 42
-- [42,45,48,51,54,57,60,63...
--
iterate :: (a -> a) -> a -> [a]
-- | <math>. Return all the elements of a list except the last one.
-- The list must be non-empty.
--
--
-- >>> init [1, 2, 3]
-- [1,2]
--
-- >>> init [1]
-- []
--
-- >>> init []
-- *** Exception: Prelude.init: empty list
--
init :: [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]
-- | 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]
-- | cycle ties a finite list into a circular one, or equivalently,
-- the infinite repetition of the original list. It is the identity on
-- infinite lists.
--
--
-- >>> cycle []
-- *** Exception: Prelude.cycle: empty list
--
-- >>> take 20 $ cycle [42]
-- [42,42,42,42,42,42,42,42,42,42...
--
-- >>> take 20 $ cycle [2, 5, 7]
-- [2,5,7,2,5,7,2,5,7,2,5,7...
--
cycle :: [a] -> [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])
-- | 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', 'b', 'c'] !! 0
-- 'a'
--
-- >>> ['a', 'b', 'c'] !! 2
-- 'c'
--
-- >>> ['a', 'b', 'c'] !! 3
-- *** Exception: Prelude.!!: index too large
--
-- >>> ['a', 'b', 'c'] !! (-1)
-- *** Exception: Prelude.!!: negative index
--
(!!) :: [a] -> Int -> a
infixl 9 !!
-- | 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.
--
-- Examples
--
-- Basic usage:
--
--
-- >>> maybe False odd (Just 3)
-- True
--
--
--
-- >>> maybe False odd Nothing
-- False
--
--
-- Read an integer from a string using readMaybe. If we succeed,
-- return twice the integer; that is, apply (*2) to it. If
-- instead we fail to parse an integer, return 0 by default:
--
--
-- >>> import Text.Read ( readMaybe )
--
-- >>> maybe 0 (*2) (readMaybe "5")
-- 10
--
-- >>> maybe 0 (*2) (readMaybe "")
-- 0
--
--
-- Apply show to a Maybe Int. If we have Just n,
-- we want to show the underlying Int n. But if we have
-- Nothing, we return the empty string instead of (for example)
-- "Nothing":
--
--
-- >>> maybe "" show (Just 5)
-- "5"
--
-- >>> maybe "" show Nothing
-- ""
--
maybe :: b -> (a -> b) -> Maybe a -> b
-- | uncurry converts a curried function to a function on pairs.
--
-- Examples
--
--
-- >>> uncurry (+) (1,2)
-- 3
--
--
--
-- >>> uncurry ($) (show, 1)
-- "1"
--
--
--
-- >>> map (uncurry max) [(1,2), (3,4), (6,8)]
-- [2,4,8]
--
uncurry :: (a -> b -> c) -> (a, b) -> c
-- | curry converts an uncurried function to a curried function.
--
-- Examples
--
--
-- >>> curry fst 1 2
-- 1
--
curry :: ((a, b) -> c) -> a -> b -> c
-- | the same as flip (-).
--
-- Because - is treated specially in the Haskell grammar,
-- (- e) is not a section, but an application of
-- prefix negation. However, (subtract
-- exp) is equivalent to the disallowed section.
subtract :: Num a => a -> a -> a
-- | until p f yields the result of applying f
-- until p holds.
until :: (a -> Bool) -> (a -> a) -> a -> a
-- | flip f takes its (first) two arguments in the reverse
-- order of f.
--
--
-- >>> flip (++) "hello" "world"
-- "worldhello"
--
flip :: (a -> b -> c) -> b -> a -> c
-- | asTypeOf is a type-restricted version of const. It is
-- usually used as an infix operator, and its typing forces its first
-- argument (which is usually overloaded) to have the same type as the
-- second.
asTypeOf :: a -> a -> a
-- | Same as >>=, but with the arguments interchanged.
(=<<) :: Monad m => (a -> m b) -> m a -> m b
infixr 1 =<<
-- | Strict (call-by-value) application operator. It takes a function and
-- an argument, evaluates the argument to weak head normal form (WHNF),
-- then calls the function with that value.
($!) :: forall (r :: RuntimeRep) a (b :: TYPE r). (a -> b) -> a -> b
infixr 0 $!
-- | 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 :: forall (r :: RuntimeRep) (a :: TYPE r). HasCallStack => a
-- | A variant of error that does not produce a stack trace.
errorWithoutStackTrace :: forall (r :: RuntimeRep) (a :: TYPE r). [Char] -> a
-- | error stops execution and displays an error message.
error :: forall (r :: RuntimeRep) (a :: TYPE r). HasCallStack => [Char] -> a
-- | Boolean "and", lazy in the second argument
(&&) :: Bool -> Bool -> Bool
infixr 3 &&
-- | Boolean "not"
not :: Bool -> Bool
-- | Boolean "or", lazy in the second argument
(||) :: Bool -> Bool -> Bool
infixr 2 ||
-- | Evaluate a state computation with the given initial state and return
-- the final value, discarding the final state.
--
--
evalState :: State s a -> s -> a
-- | Evaluate a state computation with the given initial state and return
-- the final value, discarding the final state.
--
--
evalStateT :: Monad m => StateT s m a -> s -> m a
-- | Evaluate a state computation with the given initial state and return
-- the final state, discarding the final value.
--
--
execState :: State s a -> s -> s
-- | Evaluate a state computation with the given initial state and return
-- the final state, discarding the final value.
--
--
execStateT :: Monad m => StateT s m a -> s -> m s
-- | Map both the return value and final state of a computation using the
-- given function.
--
--
mapState :: ((a, s) -> (b, s)) -> State s a -> State s b
-- | Map both the return value and final state of a computation using the
-- given function.
--
--
mapStateT :: (m (a, s) -> n (b, s)) -> StateT s m a -> StateT s n b
-- | Unwrap a state monad computation as a function. (The inverse of
-- state.)
runState :: State s a -> s -> (a, s)
-- | withState f m executes action m on a state
-- modified by applying f.
--
--
withState :: (s -> s) -> State s a -> State s a
-- | withStateT f m executes action m on a state
-- modified by applying f.
--
--
withStateT :: forall s (m :: Type -> Type) a. (s -> s) -> StateT s m a -> StateT s m a
-- | A state monad parameterized by the type s of the state to
-- carry.
--
-- The return function leaves the state unchanged, while
-- >>= uses the final state of the first computation as
-- the initial state of the second.
type State s = StateT s Identity
-- | A state transformer monad parameterized by:
--
--
-- - s - The state.
-- - m - The inner monad.
--
--
-- The return function leaves the state unchanged, while
-- >>= uses the final state of the first computation as
-- the initial state of the second.
newtype StateT s (m :: Type -> Type) a
StateT :: (s -> m (a, s)) -> StateT s (m :: Type -> Type) a
[runStateT] :: StateT s (m :: Type -> Type) a -> s -> m (a, s)
-- | Construct a state monad computation from a function. (The inverse of
-- runState.)
state :: forall (m :: Type -> Type) s a. Monad m => (s -> (a, s)) -> StateT s m a
-- | put s sets the state within the monad to s.
put :: forall (m :: Type -> Type) s. Monad m => s -> StateT s m ()
-- | A variant of modify in which the computation is strict in the
-- new state.
--
--
modify' :: forall (m :: Type -> Type) s. Monad m => (s -> s) -> StateT s m ()
-- | Lift a pass operation to the new monad.
liftPass :: Monad m => Pass w m (a, s) -> Pass w (StateT s m) a
-- | Lift a listen operation to the new monad.
liftListen :: Monad m => Listen w m (a, s) -> Listen w (StateT s m) a
-- | Lift a catchE operation to the new monad.
liftCatch :: Catch e m (a, s) -> Catch e (StateT s m) a
-- | In-situ lifting of a callCC operation to the new monad. This
-- version uses the current state on entering the continuation. It does
-- not satisfy the uniformity property (see
-- Control.Monad.Signatures).
liftCallCC' :: CallCC m (a, s) (b, s) -> CallCC (StateT s m) a b
-- | Uniform lifting of a callCC operation to the new monad. This
-- version rolls back to the original state on entering the continuation.
liftCallCC :: CallCC m (a, s) (b, s) -> CallCC (StateT s m) a b
-- | Get a specific component of the state, using a projection function
-- supplied.
--
--
gets :: forall (m :: Type -> Type) s a. Monad m => (s -> a) -> StateT s m a
-- | Fetch the current value of the state within the monad.
get :: forall (m :: Type -> Type) s. Monad m => StateT s m s
-- | The Foldable class represents data structures that can be reduced to a
-- summary value one element at a time. Strict left-associative folds are
-- a good fit for space-efficient reduction, while lazy right-associative
-- folds are a good fit for corecursive iteration, or for folds that
-- short-circuit after processing an initial subsequence of the
-- structure's elements.
--
-- Instances can be derived automatically by enabling the
-- DeriveFoldable extension. For example, a derived instance for
-- a binary tree might be:
--
--
-- {-# LANGUAGE DeriveFoldable #-}
-- data Tree a = Empty
-- | Leaf a
-- | Node (Tree a) a (Tree a)
-- deriving Foldable
--
--
-- A more detailed description can be found in the Overview
-- section of Data.Foldable#overview.
--
-- For the class laws see the Laws section of
-- Data.Foldable#laws.
class Foldable (t :: TYPE LiftedRep -> Type)
-- | Given a structure with elements whose type is a Monoid, combine
-- them via the monoid's (<>) operator. This fold
-- is right-associative and lazy in the accumulator. When you need a
-- strict left-associative fold, use foldMap' instead, with
-- id as the map.
--
-- Examples
--
-- Basic usage:
--
--
-- >>> fold [[1, 2, 3], [4, 5], [6], []]
-- [1,2,3,4,5,6]
--
--
--
-- >>> fold $ Node (Leaf (Sum 1)) (Sum 3) (Leaf (Sum 5))
-- Sum {getSum = 9}
--
--
-- Folds of unbounded structures do not terminate when the monoid's
-- (<>) operator is strict:
--
--
-- >>> fold (repeat Nothing)
-- * Hangs forever *
--
--
-- Lazy corecursive folds of unbounded structures are fine:
--
--
-- >>> take 12 $ fold $ map (\i -> [i..i+2]) [0..]
-- [0,1,2,1,2,3,2,3,4,3,4,5]
--
-- >>> sum $ take 4000000 $ fold $ map (\i -> [i..i+2]) [0..]
-- 2666668666666
--
fold :: (Foldable t, Monoid m) => t m -> m
-- | Map each element of the structure into a monoid, and combine the
-- results with (<>). This fold is
-- right-associative and lazy in the accumulator. For strict
-- left-associative folds consider foldMap' instead.
--
-- Examples
--
-- Basic usage:
--
--
-- >>> foldMap Sum [1, 3, 5]
-- Sum {getSum = 9}
--
--
--
-- >>> foldMap Product [1, 3, 5]
-- Product {getProduct = 15}
--
--
--
-- >>> foldMap (replicate 3) [1, 2, 3]
-- [1,1,1,2,2,2,3,3,3]
--
--
-- When a Monoid's (<>) is lazy in its second
-- argument, foldMap can return a result even from an unbounded
-- structure. For example, lazy accumulation enables
-- Data.ByteString.Builder to efficiently serialise large data
-- structures and produce the output incrementally:
--
--
-- >>> import qualified Data.ByteString.Lazy as L
--
-- >>> import qualified Data.ByteString.Builder as B
--
-- >>> let bld :: Int -> B.Builder; bld i = B.intDec i <> B.word8 0x20
--
-- >>> let lbs = B.toLazyByteString $ foldMap bld [0..]
--
-- >>> L.take 64 lbs
-- "0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24"
--
foldMap :: (Foldable t, Monoid m) => (a -> m) -> t a -> m
-- | A left-associative variant of foldMap that is strict in the
-- accumulator. Use this method for strict reduction when partial results
-- are merged via (<>).
--
-- Examples
--
-- Define a Monoid over finite bit strings under xor. Use
-- it to strictly compute the xor of a list of Int
-- values.
--
--
-- >>> :set -XGeneralizedNewtypeDeriving
--
-- >>> import Data.Bits (Bits, FiniteBits, xor, zeroBits)
--
-- >>> import Data.Foldable (foldMap')
--
-- >>> import Numeric (showHex)
--
-- >>>
--
-- >>> newtype X a = X a deriving (Eq, Bounded, Enum, Bits, FiniteBits)
--
-- >>> instance Bits a => Semigroup (X a) where X a <> X b = X (a `xor` b)
--
-- >>> instance Bits a => Monoid (X a) where mempty = X zeroBits
--
-- >>>
--
-- >>> let bits :: [Int]; bits = [0xcafe, 0xfeed, 0xdeaf, 0xbeef, 0x5411]
--
-- >>> (\ (X a) -> showString "0x" . showHex a $ "") $ foldMap' X bits
-- "0x42"
--
foldMap' :: (Foldable t, Monoid m) => (a -> m) -> t a -> m
-- | Right-associative fold of a structure, lazy in the accumulator.
--
-- In the case of lists, foldr, when applied to a binary operator,
-- a starting value (typically the right-identity of the operator), and a
-- list, reduces the list using the binary operator, from right to left:
--
--
-- foldr f z [x1, x2, ..., xn] == x1 `f` (x2 `f` ... (xn `f` z)...)
--
--
-- Note that since the head of the resulting expression is produced by an
-- application of the operator to the first element of the list, given an
-- operator lazy in its right argument, foldr can produce a
-- terminating expression from an unbounded list.
--
-- For a general Foldable structure this should be semantically
-- identical to,
--
--
-- foldr f z = foldr f z . toList
--
--
-- Examples
--
-- Basic usage:
--
--
-- >>> foldr (||) False [False, True, False]
-- True
--
--
--
-- >>> foldr (||) False []
-- False
--
--
--
-- >>> foldr (\c acc -> acc ++ [c]) "foo" ['a', 'b', 'c', 'd']
-- "foodcba"
--
--
-- Infinite structures
--
-- ⚠️ Applying foldr to infinite structures usually doesn't
-- terminate.
--
-- It may still terminate under one of the following conditions:
--
--
-- - the folding function is short-circuiting
-- - the folding function is lazy on its second argument
--
--
-- Short-circuiting
--
-- (||) short-circuits on True values, so the
-- following terminates because there is a True value finitely far
-- from the left side:
--
--
-- >>> foldr (||) False (True : repeat False)
-- True
--
--
-- But the following doesn't terminate:
--
--
-- >>> foldr (||) False (repeat False ++ [True])
-- * Hangs forever *
--
--
-- Laziness in the second argument
--
-- Applying foldr to infinite structures terminates when the
-- operator is lazy in its second argument (the initial accumulator is
-- never used in this case, and so could be left undefined, but
-- [] is more clear):
--
--
-- >>> take 5 $ foldr (\i acc -> i : fmap (+3) acc) [] (repeat 1)
-- [1,4,7,10,13]
--
foldr :: Foldable t => (a -> b -> b) -> b -> t a -> b
-- | Left-associative fold of a structure but with strict application of
-- the operator.
--
-- This ensures that each step of the fold is forced to Weak Head Normal
-- Form before being applied, avoiding the collection of thunks that
-- would otherwise occur. This is often what you want to strictly reduce
-- a finite structure to a single strict result (e.g. sum).
--
-- For a general Foldable structure this should be semantically
-- identical to,
--
--
-- foldl' f z = foldl' f z . toList
--
foldl' :: Foldable t => (b -> a -> b) -> b -> t a -> b
-- | A variant of foldr that has no base case, and thus may only be
-- applied to non-empty structures.
--
-- This function is non-total and will raise a runtime exception if the
-- structure happens to be empty.
--
-- Examples
--
-- Basic usage:
--
--
-- >>> foldr1 (+) [1..4]
-- 10
--
--
--
-- >>> foldr1 (+) []
-- Exception: Prelude.foldr1: empty list
--
--
--
-- >>> foldr1 (+) Nothing
-- *** Exception: foldr1: empty structure
--
--
--
-- >>> foldr1 (-) [1..4]
-- -2
--
--
--
-- >>> foldr1 (&&) [True, False, True, True]
-- False
--
--
--
-- >>> foldr1 (||) [False, False, True, True]
-- True
--
--
--
-- >>> foldr1 (+) [1..]
-- * Hangs forever *
--
foldr1 :: Foldable t => (a -> a -> a) -> t a -> a
-- | A variant of foldl that has no base case, and thus may only be
-- applied to non-empty structures.
--
-- This function is non-total and will raise a runtime exception if the
-- structure happens to be empty.
--
--
-- foldl1 f = foldl1 f . toList
--
--
-- Examples
--
-- Basic usage:
--
--
-- >>> foldl1 (+) [1..4]
-- 10
--
--
--
-- >>> foldl1 (+) []
-- *** Exception: Prelude.foldl1: empty list
--
--
--
-- >>> foldl1 (+) Nothing
-- *** Exception: foldl1: empty structure
--
--
--
-- >>> foldl1 (-) [1..4]
-- -8
--
--
--
-- >>> foldl1 (&&) [True, False, True, True]
-- False
--
--
--
-- >>> foldl1 (||) [False, False, True, True]
-- True
--
--
--
-- >>> foldl1 (+) [1..]
-- * Hangs forever *
--
foldl1 :: Foldable t => (a -> a -> a) -> t a -> a
-- | List of elements of a structure, from left to right. If the entire
-- list is intended to be reduced via a fold, just fold the structure
-- directly bypassing the list.
--
-- Examples
--
-- Basic usage:
--
--
-- >>> toList Nothing
-- []
--
--
--
-- >>> toList (Just 42)
-- [42]
--
--
--
-- >>> toList (Left "foo")
-- []
--
--
--
-- >>> toList (Node (Leaf 5) 17 (Node Empty 12 (Leaf 8)))
-- [5,17,12,8]
--
--
-- For lists, toList is the identity:
--
--
-- >>> toList [1, 2, 3]
-- [1,2,3]
--
toList :: Foldable t => t a -> [a]
-- | Test whether the structure is empty. The default implementation is
-- Left-associative and lazy in both the initial element and the
-- accumulator. Thus optimised for structures where the first element can
-- be accessed in constant time. Structures where this is not the case
-- should have a non-default implementation.
--
-- Examples
--
-- Basic usage:
--
--
-- >>> null []
-- True
--
--
--
-- >>> null [1]
-- False
--
--
-- null is expected to terminate even for infinite structures. The
-- default implementation terminates provided the structure is bounded on
-- the left (there is a leftmost element).
--
--
-- >>> null [1..]
-- False
--
null :: Foldable t => t a -> Bool
-- | Returns the size/length of a finite structure as an Int. The
-- default implementation just counts elements starting with the
-- leftmost. Instances for structures that can compute the element count
-- faster than via element-by-element counting, should provide a
-- specialised implementation.
--
-- Examples
--
-- Basic usage:
--
--
-- >>> length []
-- 0
--
--
--
-- >>> length ['a', 'b', 'c']
-- 3
--
-- >>> length [1..]
-- * Hangs forever *
--
length :: Foldable t => t a -> Int
-- | Does the element occur in the structure?
--
-- Note: elem is often used in infix form.
--
-- Examples
--
-- Basic usage:
--
--
-- >>> 3 `elem` []
-- False
--
--
--
-- >>> 3 `elem` [1,2]
-- False
--
--
--
-- >>> 3 `elem` [1,2,3,4,5]
-- True
--
--
-- For infinite structures, the default implementation of elem
-- terminates if the sought-after value exists at a finite distance from
-- the left side of the structure:
--
--
-- >>> 3 `elem` [1..]
-- True
--
--
--
-- >>> 3 `elem` ([4..] ++ [3])
-- * Hangs forever *
--
elem :: (Foldable t, Eq a) => a -> t a -> Bool
-- | The largest element of a non-empty structure.
--
-- This function is non-total and will raise a runtime exception if the
-- structure happens to be empty. A structure that supports random access
-- and maintains its elements in order should provide a specialised
-- implementation to return the maximum in faster than linear time.
--
-- Examples
--
-- Basic usage:
--
--
-- >>> maximum [1..10]
-- 10
--
--
--
-- >>> maximum []
-- *** Exception: Prelude.maximum: empty list
--
--
--
-- >>> maximum Nothing
-- *** Exception: maximum: empty structure
--
--
-- WARNING: This function is partial for possibly-empty structures like
-- lists.
maximum :: (Foldable t, Ord a) => t a -> a
-- | The least element of a non-empty structure.
--
-- This function is non-total and will raise a runtime exception if the
-- structure happens to be empty. A structure that supports random access
-- and maintains its elements in order should provide a specialised
-- implementation to return the minimum in faster than linear time.
--
-- Examples
--
-- Basic usage:
--
--
-- >>> minimum [1..10]
-- 1
--
--
--
-- >>> minimum []
-- *** Exception: Prelude.minimum: empty list
--
--
--
-- >>> minimum Nothing
-- *** Exception: minimum: empty structure
--
--
-- WARNING: This function is partial for possibly-empty structures like
-- lists.
minimum :: (Foldable t, Ord a) => t a -> a
-- | The sum function computes the sum of the numbers of a
-- structure.
--
-- Examples
--
-- Basic usage:
--
--
-- >>> sum []
-- 0
--
--
--
-- >>> sum [42]
-- 42
--
--
--
-- >>> sum [1..10]
-- 55
--
--
--
-- >>> sum [4.1, 2.0, 1.7]
-- 7.8
--
--
--
-- >>> sum [1..]
-- * Hangs forever *
--
sum :: (Foldable t, Num a) => t a -> a
-- | The product function computes the product of the numbers of a
-- structure.
--
-- Examples
--
-- Basic usage:
--
--
-- >>> product []
-- 1
--
--
--
-- >>> product [42]
-- 42
--
--
--
-- >>> product [1..10]
-- 3628800
--
--
--
-- >>> product [4.1, 2.0, 1.7]
-- 13.939999999999998
--
--
--
-- >>> product [1..]
-- * Hangs forever *
--
product :: (Foldable t, Num a) => t a -> a
infix 4 `elem`
-- | Map each element of a structure to an Applicative action,
-- evaluate these actions from left to right, and ignore the results. For
-- a version that doesn't ignore the results see traverse.
--
-- traverse_ is just like mapM_, but generalised to
-- Applicative actions.
--
-- Examples
--
-- Basic usage:
--
--
-- >>> traverse_ print ["Hello", "world", "!"]
-- "Hello"
-- "world"
-- "!"
--
traverse_ :: (Foldable t, Applicative f) => (a -> f b) -> t a -> f ()
-- | Evaluate each monadic action in the structure from left to right, and
-- ignore the results. For a version that doesn't ignore the results see
-- sequence.
--
-- sequence_ is just like sequenceA_, but specialised to
-- monadic actions.
sequence_ :: (Foldable t, Monad m) => t (m a) -> m ()
-- | Evaluate each action in the structure from left to right, and ignore
-- the results. For a version that doesn't ignore the results see
-- sequenceA.
--
-- sequenceA_ is just like sequence_, but generalised to
-- Applicative actions.
--
-- Examples
--
-- Basic usage:
--
--
-- >>> sequenceA_ [print "Hello", print "world", print "!"]
-- "Hello"
-- "world"
-- "!"
--
sequenceA_ :: (Foldable t, Applicative f) => t (f a) -> f ()
-- | 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.
--
-- Examples
--
-- Basic usage:
--
--
-- >>> or []
-- False
--
--
--
-- >>> or [True]
-- True
--
--
--
-- >>> or [False]
-- False
--
--
--
-- >>> or [True, True, False]
-- True
--
--
--
-- >>> or (True : repeat False) -- Infinite list [True,False,False,False,...
-- True
--
--
--
-- >>> or (repeat False)
-- * Hangs forever *
--
or :: Foldable t => t Bool -> Bool
-- | notElem is the negation of elem.
--
-- Examples
--
-- Basic usage:
--
--
-- >>> 3 `notElem` []
-- True
--
--
--
-- >>> 3 `notElem` [1,2]
-- True
--
--
--
-- >>> 3 `notElem` [1,2,3,4,5]
-- False
--
--
-- For infinite structures, notElem terminates if the value exists
-- at a finite distance from the left side of the structure:
--
--
-- >>> 3 `notElem` [1..]
-- False
--
--
--
-- >>> 3 `notElem` ([4..] ++ [3])
-- * Hangs forever *
--
notElem :: (Foldable t, Eq a) => a -> t a -> Bool
infix 4 `notElem`
-- | The sum of a collection of actions, generalizing concat.
--
-- msum is just like asum, but specialised to
-- MonadPlus.
msum :: (Foldable t, MonadPlus m) => t (m a) -> m a
-- | The least element of a non-empty structure with respect to the given
-- comparison function.
--
-- Examples
--
-- Basic usage:
--
--
-- >>> minimumBy (compare `on` length) ["Hello", "World", "!", "Longest", "bar"]
-- "!"
--
--
-- WARNING: This function is partial for possibly-empty structures like
-- lists.
minimumBy :: Foldable t => (a -> a -> Ordering) -> t a -> a
-- | The largest element of a non-empty structure with respect to the given
-- comparison function.
--
-- Examples
--
-- Basic usage:
--
--
-- >>> maximumBy (compare `on` length) ["Hello", "World", "!", "Longest", "bar"]
-- "Longest"
--
--
-- WARNING: This function is partial for possibly-empty structures like
-- lists.
maximumBy :: Foldable t => (a -> a -> Ordering) -> t a -> a
-- | Map each element of a structure to a monadic action, evaluate these
-- actions from left to right, and ignore the results. For a version that
-- doesn't ignore the results see mapM.
--
-- mapM_ is just like traverse_, but specialised to monadic
-- actions.
mapM_ :: (Foldable t, Monad m) => (a -> m b) -> t a -> m ()
-- | for_ is traverse_ with its arguments flipped. For a
-- version that doesn't ignore the results see for. This is
-- forM_ generalised to Applicative actions.
--
-- for_ is just like forM_, but generalised to
-- Applicative actions.
--
-- Examples
--
-- Basic usage:
--
--
-- >>> for_ [1..4] print
-- 1
-- 2
-- 3
-- 4
--
for_ :: (Foldable t, Applicative f) => t a -> (a -> f b) -> f ()
-- | forM_ is mapM_ with its arguments flipped. For a version
-- that doesn't ignore the results see forM.
--
-- forM_ is just like for_, but specialised to monadic
-- actions.
forM_ :: (Foldable t, Monad m) => t a -> (a -> m b) -> m ()
-- | Right-to-left monadic fold over the elements of a structure.
--
-- Given a structure t with elements (a, b, c, ..., x,
-- y), the result of a fold with an operator function f is
-- equivalent to:
--
--
-- foldrM f z t = do
-- yy <- f y z
-- xx <- f x yy
-- ...
-- bb <- f b cc
-- aa <- f a bb
-- return aa -- Just @return z@ when the structure is empty
--
--
-- For a Monad m, given two functions f1 :: a -> m b
-- and f2 :: b -> m c, their Kleisli composition (f1
-- >=> f2) :: a -> m c is defined by:
--
--
-- (f1 >=> f2) a = f1 a >>= f2
--
--
-- Another way of thinking about foldrM is that it amounts to an
-- application to z of a Kleisli composition:
--
--
-- foldrM f z t = f y >=> f x >=> ... >=> f b >=> f a $ z
--
--
-- The monadic effects of foldrM are sequenced from right to
-- left, and e.g. folds of infinite lists will diverge.
--
-- If at some step the bind operator (>>=)
-- short-circuits (as with, e.g., mzero in a MonadPlus),
-- the evaluated effects will be from a tail of the element sequence. If
-- you want to evaluate the monadic effects in left-to-right order, or
-- perhaps be able to short-circuit after an initial sequence of
-- elements, you'll need to use foldlM instead.
--
-- If the monadic effects don't short-circuit, the outermost application
-- of f is to the leftmost element a, so that, ignoring
-- effects, the result looks like a right fold:
--
--
-- a `f` (b `f` (c `f` (... (x `f` (y `f` z))))).
--
--
-- Examples
--
-- Basic usage:
--
--
-- >>> let f i acc = do { print i ; return $ i : acc }
--
-- >>> foldrM f [] [0..3]
-- 3
-- 2
-- 1
-- 0
-- [0,1,2,3]
--
foldrM :: (Foldable t, Monad m) => (a -> b -> m b) -> b -> t a -> m b
-- | Left-to-right monadic fold over the elements of a structure.
--
-- Given a structure t with elements (a, b, ..., w, x,
-- y), the result of a fold with an operator function f is
-- equivalent to:
--
--
-- foldlM f z t = do
-- aa <- f z a
-- bb <- f aa b
-- ...
-- xx <- f ww x
-- yy <- f xx y
-- return yy -- Just @return z@ when the structure is empty
--
--
-- For a Monad m, given two functions f1 :: a -> m b
-- and f2 :: b -> m c, their Kleisli composition (f1
-- >=> f2) :: a -> m c is defined by:
--
--
-- (f1 >=> f2) a = f1 a >>= f2
--
--
-- Another way of thinking about foldlM is that it amounts to an
-- application to z of a Kleisli composition:
--
--
-- foldlM f z t =
-- flip f a >=> flip f b >=> ... >=> flip f x >=> flip f y $ z
--
--
-- The monadic effects of foldlM are sequenced from left to
-- right.
--
-- If at some step the bind operator (>>=)
-- short-circuits (as with, e.g., mzero in a MonadPlus),
-- the evaluated effects will be from an initial segment of the element
-- sequence. If you want to evaluate the monadic effects in right-to-left
-- order, or perhaps be able to short-circuit after processing a tail of
-- the sequence of elements, you'll need to use foldrM instead.
--
-- If the monadic effects don't short-circuit, the outermost application
-- of f is to the rightmost element y, so that,
-- ignoring effects, the result looks like a left fold:
--
--
-- ((((z `f` a) `f` b) ... `f` w) `f` x) `f` y
--
--
-- Examples
--
-- Basic usage:
--
--
-- >>> let f a e = do { print e ; return $ e : a }
--
-- >>> foldlM f [] [0..3]
-- 0
-- 1
-- 2
-- 3
-- [3,2,1,0]
--
foldlM :: (Foldable t, Monad m) => (b -> a -> m b) -> b -> t a -> m b
-- | 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.
--
-- Examples
--
-- Basic usage:
--
--
-- >>> find (> 42) [0, 5..]
-- Just 45
--
--
--
-- >>> find (> 12) [1..7]
-- Nothing
--
find :: Foldable t => (a -> Bool) -> t a -> Maybe a
-- | Map a function over all the elements of a container and concatenate
-- the resulting lists.
--
-- Examples
--
-- Basic usage:
--
--
-- >>> concatMap (take 3) [[1..], [10..], [100..], [1000..]]
-- [1,2,3,10,11,12,100,101,102,1000,1001,1002]
--
--
--
-- >>> concatMap (take 3) (Just [1..])
-- [1,2,3]
--
concatMap :: Foldable t => (a -> [b]) -> t a -> [b]
-- | The concatenation of all the elements of a container of lists.
--
-- Examples
--
-- Basic usage:
--
--
-- >>> concat (Just [1, 2, 3])
-- [1,2,3]
--
--
--
-- >>> concat (Left 42)
-- []
--
--
--
-- >>> concat [[1, 2, 3], [4, 5], [6], []]
-- [1,2,3,4,5,6]
--
concat :: Foldable t => t [a] -> [a]
-- | The sum of a collection of actions, generalizing concat.
--
-- asum is just like msum, but generalised to
-- Alternative.
--
-- Examples
--
-- Basic usage:
--
--
-- >>> asum [Just "Hello", Nothing, Just "World"]
-- Just "Hello"
--
asum :: (Foldable t, Alternative f) => t (f a) -> f a
-- | Determines whether any element of the structure satisfies the
-- predicate.
--
-- Examples
--
-- Basic usage:
--
--
-- >>> any (> 3) []
-- False
--
--
--
-- >>> any (> 3) [1,2]
-- False
--
--
--
-- >>> any (> 3) [1,2,3,4,5]
-- True
--
--
--
-- >>> any (> 3) [1..]
-- True
--
--
--
-- >>> any (> 3) [0, -1..]
-- * Hangs forever *
--
any :: 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.
--
-- Examples
--
-- Basic usage:
--
--
-- >>> and []
-- True
--
--
--
-- >>> and [True]
-- True
--
--
--
-- >>> and [False]
-- False
--
--
--
-- >>> and [True, True, False]
-- False
--
--
--
-- >>> and (False : repeat True) -- Infinite list [False,True,True,True,...
-- False
--
--
--
-- >>> and (repeat True)
-- * Hangs forever *
--
and :: Foldable t => t Bool -> Bool
-- | Determines whether all elements of the structure satisfy the
-- predicate.
--
-- Examples
--
-- Basic usage:
--
--
-- >>> all (> 3) []
-- True
--
--
--
-- >>> all (> 3) [1,2]
-- False
--
--
--
-- >>> all (> 3) [1,2,3,4,5]
-- False
--
--
--
-- >>> all (> 3) [1..]
-- False
--
--
--
-- >>> all (> 3) [4..]
-- * Hangs forever *
--
all :: Foldable t => (a -> Bool) -> t a -> Bool
-- | const x is a unary function which evaluates to x for
-- all inputs.
--
--
-- >>> const 42 "hello"
-- 42
--
--
--
-- >>> map (const 42) [0..3]
-- [42,42,42,42]
--
const :: a -> b -> a
-- | Function composition.
(.) :: (b -> c) -> (a -> b) -> a -> c
infixr 9 .
-- | Identity function.
--
--
-- id x = x
--
id :: a -> a
-- | on b u x y runs the binary function b
-- on the results of applying unary function u to two
-- arguments x and y. From the opposite perspective, it
-- transforms two inputs and combines the outputs.
--
--
-- ((+) `on` f) x y = f x + f y
--
--
-- Typical usage: sortBy (compare `on`
-- fst).
--
-- Algebraic properties:
--
--
-- (*) `on` id = (*) -- (if (*) ∉ {⊥, const
-- ⊥})((*) `on` f) `on` g = (*) `on` (f . g)
flip on f . flip on g = flip on (g .
-- f)
on :: (b -> b -> c) -> (a -> b) -> a -> a -> c
infixl 0 `on`
-- | fix f is the least fixed point of the function
-- f, i.e. the least defined x such that f x =
-- x.
--
-- For example, we can write the factorial function using direct
-- recursion as
--
--
-- >>> let fac n = if n <= 1 then 1 else n * fac (n-1) in fac 5
-- 120
--
--
-- This uses the fact that Haskell’s let introduces recursive
-- bindings. We can rewrite this definition using fix,
--
--
-- >>> fix (\rec n -> if n <= 1 then 1 else n * rec (n-1)) 5
-- 120
--
--
-- Instead of making a recursive call, we introduce a dummy parameter
-- rec; when used within fix, this parameter then refers
-- to fix’s argument, hence the recursion is reintroduced.
fix :: (a -> a) -> a
-- | & 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 $.
--
--
-- >>> 5 & (+1) & show
-- "6"
--
(&) :: a -> (a -> b) -> b
infixl 1 &
-- | flip f takes its (first) two arguments in the reverse
-- order of f.
--
--
-- >>> flip (++) "hello" "world"
-- "worldhello"
--
flip :: (a -> b -> c) -> b -> a -> c
-- | The Ix class is used to map a contiguous subrange of values in
-- a type onto integers. It is used primarily for array indexing (see the
-- array package).
--
-- The first argument (l,u) of each of these operations is a
-- pair specifying the lower and upper bounds of a contiguous subrange of
-- values.
--
-- An implementation is entitled to assume the following laws about these
-- operations:
--
--
-- - inRange (l,u) i == elem i (range
-- (l,u))
-- - range (l,u) !! index (l,u) i == i,
-- when inRange (l,u) i
-- - map (index (l,u)) (range (l,u))) ==
-- [0..rangeSize (l,u)-1]
-- - rangeSize (l,u) == length (range
-- (l,u))
--
class Ord a => Ix a
-- | The kind of types with lifted values. For example Int ::
-- Type.
type Type = TYPE LiftedRep
-- | Non-empty (and non-strict) list type.
data NonEmpty a
(:|) :: a -> [a] -> NonEmpty a
infixr 5 :|
-- | The Down type allows you to reverse sort order conveniently. A
-- value of type Down a contains a value of type
-- a (represented as Down a).
--
-- If a has an Ord instance associated with it
-- then comparing two values thus wrapped will give you the opposite of
-- their normal sort order. This is particularly useful when sorting in
-- generalised list comprehensions, as in: then sortWith by
-- Down x.
--
--
-- >>> compare True False
-- GT
--
--
--
-- >>> compare (Down True) (Down False)
-- LT
--
--
-- If a has a Bounded instance then the wrapped
-- instance also respects the reversed ordering by exchanging the values
-- of minBound and maxBound.
--
--
-- >>> minBound :: Int
-- -9223372036854775808
--
--
--
-- >>> minBound :: Down Int
-- Down 9223372036854775807
--
--
-- All other instances of Down a behave as they do for
-- a.
newtype Down a
Down :: a -> Down a
[getDown] :: Down a -> a
-- | Proxy is a type that holds no data, but has a phantom parameter
-- of arbitrary type (or even kind). Its use is to provide type
-- information, even though there is no value available of that type (or
-- it may be too costly to create one).
--
-- Historically, Proxy :: Proxy a is a safer
-- alternative to the undefined :: a idiom.
--
--
-- >>> Proxy :: Proxy (Void, Int -> Int)
-- Proxy
--
--
-- Proxy can even hold types of higher kinds,
--
--
-- >>> Proxy :: Proxy Either
-- Proxy
--
--
--
-- >>> Proxy :: Proxy Functor
-- Proxy
--
--
--
-- >>> Proxy :: Proxy complicatedStructure
-- Proxy
--
data Proxy (t :: k)
Proxy :: Proxy (t :: k)
-- | The class Typeable allows a concrete representation of a type
-- to be calculated.
class Typeable (a :: k)
-- | A Word is an unsigned integral type, with the same size as
-- Int.
data Word
-- | 8-bit unsigned integer type
data Word8
module Language.Lexer.Tlex.Machine.State
data StateNum
initialStateNum :: StateNum
data StateSet
emptySet :: StateSet
singletonSet :: StateNum -> StateSet
listToSet :: [StateNum] -> StateSet
setToList :: StateSet -> [StateNum]
nullSet :: StateSet -> Bool
insertSet :: StateNum -> StateSet -> StateSet
intersectSet :: StateSet -> StateSet -> StateSet
diffSet :: StateSet -> StateSet -> StateSet
unionSet :: StateSet -> StateSet -> StateSet
lengthSet :: StateSet -> Int
memberSet :: StateNum -> StateSet -> Bool
data StateMap a
emptyMap :: StateMap a
insertOrUpdateMap :: StateNum -> a -> (a -> a) -> StateMap a -> StateMap a
insertMap :: StateNum -> a -> StateMap a -> StateMap a
lookupMap :: StateNum -> StateMap a -> Maybe a
assocsMap :: StateMap a -> [(StateNum, a)]
data StateArray a
totalStateMapToArray :: StateNum -> StateMap a -> StateArray a
mapArrayWithIx :: (StateNum -> a -> a) -> StateArray a -> StateArray a
indexArray :: StateArray a -> StateNum -> a
arrayAssocs :: StateArray a -> [(StateNum, a)]
data StateGraph
stateArrayToGraph :: StateArray [StateNum] -> StateGraph
liftGraphOp :: (Graph -> Graph) -> StateGraph -> StateGraph
indexGraph :: StateGraph -> StateNum -> [StateNum]
instance GHC.Enum.Enum Language.Lexer.Tlex.Machine.State.StateNum
instance Data.Hashable.Class.Hashable Language.Lexer.Tlex.Machine.State.StateNum
instance GHC.Ix.Ix Language.Lexer.Tlex.Machine.State.StateNum
instance GHC.Show.Show Language.Lexer.Tlex.Machine.State.StateNum
instance GHC.Classes.Ord Language.Lexer.Tlex.Machine.State.StateNum
instance GHC.Classes.Eq Language.Lexer.Tlex.Machine.State.StateNum
instance GHC.Show.Show Language.Lexer.Tlex.Machine.State.StateSet
instance GHC.Classes.Eq Language.Lexer.Tlex.Machine.State.StateSet
instance GHC.Base.Functor Language.Lexer.Tlex.Machine.State.StateMap
instance GHC.Show.Show a => GHC.Show.Show (Language.Lexer.Tlex.Machine.State.StateMap a)
instance GHC.Classes.Eq a => GHC.Classes.Eq (Language.Lexer.Tlex.Machine.State.StateMap a)
instance Data.Foldable.Foldable Language.Lexer.Tlex.Machine.State.StateArray
instance GHC.Base.Functor Language.Lexer.Tlex.Machine.State.StateArray
instance GHC.Show.Show a => GHC.Show.Show (Language.Lexer.Tlex.Machine.State.StateArray a)
instance GHC.Classes.Eq a => GHC.Classes.Eq (Language.Lexer.Tlex.Machine.State.StateArray a)
instance Data.Hashable.Class.Hashable Language.Lexer.Tlex.Machine.State.StateSet
module Language.Lexer.Tlex.Machine.Pattern
data Pattern e
Epsilon :: Pattern e
(:^:) :: Pattern e -> Pattern e -> Pattern e
(:|:) :: Pattern e -> Pattern e -> Pattern e
Many :: Pattern e -> Pattern e
Range :: SymEnumSet e -> Pattern e
enumsP :: Enum e => [e] -> Pattern e
straightEnumSetP :: Enum e => EnumSet e -> Pattern e
anyoneP :: Enum e => Pattern e
newtype AcceptPriority
AcceptPriority :: Int -> AcceptPriority
mostPriority :: AcceptPriority
data Accept a
Accept :: AcceptPriority -> a -> Accept a
[$sel:accPriority:Accept] :: Accept a -> AcceptPriority
[$sel:accSemanticAction:Accept] :: Accept a -> a
compareAcceptsByPriority :: Accept a -> Accept a -> Ordering
newtype StartState
StartState :: Int -> StartState
startStateFromEnum :: Enum s => s -> StartState
instance GHC.Enum.Enum Language.Lexer.Tlex.Machine.Pattern.StartState
instance GHC.Show.Show Language.Lexer.Tlex.Machine.Pattern.StartState
instance GHC.Classes.Eq Language.Lexer.Tlex.Machine.Pattern.StartState
instance GHC.Enum.Enum Language.Lexer.Tlex.Machine.Pattern.AcceptPriority
instance Data.Hashable.Class.Hashable Language.Lexer.Tlex.Machine.Pattern.AcceptPriority
instance GHC.Classes.Ord Language.Lexer.Tlex.Machine.Pattern.AcceptPriority
instance GHC.Show.Show Language.Lexer.Tlex.Machine.Pattern.AcceptPriority
instance GHC.Classes.Eq Language.Lexer.Tlex.Machine.Pattern.AcceptPriority
instance GHC.Base.Functor Language.Lexer.Tlex.Machine.Pattern.Accept
instance GHC.Show.Show a => GHC.Show.Show (Language.Lexer.Tlex.Machine.Pattern.Accept a)
instance GHC.Classes.Eq a => GHC.Classes.Eq (Language.Lexer.Tlex.Machine.Pattern.Accept a)
instance (GHC.Enum.Enum e, GHC.Show.Show e) => GHC.Show.Show (Language.Lexer.Tlex.Machine.Pattern.Pattern e)
instance GHC.Classes.Eq (Language.Lexer.Tlex.Machine.Pattern.Pattern e)
instance GHC.Enum.Enum e => GHC.Base.Semigroup (Language.Lexer.Tlex.Machine.Pattern.Pattern e)
instance GHC.Enum.Enum e => GHC.Base.Monoid (Language.Lexer.Tlex.Machine.Pattern.Pattern e)
module Language.Lexer.Tlex.Machine.NFA
data NFA a
NFA :: [(StateNum, StartState)] -> StateArray (NFAState a) -> NFA a
[$sel:nfaInitials:NFA] :: NFA a -> [(StateNum, StartState)]
[$sel:nfaTrans:NFA] :: NFA a -> StateArray (NFAState a)
data NFAState a
NState :: [Accept a] -> [StateNum] -> [NFAStateTrans] -> NFAState a
[$sel:nstAccepts:NState] :: NFAState a -> [Accept a]
[$sel:nstEpsilonTrans:NState] :: NFAState a -> [StateNum]
[$sel:nstTrans:NState] :: NFAState a -> [NFAStateTrans]
data NFAStateTrans
NFAStateTrans :: Bool -> IntSet -> StateNum -> NFAStateTrans
[$sel:nstTransIsStraight:NFAStateTrans] :: NFAStateTrans -> Bool
[$sel:nstTransRange:NFAStateTrans] :: NFAStateTrans -> IntSet
[$sel:nstTransNextState:NFAStateTrans] :: NFAStateTrans -> StateNum
type NFABuilder m = State (NFABuilderContext m)
data NFABuilderContext m
buildNFA :: NFABuilder m () -> NFA m
epsilonClosed :: NFA a -> NFA a
newStateNum :: NFABuilder m StateNum
epsilonTrans :: StateNum -> StateNum -> NFABuilder m ()
condTrans :: StateNum -> NFAStateTrans -> NFABuilder m ()
accept :: StateNum -> Accept m -> NFABuilder m ()
initial :: StateNum -> StartState -> NFABuilder m ()
instance GHC.Show.Show Language.Lexer.Tlex.Machine.NFA.NFAStateTrans
instance GHC.Classes.Eq Language.Lexer.Tlex.Machine.NFA.NFAStateTrans
instance GHC.Base.Functor Language.Lexer.Tlex.Machine.NFA.NFAState
instance GHC.Show.Show a => GHC.Show.Show (Language.Lexer.Tlex.Machine.NFA.NFAState a)
instance GHC.Classes.Eq a => GHC.Classes.Eq (Language.Lexer.Tlex.Machine.NFA.NFAState a)
instance GHC.Base.Functor Language.Lexer.Tlex.Machine.NFA.NFA
instance GHC.Show.Show a => GHC.Show.Show (Language.Lexer.Tlex.Machine.NFA.NFA a)
instance GHC.Classes.Eq a => GHC.Classes.Eq (Language.Lexer.Tlex.Machine.NFA.NFA a)
module Language.Lexer.Tlex.Pipeline.Pattern2Nfa
pattern2Nfa :: Enum e => StateNum -> StateNum -> Pattern e -> NFABuilder m ()
module Language.Lexer.Tlex.Machine.DFA
data DFA a
DFA :: EnumMap StartState StateNum -> StateArray (DFAState a) -> DFA a
[$sel:dfaInitials:DFA] :: DFA a -> EnumMap StartState StateNum
[$sel:dfaTrans:DFA] :: DFA a -> StateArray (DFAState a)
data DFAState a
DState :: [Accept a] -> IntMap StateNum -> Maybe StateNum -> DFAState a
[$sel:dstAccepts:DState] :: DFAState a -> [Accept a]
[$sel:dstTrans:DState] :: DFAState a -> IntMap StateNum
[$sel:dstOtherTrans:DState] :: DFAState a -> Maybe StateNum
type DFABuilder m = State (DFABuilderContext m)
data DFABuilderContext m
buildDFA :: DFABuilder m () -> DFA m
newStateNum :: DFABuilder m StateNum
insertTrans :: StateNum -> DFAState m -> DFABuilder m ()
accept :: StateNum -> Accept m -> DFABuilder m ()
initial :: StateNum -> StartState -> DFABuilder m ()
instance GHC.Base.Functor Language.Lexer.Tlex.Machine.DFA.DFAState
instance GHC.Show.Show a => GHC.Show.Show (Language.Lexer.Tlex.Machine.DFA.DFAState a)
instance GHC.Classes.Eq a => GHC.Classes.Eq (Language.Lexer.Tlex.Machine.DFA.DFAState a)
instance GHC.Base.Functor Language.Lexer.Tlex.Machine.DFA.DFA
instance GHC.Show.Show a => GHC.Show.Show (Language.Lexer.Tlex.Machine.DFA.DFA a)
instance GHC.Classes.Eq a => GHC.Classes.Eq (Language.Lexer.Tlex.Machine.DFA.DFA a)
instance GHC.Base.Functor Language.Lexer.Tlex.Machine.DFA.DFABuilderContext
instance GHC.Show.Show m => GHC.Show.Show (Language.Lexer.Tlex.Machine.DFA.DFABuilderContext m)
instance GHC.Classes.Eq m => GHC.Classes.Eq (Language.Lexer.Tlex.Machine.DFA.DFABuilderContext m)
module Language.Lexer.Tlex.Pipeline.Nfa2Dfa
nfa2Dfa :: NFA a -> DFA a
module Language.Lexer.Tlex.Pipeline.MinDfa
minDfa :: DFA a -> DFA a
instance GHC.Base.Functor Language.Lexer.Tlex.Pipeline.MinDfa.MinDfaContext
instance GHC.Show.Show m => GHC.Show.Show (Language.Lexer.Tlex.Pipeline.MinDfa.MinDfaContext m)
instance GHC.Classes.Eq m => GHC.Classes.Eq (Language.Lexer.Tlex.Pipeline.MinDfa.MinDfaContext m)
instance GHC.Base.Functor Language.Lexer.Tlex.Pipeline.MinDfa.DFAStateBuilderContext
instance GHC.Show.Show a => GHC.Show.Show (Language.Lexer.Tlex.Pipeline.MinDfa.DFAStateBuilderContext a)
instance GHC.Classes.Eq a => GHC.Classes.Eq (Language.Lexer.Tlex.Pipeline.MinDfa.DFAStateBuilderContext a)
instance GHC.Show.Show Language.Lexer.Tlex.Pipeline.MinDfa.Partition
instance GHC.Classes.Eq Language.Lexer.Tlex.Pipeline.MinDfa.Partition
module Language.Lexer.Tlex.Data.Bag
data Bag a
fromList :: [a] -> Bag a
singleton :: a -> Bag a
instance GHC.Base.Functor Language.Lexer.Tlex.Data.Bag.Bag
instance GHC.Show.Show a => GHC.Show.Show (Language.Lexer.Tlex.Data.Bag.Bag a)
instance Data.Foldable.Foldable Language.Lexer.Tlex.Data.Bag.Bag
instance GHC.Classes.Eq a => GHC.Classes.Eq (Language.Lexer.Tlex.Data.Bag.Bag a)
instance GHC.Base.Semigroup (Language.Lexer.Tlex.Data.Bag.Bag a)
instance GHC.Base.Monoid (Language.Lexer.Tlex.Data.Bag.Bag a)