-- Hoogle documentation, generated by Haddock -- See Hoogle, http://www.haskell.org/hoogle/ -- | Deterministic serialisation and signatures with proto-lens support -- -- You can find documentation at hackage @package signable @version 0.4 module Data.Signable.Util safeFromIntegral :: forall a b. (Integral a, Integral b, Bounded b) => a -> Maybe b liftEither :: (MonadFail m, Show a) => Either a b -> m b ifThenElse :: (a -> Bool) -> (a -> b) -> (a -> b) -> a -> b module Data.Signable.Import -- | 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 :: () => a -> b -> b -- | filter, applied to a predicate and a list, returns the list of -- those elements that satisfy the predicate; i.e., -- -- 
--   filter p xs = [ x | x <- xs, p x]
--
filter :: () => (a -> Bool) -> [a] -> [a] -- | 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 short, excess elements of the longer list are -- discarded: -- -- 
--   zip [1] ['a', 'b'] = [(1, 'a')]
--   zip [1, 2] ['a'] = [(1, 'a')]
--
-- -- zip is right-lazy: -- -- 
--   zip [] _|_ = []
--   zip _|_ [] = _|_
--
zip :: () => [a] -> [b] -> [(a, b)] -- | 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 -- | Application operator. This operator is redundant, since ordinary -- application (f x) means the same as (f $ x). -- However, $ has low, right-associative binding precedence, so it -- sometimes allows parentheses to be omitted; for example: -- -- 
--   f $ g $ h x  =  f (g (h x))
--
-- -- It is also useful in higher-order situations, such as map -- ($ 0) xs, or zipWith ($) fs xs. -- -- Note that ($) is levity-polymorphic in its result type, so -- that foo $ True where foo :: Bool -> Int# is well-typed ($) :: () => (a -> b) -> a -> b infixr 0 $ -- | The function coerce allows you to safely convert between -- values of types that have the same representation with no run-time -- overhead. In the simplest case you can use it instead of a newtype -- constructor, to go from the newtype's concrete type to the abstract -- type. But it also works in more complicated settings, e.g. converting -- a list of newtypes to a list of concrete types. coerce :: Coercible 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 -- | Conditional failure of Alternative computations. Defined by -- -- 
--   guard True  = pure ()
--   guard False = empty
--
-- --

Examples

-- -- Common uses of guard include conditionally signaling an error -- in an error monad and conditionally rejecting the current choice in an -- Alternative-based parser. -- -- As an example of signaling an error in the error monad Maybe, -- consider a safe division function safeDiv x y that returns -- Nothing when the denominator y is zero and -- Just (x `div` y) otherwise. For example: -- -- 
--   >>> safeDiv 4 0
--   Nothing
--   >>> safeDiv 4 2
--   Just 2
--
-- -- A definition of safeDiv using guards, but not guard: -- -- 
--   safeDiv :: Int -> Int -> Maybe Int
--   safeDiv x y | y /= 0    = Just (x `div` y)
--               | otherwise = Nothing
--
-- -- A definition of safeDiv using guard and Monad -- do-notation: -- -- 
--   safeDiv :: Int -> Int -> Maybe Int
--   safeDiv x y = do
--     guard (y /= 0)
--     return (x `div` y)
--
guard :: Alternative f => Bool -> f () -- | The join function is the conventional monad join operator. It -- is used to remove one level of monadic structure, projecting its bound -- argument into the outer level. -- --

Examples

-- -- A common use of join is to run an IO computation -- returned from an STM transaction, since STM transactions -- can't perform IO directly. Recall that -- -- 
--   atomically :: STM a -> IO a
--
-- -- is used to run STM transactions atomically. So, by specializing -- the types of atomically and join to -- -- 
--   atomically :: STM (IO b) -> IO (IO b)
--   join       :: IO (IO b)  -> IO b
--
-- -- we can compose them as -- -- 
--   join . atomically :: STM (IO b) -> IO b
--
-- -- to run an STM transaction and the IO action it returns. join :: Monad m => m (m a) -> m a -- | The Bounded class is used to name the upper and lower limits of -- a type. Ord is not a superclass of Bounded since types -- that are not totally ordered may also have upper and lower bounds. -- -- The Bounded class may be derived for any enumeration type; -- minBound is the first constructor listed in the data -- declaration and maxBound is the last. Bounded may also -- be derived for single-constructor datatypes whose constituent types -- are in Bounded. class Bounded a minBound :: Bounded a => a maxBound :: Bounded a => a -- | Class Enum defines operations on sequentially ordered types. -- -- The enumFrom... methods are used in Haskell's translation of -- arithmetic sequences. -- -- Instances of Enum may be derived for any enumeration type -- (types whose constructors have no fields). The nullary constructors -- are assumed to be numbered left-to-right by fromEnum from -- 0 through n-1. See Chapter 10 of the Haskell -- Report for more details. -- -- For any type that is an instance of class Bounded as well as -- Enum, the following should hold: -- -- -- -- 
--   enumFrom     x   = enumFromTo     x maxBound
--   enumFromThen x y = enumFromThenTo x y bound
--     where
--       bound | fromEnum y >= fromEnum x = maxBound
--             | otherwise                = minBound
--
class Enum a -- | 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 :: 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 :: 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 :: 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 :: 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, == -- is customarily expected to implement an equivalence relationship where -- two values comparing equal are indistinguishable by "public" -- functions, with a "public" function being one not allowing to see -- implementation details. For example, for a type representing -- non-normalised natural numbers modulo 100, a "public" function doesn't -- make the difference between 1 and 201. It is expected to have the -- following properties: -- -- -- -- 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: -- -- class Fractional a => Floating a pi :: Floating a => a exp :: 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: -- -- -- -- 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: -- -- -- -- 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 `quot` infixl 7 `rem` infixl 7 `div` infixl 7 `mod` -- | 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 laws: -- -- -- -- 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. (>>=) :: 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. (>>) :: 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 >> -- | The Functor class is used for types that can be mapped over. -- Instances of Functor should satisfy the following laws: -- -- 
--   fmap id  ==  id
--   fmap (f . g)  ==  fmap f . fmap g
--
-- -- The instances of Functor for lists, Maybe and IO -- satisfy these laws. class Functor (f :: Type -> Type) 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: -- -- -- -- 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 6 + infixl 7 * 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. -- -- The Haskell Report defines no laws for Ord. However, -- <= is customarily expected to implement a non-strict partial -- order and have the following properties: -- -- -- -- Note that the following operator interactions are expected to hold: -- --
    --
  1. x >= y = y <= x
    2. --
  2. x < y = x <= y && x /= y
    3. --
  3. x > y = y < x
    4. --
  4. x < y = compare x y == LT
    5. --
  5. x > y = compare x y == GT
    6. --
  6. x == y = compare x y == EQ
    7. --
  7. min x y == if x <= y then x else y = True
    8. --
  8. max x y == if x >= y then x else y = True
    9. --
-- -- 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: -- -- -- -- 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 class (Num a, Ord a) => Real a -- | the rational equivalent of its real argument with full precision toRational :: Real a => a -> Rational -- | 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: -- -- -- -- 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: -- -- -- -- 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, -- -- class Show a -- | The class Typeable allows a concrete representation of a type -- to be calculated. class Typeable (a :: k) -- | 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 -- | Class for string-like datastructures; used by the overloaded string -- extension (-XOverloadedStrings in GHC). class IsString a fromString :: IsString a => String -> a -- | A functor with application, providing operations to -- -- -- -- 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. (<*>) :: Applicative f => f (a -> b) -> f a -> f b -- | Lift a binary function to actions. -- -- Some functors support an implementation of liftA2 that is more -- efficient than the default one. In particular, if fmap is an -- expensive operation, it is likely better to use liftA2 than to -- fmap over the structure and then use <*>. liftA2 :: Applicative f => (a -> b -> c) -> f a -> f b -> f c -- | Sequence actions, discarding the value of the first argument. (*>) :: 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 <* -- | Data structures that can be folded. -- -- For example, given a data type -- -- 
--   data Tree a = Empty | Leaf a | Node (Tree a) a (Tree a)
--
-- -- a suitable instance would be -- -- 
--   instance Foldable Tree where
--      foldMap f Empty = mempty
--      foldMap f (Leaf x) = f x
--      foldMap f (Node l k r) = foldMap f l `mappend` f k `mappend` foldMap f r
--
-- -- This is suitable even for abstract types, as the monoid is assumed to -- satisfy the monoid laws. Alternatively, one could define -- foldr: -- -- 
--   instance Foldable Tree where
--      foldr f z Empty = z
--      foldr f z (Leaf x) = f x z
--      foldr f z (Node l k r) = foldr f (f k (foldr f z r)) l
--
-- -- Foldable instances are expected to satisfy the following -- laws: -- -- 
--   foldr f z t = appEndo (foldMap (Endo . f) t ) z
--
-- -- 
--   foldl f z t = appEndo (getDual (foldMap (Dual . Endo . flip f) t)) z
--
-- -- 
--   fold = foldMap id
--
-- -- 
--   length = getSum . foldMap (Sum . const  1)
--
-- -- sum, product, maximum, and minimum -- should all be essentially equivalent to foldMap forms, such -- as -- -- 
--   sum = getSum . foldMap Sum
--
-- -- but may be less defined. -- -- If the type is also a Functor instance, it should satisfy -- -- 
--   foldMap f = fold . fmap f
--
-- -- which implies that -- -- 
--   foldMap f . fmap g = foldMap (f . g)
--
class Foldable (t :: Type -> Type) -- | Functors representing data structures that can be traversed from left -- to right. -- -- A definition of traverse must satisfy the following laws: -- -- -- -- A definition of sequenceA must satisfy the following laws: -- -- -- -- where an applicative transformation is a function -- -- 
--   t :: (Applicative f, Applicative g) => f a -> g a
--
-- -- preserving the Applicative operations, i.e. -- -- -- -- and the identity functor Identity and composition of functors -- Compose are defined as -- -- 
--   newtype Identity a = Identity a
--   
--   instance Functor Identity where
--     fmap f (Identity x) = Identity (f x)
--   
--   instance Applicative Identity where
--     pure x = Identity x
--     Identity f <*> Identity x = Identity (f x)
--   
--   newtype Compose f g a = Compose (f (g a))
--   
--   instance (Functor f, Functor g) => Functor (Compose f g) where
--     fmap f (Compose x) = Compose (fmap (fmap f) x)
--   
--   instance (Applicative f, Applicative g) => Applicative (Compose f g) where
--     pure x = Compose (pure (pure x))
--     Compose f <*> Compose x = Compose ((<*>) <$> f <*> x)
--
-- -- (The naturality law is implied by parametricity.) -- -- Instances are similar to Functor, e.g. given a data type -- -- 
--   data Tree a = Empty | Leaf a | Node (Tree a) a (Tree a)
--
-- -- a suitable instance would be -- -- 
--   instance Traversable Tree where
--      traverse f Empty = pure Empty
--      traverse f (Leaf x) = Leaf <$> f x
--      traverse f (Node l k r) = Node <$> traverse f l <*> f k <*> traverse f r
--
-- -- This is suitable even for abstract types, as the laws for -- <*> imply a form of associativity. -- -- The superclass instances should satisfy the following: -- -- 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_. 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_. 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_. 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_. sequence :: (Traversable t, Monad m) => t (m a) -> m (t a) -- | Representable types of kind *. This class is derivable in GHC -- with the DeriveGeneric flag on. -- -- A Generic instance must satisfy the following laws: -- -- 
--   from . to ≡ id
--   to . from ≡ id
--
class Generic a -- | This class gives the integer associated with a type-level natural. -- There are instances of the class for every concrete literal: 0, 1, 2, -- etc. class KnownNat (n :: Nat) class IsLabel (x :: Symbol) a fromLabel :: IsLabel x a => a -- | The class of semigroups (types with an associative binary operation). -- -- Instances should satisfy the associativity law: -- -- class Semigroup a -- | An associative operation. (<>) :: Semigroup a => a -> a -> a -- | Reduce a non-empty list with <> -- -- The default definition should be sufficient, but this can be -- overridden for efficiency. sconcat :: Semigroup a => NonEmpty a -> a -- | Repeat a value n times. -- -- Given that this works on a Semigroup it is allowed to fail if -- you request 0 or fewer repetitions, and the default definition will do -- so. -- -- By making this a member of the class, idempotent semigroups and -- monoids can upgrade this to execute in O(1) by picking -- stimes = stimesIdempotent or stimes = -- stimesIdempotentMonoid respectively. stimes :: (Semigroup a, Integral b) => b -> a -> a infixr 6 <> -- | The class of monoids (types with an associative binary operation that -- has an identity). Instances should satisfy the following laws: -- -- -- -- The method names refer to the monoid of lists under concatenation, but -- there are many other instances. -- -- 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 mempty :: Monoid a => a -- | An associative operation -- -- NOTE: This method is redundant and has the default -- implementation mappend = '(<>)' since -- base-4.11.0.0. mappend :: Monoid a => a -> a -> a -- | Fold a list using the monoid. -- -- For most types, the default definition for mconcat will be -- used, but the function is included in the class definition so that an -- optimized version can be provided for specific types. mconcat :: Monoid a => [a] -> a 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 D# :: Double# -> 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 F# :: Float# -> 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 -- | 8-bit signed integer type data Int8 -- | 16-bit signed integer type data Int16 -- | 32-bit signed integer type data Int32 -- | 64-bit signed integer type data Int64 -- | Invariant: Jn# and Jp# are used iff value doesn't fit in -- S# -- -- Useful properties resulting from the invariants: -- -- data Integer -- | Type representing arbitrary-precision non-negative integers. -- -- 
--   >>> 2^100 :: Natural
--   1267650600228229401496703205376
--
-- -- Operations whose result would be negative throw -- (Underflow :: ArithException), -- -- 
--   >>> -1 :: Natural
--   *** Exception: arithmetic underflow
--
data Natural -- | 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 -- | Rational numbers, with numerator and denominator of some -- Integral type. -- -- Note that Ratio's instances inherit the deficiencies from the -- type parameter's. For example, Ratio Natural's Num -- instance has similar problems to Natural's. data Ratio a (:%) :: !a -> !a -> Ratio a -- | 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 -- | 8-bit unsigned integer type data Word8 -- | 16-bit unsigned integer type data Word16 -- | 32-bit unsigned integer type data Word32 -- | 64-bit unsigned integer type data Word64 -- | A value of type Ptr a represents a pointer to an -- object, or an array of objects, which may be marshalled to or from -- Haskell values of type a. -- -- The type a will often be an instance of class Storable -- which provides the marshalling operations. However this is not -- essential, and you can provide your own operations to access the -- pointer. For example you might write small foreign functions to get or -- set the fields of a C struct. data Ptr a -- | A value of type FunPtr a is a pointer to a function -- callable from foreign code. The type a will normally be a -- foreign type, a function type with zero or more arguments where -- -- -- -- A value of type FunPtr a may be a pointer to a foreign -- function, either returned by another foreign function or imported with -- a a static address import like -- -- 
--   foreign import ccall "stdlib.h &free"
--     p_free :: FunPtr (Ptr a -> IO ())
--
-- -- or a pointer to a Haskell function created using a wrapper stub -- declared to produce a FunPtr of the correct type. For example: -- -- 
--   type Compare = Int -> Int -> Bool
--   foreign import ccall "wrapper"
--     mkCompare :: Compare -> IO (FunPtr Compare)
--
-- -- Calls to wrapper stubs like mkCompare allocate storage, which -- should be released with freeHaskellFunPtr when no longer -- required. -- -- To convert FunPtr values to corresponding Haskell functions, -- one can define a dynamic stub for the specific foreign type, -- e.g. -- -- 
--   type IntFunction = CInt -> IO ()
--   foreign import ccall "dynamic"
--     mkFun :: FunPtr IntFunction -> IntFunction
--
data FunPtr a -- | 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 -- | The kind of types with values. For example Int :: Type. type Type = Type -- | The kind of constraints, like Show a data Constraint -- | (Kind) This is the kind of type-level natural numbers. data Nat -- | Comparison of type-level naturals, as a function. type family CmpNat (a :: Nat) (b :: Nat) :: Ordering -- | Coercible is a two-parameter class that has instances for -- types a and b if the compiler can infer that they -- have the same representation. This class does not have regular -- instances; instead they are created on-the-fly during type-checking. -- Trying to manually declare an instance of Coercible is an -- error. -- -- Nevertheless one can pretend that the following three kinds of -- instances exist. First, as a trivial base-case: -- -- 
--   instance Coercible a a
--
-- -- Furthermore, for every type constructor there is an instance that -- allows to coerce under the type constructor. For example, let -- D be a prototypical type constructor (data or -- newtype) with three type arguments, which have roles -- nominal, representational resp. phantom. -- Then there is an instance of the form -- -- 
--   instance Coercible b b' => Coercible (D a b c) (D a b' c')
--
-- -- Note that the nominal type arguments are equal, the -- representational type arguments can differ, but need to have -- a Coercible instance themself, and the phantom type -- arguments can be changed arbitrarily. -- -- The third kind of instance exists for every newtype NT = MkNT -- T and comes in two variants, namely -- -- 
--   instance Coercible a T => Coercible a NT
--
-- -- 
--   instance Coercible T b => Coercible NT b
--
-- -- This instance is only usable if the constructor MkNT is in -- scope. -- -- If, as a library author of a type constructor like Set a, you -- want to prevent a user of your module to write coerce :: Set T -- -> Set NT, you need to set the role of Set's type -- parameter to nominal, by writing -- -- 
--   type role Set nominal
--
-- -- For more details about this feature, please refer to Safe -- Coercions by Joachim Breitner, Richard A. Eisenberg, Simon Peyton -- Jones and Stephanie Weirich. class a ~R# b => Coercible (a :: k0) (b :: k0) -- | CallStacks are a lightweight method of obtaining a partial -- call-stack at any point in the program. -- -- A function can request its call-site with the HasCallStack -- constraint. For example, we can define -- -- 
--   putStrLnWithCallStack :: HasCallStack => String -> IO ()
--
-- -- as a variant of putStrLn that will get its call-site and -- print it, along with the string given as argument. We can access the -- call-stack inside putStrLnWithCallStack with -- callStack. -- -- 
--   putStrLnWithCallStack :: HasCallStack => String -> IO ()
--   putStrLnWithCallStack msg = do
--     putStrLn msg
--     putStrLn (prettyCallStack callStack)
--
-- -- Thus, if we call putStrLnWithCallStack we will get a -- formatted call-stack alongside our string. -- -- 
--   >>> putStrLnWithCallStack "hello"
--   hello
--   CallStack (from HasCallStack):
--     putStrLnWithCallStack, called at <interactive>:2:1 in interactive:Ghci1
--
-- -- GHC solves HasCallStack constraints in three steps: -- --
    --
  1. If there is a CallStack in scope -- i.e. the enclosing -- function has a HasCallStack constraint -- GHC will append the -- new call-site to the existing CallStack.
    2. --
  2. If there is no CallStack in scope -- e.g. in the GHCi -- session above -- and the enclosing definition does not have an -- explicit type signature, GHC will infer a HasCallStack -- constraint for the enclosing definition (subject to the monomorphism -- restriction).
    3. --
  3. If there is no CallStack in scope and the enclosing -- definition has an explicit type signature, GHC will solve the -- HasCallStack constraint for the singleton CallStack -- containing just the current call-site.
    4. --
-- -- CallStacks do not interact with the RTS and do not require -- compilation with -prof. On the other hand, as they are built -- up explicitly via the HasCallStack constraints, they will -- generally not contain as much information as the simulated call-stacks -- maintained by the RTS. -- -- A CallStack is a [(String, SrcLoc)]. The -- String is the name of function that was called, the -- SrcLoc is the call-site. The list is ordered with the most -- recently called function at the head. -- -- NOTE: The intrepid user may notice that HasCallStack is just an -- alias for an implicit parameter ?callStack :: CallStack. This -- is an implementation detail and should not be considered part -- of the CallStack API, we may decide to change the -- implementation in the future. data CallStack -- | Haskell defines operations to read and write characters from and to -- files, represented by values of type Handle. Each value of -- this type is a handle: a record used by the Haskell run-time -- system to manage I/O with file system objects. A handle has at -- least the following properties: -- -- -- -- Most handles will also have a current I/O position indicating where -- the next input or output operation will occur. A handle is -- readable if it manages only input or both input and output; -- likewise, it is writable if it manages only output or both -- input and output. A handle is open when first allocated. Once -- it is closed it can no longer be used for either input or output, -- though an implementation cannot re-use its storage while references -- remain to it. Handles are in the Show and Eq classes. -- The string produced by showing a handle is system dependent; it should -- include enough information to identify the handle for debugging. A -- handle is equal according to == only to itself; no attempt is -- made to compare the internal state of different handles for equality. data Handle integralEnumFromThenTo :: Integral a => a -> a -> a -> [a] integralEnumFromTo :: Integral a => a -> a -> [a] integralEnumFromThen :: (Integral a, Bounded a) => a -> a -> [a] integralEnumFrom :: (Integral a, Bounded a) => a -> [a] gcdWord' :: Word -> Word -> Word gcdInt' :: Int -> Int -> Int (^^%^^) :: Integral a => Rational -> a -> Rational (^%^) :: Integral a => Rational -> a -> Rational numericEnumFromThenTo :: (Ord a, Fractional a) => a -> a -> a -> [a] numericEnumFromTo :: (Ord a, Fractional a) => a -> a -> [a] numericEnumFromThen :: Fractional a => a -> a -> [a] numericEnumFrom :: Fractional a => a -> [a] notANumber :: Rational infinity :: Rational ratioPrec1 :: Int ratioPrec :: Int underflowError :: () => a overflowError :: () => a ratioZeroDenominatorError :: () => a divZeroError :: () => a -- | reduce is a subsidiary function used only in this module. It -- normalises a ratio by dividing both numerator and denominator by their -- greatest common divisor. reduce :: Integral a => a -> a -> Ratio a boundedEnumFromThen :: (Enum a, Bounded a) => a -> a -> [a] boundedEnumFrom :: (Enum a, Bounded a) => a -> [a] maxInt :: Int minInt :: Int -- | Right-to-left composition of functors. The composition of applicative -- functors is always applicative, but the composition of monads is not -- always a monad. newtype Compose (f :: k -> Type) (g :: k1 -> k) (a :: k1) :: forall k k1. () => k -> Type -> k1 -> k -> k1 -> Type Compose :: f (g a) -> Compose [getCompose] :: Compose -> f (g a) infixr 9 `Compose` infixr 9 `Compose` -- | If Void is uninhabited then any Functor that holds only -- values of type Void is holding no values. vacuous :: Functor f => f Void -> f a -- | Since Void values logically don't exist, this witnesses the -- logical reasoning tool of "ex falso quodlibet". -- -- 
--   >>> let x :: Either Void Int; x = Right 5
--   
--   >>> :{
--   case x of
--       Right r -> r
--       Left l  -> absurd l
--   :}
--   5
--
absurd :: () => Void -> a -- | Uninhabited data type data Void -- | Repeat a value n times. -- -- 
--   mtimesDefault n a = a <> a <> ... <> a  -- using <> (n-1) times
--
-- -- Implemented using stimes and mempty. -- -- This is a suitable definition for an mtimes member of -- Monoid. mtimesDefault :: (Integral b, Monoid a) => b -> a -> a -- | A generalization of cycle to an arbitrary Semigroup. May -- fail to terminate for some values in some semigroups. cycle1 :: Semigroup m => m -> m -- | Provide a Semigroup for an arbitrary Monoid. -- -- NOTE: This is not needed anymore since Semigroup became -- a superclass of Monoid in base-4.11 and this newtype be -- deprecated at some point in the future. data WrappedMonoid m -- | Option is effectively Maybe with a better instance of -- Monoid, built off of an underlying Semigroup instead of -- an underlying Monoid. -- -- Ideally, this type would not exist at all and we would just fix the -- Monoid instance of Maybe. -- -- In GHC 8.4 and higher, the Monoid instance for Maybe has -- been corrected to lift a Semigroup instance instead of a -- Monoid instance. Consequently, this type is no longer useful. -- It will be marked deprecated in GHC 8.8 and removed in GHC 8.10. newtype Option a Option :: Maybe a -> Option a [getOption] :: Option a -> Maybe a -- | The sortWith function sorts a list of elements using the user -- supplied function to project something out of each element sortWith :: Ord b => (a -> b) -> [a] -> [a] -- | A bifunctor is a type constructor that takes two type arguments and is -- a functor in both arguments. That is, unlike with -- Functor, a type constructor such as Either does not need -- to be partially applied for a Bifunctor instance, and the -- methods in this class permit mapping functions over the Left -- value or the Right value, or both at the same time. -- -- Formally, the class Bifunctor represents a bifunctor from -- Hask -> Hask. -- -- Intuitively it is a bifunctor where both the first and second -- arguments are covariant. -- -- You can define a Bifunctor by either defining bimap or -- by defining both first and second. -- -- If you supply bimap, you should ensure that: -- -- 
--   bimap id id ≡ id
--
-- -- If you supply first and second, ensure: -- -- 
--   first id ≡ id
--   second id ≡ id
--
-- -- If you supply both, you should also ensure: -- -- 
--   bimap f g ≡ first f . second g
--
-- -- These ensure by parametricity: -- -- 
--   bimap  (f . g) (h . i) ≡ bimap f h . bimap g i
--   first  (f . g) ≡ first  f . first  g
--   second (f . g) ≡ second f . second g
--
class Bifunctor (p :: Type -> Type -> Type) -- | Map over both arguments at the same time. -- -- 
--   bimap f g ≡ first f . second g
--
-- --

Examples

-- -- 
--   >>> bimap toUpper (+1) ('j', 3)
--   ('J',4)
--
-- -- 
--   >>> bimap toUpper (+1) (Left 'j')
--   Left 'J'
--
-- -- 
--   >>> bimap toUpper (+1) (Right 3)
--   Right 4
--
bimap :: Bifunctor p => (a -> b) -> (c -> d) -> p a c -> p b d -- | Map covariantly over the first argument. -- -- 
--   first f ≡ bimap f id
--
-- --

Examples

-- -- 
--   >>> first toUpper ('j', 3)
--   ('J',3)
--
-- -- 
--   >>> first toUpper (Left 'j')
--   Left 'J'
--
first :: Bifunctor p => (a -> b) -> p a c -> p b c -- | Map covariantly over the second argument. -- -- 
--   second ≡ bimap id
--
-- --

Examples

-- -- 
--   >>> second (+1) ('j', 3)
--   ('j',4)
--
-- -- 
--   >>> second (+1) (Right 3)
--   Right 4
--
second :: Bifunctor p => (b -> c) -> p a b -> p a c -- | Extract everything except the last element of the stream. init :: () => NonEmpty a -> [a] -- | Extract the last element of the stream. last :: () => NonEmpty a -> a -- | Extract the possibly-empty tail of the stream. tail :: () => NonEmpty a -> [a] -- | Extract the first element of the stream. head :: () => NonEmpty a -> a -- | nonEmpty efficiently turns a normal list into a NonEmpty -- stream, producing Nothing if the input is empty. nonEmpty :: () => [a] -> Maybe (NonEmpty a) -- | Get a string representation of the current execution stack state. showStackTrace :: IO (Maybe String) -- | Get a trace of the current execution stack state. -- -- Returns Nothing if stack trace support isn't available on -- host machine. getStackTrace :: IO (Maybe [Location]) -- | Monads in which IO computations may be embedded. Any monad -- built by applying a sequence of monad transformers to the IO -- monad will be an instance of this class. -- -- Instances should satisfy the following laws, which state that -- liftIO is a transformer of monads: -- -- class Monad m => MonadIO (m :: Type -> Type) -- | Lift a computation from the IO monad. liftIO :: MonadIO m => IO a -> m a -- | Direct MonadPlus equivalent of filter. -- --

Examples

-- -- The filter function is just mfilter specialized to the -- list monad: -- -- 
--   filter = ( mfilter :: (a -> Bool) -> [a] -> [a] )
--
-- -- An example using mfilter with the Maybe monad: -- -- 
--   >>> mfilter odd (Just 1)
--   Just 1
--   >>> mfilter odd (Just 2)
--   Nothing
--
mfilter :: MonadPlus m => (a -> Bool) -> m a -> m a -- | Strict version of <$>. (<$!>) :: Monad m => (a -> b) -> m a -> m b infixl 4 <$!> -- | The reverse of when. unless :: Applicative f => Bool -> f () -> f () -- | Like replicateM, but discards the result. replicateM_ :: Applicative m => Int -> m a -> m () -- | replicateM n act performs the action n times, -- gathering the results. replicateM :: Applicative m => Int -> m a -> m [a] -- | Like foldM, but discards the result. foldM_ :: (Foldable t, Monad m) => (b -> a -> m b) -> b -> t a -> m () -- | The foldM function is analogous to foldl, except that -- its result is encapsulated in a monad. Note that foldM works -- from left-to-right over the list arguments. This could be an issue -- where (>>) and the `folded function' are not -- commutative. -- -- 
--   foldM f a1 [x1, x2, ..., xm]
--   
--   ==
--   
--   do
--     a2 <- f a1 x1
--     a3 <- f a2 x2
--     ...
--     f am xm
--
-- -- If right-to-left evaluation is required, the input list should be -- reversed. -- -- Note: foldM is the same as foldlM foldM :: (Foldable t, Monad m) => (b -> a -> m b) -> b -> t a -> m b -- | zipWithM_ is the extension of zipWithM which ignores the -- final result. zipWithM_ :: Applicative m => (a -> b -> m c) -> [a] -> [b] -> m () -- | The zipWithM function generalizes zipWith to arbitrary -- applicative functors. zipWithM :: Applicative m => (a -> b -> m c) -> [a] -> [b] -> m [c] -- | The mapAndUnzipM function maps its first argument over a list, -- returning the result as a pair of lists. This function is mainly used -- with complicated data structures or a state-transforming monad. mapAndUnzipM :: Applicative m => (a -> m (b, c)) -> [a] -> m ([b], [c]) -- | Repeat an action indefinitely. -- --

Examples

-- -- A common use of forever is to process input from network -- sockets, Handles, and channels (e.g. MVar and -- Chan). -- -- For example, here is how we might implement an echo server, -- using forever both to listen for client connections on a -- network socket and to echo client input on client connection handles: -- -- 
--   echoServer :: Socket -> IO ()
--   echoServer socket = forever $ do
--     client <- accept socket
--     forkFinally (echo client) (\_ -> hClose client)
--     where
--       echo :: Handle -> IO ()
--       echo client = forever $
--         hGetLine client >>= hPutStrLn client
--
forever :: Applicative f => f a -> f b -- | Right-to-left composition of Kleisli arrows. -- (>=>), with the arguments flipped. -- -- Note how this operator resembles function composition -- (.): -- -- 
--   (.)   ::            (b ->   c) -> (a ->   b) -> a ->   c
--   (<=<) :: Monad m => (b -> m c) -> (a -> m b) -> a -> m c
--
(<=<) :: Monad m => (b -> m c) -> (a -> m b) -> a -> m c infixr 1 <=< -- | Left-to-right composition of Kleisli arrows. (>=>) :: Monad m => (a -> m b) -> (b -> m c) -> a -> m c infixr 1 >=> -- | This generalizes the list-based filter function. filterM :: Applicative m => (a -> m Bool) -> [a] -> m [a] -- | This function may be used as a value for foldMap in a -- Foldable instance. -- -- 
--   foldMapDefault f ≡ getConst . traverse (Const . f)
--
foldMapDefault :: (Traversable t, Monoid m) => (a -> m) -> t a -> m -- | This function may be used as a value for fmap in a -- Functor instance, provided that traverse is defined. -- (Using fmapDefault with a Traversable instance defined -- only by sequenceA will result in infinite recursion.) -- -- 
--   fmapDefault f ≡ runIdentity . traverse (Identity . f)
--
fmapDefault :: Traversable t => (a -> b) -> t a -> t b -- | The mapAccumR function behaves like a combination of -- fmap and foldr; it applies a function to each element -- of a structure, passing an accumulating parameter from right to left, -- and returning a final value of this accumulator together with the new -- structure. mapAccumR :: Traversable t => (a -> b -> (a, c)) -> a -> t b -> (a, t c) -- | The mapAccumL function behaves like a combination of -- fmap and foldl; it applies a function to each element -- of a structure, passing an accumulating parameter from left to right, -- and returning a final value of this accumulator together with the new -- structure. mapAccumL :: Traversable t => (a -> b -> (a, c)) -> a -> t b -> (a, t c) -- | forM is mapM with its arguments flipped. For a version -- that ignores the results see forM_. forM :: (Traversable t, Monad m) => t a -> (a -> m b) -> m (t b) -- | One or none. optional :: Alternative f => f a -> f (Maybe a) -- | Lists, but with an Applicative functor based on zipping. newtype ZipList a ZipList :: [a] -> ZipList a [getZipList] :: ZipList a -> [a] -- | Fanout: send the input to both argument arrows and combine their -- output. -- -- The default definition may be overridden with a more efficient version -- if desired. (&&&) :: Arrow a => a b c -> a b c' -> a b (c, c') infixr 3 &&& -- | Identity functor and monad. (a non-strict monad) newtype Identity a Identity :: a -> Identity a [runIdentity] :: Identity a -> a -- | A handle managing output to the Haskell program's standard error -- channel. stderr :: Handle -- | A handle managing input from the Haskell program's standard input -- channel. stdin :: Handle -- | Perform some computation without adding new entries to the -- CallStack. withFrozenCallStack :: HasCallStack => (HasCallStack -> a) -> a -- | Return the current CallStack. -- -- Does *not* include the call-site of callStack. callStack :: HasCallStack -> CallStack -- | Write the supplied value into a TVar. writeTVar :: () => TVar a -> a -> STM () -- | Return the current value stored in a TVar. readTVar :: () => TVar a -> STM a -- | Create a new TVar holding a value supplied newTVar :: () => a -> STM (TVar a) -- | A monad supporting atomic memory transactions. data STM a -- | Shared memory locations that support atomic memory transactions. data TVar a -- | A handle managing output to the Haskell program's standard output -- channel. stdout :: Handle -- | A mutable variable in the IO monad data IORef 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 -- | Pretty print a CallStack. prettyCallStack :: CallStack -> String -- | Pretty print a SrcLoc. prettySrcLoc :: SrcLoc -> String -- | Any type that you wish to throw or catch as an exception must be an -- instance of the Exception class. The simplest case is a new -- exception type directly below the root: -- -- 
--   data MyException = ThisException | ThatException
--       deriving Show
--   
--   instance Exception MyException
--
-- -- The default method definitions in the Exception class do what -- we need in this case. You can now throw and catch -- ThisException and ThatException as exceptions: -- -- 
--   *Main> throw ThisException `catch` \e -> putStrLn ("Caught " ++ show (e :: MyException))
--   Caught ThisException
--
-- -- In more complicated examples, you may wish to define a whole hierarchy -- of exceptions: -- -- 
--   ---------------------------------------------------------------------
--   -- Make the root exception type for all the exceptions in a compiler
--   
--   data SomeCompilerException = forall e . Exception e => SomeCompilerException e
--   
--   instance Show SomeCompilerException where
--       show (SomeCompilerException e) = show e
--   
--   instance Exception SomeCompilerException
--   
--   compilerExceptionToException :: Exception e => e -> SomeException
--   compilerExceptionToException = toException . SomeCompilerException
--   
--   compilerExceptionFromException :: Exception e => SomeException -> Maybe e
--   compilerExceptionFromException x = do
--       SomeCompilerException a <- fromException x
--       cast a
--   
--   ---------------------------------------------------------------------
--   -- Make a subhierarchy for exceptions in the frontend of the compiler
--   
--   data SomeFrontendException = forall e . Exception e => SomeFrontendException e
--   
--   instance Show SomeFrontendException where
--       show (SomeFrontendException e) = show e
--   
--   instance Exception SomeFrontendException where
--       toException = compilerExceptionToException
--       fromException = compilerExceptionFromException
--   
--   frontendExceptionToException :: Exception e => e -> SomeException
--   frontendExceptionToException = toException . SomeFrontendException
--   
--   frontendExceptionFromException :: Exception e => SomeException -> Maybe e
--   frontendExceptionFromException x = do
--       SomeFrontendException a <- fromException x
--       cast a
--   
--   ---------------------------------------------------------------------
--   -- Make an exception type for a particular frontend compiler exception
--   
--   data MismatchedParentheses = MismatchedParentheses
--       deriving Show
--   
--   instance Exception MismatchedParentheses where
--       toException   = frontendExceptionToException
--       fromException = frontendExceptionFromException
--
-- -- We can now catch a MismatchedParentheses exception as -- MismatchedParentheses, SomeFrontendException or -- SomeCompilerException, but not other types, e.g. -- IOException: -- -- 
--   *Main> throw MismatchedParentheses `catch` \e -> putStrLn ("Caught " ++ show (e :: MismatchedParentheses))
--   Caught MismatchedParentheses
--   *Main> throw MismatchedParentheses `catch` \e -> putStrLn ("Caught " ++ show (e :: SomeFrontendException))
--   Caught MismatchedParentheses
--   *Main> throw MismatchedParentheses `catch` \e -> putStrLn ("Caught " ++ show (e :: SomeCompilerException))
--   Caught MismatchedParentheses
--   *Main> throw MismatchedParentheses `catch` \e -> putStrLn ("Caught " ++ show (e :: IOException))
--   *** Exception: MismatchedParentheses
--
class (Typeable e, Show e) => Exception e toException :: Exception e => e -> SomeException fromException :: Exception e => SomeException -> Maybe e -- | Render this exception value in a human-friendly manner. -- -- Default implementation: show. displayException :: Exception e => e -> String -- | The Const functor. newtype Const a (b :: k) :: forall k. () => Type -> k -> Type Const :: a -> Const a [getConst] :: Const a -> a -- | The least element of a non-empty structure with respect to the given -- comparison function. minimumBy :: Foldable t => (a -> a -> Ordering) -> t a -> a -- | The largest element of a non-empty structure with respect to the given -- comparison function. maximumBy :: Foldable t => (a -> a -> Ordering) -> t a -> a -- | Map a function over all the elements of a container and concatenate -- the resulting lists. concatMap :: Foldable t => (a -> [b]) -> t a -> [b] -- | The concatenation of all the elements of a container of lists. concat :: Foldable t => t [a] -> [a] -- | Monadic fold over the elements of a structure, associating to the -- left, i.e. from left to right. foldlM :: (Foldable t, Monad m) => (b -> a -> m b) -> b -> t a -> m b -- | Monadic fold over the elements of a structure, associating to the -- right, i.e. from right to left. foldrM :: (Foldable t, Monad m) => (a -> b -> m b) -> b -> t a -> m b -- | Maybe monoid returning the leftmost non-Nothing value. -- -- First a is isomorphic to Alt Maybe -- a, but precedes it historically. -- -- 
--   >>> getFirst (First (Just "hello") <> First Nothing <> First (Just "world"))
--   Just "hello"
--
-- -- Use of this type is discouraged. Note the following equivalence: -- -- 
--   Data.Monoid.First x === Maybe (Data.Semigroup.First x)
--
-- -- In addition to being equivalent in the structural sense, the two also -- have Monoid instances that behave the same. This type will be -- marked deprecated in GHC 8.8, and removed in GHC 8.10. Users are -- advised to use the variant from Data.Semigroup and wrap it in -- Maybe. newtype First a First :: Maybe a -> First a [getFirst] :: First a -> Maybe a -- | Maybe monoid returning the rightmost non-Nothing value. -- -- Last a is isomorphic to Dual (First -- a), and thus to Dual (Alt Maybe a) -- -- 
--   >>> getLast (Last (Just "hello") <> Last Nothing <> Last (Just "world"))
--   Just "world"
--
-- -- Use of this type is discouraged. Note the following equivalence: -- -- 
--   Data.Monoid.Last x === Maybe (Data.Semigroup.Last x)
--
-- -- In addition to being equivalent in the structural sense, the two also -- have Monoid instances that behave the same. This type will be -- marked deprecated in GHC 8.8, and removed in GHC 8.10. Users are -- advised to use the variant from Data.Semigroup and wrap it in -- Maybe. newtype Last a Last :: Maybe a -> Last a [getLast] :: Last a -> Maybe a -- | This is a valid definition of stimes for a Monoid. -- -- Unlike the default definition of stimes, it is defined for 0 -- and so it should be preferred where possible. stimesMonoid :: (Integral b, Monoid a) => b -> a -> a -- | This is a valid definition of stimes for an idempotent -- Semigroup. -- -- When x <> x = x, this definition should be preferred, -- because it works in O(1) rather than O(log n). stimesIdempotent :: Integral b => b -> a -> a -- | The dual of a Monoid, obtained by swapping the arguments of -- mappend. -- -- 
--   >>> getDual (mappend (Dual "Hello") (Dual "World"))
--   "WorldHello"
--
newtype Dual a Dual :: a -> Dual a [getDual] :: Dual a -> a -- | The monoid of endomorphisms under composition. -- -- 
--   >>> let computation = Endo ("Hello, " ++) <> Endo (++ "!")
--   
--   >>> appEndo computation "Haskell"
--   "Hello, Haskell!"
--
newtype Endo a Endo :: (a -> a) -> Endo a [appEndo] :: Endo a -> a -> a -- | Boolean monoid under conjunction (&&). -- -- 
--   >>> getAll (All True <> mempty <> All False)
--   False
--
-- -- 
--   >>> getAll (mconcat (map (\x -> All (even x)) [2,4,6,7,8]))
--   False
--
newtype All All :: Bool -> All [getAll] :: All -> Bool -- | Boolean monoid under disjunction (||). -- -- 
--   >>> getAny (Any True <> mempty <> Any False)
--   True
--
-- -- 
--   >>> getAny (mconcat (map (\x -> Any (even x)) [2,4,6,7,8]))
--   True
--
newtype Any Any :: Bool -> Any [getAny] :: Any -> Bool -- | Monoid under addition. -- -- 
--   >>> getSum (Sum 1 <> Sum 2 <> mempty)
--   3
--
newtype Sum a Sum :: a -> Sum a [getSum] :: Sum a -> a -- | Monoid under multiplication. -- -- 
--   >>> getProduct (Product 3 <> Product 4 <> mempty)
--   12
--
newtype Product a Product :: a -> Product a [getProduct] :: Product a -> a -- | Monoid under <|>. newtype Alt (f :: k -> Type) (a :: k) :: forall k. () => k -> Type -> k -> Type Alt :: f a -> Alt [getAlt] :: Alt -> f a -- | Convert an integer into an unknown type-level natural. someNatVal :: Natural -> SomeNat natVal :: KnownNat n => proxy n -> Natural -- | This type represents unknown type-level natural numbers. data SomeNat [SomeNat] :: forall (n :: Nat). KnownNat n => Proxy n -> SomeNat -- | The unfoldr function is a `dual' to foldr: while -- foldr reduces a list to a summary value, unfoldr builds -- a list from a seed value. The function takes the element and returns -- Nothing if it is done producing the list or returns Just -- (a,b), in which case, a is a prepended to the list -- and b is used as the next element in a recursive call. For -- example, -- -- 
--   iterate f == unfoldr (\x -> Just (x, f x))
--
-- -- In some cases, unfoldr can undo a foldr operation: -- -- 
--   unfoldr f' (foldr f z xs) == xs
--
-- -- if the following holds: -- -- 
--   f' (f x y) = Just (x,y)
--   f' z       = Nothing
--
-- -- A simple use of unfoldr: -- -- 
--   >>> unfoldr (\b -> if b == 0 then Nothing else Just (b, b-1)) 10
--   [10,9,8,7,6,5,4,3,2,1]
--
unfoldr :: () => (b -> Maybe (a, b)) -> b -> [a] -- | Sort a list by comparing the results of a key function applied to each -- element. sortOn f is equivalent to sortBy (comparing -- f), but has the performance advantage of only evaluating -- f once for each element in the input list. This is called the -- decorate-sort-undecorate paradigm, or Schwartzian transform. -- -- Elements are arranged from from lowest to highest, keeping duplicates -- in the order they appeared in the input. -- -- 
--   >>> sortOn fst [(2, "world"), (4, "!"), (1, "Hello")]
--   [(1,"Hello"),(2,"world"),(4,"!")]
--
sortOn :: Ord b => (a -> b) -> [a] -> [a] -- | The sortBy function is the non-overloaded version of -- sort. -- -- 
--   >>> sortBy (\(a,_) (b,_) -> compare a b) [(2, "world"), (4, "!"), (1, "Hello")]
--   [(1,"Hello"),(2,"world"),(4,"!")]
--
sortBy :: () => (a -> a -> Ordering) -> [a] -> [a] -- | The sort function implements a stable sorting algorithm. It is -- a special case of sortBy, which allows the programmer to supply -- their own comparison function. -- -- Elements are arranged from from lowest to highest, keeping duplicates -- in the order they appeared in the input. -- -- 
--   >>> sort [1,6,4,3,2,5]
--   [1,2,3,4,5,6]
--
sort :: Ord a => [a] -> [a] -- | The permutations function returns the list of all permutations -- of the argument. -- -- 
--   >>> permutations "abc"
--   ["abc","bac","cba","bca","cab","acb"]
--
permutations :: () => [a] -> [[a]] -- | The subsequences function returns the list of all subsequences -- of the argument. -- -- 
--   >>> subsequences "abc"
--   ["","a","b","ab","c","ac","bc","abc"]
--
subsequences :: () => [a] -> [[a]] -- | The tails function returns all final segments of the argument, -- longest first. For example, -- -- 
--   >>> tails "abc"
--   ["abc","bc","c",""]
--
-- -- Note that tails has the following strictness property: -- tails _|_ = _|_ : _|_ tails :: () => [a] -> [[a]] -- | The inits function returns all initial segments of the -- argument, shortest first. For example, -- -- 
--   >>> inits "abc"
--   ["","a","ab","abc"]
--
-- -- Note that inits has the following strictness property: -- inits (xs ++ _|_) = inits xs ++ _|_ -- -- In particular, inits _|_ = [] : _|_ inits :: () => [a] -> [[a]] -- | The group function takes a list and returns a list of lists -- such that the concatenation of the result is equal to the argument. -- Moreover, each sublist in the result contains only equal elements. For -- example, -- -- 
--   >>> group "Mississippi"
--   ["M","i","ss","i","ss","i","pp","i"]
--
-- -- It is a special case of groupBy, which allows the programmer to -- supply their own equality test. group :: Eq a => [a] -> [[a]] -- | The genericReplicate function is an overloaded version of -- replicate, which accepts any Integral value as the -- number of repetitions to make. genericReplicate :: Integral i => i -> a -> [a] -- | The genericSplitAt function is an overloaded version of -- splitAt, which accepts any Integral value as the -- position at which to split. genericSplitAt :: Integral i => i -> [a] -> ([a], [a]) -- | The genericDrop function is an overloaded version of -- drop, which accepts any Integral value as the number of -- elements to drop. genericDrop :: Integral i => i -> [a] -> [a] -- | The genericTake function is an overloaded version of -- take, which accepts any Integral value as the number of -- elements to take. genericTake :: Integral i => i -> [a] -> [a] -- | The genericLength function is an overloaded version of -- length. In particular, instead of returning an Int, it -- returns any type which is an instance of Num. It is, however, -- less efficient than length. genericLength :: Num i => [a] -> i -- | The partition function takes a predicate a list and returns the -- pair of lists of elements which do and do not satisfy the predicate, -- respectively; i.e., -- -- 
--   partition p xs == (filter p xs, filter (not . p) xs)
--
-- -- 
--   >>> partition (`elem` "aeiou") "Hello World!"
--   ("eoo","Hll Wrld!")
--
partition :: () => (a -> Bool) -> [a] -> ([a], [a]) -- | The transpose function transposes the rows and columns of its -- argument. For example, -- -- 
--   >>> transpose [[1,2,3],[4,5,6]]
--   [[1,4],[2,5],[3,6]]
--
-- -- If some of the rows are shorter than the following rows, their -- elements are skipped: -- -- 
--   >>> transpose [[10,11],[20],[],[30,31,32]]
--   [[10,20,30],[11,31],[32]]
--
transpose :: () => [[a]] -> [[a]] -- | intercalate xs xss is equivalent to (concat -- (intersperse xs xss)). It inserts the list xs in -- between the lists in xss and concatenates the result. -- -- 
--   >>> intercalate ", " ["Lorem", "ipsum", "dolor"]
--   "Lorem, ipsum, dolor"
--
intercalate :: () => [a] -> [[a]] -> [a] -- | The intersperse function takes an element and a list and -- `intersperses' that element between the elements of the list. For -- example, -- -- 
--   >>> intersperse ',' "abcde"
--   "a,b,c,d,e"
--
intersperse :: () => a -> [a] -> [a] -- | The isPrefixOf function takes two lists and returns True -- iff the first list is a prefix of the second. -- -- 
--   >>> "Hello" `isPrefixOf` "Hello World!"
--   True
--
-- -- 
--   >>> "Hello" `isPrefixOf` "Wello Horld!"
--   False
--
isPrefixOf :: Eq a => [a] -> [a] -> Bool -- | Parse a string using the Read instance. Succeeds if there is -- exactly one valid result. -- -- 
--   >>> readMaybe "123" :: Maybe Int
--   Just 123
--
-- -- 
--   >>> readMaybe "hello" :: Maybe Int
--   Nothing
--
readMaybe :: Read a => String -> Maybe a -- | equivalent to readsPrec with a precedence of 0. reads :: Read a => ReadS a -- | Return True if the given value is a Right-value, -- False otherwise. -- --

Examples

-- -- Basic usage: -- -- 
--   >>> isRight (Left "foo")
--   False
--   
--   >>> isRight (Right 3)
--   True
--
-- -- Assuming a Left value signifies some sort of error, we can use -- isRight to write a very simple reporting function that only -- outputs "SUCCESS" when a computation has succeeded. -- -- This example shows how isRight might be used to avoid pattern -- matching when one does not care about the value contained in the -- constructor: -- -- 
--   >>> import Control.Monad ( when )
--   
--   >>> let report e = when (isRight e) $ putStrLn "SUCCESS"
--   
--   >>> report (Left "parse error")
--   
--   >>> report (Right 1)
--   SUCCESS
--
isRight :: () => Either a b -> Bool -- | Return True if the given value is a Left-value, -- False otherwise. -- --

Examples

-- -- Basic usage: -- -- 
--   >>> isLeft (Left "foo")
--   True
--   
--   >>> isLeft (Right 3)
--   False
--
-- -- Assuming a Left value signifies some sort of error, we can use -- isLeft to write a very simple error-reporting function that -- does absolutely nothing in the case of success, and outputs "ERROR" if -- any error occurred. -- -- This example shows how isLeft might be used to avoid pattern -- matching when one does not care about the value contained in the -- constructor: -- -- 
--   >>> import Control.Monad ( when )
--   
--   >>> let report e = when (isLeft e) $ putStrLn "ERROR"
--   
--   >>> report (Right 1)
--   
--   >>> report (Left "parse error")
--   ERROR
--
isLeft :: () => Either a b -> Bool -- | Partitions a list of Either into two lists. All the Left -- elements are extracted, in order, to the first component of the -- output. Similarly the Right elements are extracted to the -- second component of the output. -- --

Examples

-- -- Basic usage: -- -- 
--   >>> let list = [ Left "foo", Right 3, Left "bar", Right 7, Left "baz" ]
--   
--   >>> partitionEithers list
--   (["foo","bar","baz"],[3,7])
--
-- -- The pair returned by partitionEithers x should be the -- same pair as (lefts x, rights x): -- -- 
--   >>> let list = [ Left "foo", Right 3, Left "bar", Right 7, Left "baz" ]
--   
--   >>> partitionEithers list == (lefts list, rights list)
--   True
--
partitionEithers :: () => [Either a b] -> ([a], [b]) -- | Extracts from a list of Either all the Right elements. -- All the Right elements are extracted in order. -- --

Examples

-- -- Basic usage: -- -- 
--   >>> let list = [ Left "foo", Right 3, Left "bar", Right 7, Left "baz" ]
--   
--   >>> rights list
--   [3,7]
--
rights :: () => [Either a b] -> [b] -- | Extracts from a list of Either all the Left elements. -- All the Left elements are extracted in order. -- --

Examples

-- -- Basic usage: -- -- 
--   >>> let list = [ Left "foo", Right 3, Left "bar", Right 7, Left "baz" ]
--   
--   >>> lefts list
--   ["foo","bar","baz"]
--
lefts :: () => [Either a b] -> [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 -- | 
--   comparing p x y = compare (p x) (p y)
--
-- -- Useful combinator for use in conjunction with the xxxBy -- family of functions from Data.List, for example: -- -- 
--   ... sortBy (comparing fst) ...
--
comparing :: Ord a => (b -> a) -> b -> b -> Ordering -- | 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 newtype Down a Down :: a -> Down 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) :: forall k. () => k -> Type Proxy :: Proxy -- | See openFile data IOMode ReadMode :: IOMode WriteMode :: IOMode AppendMode :: IOMode ReadWriteMode :: IOMode -- | Reverse order of bytes in Word64. byteSwap64 :: Word64 -> Word64 -- | Reverse order of bytes in Word32. byteSwap32 :: Word32 -> Word32 -- | Swap bytes in Word16. byteSwap16 :: Word16 -> Word16 -- | Bitwise "xor" xor :: Bits a => a -> a -> a infixl 6 `xor` -- | Case analysis for the Bool type. bool x y p -- evaluates to x when p is False, and evaluates -- to y when p is True. -- -- This is equivalent to if p then y else x; that is, one can -- think of it as an if-then-else construct with its arguments reordered. -- --

Examples

-- -- Basic usage: -- -- 
--   >>> bool "foo" "bar" True
--   "bar"
--   
--   >>> bool "foo" "bar" False
--   "foo"
--
-- -- Confirm that bool x y p and if p then y else -- x are equivalent: -- -- 
--   >>> let p = True; x = "bar"; y = "foo"
--   
--   >>> bool x y p == if p then y else x
--   True
--   
--   >>> let p = False
--   
--   >>> bool x y p == if p then y else x
--   True
--
bool :: () => a -> a -> Bool -> 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 & -- | 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 :: () => (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' argument, hence the recursion is reintroduced. fix :: () => (a -> a) -> a -- | void value discards or ignores the result of -- evaluation, such as the return value of an IO action. -- --

Examples

-- -- Replace the contents of a Maybe Int with -- unit: -- -- 
--   >>> void Nothing
--   Nothing
--   
--   >>> void (Just 3)
--   Just ()
--
-- -- Replace the contents of an Either Int -- Int with unit, resulting in an Either -- Int '()': -- -- 
--   >>> void (Left 8675309)
--   Left 8675309
--   
--   >>> void (Right 8675309)
--   Right ()
--
-- -- Replace every element of a list with unit: -- -- 
--   >>> void [1,2,3]
--   [(),(),()]
--
-- -- Replace the second element of a pair with unit: -- -- 
--   >>> void (1,2)
--   (1,())
--
-- -- Discard the result of an IO action: -- -- 
--   >>> mapM print [1,2]
--   1
--   2
--   [(),()]
--   
--   >>> void $ mapM print [1,2]
--   1
--   2
--
void :: Functor f => f a -> f () -- | Flipped version of <$. -- --

Examples

-- -- Replace the contents of a Maybe Int with a -- constant String: -- -- 
--   >>> Nothing $> "foo"
--   Nothing
--   
--   >>> Just 90210 $> "foo"
--   Just "foo"
--
-- -- Replace the contents of an Either Int -- Int with a constant String, resulting in an -- Either Int String: -- -- 
--   >>> Left 8675309 $> "foo"
--   Left 8675309
--   
--   >>> Right 8675309 $> "foo"
--   Right "foo"
--
-- -- Replace each element of a list with a constant String: -- -- 
--   >>> [1,2,3] $> "foo"
--   ["foo","foo","foo"]
--
-- -- Replace the second element of a pair with a constant String: -- -- 
--   >>> (1,2) $> "foo"
--   (1,"foo")
--
($>) :: Functor f => f a -> b -> f b infixl 4 $> -- | Flipped version of <$>. -- -- 
--   (<&>) = flip fmap
--
-- --

Examples

-- -- Apply (+1) to a list, a Just and a Right: -- -- 
--   >>> Just 2 <&> (+1)
--   Just 3
--
-- -- 
--   >>> [1,2,3] <&> (+1)
--   [2,3,4]
--
-- -- 
--   >>> Right 3 <&> (+1)
--   Right 4
--
(<&>) :: Functor f => f a -> (a -> b) -> f b infixl 1 <&> -- | 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)
--
(<$>) :: Functor f => (a -> b) -> f a -> f b infixl 4 <$> -- | 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 -- | 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 ^ odd :: Integral a => a -> Bool even :: Integral a => a -> Bool -- | Extract the denominator of the ratio in reduced form: the numerator -- and denominator have no common factor and the denominator is positive. denominator :: () => Ratio a -> a -- | Extract the numerator of the ratio in reduced form: the numerator and -- denominator have no common factor and the denominator is positive. numerator :: () => Ratio a -> a -- | Forms the ratio of two integral numbers. (%) :: Integral a => a -> a -> Ratio a infixl 7 % -- | The toEnum method restricted to the type Char. chr :: Int -> Char -- | The unzip3 function takes a list of triples and returns three -- lists, analogous to unzip. 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 :: () => [(a, b)] -> ([a], [b]) -- | zipWith generalises zip by zipping with the function -- given as the first argument, instead of a tupling function. For -- example, zipWith (+) is applied to two lists to -- produce the list of corresponding sums. -- -- zipWith is right-lazy: -- -- 
--   zipWith f [] _|_ = []
--
zipWith :: () => (a -> b -> c) -> [a] -> [b] -> [c] -- | zip3 takes three lists and returns a list of triples, analogous -- to zip. zip3 :: () => [a] -> [b] -> [c] -> [(a, b, c)] -- | reverse xs returns the elements of xs in -- reverse order. xs must be finite. reverse :: () => [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]) -- | 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]) -- | 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] -- | 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] -- | 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] -- | 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] -- | cycle ties a finite list into a circular one, or equivalently, -- the infinite repetition of the original list. It is the identity on -- infinite lists. cycle :: () => [a] -> [a] -- | replicate n x is a list of length n with -- x the value of every element. It is an instance of the more -- general genericReplicate, in which n may be of any -- integral type. replicate :: () => Int -> a -> [a] -- | repeat x is an infinite list, with x the -- value of every element. repeat :: () => 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. iterate :: () => (a -> a) -> a -> [a] -- | scanr is the right-to-left dual of scanl. Note that -- -- 
--   head (scanr f z xs) == foldr f z xs.
--
scanr :: () => (a -> b -> b) -> b -> [a] -> [b] -- | scanl is similar to foldl, but returns a list of -- successive reduced values from the left: -- -- 
--   scanl f z [x1, x2, ...] == [z, z `f` x1, (z `f` x1) `f` x2, ...]
--
-- -- Note that -- -- 
--   last (scanl f z xs) == foldl f z xs.
--
scanl :: () => (b -> a -> b) -> b -> [a] -> [b] -- | The mapMaybe function is a version of map which can -- throw out elements. In particular, the functional argument returns -- something of type Maybe b. If this is Nothing, -- no element is added on to the result list. If it is Just -- b, then b is included in the result list. -- --

Examples

-- -- Using mapMaybe f x is a shortcut for -- catMaybes $ map f x in most cases: -- -- 
--   >>> import Text.Read ( readMaybe )
--   
--   >>> let readMaybeInt = readMaybe :: String -> Maybe Int
--   
--   >>> mapMaybe readMaybeInt ["1", "Foo", "3"]
--   [1,3]
--   
--   >>> catMaybes $ map readMaybeInt ["1", "Foo", "3"]
--   [1,3]
--
-- -- If we map the Just constructor, the entire list should be -- returned: -- -- 
--   >>> mapMaybe Just [1,2,3]
--   [1,2,3]
--
mapMaybe :: () => (a -> Maybe b) -> [a] -> [b] -- | The catMaybes function takes a list of Maybes and -- returns a list of all the Just values. -- --

Examples

-- -- Basic usage: -- -- 
--   >>> catMaybes [Just 1, Nothing, Just 3]
--   [1,3]
--
-- -- When constructing a list of Maybe values, catMaybes can -- be used to return all of the "success" results (if the list is the -- result of a map, then mapMaybe would be more -- appropriate): -- -- 
--   >>> import Text.Read ( readMaybe )
--   
--   >>> [readMaybe x :: Maybe Int | x <- ["1", "Foo", "3"] ]
--   [Just 1,Nothing,Just 3]
--   
--   >>> catMaybes $ [readMaybe x :: Maybe Int | x <- ["1", "Foo", "3"] ]
--   [1,3]
--
catMaybes :: () => [Maybe a] -> [a] -- | The listToMaybe function returns Nothing on an empty -- list or Just a where a is the first element -- of the list. -- --

Examples

-- -- Basic usage: -- -- 
--   >>> listToMaybe []
--   Nothing
--
-- -- 
--   >>> listToMaybe [9]
--   Just 9
--
-- -- 
--   >>> listToMaybe [1,2,3]
--   Just 1
--
-- -- Composing maybeToList with listToMaybe should be the -- identity on singleton/empty lists: -- -- 
--   >>> maybeToList $ listToMaybe [5]
--   [5]
--   
--   >>> maybeToList $ listToMaybe []
--   []
--
-- -- But not on lists with more than one element: -- -- 
--   >>> maybeToList $ listToMaybe [1,2,3]
--   [1]
--
listToMaybe :: () => [a] -> Maybe a -- | The maybeToList function returns an empty list when given -- Nothing or a singleton list when not given Nothing. -- --

Examples

-- -- Basic usage: -- -- 
--   >>> maybeToList (Just 7)
--   [7]
--
-- -- 
--   >>> maybeToList Nothing
--   []
--
-- -- One can use maybeToList to avoid pattern matching when combined -- with a function that (safely) works on lists: -- -- 
--   >>> import Text.Read ( readMaybe )
--   
--   >>> sum $ maybeToList (readMaybe "3")
--   3
--   
--   >>> sum $ maybeToList (readMaybe "")
--   0
--
maybeToList :: () => Maybe a -> [a] -- | The fromMaybe function takes a default value and and -- Maybe value. If the Maybe is Nothing, it returns -- the default values; otherwise, it returns the value contained in the -- Maybe. -- --

Examples

-- -- Basic usage: -- -- 
--   >>> fromMaybe "" (Just "Hello, World!")
--   "Hello, World!"
--
-- -- 
--   >>> fromMaybe "" Nothing
--   ""
--
-- -- Read an integer from a string using readMaybe. If we fail to -- parse an integer, we want to return 0 by default: -- -- 
--   >>> import Text.Read ( readMaybe )
--   
--   >>> fromMaybe 0 (readMaybe "5")
--   5
--   
--   >>> fromMaybe 0 (readMaybe "")
--   0
--
fromMaybe :: () => a -> Maybe a -> a -- | The isNothing function returns True iff its argument is -- Nothing. -- --

Examples

-- -- Basic usage: -- -- 
--   >>> isNothing (Just 3)
--   False
--
-- -- 
--   >>> isNothing (Just ())
--   False
--
-- -- 
--   >>> isNothing Nothing
--   True
--
-- -- Only the outer constructor is taken into consideration: -- -- 
--   >>> isNothing (Just Nothing)
--   False
--
isNothing :: () => Maybe a -> Bool -- | The isJust function returns True iff its argument is of -- the form Just _. -- --

Examples

-- -- Basic usage: -- -- 
--   >>> isJust (Just 3)
--   True
--
-- -- 
--   >>> isJust (Just ())
--   True
--
-- -- 
--   >>> isJust Nothing
--   False
--
-- -- Only the outer constructor is taken into consideration: -- -- 
--   >>> isJust (Just Nothing)
--   True
--
isJust :: () => Maybe a -> Bool -- | 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 -- | Swap the components of a pair. swap :: () => (a, b) -> (b, a) -- | 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 -- | An MVar (pronounced "em-var") is a synchronising variable, used -- for communication between concurrent threads. It can be thought of as -- a box, which may be empty or full. data MVar a -- | 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 -- | Returns a [String] representing the current call stack. This -- can be useful for debugging. -- -- The implementation uses the call-stack simulation maintained by the -- profiler, so it only works if the program was compiled with -- -prof and contains suitable SCC annotations (e.g. by using -- -fprof-auto). Otherwise, the list returned is likely to be -- empty or uninformative. currentCallStack :: IO [String] -- | 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 -- | flip f takes its (first) two arguments in the reverse -- order of f. -- -- 
--   >>> flip (++) "hello" "world"
--   "worldhello"
--
flip :: () => (a -> b -> c) -> b -> a -> c -- | Function composition. (.) :: () => (b -> c) -> (a -> b) -> a -> c infixr 9 . -- | 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 -- | Identity function. -- -- 
--   id x = x
--
id :: () => a -> a -- | The fromEnum method restricted to the type Char. ord :: Char -> Int -- | In many situations, the liftM operations can be replaced by -- uses of ap, which promotes function application. -- -- 
--   return f `ap` x1 `ap` ... `ap` xn
--
-- -- is equivalent to -- -- 
--   liftMn f x1 x2 ... xn
--
ap :: Monad m => m (a -> b) -> m a -> m b -- | Promote a function to a monad, scanning the monadic arguments from -- left to right (cf. liftM2). liftM5 :: Monad m => (a1 -> a2 -> a3 -> a4 -> a5 -> r) -> m a1 -> m a2 -> m a3 -> m a4 -> m a5 -> m r -- | Promote a function to a monad, scanning the monadic arguments from -- left to right (cf. liftM2). liftM4 :: Monad m => (a1 -> a2 -> a3 -> a4 -> r) -> m a1 -> m a2 -> m a3 -> m a4 -> m r -- | Promote a function to a monad, scanning the monadic arguments from -- left to right (cf. liftM2). liftM3 :: Monad m => (a1 -> a2 -> a3 -> r) -> m a1 -> m a2 -> m a3 -> m r -- | Promote a function to a monad, scanning the monadic arguments from -- left to right. For example, -- -- 
--   liftM2 (+) [0,1] [0,2] = [0,2,1,3]
--   liftM2 (+) (Just 1) Nothing = Nothing
--
liftM2 :: Monad m => (a1 -> a2 -> r) -> m a1 -> m a2 -> m r -- | Conditional execution of Applicative expressions. For example, -- -- 
--   when debug (putStrLn "Debugging")
--
-- -- will output the string Debugging if the Boolean value -- debug is True, and otherwise do nothing. when :: Applicative f => Bool -> f () -> f () -- | Same as >>=, but with the arguments interchanged. (=<<) :: Monad m => (a -> m b) -> m a -> m b infixr 1 =<< -- | Lift a ternary function to actions. liftA3 :: Applicative f => (a -> b -> c -> d) -> f a -> f b -> f c -> f d -- | A variant of <*> with the arguments reversed. (<**>) :: Applicative f => f a -> f (a -> b) -> f b infixl 4 <**> -- | A monoid on applicative functors. -- -- If defined, some and many should be the least solutions -- of the equations: -- -- class Applicative f => Alternative (f :: Type -> Type) -- | The identity of <|> empty :: Alternative f => f a -- | An associative binary operation (<|>) :: Alternative f => f a -> f a -> f a -- | One or more. some :: Alternative f => f a -> f [a] -- | Zero or more. many :: Alternative f => f a -> f [a] infixl 3 <|> -- | Monads that also support choice and failure. class (Alternative m, Monad m) => MonadPlus (m :: Type -> Type) -- | The identity of mplus. It should also satisfy the equations -- -- 
--   mzero >>= f  =  mzero
--   v >> mzero   =  mzero
--
-- -- The default definition is -- -- 
--   mzero = empty
--
mzero :: MonadPlus m => m a -- | An associative operation. The default definition is -- -- 
--   mplus = (<|>)
--
mplus :: MonadPlus m => m a -> m a -> m a -- | Non-empty (and non-strict) list type. data NonEmpty a (:|) :: a -> [a] -> NonEmpty a infixr 5 :| -- | A String is a list of characters. String constants in Haskell -- are values of type String. type String = [Char] -- | Extract a list of call-sites from the CallStack. -- -- The list is ordered by most recent call. getCallStack :: CallStack -> [([Char], SrcLoc)] -- | Request a CallStack. -- -- NOTE: The implicit parameter ?callStack :: CallStack is an -- implementation detail and should not be considered part of the -- CallStack API, we may decide to change the implementation in -- the future. type HasCallStack = ?callStack :: CallStack -- | This is a valid definition of stimes for an idempotent -- Monoid. -- -- When mappend x x = x, this definition should be preferred, -- because it works in O(1) rather than O(log n) stimesIdempotentMonoid :: (Integral b, Monoid a) => b -> a -> a -- | The SomeException type is the root of the exception type -- hierarchy. When an exception of type e is thrown, behind the -- scenes it is encapsulated in a SomeException. data SomeException [SomeException] :: forall e. Exception e => e -> SomeException -- | Boolean "and" (&&) :: Bool -> Bool -> Bool infixr 3 && -- | Boolean "or" (||) :: Bool -> Bool -> Bool infixr 2 || -- | Boolean "not" not :: Bool -> Bool -- | A space-efficient representation of a Word8 vector, supporting -- many efficient operations. -- -- A ByteString contains 8-bit bytes, or by using the operations -- from Data.ByteString.Char8 it can be interpreted as containing -- 8-bit characters. data ByteString -- | A map of integers to values a. data IntMap a -- | A set of integers. data IntSet -- | A Map from keys k to values a. data Map k a -- | General-purpose finite sequences. data Seq a -- | A set of values a. data Set a -- | a variant of deepseq that is useful in some circumstances: -- -- 
--   force x = x `deepseq` x
--
-- -- force x fully evaluates x, and then returns it. Note -- that force x only performs evaluation when the value of -- force x itself is demanded, so essentially it turns shallow -- evaluation into deep evaluation. -- -- force can be conveniently used in combination with -- ViewPatterns: -- -- 
--   {-# LANGUAGE BangPatterns, ViewPatterns #-}
--   import Control.DeepSeq
--   
--   someFun :: ComplexData -> SomeResult
--   someFun (force -> !arg) = {- 'arg' will be fully evaluated -}
--
-- -- Another useful application is to combine force with -- evaluate in order to force deep evaluation relative to other -- IO operations: -- -- 
--   import Control.Exception (evaluate)
--   import Control.DeepSeq
--   
--   main = do
--     result <- evaluate $ force $ pureComputation
--     {- 'result' will be fully evaluated at this point -}
--     return ()
--
-- -- Finally, here's an exception safe variant of the readFile' -- example: -- -- 
--   readFile' :: FilePath -> IO String
--   readFile' fn = bracket (openFile fn ReadMode) hClose $ \h ->
--                          evaluate . force =<< hGetContents h
--
force :: NFData a => a -> a -- | the deep analogue of $!. In the expression f $!! x, -- x is fully evaluated before the function f is -- applied to it. ($!!) :: NFData a => (a -> b) -> a -> b infixr 0 $!! -- | deepseq: fully evaluates the first argument, before returning -- the second. -- -- The name deepseq is used to illustrate the relationship to -- seq: where seq is shallow in the sense that it only -- evaluates the top level of its argument, deepseq traverses the -- entire data structure evaluating it completely. -- -- deepseq can be useful for forcing pending exceptions, -- eradicating space leaks, or forcing lazy I/O to happen. It is also -- useful in conjunction with parallel Strategies (see the -- parallel package). -- -- There is no guarantee about the ordering of evaluation. The -- implementation may evaluate the components of the structure in any -- order or in parallel. To impose an actual order on evaluation, use -- pseq from Control.Parallel in the parallel -- package. deepseq :: NFData a => a -> b -> b -- | A class of types that can be fully evaluated. class NFData a -- | rnf should reduce its argument to normal form (that is, fully -- evaluate all sub-components), and then return '()'. -- --

Generic NFData deriving

-- -- Starting with GHC 7.2, you can automatically derive instances for -- types possessing a Generic instance. -- -- Note: Generic1 can be auto-derived starting with GHC 7.4 -- -- 
--   {-# LANGUAGE DeriveGeneric #-}
--   
--   import GHC.Generics (Generic, Generic1)
--   import Control.DeepSeq
--   
--   data Foo a = Foo a String
--                deriving (Eq, Generic, Generic1)
--   
--   instance NFData a => NFData (Foo a)
--   instance NFData1 Foo
--   
--   data Colour = Red | Green | Blue
--                 deriving Generic
--   
--   instance NFData Colour
--
-- -- Starting with GHC 7.10, the example above can be written more -- concisely by enabling the new DeriveAnyClass extension: -- -- 
--   {-# LANGUAGE DeriveGeneric, DeriveAnyClass #-}
--   
--   import GHC.Generics (Generic)
--   import Control.DeepSeq
--   
--   data Foo a = Foo a String
--                deriving (Eq, Generic, Generic1, NFData, NFData1)
--   
--   data Colour = Red | Green | Blue
--                 deriving (Generic, NFData)
--
-- --

Compatibility with previous deepseq versions

-- -- Prior to version 1.4.0.0, the default implementation of the rnf -- method was defined as -- -- 
--   rnf a = seq a ()
--
-- -- However, starting with deepseq-1.4.0.0, the default -- implementation is based on DefaultSignatures allowing for -- more accurate auto-derived NFData instances. If you need the -- previously used exact default rnf method implementation -- semantics, use -- -- 
--   instance NFData Colour where rnf x = seq x ()
--
-- -- or alternatively -- -- 
--   instance NFData Colour where rnf = rwhnf
--
-- -- or -- -- 
--   {-# LANGUAGE BangPatterns #-}
--   instance NFData Colour where rnf !_ = ()
--
rnf :: NFData a => a -> () -- | The class of monad transformers. Instances should satisfy the -- following laws, which state that lift is a monad -- transformation: -- -- class MonadTrans (t :: Type -> Type -> Type -> Type) -- | Lift a computation from the argument monad to the constructed monad. lift :: (MonadTrans t, Monad m) => m a -> t m a -- | The trivial monad transformer, which maps a monad to an equivalent -- monad. data IdentityT (f :: k -> Type) (a :: k) :: forall k. () => k -> Type -> k -> Type -- | Gets specific component of the state, using a projection function -- supplied. gets :: MonadState s m => (s -> a) -> m a -- | A variant of modify in which the computation is strict in the -- new state. modify' :: MonadState s m => (s -> s) -> m () -- | Monadic state transformer. -- -- Maps an old state to a new state inside a state monad. The old state -- is thrown away. -- -- 
--   Main> :t modify ((+1) :: Int -> Int)
--   modify (...) :: (MonadState Int a) => a ()
--
-- -- This says that modify (+1) acts over any Monad that is a -- member of the MonadState class, with an Int state. modify :: MonadState s m => (s -> s) -> m () -- | Minimal definition is either both of get and put or -- just state class Monad m => MonadState s (m :: Type -> Type) | m -> s -- | Return the state from the internals of the monad. get :: MonadState s m => m s -- | Replace the state inside the monad. put :: MonadState s m => s -> m () -- | Embed a simple state action into the monad. state :: MonadState s m => (s -> (a, s)) -> m a -- | Retrieves a function of the current environment. asks :: MonadReader r m => (r -> a) -> m a -- | See examples in Control.Monad.Reader. Note, the partially -- applied function type (->) r is a simple reader monad. See -- the instance declaration below. class Monad m => MonadReader r (m :: Type -> Type) | m -> r -- | Retrieves the monad environment. ask :: MonadReader r m => m r -- | Executes a computation in a modified environment. local :: MonadReader r m => (r -> r) -> m a -> m a -- | Retrieves a function of the current environment. reader :: MonadReader r m => (r -> a) -> m a -- | A monad transformer that adds exceptions to other monads. -- -- ExceptT constructs a monad parameterized over two things: -- -- -- -- The return function yields a computation that produces the -- given value, while >>= sequences two subcomputations, -- exiting on the first exception. newtype ExceptT e (m :: Type -> Type) a ExceptT :: m (Either e a) -> ExceptT e a -- | The inverse of ExceptT. runExceptT :: () => ExceptT e m a -> m (Either e a) -- | The reader monad transformer, which adds a read-only environment to -- the given monad. -- -- The return function ignores the environment, while -- >>= passes the inherited environment to both -- subcomputations. newtype ReaderT r (m :: Type -> Type) a ReaderT :: (r -> m a) -> ReaderT r a [runReaderT] :: ReaderT r a -> r -> m a -- | The parameterizable reader monad. -- -- Computations are functions of a shared environment. -- -- The return function ignores the environment, while -- >>= passes the inherited environment to both -- subcomputations. type Reader r = ReaderT r Identity -- | Runs a Reader and extracts the final value from it. (The -- inverse of reader.) runReader :: () => Reader r a -> r -> a -- | A state transformer monad parameterized by: -- -- -- -- 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 a [runStateT] :: StateT s a -> s -> m (a, s) -- | 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 -- | Unwrap a state monad computation as a function. (The inverse of -- state.) runState :: () => State s a -> s -> (a, s) -- | 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 state, discarding the final value. -- -- execState :: () => State s a -> s -> s -- | withState f m executes action m on a state -- modified by applying f. -- -- withState :: () => (s -> s) -> State s a -> State 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. -- -- execStateT :: Monad m => StateT s m a -> s -> m s -- | Strict version of modifyTVar. modifyTVar' :: () => TVar a -> (a -> a) -> STM () -- | O(c) Convert a strict Text into a lazy Text. fromStrict :: Text -> Text -- | O(n) Convert a lazy Text into a strict Text. toStrict :: Text -> Text -- | O(n) Joins words using single space characters. unwords :: [Text] -> Text -- | O(n) Joins lines, after appending a terminating newline to -- each. unlines :: [Text] -> Text -- | O(n) Breaks a Text up into a list of Texts at -- newline Chars. The resulting strings do not contain newlines. lines :: Text -> [Text] -- | O(n) Breaks a Text up into a list of words, delimited by -- Chars representing white space. words :: Text -> [Text] -- | O(n) Convert a String into a Text. Subject to -- fusion. Performs replacement on invalid scalar values. pack :: String -> Text -- | Decode a ByteString containing UTF-8 encoded text. -- -- If the input contains any invalid UTF-8 data, the relevant exception -- will be returned, otherwise the decoded text. decodeUtf8' :: ByteString -> Either UnicodeException Text -- | Decode a ByteString containing UTF-8 encoded text. -- -- NOTE: The replacement character returned by -- OnDecodeError MUST be within the BMP plane; surrogate code -- points will automatically be remapped to the replacement char -- U+FFFD (since 0.11.3.0), whereas code points beyond -- the BMP will throw an error (since 1.2.3.1); For earlier -- versions of text using those unsupported code points would -- result in undefined behavior. decodeUtf8With :: OnDecodeError -> ByteString -> Text -- | A space efficient, packed, unboxed Unicode text type. data Text -- | Replace an invalid input byte with the Unicode replacement character -- U+FFFD. lenientDecode :: OnDecodeError -- | Throw a UnicodeException if decoding fails. strictDecode :: OnDecodeError -- | Function type for handling a coding error. It is supplied with two -- inputs: -- -- -- -- If the handler returns a value wrapped with Just, that value -- will be used in the output as the replacement for the invalid input. -- If it returns Nothing, no value will be used in the output. -- -- Should the handler need to abort processing, it should use -- error or throw an exception (preferably a -- UnicodeException). It may use the description provided to -- construct a more helpful error report. type OnError a b = String -> Maybe a -> Maybe b -- | A handler for a decoding error. type OnDecodeError = OnError Word8 Char -- | An exception type for representing Unicode encoding errors. data UnicodeException -- | Convert a ExceptT computation to MaybeT, discarding the -- value of any exception. exceptToMaybeT :: Functor m => ExceptT e m a -> MaybeT m a -- | Convert a MaybeT computation to ExceptT, with a default -- exception value. maybeToExceptT :: Functor m => e -> MaybeT m a -> ExceptT e m a -- | The parameterizable maybe monad, obtained by composing an arbitrary -- monad with the Maybe monad. -- -- Computations are actions that may produce a value or exit. -- -- The return function yields a computation that produces that -- value, while >>= sequences two subcomputations, exiting -- if either computation does. newtype MaybeT (m :: Type -> Type) a MaybeT :: m (Maybe a) -> MaybeT a [runMaybeT] :: MaybeT a -> m (Maybe a) (%~) :: () => ASetter s t a b -> (a -> b) -> s -> t (.~) :: () => ASetter s t a b -> b -> s -> t (^.) :: () => s -> Getting a s a -> a (^..) :: () => s -> Getting (Endo [a]) s a -> [a] (^?) :: () => s -> Getting (First a) s a -> Maybe a over :: () => ASetter s t a b -> (a -> b) -> s -> t set :: () => ASetter s t a b -> b -> s -> t preuse :: MonadState s m => Getting (First a) s a -> m (Maybe a) preview :: MonadReader s m => Getting (First a) s a -> m (Maybe a) use :: MonadState s m => Getting a s a -> m a view :: MonadReader s m => Getting a s a -> m a bracket :: MonadMask m => m a -> (a -> m b) -> (a -> m c) -> m c bracketOnError :: MonadMask m => m a -> (a -> m b) -> (a -> m c) -> m c bracket_ :: MonadMask m => m a -> m b -> m c -> m c catch :: (MonadCatch m, Exception e) => m a -> (e -> m a) -> m a catchAny :: MonadCatch m => m a -> (SomeException -> m a) -> m a finally :: MonadMask m => m a -> m b -> m a handleAny :: MonadCatch m => (SomeException -> m a) -> m a -> m a onException :: MonadMask m => m a -> m b -> m a throwM :: (MonadThrow m, Exception e) => e -> m a try :: (MonadCatch m, Exception e) => m a -> m (Either e a) tryAny :: MonadCatch m => m a -> m (Either SomeException a) pass :: Applicative f => f () ($!) :: () => (a -> b) -> a -> b guardM :: MonadPlus m => m Bool -> m () ifM :: Monad m => m Bool -> m a -> m a -> m a unlessM :: Monad m => m Bool -> m () -> m () whenM :: Monad m => m Bool -> m () -> m () asum :: (Container t, Alternative f, Element t ~ f a) => t -> f a flipfoldl' :: (Container t, Element t ~ a) => (a -> b -> b) -> b -> t -> b forM_ :: (Container t, Monad m) => t -> (Element t -> m b) -> m () for_ :: (Container t, Applicative f) => t -> (Element t -> f b) -> f () mapM_ :: (Container t, Monad m) => (Element t -> m b) -> t -> m () product :: (Container t, Num (Element t)) => t -> Element t sequenceA_ :: (Container t, Applicative f, Element t ~ f a) => t -> f () sequence_ :: (Container t, Monad m, Element t ~ m a) => t -> m () sum :: (Container t, Num (Element t)) => t -> Element t traverse_ :: (Container t, Applicative f) => (Element t -> f b) -> t -> f () error :: HasCallStack => Text -> a trace :: () => Text -> a -> a traceId :: Text -> Text traceIdWith :: () => (a -> Text) -> a -> a traceM :: Monad m => Text -> m () traceShow :: Show a => a -> b -> b traceShowId :: Show a => a -> a traceShowIdWith :: Show s => (a -> s) -> a -> a traceShowM :: (Show a, Monad m) => a -> m () undefined :: HasCallStack => a evaluateNF :: (NFData a, MonadIO m) => a -> m a evaluateNF_ :: (NFData a, MonadIO m) => a -> m () evaluateWHNF :: MonadIO m => a -> m a evaluateWHNF_ :: MonadIO m => a -> m () pattern Exc :: forall e. Exception e => () => e -> SomeException bug :: (HasCallStack, Exception e) => e -> a note :: MonadError e m => e -> Maybe a -> m a (<<$>>) :: (Functor f, Functor g) => (a -> b) -> f (g a) -> f (g b) map :: Functor f => (a -> b) -> f a -> f b atomically :: MonadIO m => STM a -> m a newEmptyMVar :: MonadIO m => m (MVar a) newMVar :: MonadIO m => a -> m (MVar a) newTVarIO :: MonadIO m => a -> m (TVar a) putMVar :: MonadIO m => MVar a -> a -> m () readMVar :: MonadIO m => MVar a -> m a readTVarIO :: MonadIO m => TVar a -> m a swapMVar :: MonadIO m => MVar a -> a -> m a takeMVar :: MonadIO m => MVar a -> m a tryPutMVar :: MonadIO m => MVar a -> a -> m Bool tryReadMVar :: MonadIO m => MVar a -> m (Maybe a) tryTakeMVar :: MonadIO m => MVar a -> m (Maybe a) die :: MonadIO m => String -> m a exitFailure :: MonadIO m => m a exitSuccess :: MonadIO m => m a exitWith :: MonadIO m => ExitCode -> m a appendFile :: MonadIO m => FilePath -> Text -> m () getLine :: MonadIO m => m Text hClose :: MonadIO m => Handle -> m () openFile :: MonadIO m => FilePath -> IOMode -> m Handle readFile :: MonadIO m => FilePath -> m Text withFile :: (MonadIO m, MonadMask m) => FilePath -> IOMode -> (Handle -> m a) -> m a writeFile :: MonadIO m => FilePath -> Text -> m () atomicModifyIORef :: MonadIO m => IORef a -> (a -> (a, b)) -> m b atomicModifyIORef' :: MonadIO m => IORef a -> (a -> (a, b)) -> m b atomicWriteIORef :: MonadIO m => IORef a -> a -> m () modifyIORef :: MonadIO m => IORef a -> (a -> a) -> m () modifyIORef' :: MonadIO m => IORef a -> (a -> a) -> m () newIORef :: MonadIO m => a -> m (IORef a) readIORef :: MonadIO m => IORef a -> m a writeIORef :: MonadIO m => IORef a -> a -> m () uncons :: () => [a] -> Maybe (a, [a]) whenNotNull :: Applicative f => [a] -> (NonEmpty a -> f ()) -> f () whenNotNullM :: Monad m => m [a] -> (NonEmpty a -> m ()) -> m () allM :: (Container f, Monad m) => (Element f -> m Bool) -> f -> m Bool andM :: (Container f, Element f ~ m Bool, Monad m) => f -> m Bool anyM :: (Container f, Monad m) => (Element f -> m Bool) -> f -> m Bool concatForM :: (Applicative f, Monoid m, Container (l m), Element (l m) ~ m, Traversable l) => l a -> (a -> f m) -> f m concatMapM :: (Applicative f, Monoid m, Container (l m), Element (l m) ~ m, Traversable l) => (a -> f m) -> l a -> f m orM :: (Container f, Element f ~ m Bool, Monad m) => f -> m Bool fromLeft :: () => a -> Either a b -> a fromRight :: () => b -> Either a b -> b leftToMaybe :: () => Either l r -> Maybe l maybeToLeft :: () => r -> Maybe l -> Either l r maybeToRight :: () => l -> Maybe r -> Either l r rightToMaybe :: () => Either l r -> Maybe r whenLeft :: Applicative f => Either l r -> (l -> f ()) -> f () whenLeftM :: Monad m => m (Either l r) -> (l -> m ()) -> m () whenRight :: Applicative f => Either l r -> (r -> f ()) -> f () whenRightM :: Monad m => m (Either l r) -> (r -> m ()) -> m () (?:) :: () => Maybe a -> a -> a whenJust :: Applicative f => Maybe a -> (a -> f ()) -> f () whenJustM :: Monad m => m (Maybe a) -> (a -> m ()) -> m () whenNothing :: Applicative f => Maybe a -> f a -> f a whenNothingM :: Monad m => m (Maybe a) -> m a -> m a whenNothingM_ :: Monad m => m (Maybe a) -> m () -> m () whenNothing_ :: Applicative f => Maybe a -> f () -> f () evaluatingState :: () => s -> State s a -> a evaluatingStateT :: Functor f => s -> StateT s f a -> f a executingState :: () => s -> State s a -> s executingStateT :: Functor f => s -> StateT s f a -> f s usingReader :: () => r -> Reader r a -> a usingReaderT :: () => r -> ReaderT r m a -> m a usingState :: () => s -> State s a -> (a, s) usingStateT :: () => s -> StateT s m a -> m (a, s) maybeToMonoid :: Monoid m => Maybe m -> m hashNub :: (Eq a, Hashable a) => [a] -> [a] ordNub :: Ord a => [a] -> [a] sortNub :: Ord a => [a] -> [a] unstableNub :: (Eq a, Hashable a) => [a] -> [a] hPrint :: (MonadIO m, Show a) => Handle -> a -> m () hPutStr :: (Print a, MonadIO m) => Handle -> a -> m () hPutStrLn :: (Print a, MonadIO m) => Handle -> a -> m () print :: (MonadIO m, Show a) => a -> m () putLText :: MonadIO m => Text -> m () putLTextLn :: MonadIO m => Text -> m () putStr :: (Print a, MonadIO m) => a -> m () putStrLn :: (Print a, MonadIO m) => a -> m () putText :: MonadIO m => Text -> m () putTextLn :: MonadIO m => Text -> m () readEither :: (ToString a, Read b) => a -> Either Text b show :: (Show a, IsString b) => a -> b class MonadThrow m => MonadCatch (m :: Type -> Type) class MonadCatch m => MonadMask (m :: Type -> Type) mask :: MonadMask m => ((forall a. () => m a -> m a) -> m b) -> m b uninterruptibleMask :: MonadMask m => ((forall a. () => m a -> m a) -> m b) -> m b generalBracket :: MonadMask m => m a -> (a -> ExitCase b -> m c) -> (a -> m b) -> m (b, c) class Monad m => MonadThrow (m :: Type -> Type) class Hashable a hashWithSalt :: Hashable a => Int -> a -> Int _1 :: Field1 s t a b => Lens s t a b _2 :: Field2 s t a b => Lens s t a b _3 :: Field3 s t a b => Lens s t a b _4 :: Field4 s t a b => Lens s t a b _5 :: Field5 s t a b => Lens s t a b type Lens s t a b = forall (f :: Type -> Type). Functor f => a -> f b -> s -> f t type Lens' s a = Lens s s a a type Traversal s t a b = forall (f :: Type -> Type). Applicative f => a -> f b -> s -> f t type Traversal' s a = Traversal s s a a class Container t where { type family Element t :: Type; } toList :: Container t => t -> [Element t] null :: Container t => t -> Bool foldr :: Container t => (Element t -> b -> b) -> b -> t -> b foldl :: Container t => (b -> Element t -> b) -> b -> t -> b foldl' :: Container t => (b -> Element t -> b) -> b -> t -> b length :: Container t => t -> Int elem :: Container t => Element t -> t -> Bool maximum :: Container t => t -> Element t minimum :: Container t => t -> Element t foldMap :: (Container t, Monoid m) => (Element t -> m) -> t -> m fold :: Container t => t -> Element t foldr' :: Container t => (Element t -> b -> b) -> b -> t -> b foldr1 :: Container t => (Element t -> Element t -> Element t) -> t -> Element t foldl1 :: Container t => (Element t -> Element t -> Element t) -> t -> Element t notElem :: Container t => Element t -> t -> Bool all :: Container t => (Element t -> Bool) -> t -> Bool any :: Container t => (Element t -> Bool) -> t -> Bool and :: Container t => t -> Bool or :: Container t => t -> Bool find :: Container t => (Element t -> Bool) -> t -> Maybe (Element t) safeHead :: Container t => t -> Maybe (Element t) class One x where { type family OneItem x :: Type; } one :: One x => OneItem x -> x class ToPairs t where { type family Key t :: Type; type family Val t :: Type; } toPairs :: ToPairs t => t -> [(Key t, Val t)] keys :: ToPairs t => t -> [Key t] elems :: ToPairs t => t -> [Val t] data Undefined Undefined :: Undefined data Bug Bug :: SomeException -> CallStack -> Bug class Print a class ConvertUtf8 a b encodeUtf8 :: ConvertUtf8 a b => a -> b decodeUtf8 :: ConvertUtf8 a b => b -> a decodeUtf8Strict :: ConvertUtf8 a b => b -> Either UnicodeException a type LByteString = ByteString type LText = Text class ToLText a toLText :: ToLText a => a -> Text class ToString a toString :: ToString a => a -> String class ToText a toText :: ToText a => a -> Text type ($) (f :: k -> k1) (a :: k) = f a type family Each (c :: [k -> Constraint]) (as :: [k]) :: Constraint type With (a :: [k -> Constraint]) (b :: k) = a <+> b class SuperComposition a b c | a b -> c (...) :: SuperComposition a b c => a -> b -> c data HashMap k v data HashSet a data Vector a safeFromIntegral :: forall a b. (Integral a, Integral b, Bounded b) => a -> Maybe b liftEither :: (MonadFail m, Show a) => Either a b -> m b hashWith :: (ByteArrayAccess ba, HashAlgorithm alg) => alg -> ba -> Digest alg hashlazy :: HashAlgorithm a => ByteString -> Digest a data SHA256 SHA256 :: SHA256 data Digest a getRandomBytes :: (MonadRandom m, ByteArray byteArray) => Int -> m byteArray camel :: String -> String fromSnake :: String -> Identifier String pascal :: String -> String toPascal :: Identifier String -> String module Data.Signable.Class data PubKey data PrvKey importPubKeyDer :: Alg -> ByteString -> Maybe PubKey importPubKeyPem :: Alg -> ByteString -> Either SignableError PubKey exportPubKeyDer :: ECPointFormat -> PubKey -> ByteString derivePubKey :: PrvKey -> PubKey importPrvKeyRaw :: Alg -> ByteString -> Maybe PrvKey importPrvKeyPem :: Alg -> ByteString -> Either SignableError PrvKey exportPrvKeyRaw :: PrvKey -> ByteString newRandomPrvKey :: (MonadIO m, MonadFail m) => Alg -> m PrvKey data Sig sign :: Signable a => PrvKey -> a -> Sig verify :: Signable a => PubKey -> Sig -> a -> Bool importSigDer :: Alg -> ByteString -> Maybe Sig exportSigDer :: Sig -> ByteString class Signable a toBinary :: Signable a => a -> ByteString pubKey2Alg :: PubKey -> Alg prvKey2Alg :: PrvKey -> Alg sig2Alg :: Sig -> Alg data Alg AlgSecp256k1 :: Alg data SignableError InvalidPem :: SignableError TooFewPemChunks :: SignableError TooManyPemChunks :: SignableError InvalidAsn1 :: SignableError TooFewAsn1Chunks :: SignableError TooManyAsn1Chunks :: SignableError InvalidPubKeyDer :: SignableError InvalidPrvKeyRaw :: SignableError data ECPointFormat ECPointCompressed :: ECPointFormat ECPointUncompressed :: ECPointFormat instance GHC.Show.Show Data.Signable.Class.Sig instance GHC.Classes.Eq Data.Signable.Class.Sig instance GHC.Show.Show Data.Signable.Class.Sha256 instance GHC.Classes.Ord Data.Signable.Class.Sha256 instance GHC.Classes.Eq Data.Signable.Class.Sha256 instance GHC.Classes.Eq Data.Signable.Class.PrvKey instance GHC.Show.Show Data.Signable.Class.PubKey instance GHC.Classes.Eq Data.Signable.Class.PubKey instance GHC.Show.Show Data.Signable.Class.ECPointFormat instance GHC.Classes.Ord Data.Signable.Class.ECPointFormat instance GHC.Classes.Eq Data.Signable.Class.ECPointFormat instance GHC.Show.Show Data.Signable.Class.SignableError instance GHC.Classes.Ord Data.Signable.Class.SignableError instance GHC.Classes.Eq Data.Signable.Class.SignableError instance GHC.Show.Show Data.Signable.Class.Alg instance GHC.Classes.Ord Data.Signable.Class.Alg instance GHC.Classes.Eq Data.Signable.Class.Alg instance Data.Signable.Class.Signable Data.ByteString.Internal.ByteString instance Data.Signable.Class.Signable Data.ByteString.Lazy.Internal.ByteString instance Data.Signable.Class.Signable GHC.Int.Int32 instance Data.Signable.Class.Signable GHC.Int.Int64 instance Data.Signable.Class.Signable GHC.Word.Word32 instance Data.Signable.Class.Signable GHC.Word.Word64 instance Data.Signable.Class.Signable GHC.Types.Double instance Data.Signable.Class.Signable GHC.Types.Float instance Data.Signable.Class.Signable GHC.Types.Bool instance Data.Signable.Class.Signable Data.Text.Internal.Text instance (Data.Foldable.Foldable f, Data.Signable.Class.Signable a) => Data.Signable.Class.Signable (f a) instance GHC.Show.Show Data.Signable.Class.PrvKey -- | Digital signature is common security-related practice. One of the main -- difficulties of digital signature usage is necessity of determenistic -- data serialization agreement. This library provides Signable -- class which represents the idea of such agreement. Also worth -- mentioning generic proto-lens compatible implementation of -- serialization/signing algorithm described here. It's -- implemented as separate protoc plugin signable-haskell-protoc -- which generates Signable class instances for given proto-lens -- messages and enums. module Data.Signable safeFromIntegral :: forall a b. (Integral a, Integral b, Bounded b) => a -> Maybe b ifThenElse :: (a -> Bool) -> (a -> b) -> (a -> b) -> a -> b class Signable a toBinary :: Signable a => a -> ByteString data Sig data PrvKey data PubKey data ECPointFormat ECPointCompressed :: ECPointFormat ECPointUncompressed :: ECPointFormat data SignableError InvalidPem :: SignableError TooFewPemChunks :: SignableError TooManyPemChunks :: SignableError InvalidAsn1 :: SignableError TooFewAsn1Chunks :: SignableError TooManyAsn1Chunks :: SignableError InvalidPubKeyDer :: SignableError InvalidPrvKeyRaw :: SignableError data Alg AlgSecp256k1 :: Alg pubKey2Alg :: PubKey -> Alg prvKey2Alg :: PrvKey -> Alg sig2Alg :: Sig -> Alg importPubKeyDer :: Alg -> ByteString -> Maybe PubKey importPubKeyPem :: Alg -> ByteString -> Either SignableError PubKey exportPubKeyDer :: ECPointFormat -> PubKey -> ByteString derivePubKey :: PrvKey -> PubKey importPrvKeyRaw :: Alg -> ByteString -> Maybe PrvKey importPrvKeyPem :: Alg -> ByteString -> Either SignableError PrvKey exportPrvKeyRaw :: PrvKey -> ByteString newRandomPrvKey :: (MonadIO m, MonadFail m) => Alg -> m PrvKey importSigDer :: Alg -> ByteString -> Maybe Sig exportSigDer :: Sig -> ByteString sign :: Signable a => PrvKey -> a -> Sig verify :: Signable a => PubKey -> Sig -> a -> Bool