-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/
-- | Generate an installation access token for a GitHub App
--
-- Please see README.md
@package github-app-token
@version 0.0.3.0
module GitHub.App.Token.Prelude
-- | Path of some base and type.
--
-- The type variables are:
--
--
-- - b — base, the base location of the path; absolute or
-- relative.
-- - t — type, whether file or directory.
--
--
-- Internally is a string. The string can be of two formats only:
--
--
-- - File format: file.txt, foo/bar.txt,
-- /foo/bar.txt
-- - Directory format: foo/, /foo/bar/
--
--
-- All directories end in a trailing separator. There are no duplicate
-- path separators //, no .., no ./, no
-- ~/, etc.
data () => Path b t
data () => Bool
False :: Bool
True :: Bool
-- | The character type Char is an enumeration whose values
-- represent Unicode (or equivalently ISO/IEC 10646) code points (i.e.
-- characters, see http://www.unicode.org/ for details). This set
-- extends the ISO 8859-1 (Latin-1) character set (the first 256
-- characters), which is itself an extension of the ASCII character set
-- (the first 128 characters). A character literal in Haskell has type
-- Char.
--
-- To convert a Char to or from the corresponding Int value
-- defined by Unicode, use toEnum and fromEnum from the
-- Enum class respectively (or equivalently ord and
-- chr).
data () => Char
-- | Double-precision floating point numbers. It is desirable that this
-- type be at least equal in range and precision to the IEEE
-- double-precision type.
data () => Double
-- | Single-precision floating point numbers. It is desirable that this
-- type be at least equal in range and precision to the IEEE
-- single-precision type.
data () => Float
-- | A fixed-precision integer type with at least the range [-2^29 ..
-- 2^29-1]. The exact range for a given implementation can be
-- determined by using minBound and maxBound from the
-- Bounded class.
data () => Int
-- | A Word is an unsigned integral type, with the same size as
-- Int.
data () => Word
data () => Ordering
LT :: Ordering
EQ :: Ordering
GT :: Ordering
-- | 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
-- | Lifted, homogeneous equality. By lifted, we mean that it can be bogus
-- (deferred type error). By homogeneous, the two types a and
-- b must have the same kinds.
class a ~# b => (a :: k) ~ (b :: k)
infix 4 ~
-- | Arbitrary precision integers. In contrast with fixed-size integral
-- types such as Int, the Integer type represents the
-- entire infinite range of integers.
--
-- Integers are stored in a kind of sign-magnitude form, hence do not
-- expect two's complement form when using bit operations.
--
-- If the value is small (fit into an Int), IS constructor
-- is used. Otherwise Integer and IN constructors are used
-- to store a BigNat representing respectively the positive or the
-- negative value magnitude.
--
-- Invariant: Integer and IN are used iff value doesn't fit
-- in IS
data () => Integer
-- | 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
-- | Conversion of values to readable Strings.
--
-- Derived instances of Show have the following properties, which
-- are compatible with derived instances of Read:
--
--
-- - The result of show is a syntactically correct Haskell
-- expression containing only constants, given the fixity declarations in
-- force at the point where the type is declared. It contains only the
-- constructor names defined in the data type, parentheses, and spaces.
-- When labelled constructor fields are used, braces, commas, field
-- names, and equal signs are also used.
-- - If the constructor is defined to be an infix operator, then
-- showsPrec will produce infix applications of the
-- constructor.
-- - the representation will be enclosed in parentheses if the
-- precedence of the top-level constructor in x is less than
-- d (associativity is ignored). Thus, if d is
-- 0 then the result is never surrounded in parentheses; if
-- d is 11 it is always surrounded in parentheses,
-- unless it is an atomic expression.
-- - If the constructor is defined using record syntax, then
-- show will produce the record-syntax form, with the fields given
-- in the same order as the original declaration.
--
--
-- For example, given the declarations
--
--
-- infixr 5 :^:
-- data Tree a = Leaf a | Tree a :^: Tree a
--
--
-- the derived instance of Show is equivalent to
--
--
-- instance (Show a) => Show (Tree a) where
--
-- showsPrec d (Leaf m) = showParen (d > app_prec) $
-- showString "Leaf " . showsPrec (app_prec+1) m
-- where app_prec = 10
--
-- showsPrec d (u :^: v) = showParen (d > up_prec) $
-- showsPrec (up_prec+1) u .
-- showString " :^: " .
-- showsPrec (up_prec+1) v
-- where up_prec = 5
--
--
-- Note that right-associativity of :^: is ignored. For example,
--
--
-- - show (Leaf 1 :^: Leaf 2 :^: Leaf 3) produces the
-- string "Leaf 1 :^: (Leaf 2 :^: Leaf 3)".
--
class () => Show a
-- | Convert a value to a readable String.
--
-- showsPrec should satisfy the law
--
--
-- showsPrec d x r ++ s == showsPrec d x (r ++ s)
--
--
-- Derived instances of Read and Show satisfy the
-- following:
--
--
--
-- That is, readsPrec parses the string produced by
-- showsPrec, and delivers the value that showsPrec started
-- with.
showsPrec :: Show a => Int -> a -> ShowS
-- | A specialised variant of showsPrec, using precedence context
-- zero, and returning an ordinary String.
show :: Show a => a -> String
-- | The method showList is provided to allow the programmer to give
-- a specialised way of showing lists of values. For example, this is
-- used by the predefined Show instance of the Char type,
-- where values of type String should be shown in double quotes,
-- rather than between square brackets.
showList :: Show a => [a] -> ShowS
-- | The Bounded class is used to name the upper and lower limits of
-- a type. Ord is not a superclass of Bounded since types
-- that are not totally ordered may also have upper and lower bounds.
--
-- The Bounded class may be derived for any enumeration type;
-- minBound is the first constructor listed in the data
-- declaration and maxBound is the last. Bounded may also
-- be derived for single-constructor datatypes whose constituent types
-- are in Bounded.
class () => Bounded a
minBound :: Bounded a => a
maxBound :: Bounded a => a
-- | Class Enum defines operations on sequentially ordered types.
--
-- The enumFrom... methods are used in Haskell's translation of
-- arithmetic sequences.
--
-- Instances of Enum may be derived for any enumeration type
-- (types whose constructors have no fields). The nullary constructors
-- are assumed to be numbered left-to-right by fromEnum from
-- 0 through n-1. See Chapter 10 of the Haskell
-- Report for more details.
--
-- For any type that is an instance of class Bounded as well as
-- Enum, the following should hold:
--
--
--
--
-- enumFrom x = enumFromTo x maxBound
-- enumFromThen x y = enumFromThenTo x y bound
-- where
-- bound | fromEnum y >= fromEnum x = maxBound
-- | otherwise = minBound
--
class () => Enum a
-- | the successor of a value. For numeric types, succ adds 1.
succ :: Enum a => a -> a
-- | the predecessor of a value. For numeric types, pred subtracts
-- 1.
pred :: Enum a => a -> a
-- | Convert from an Int.
toEnum :: Enum a => Int -> a
-- | Convert to an Int. It is implementation-dependent what
-- fromEnum returns when applied to a value that is too large to
-- fit in an Int.
fromEnum :: Enum a => a -> Int
-- | Used in Haskell's translation of [n..] with [n..] =
-- enumFrom n, a possible implementation being enumFrom n = n :
-- enumFrom (succ n). For example:
--
--
-- enumFrom 4 :: [Integer] = [4,5,6,7,...]
enumFrom 6 :: [Int] = [6,7,8,9,...,maxBound ::
-- Int]
enumFrom :: Enum a => a -> [a]
-- | Used in Haskell's translation of [n,n'..] with [n,n'..] =
-- enumFromThen n n', a possible implementation being
-- enumFromThen n n' = n : n' : worker (f x) (f x n'),
-- worker s v = v : worker s (s v), x = fromEnum n' -
-- fromEnum n and f n y | n > 0 = f (n - 1) (succ y) | n <
-- 0 = f (n + 1) (pred y) | otherwise = y For example:
--
--
-- enumFromThen 4 6 :: [Integer] = [4,6,8,10...]
enumFromThen 6 2 :: [Int] = [6,2,-2,-6,...,minBound ::
-- Int]
enumFromThen :: Enum a => a -> a -> [a]
-- | Used in Haskell's translation of [n..m] with [n..m] =
-- enumFromTo n m, a possible implementation being enumFromTo n
-- m | n <= m = n : enumFromTo (succ n) m | otherwise = []. For
-- example:
--
--
-- enumFromTo 6 10 :: [Int] = [6,7,8,9,10]
enumFromTo 42 1 :: [Integer] = []
enumFromTo :: Enum a => a -> a -> [a]
-- | Used in Haskell's translation of [n,n'..m] with [n,n'..m]
-- = enumFromThenTo n n' m, a possible implementation being
-- enumFromThenTo n n' m = worker (f x) (c x) n m, x =
-- fromEnum n' - fromEnum n, c x = bool (>=) ((x
-- 0) f n y | n > 0 = f (n - 1) (succ y) | n < 0 = f (n +
-- 1) (pred y) | otherwise = y and worker s c v m | c v m = v :
-- worker s c (s v) m | otherwise = [] For example:
--
--
-- enumFromThenTo 4 2 -6 :: [Integer] =
-- [4,2,0,-2,-4,-6]
enumFromThenTo 6 8 2 :: [Int] = []
enumFromThenTo :: Enum a => a -> a -> a -> [a]
-- | Extracting components of fractions.
class (Real a, Fractional a) => RealFrac a
-- | The function properFraction takes a real fractional number
-- x and returns a pair (n,f) such that x =
-- n+f, and:
--
--
-- - n is an integral number with the same sign as x;
-- and
-- - f is a fraction with the same type and sign as
-- x, and with absolute value less than 1.
--
--
-- The default definitions of the ceiling, floor,
-- truncate and round functions are in terms of
-- properFraction.
properFraction :: (RealFrac a, Integral b) => a -> (b, a)
-- | truncate x returns the integer nearest x
-- between zero and x
truncate :: (RealFrac a, Integral b) => a -> b
-- | round x returns the nearest integer to x; the
-- even integer if x is equidistant between two integers
round :: (RealFrac a, Integral b) => a -> b
-- | ceiling x returns the least integer not less than
-- x
ceiling :: (RealFrac a, Integral b) => a -> b
-- | floor x returns the greatest integer not greater than
-- x
floor :: (RealFrac a, Integral b) => a -> b
-- | Integral numbers, supporting integer division.
--
-- The Haskell Report defines no laws for Integral. However,
-- Integral instances are customarily expected to define a
-- Euclidean domain and have the following properties for the
-- div/mod and quot/rem pairs, given suitable
-- Euclidean functions f and g:
--
--
-- - x = y * quot x y + rem x y with rem x y
-- = fromInteger 0 or g (rem x y) < g
-- y
-- - x = y * div x y + mod x y with mod x y
-- = fromInteger 0 or f (mod x y) < f
-- y
--
--
-- An example of a suitable Euclidean function, for Integer's
-- instance, is abs.
--
-- In addition, toInteger should be total, and fromInteger
-- should be a left inverse for it, i.e. fromInteger (toInteger i) =
-- i.
class (Real a, Enum a) => Integral a
-- | integer division truncated toward zero
--
-- WARNING: This function is partial (because it throws when 0 is passed
-- as the divisor) for all the integer types in base.
quot :: Integral a => a -> a -> a
-- | integer remainder, satisfying
--
--
-- (x `quot` y)*y + (x `rem` y) == x
--
--
-- WARNING: This function is partial (because it throws when 0 is passed
-- as the divisor) for all the integer types in base.
rem :: Integral a => a -> a -> a
-- | integer division truncated toward negative infinity
--
-- WARNING: This function is partial (because it throws when 0 is passed
-- as the divisor) for all the integer types in base.
div :: Integral a => a -> a -> a
-- | integer modulus, satisfying
--
--
-- (x `div` y)*y + (x `mod` y) == x
--
--
-- WARNING: This function is partial (because it throws when 0 is passed
-- as the divisor) for all the integer types in base.
mod :: Integral a => a -> a -> a
-- | simultaneous quot and rem
--
-- WARNING: This function is partial (because it throws when 0 is passed
-- as the divisor) for all the integer types in base.
quotRem :: Integral a => a -> a -> (a, a)
-- | simultaneous div and mod
--
-- WARNING: This function is partial (because it throws when 0 is passed
-- as the divisor) for all the integer types in base.
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`
-- | Parsing of Strings, producing values.
--
-- Derived instances of Read make the following assumptions, which
-- derived instances of Show obey:
--
--
-- - If the constructor is defined to be an infix operator, then the
-- derived Read instance will parse only infix applications of the
-- constructor (not the prefix form).
-- - Associativity is not used to reduce the occurrence of parentheses,
-- although precedence may be.
-- - If the constructor is defined using record syntax, the derived
-- Read will parse only the record-syntax form, and furthermore,
-- the fields must be given in the same order as the original
-- declaration.
-- - The derived Read instance allows arbitrary Haskell
-- whitespace between tokens of the input string. Extra parentheses are
-- also allowed.
--
--
-- For example, given the declarations
--
--
-- infixr 5 :^:
-- data Tree a = Leaf a | Tree a :^: Tree a
--
--
-- the derived instance of Read in Haskell 2010 is equivalent to
--
--
-- instance (Read a) => Read (Tree a) where
--
-- readsPrec d r = readParen (d > app_prec)
-- (\r -> [(Leaf m,t) |
-- ("Leaf",s) <- lex r,
-- (m,t) <- readsPrec (app_prec+1) s]) r
--
-- ++ readParen (d > up_prec)
-- (\r -> [(u:^:v,w) |
-- (u,s) <- readsPrec (up_prec+1) r,
-- (":^:",t) <- lex s,
-- (v,w) <- readsPrec (up_prec+1) t]) r
--
-- where app_prec = 10
-- up_prec = 5
--
--
-- Note that right-associativity of :^: is unused.
--
-- The derived instance in GHC is equivalent to
--
--
-- instance (Read a) => Read (Tree a) where
--
-- readPrec = parens $ (prec app_prec $ do
-- Ident "Leaf" <- lexP
-- m <- step readPrec
-- return (Leaf m))
--
-- +++ (prec up_prec $ do
-- u <- step readPrec
-- Symbol ":^:" <- lexP
-- v <- step readPrec
-- return (u :^: v))
--
-- where app_prec = 10
-- up_prec = 5
--
-- readListPrec = readListPrecDefault
--
--
-- Why do both readsPrec and readPrec exist, and why does
-- GHC opt to implement readPrec in derived Read instances
-- instead of readsPrec? The reason is that readsPrec is
-- based on the ReadS type, and although ReadS is mentioned
-- in the Haskell 2010 Report, it is not a very efficient parser data
-- structure.
--
-- readPrec, on the other hand, is based on a much more efficient
-- ReadPrec datatype (a.k.a "new-style parsers"), but its
-- definition relies on the use of the RankNTypes language
-- extension. Therefore, readPrec (and its cousin,
-- readListPrec) are marked as GHC-only. Nevertheless, it is
-- recommended to use readPrec instead of readsPrec
-- whenever possible for the efficiency improvements it brings.
--
-- As mentioned above, derived Read instances in GHC will
-- implement readPrec instead of readsPrec. The default
-- implementations of readsPrec (and its cousin, readList)
-- will simply use readPrec under the hood. If you are writing a
-- Read instance by hand, it is recommended to write it like so:
--
--
-- instance Read T where
-- readPrec = ...
-- readListPrec = readListPrecDefault
--
class () => Read a
-- | attempts to parse a value from the front of the string, returning a
-- list of (parsed value, remaining string) pairs. If there is no
-- successful parse, the returned list is empty.
--
-- Derived instances of Read and Show satisfy the
-- following:
--
--
--
-- That is, readsPrec parses the string produced by
-- showsPrec, and delivers the value that showsPrec started
-- with.
readsPrec :: Read a => Int -> ReadS a
-- | The method readList is provided to allow the programmer to give
-- a specialised way of parsing lists of values. For example, this is
-- used by the predefined Read instance of the Char type,
-- where values of type String should be are expected to use
-- double quotes, rather than square brackets.
readList :: Read a => ReadS [a]
-- | A value of type IO a is a computation which, when
-- performed, does some I/O before returning a value of type a.
--
-- There is really only one way to "perform" an I/O action: bind it to
-- Main.main in your program. When your program is run, the I/O
-- will be performed. It isn't possible to perform I/O from an arbitrary
-- function, unless that function is itself in the IO monad and
-- called at some point, directly or indirectly, from Main.main.
--
-- IO is a monad, so IO actions can be combined using
-- either the do-notation or the >> and >>=
-- operations from the Monad class.
data () => IO a
-- | The Ord class is used for totally ordered datatypes.
--
-- Instances of Ord can be derived for any user-defined datatype
-- whose constituent types are in Ord. The declared order of the
-- constructors in the data declaration determines the ordering in
-- derived Ord instances. The Ordering datatype allows a
-- single comparison to determine the precise ordering of two objects.
--
-- Ord, as defined by the Haskell report, implements a total order
-- and has the following properties:
--
--
-- - Comparability x <= y || y <= x =
-- True
-- - Transitivity if x <= y && y <=
-- z = True, then x <= z = True
-- - Reflexivity x <= x = True
-- - Antisymmetry if x <= y && y <=
-- x = True, then x == y = True
--
--
-- The following operator interactions are expected to hold:
--
--
-- - x >= y = y <= x
-- - x < y = x <= y && x /= y
-- - x > y = y < x
-- - x < y = compare x y == LT
-- - x > y = compare x y == GT
-- - x == y = compare x y == EQ
-- - min x y == if x <= y then x else y = True
-- - max x y == if x >= y then x else y = True
--
--
-- Note that (7.) and (8.) do not require min and
-- max to return either of their arguments. The result is merely
-- required to equal one of the arguments in terms of (==).
--
-- Minimal complete definition: either compare or <=.
-- Using compare can be more efficient for complex types.
class Eq a => Ord a
compare :: Ord a => a -> a -> Ordering
(<) :: Ord a => a -> a -> Bool
(<=) :: Ord a => a -> a -> Bool
(>) :: Ord a => a -> a -> Bool
(>=) :: Ord a => a -> a -> Bool
max :: Ord a => a -> a -> a
min :: Ord a => a -> a -> a
infix 4 >=
infix 4 <
infix 4 <=
infix 4 >
-- | A String is a list of characters. String constants in Haskell
-- are values of type String.
--
-- See Data.List for operations on lists.
type String = [Char]
-- | 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
-- | 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 /
-- | Real numbers.
--
-- The Haskell report defines no laws for Real, however
-- Real instances are customarily expected to adhere to the
-- following law:
--
--
class (Num a, Ord a) => Real a
-- | the rational equivalent of its real argument with full precision
toRational :: Real a => a -> Rational
-- | The Eq class defines equality (==) and inequality
-- (/=). All the basic datatypes exported by the Prelude
-- are instances of Eq, and Eq may be derived for any
-- datatype whose constituents are also instances of Eq.
--
-- The Haskell Report defines no laws for Eq. However, instances
-- are encouraged to follow these properties:
--
--
-- - Reflexivity x == x = True
-- - Symmetry x == y = y == x
-- - Transitivity if x == y && y == z =
-- True, then x == z = True
-- - Extensionality if x == y = True and
-- f is a function whose return type is an instance of
-- Eq, then f x == f y = True
-- - Negation x /= y = not (x ==
-- y)
--
--
-- Minimal complete definition: either == or /=.
class () => Eq a
(==) :: Eq a => a -> a -> Bool
(/=) :: Eq a => a -> a -> Bool
infix 4 ==
infix 4 /=
-- | The class of monoids (types with an associative binary operation that
-- has an identity). Instances should satisfy the following:
--
--
--
-- You can alternatively define mconcat instead of mempty,
-- in which case the laws are:
--
--
--
-- The method names refer to the monoid of lists under concatenation, but
-- there are many other instances.
--
-- Some types can be viewed as a monoid in more than one way, e.g. both
-- addition and multiplication on numbers. In such cases we often define
-- newtypes and make those instances of Monoid, e.g.
-- Sum and Product.
--
-- NOTE: Semigroup is a superclass of Monoid since
-- base-4.11.0.0.
class Semigroup a => Monoid a
-- | Identity of mappend
--
--
-- >>> "Hello world" <> mempty
-- "Hello world"
--
mempty :: Monoid a => a
-- | An associative operation
--
-- NOTE: This method is redundant and has the default
-- implementation mappend = (<>) since
-- base-4.11.0.0. Should it be implemented manually, since
-- mappend is a synonym for (<>), it is expected that
-- the two functions are defined the same way. In a future GHC release
-- mappend will be removed from Monoid.
mappend :: Monoid a => a -> a -> a
-- | Fold a list using the monoid.
--
-- For most types, the default definition for mconcat will be
-- used, but the function is included in the class definition so that an
-- optimized version can be provided for specific types.
--
--
-- >>> mconcat ["Hello", " ", "Haskell", "!"]
-- "Hello Haskell!"
--
mconcat :: Monoid a => [a] -> a
-- | The class of semigroups (types with an associative binary operation).
--
-- Instances should satisfy the following:
--
--
-- - Associativity x <> (y <> z) =
-- (x <> y) <> z
--
--
-- You can alternatively define sconcat instead of
-- (<>), in which case the laws are:
--
--
class () => Semigroup a
-- | An associative operation.
--
--
-- >>> [1,2,3] <> [4,5,6]
-- [1,2,3,4,5,6]
--
(<>) :: Semigroup a => a -> a -> a
infixr 6 <>
-- | A functor with application, providing operations to
--
--
-- - embed pure expressions (pure), and
-- - sequence computations and combine their results (<*>
-- and liftA2).
--
--
-- A minimal complete definition must include implementations of
-- pure and of either <*> or liftA2. If it
-- defines both, then they must behave the same as their default
-- definitions:
--
--
-- (<*>) = liftA2 id
--
--
--
-- liftA2 f x y = f <$> x <*> y
--
--
-- Further, any definition must satisfy the following:
--
--
--
-- The other methods have the following default definitions, which may be
-- overridden with equivalent specialized implementations:
--
--
--
-- As a consequence of these laws, the Functor instance for
-- f will satisfy
--
--
--
-- It may be useful to note that supposing
--
--
-- forall x y. p (q x y) = f x . g y
--
--
-- it follows from the above that
--
--
-- liftA2 p (liftA2 q u v) = liftA2 f u . liftA2 g v
--
--
-- If f is also a Monad, it should satisfy
--
--
--
-- (which implies that pure and <*> satisfy the
-- applicative functor laws).
class Functor f => Applicative (f :: Type -> Type)
-- | Lift a value.
pure :: Applicative f => a -> f a
-- | Sequential application.
--
-- A few functors support an implementation of <*> that is
-- more efficient than the default one.
--
-- Example
--
-- Used in combination with (<$>),
-- (<*>) can be used to build a record.
--
--
-- >>> data MyState = MyState {arg1 :: Foo, arg2 :: Bar, arg3 :: Baz}
--
--
--
-- >>> produceFoo :: Applicative f => f Foo
--
--
--
-- >>> produceBar :: Applicative f => f Bar
--
-- >>> produceBaz :: Applicative f => f Baz
--
--
--
-- >>> mkState :: Applicative f => f MyState
--
-- >>> mkState = MyState <$> produceFoo <*> produceBar <*> produceBaz
--
(<*>) :: Applicative f => f (a -> b) -> f a -> f b
-- | 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 <*>.
--
-- This became a typeclass method in 4.10.0.0. Prior to that, it was a
-- function defined in terms of <*> and fmap.
--
-- Example
--
--
-- >>> liftA2 (,) (Just 3) (Just 5)
-- Just (3,5)
--
liftA2 :: Applicative f => (a -> b -> c) -> f a -> f b -> f c
-- | Sequence actions, discarding the value of the first argument.
--
-- Examples
--
-- If used in conjunction with the Applicative instance for Maybe,
-- you can chain Maybe computations, with a possible "early return" in
-- case of Nothing.
--
--
-- >>> Just 2 *> Just 3
-- Just 3
--
--
--
-- >>> Nothing *> Just 3
-- Nothing
--
--
-- Of course a more interesting use case would be to have effectful
-- computations instead of just returning pure values.
--
--
-- >>> import Data.Char
--
-- >>> import Text.ParserCombinators.ReadP
--
-- >>> let p = string "my name is " *> munch1 isAlpha <* eof
--
-- >>> readP_to_S p "my name is Simon"
-- [("Simon","")]
--
(*>) :: Applicative f => f a -> f b -> f b
-- | Sequence actions, discarding the value of the second argument.
(<*) :: Applicative f => f a -> f b -> f a
infixl 4 <*>
infixl 4 *>
infixl 4 <*
-- | A type f is a Functor if it provides a function fmap
-- which, given any types a and b lets you apply any
-- function from (a -> b) to turn an f a into an
-- f b, preserving the structure of f. Furthermore
-- f needs to adhere to the following:
--
--
--
-- Note, that the second law follows from the free theorem of the type
-- fmap and the first law, so you need only check that the former
-- condition holds. See
-- https://www.schoolofhaskell.com/user/edwardk/snippets/fmap or
-- https://github.com/quchen/articles/blob/master/second_functor_law.md
-- for an explanation.
class () => Functor (f :: Type -> Type)
-- | fmap is used to apply a function of type (a -> b)
-- to a value of type f a, where f is a functor, to produce a
-- value of type f b. Note that for any type constructor with
-- more than one parameter (e.g., Either), only the last type
-- parameter can be modified with fmap (e.g., b in
-- `Either a b`).
--
-- Some type constructors with two parameters or more have a
-- Bifunctor instance that allows both the last and the
-- penultimate parameters to be mapped over.
--
-- Examples
--
-- Convert from a Maybe Int to a Maybe String
-- using show:
--
--
-- >>> fmap show Nothing
-- Nothing
--
-- >>> fmap show (Just 3)
-- Just "3"
--
--
-- Convert from an Either Int Int to an Either Int
-- String using show:
--
--
-- >>> fmap show (Left 17)
-- Left 17
--
-- >>> fmap show (Right 17)
-- Right "17"
--
--
-- Double each element of a list:
--
--
-- >>> fmap (*2) [1,2,3]
-- [2,4,6]
--
--
-- Apply even to the second element of a pair:
--
--
-- >>> fmap even (2,2)
-- (2,True)
--
--
-- It may seem surprising that the function is only applied to the last
-- element of the tuple compared to the list example above which applies
-- it to every element in the list. To understand, remember that tuples
-- are type constructors with multiple type parameters: a tuple of 3
-- elements (a,b,c) can also be written (,,) a b c and
-- its Functor instance is defined for Functor ((,,) a
-- b) (i.e., only the third parameter is free to be mapped over with
-- fmap).
--
-- It explains why fmap can be used with tuples containing
-- values of different types as in the following example:
--
--
-- >>> fmap even ("hello", 1.0, 4)
-- ("hello",1.0,True)
--
fmap :: Functor f => (a -> b) -> f a -> f b
-- | Replace all locations in the input with the same value. The default
-- definition is fmap . const, but this may be
-- overridden with a more efficient version.
--
-- Examples
--
-- Perform a computation with Maybe and replace the result with a
-- constant value if it is Just:
--
--
-- >>> 'a' <$ Just 2
-- Just 'a'
--
-- >>> 'a' <$ Nothing
-- Nothing
--
(<$) :: Functor f => a -> f b -> f a
infixl 4 <$
-- | The Monad class defines the basic operations over a
-- monad, a concept from a branch of mathematics known as
-- category theory. From the perspective of a Haskell programmer,
-- however, it is best to think of a monad as an abstract datatype
-- of actions. Haskell's do expressions provide a convenient
-- syntax for writing monadic expressions.
--
-- Instances of Monad should satisfy the following:
--
--
--
-- Furthermore, the Monad and Applicative operations should
-- relate as follows:
--
--
--
-- The above laws imply:
--
--
--
-- and that pure and (<*>) satisfy the applicative
-- functor laws.
--
-- The instances of Monad for lists, Maybe and IO
-- defined in the Prelude satisfy these laws.
class Applicative m => Monad (m :: Type -> Type)
-- | Sequentially compose two actions, passing any value produced by the
-- first as an argument to the second.
--
-- 'as >>= bs' can be understood as the do
-- expression
--
--
-- do a <- as
-- bs a
--
(>>=) :: Monad m => m a -> (a -> m b) -> m b
-- | Sequentially compose two actions, discarding any value produced by the
-- first, like sequencing operators (such as the semicolon) in imperative
-- languages.
--
-- 'as >> bs' can be understood as the do
-- expression
--
--
-- do as
-- bs
--
(>>) :: Monad m => m a -> m b -> m b
-- | Inject a value into the monadic type.
return :: Monad m => a -> m a
infixl 1 >>=
infixl 1 >>
-- | 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
-- | 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 space efficient, packed, unboxed Unicode text type.
data () => Text
-- | This is the simplest representation of UTC. It consists of the day
-- number, and a time offset from midnight. Note that if a day has a leap
-- second added to it, it will have 86401 seconds.
data () => UTCTime
-- | The Foldable class represents data structures that can be reduced to a
-- summary value one element at a time. Strict left-associative folds are
-- a good fit for space-efficient reduction, while lazy right-associative
-- folds are a good fit for corecursive iteration, or for folds that
-- short-circuit after processing an initial subsequence of the
-- structure's elements.
--
-- Instances can be derived automatically by enabling the
-- DeriveFoldable extension. For example, a derived instance for
-- a binary tree might be:
--
--
-- {-# LANGUAGE DeriveFoldable #-}
-- data Tree a = Empty
-- | Leaf a
-- | Node (Tree a) a (Tree a)
-- deriving Foldable
--
--
-- A more detailed description can be found in the Overview
-- section of Data.Foldable#overview.
--
-- For the class laws see the Laws section of
-- Data.Foldable#laws.
class () => Foldable (t :: Type -> Type)
-- | Map each element of the structure into a monoid, and combine the
-- results with (<>). This fold is
-- right-associative and lazy in the accumulator. For strict
-- left-associative folds consider foldMap' instead.
--
-- Examples
--
-- Basic usage:
--
--
-- >>> foldMap Sum [1, 3, 5]
-- Sum {getSum = 9}
--
--
--
-- >>> foldMap Product [1, 3, 5]
-- Product {getProduct = 15}
--
--
--
-- >>> foldMap (replicate 3) [1, 2, 3]
-- [1,1,1,2,2,2,3,3,3]
--
--
-- When a Monoid's (<>) is lazy in its second
-- argument, foldMap can return a result even from an unbounded
-- structure. For example, lazy accumulation enables
-- Data.ByteString.Builder to efficiently serialise large data
-- structures and produce the output incrementally:
--
--
-- >>> import qualified Data.ByteString.Lazy as L
--
-- >>> import qualified Data.ByteString.Builder as B
--
-- >>> let bld :: Int -> B.Builder; bld i = B.intDec i <> B.word8 0x20
--
-- >>> let lbs = B.toLazyByteString $ foldMap bld [0..]
--
-- >>> L.take 64 lbs
-- "0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24"
--
foldMap :: (Foldable t, Monoid m) => (a -> m) -> t a -> m
-- | Right-associative fold of a structure, lazy in the accumulator.
--
-- In the case of lists, foldr, when applied to a binary operator,
-- a starting value (typically the right-identity of the operator), and a
-- list, reduces the list using the binary operator, from right to left:
--
--
-- foldr f z [x1, x2, ..., xn] == x1 `f` (x2 `f` ... (xn `f` z)...)
--
--
-- Note that since the head of the resulting expression is produced by an
-- application of the operator to the first element of the list, given an
-- operator lazy in its right argument, foldr can produce a
-- terminating expression from an unbounded list.
--
-- For a general Foldable structure this should be semantically
-- identical to,
--
--
-- foldr f z = foldr f z . toList
--
--
-- Examples
--
-- Basic usage:
--
--
-- >>> foldr (||) False [False, True, False]
-- True
--
--
--
-- >>> foldr (||) False []
-- False
--
--
--
-- >>> foldr (\c acc -> acc ++ [c]) "foo" ['a', 'b', 'c', 'd']
-- "foodcba"
--
--
-- Infinite structures
--
-- ⚠️ Applying foldr to infinite structures usually doesn't
-- terminate.
--
-- It may still terminate under one of the following conditions:
--
--
-- - the folding function is short-circuiting
-- - the folding function is lazy on its second argument
--
--
-- Short-circuiting
--
-- (||) short-circuits on True values, so the
-- following terminates because there is a True value finitely far
-- from the left side:
--
--
-- >>> foldr (||) False (True : repeat False)
-- True
--
--
-- But the following doesn't terminate:
--
--
-- >>> foldr (||) False (repeat False ++ [True])
-- * Hangs forever *
--
--
-- Laziness in the second argument
--
-- Applying foldr to infinite structures terminates when the
-- operator is lazy in its second argument (the initial accumulator is
-- never used in this case, and so could be left undefined, but
-- [] is more clear):
--
--
-- >>> take 5 $ foldr (\i acc -> i : fmap (+3) acc) [] (repeat 1)
-- [1,4,7,10,13]
--
foldr :: Foldable t => (a -> b -> b) -> b -> t a -> b
-- | Left-associative fold of a structure, lazy in the accumulator. This is
-- rarely what you want, but can work well for structures with efficient
-- right-to-left sequencing and an operator that is lazy in its left
-- argument.
--
-- In the case of lists, foldl, when applied to a binary operator,
-- a starting value (typically the left-identity of the operator), and a
-- list, reduces the list using the binary operator, from left to right:
--
--
-- foldl f z [x1, x2, ..., xn] == (...((z `f` x1) `f` x2) `f`...) `f` xn
--
--
-- Note that to produce the outermost application of the operator the
-- entire input list must be traversed. Like all left-associative folds,
-- foldl will diverge if given an infinite list.
--
-- If you want an efficient strict left-fold, you probably want to use
-- foldl' instead of foldl. The reason for this is that the
-- latter does not force the inner results (e.g. z `f` x1
-- in the above example) before applying them to the operator (e.g. to
-- (`f` x2)). This results in a thunk chain O(n) elements
-- long, which then must be evaluated from the outside-in.
--
-- For a general Foldable structure this should be semantically
-- identical to:
--
--
-- foldl f z = foldl f z . toList
--
--
-- Examples
--
-- The first example is a strict fold, which in practice is best
-- performed with foldl'.
--
--
-- >>> foldl (+) 42 [1,2,3,4]
-- 52
--
--
-- Though the result below is lazy, the input is reversed before
-- prepending it to the initial accumulator, so corecursion begins only
-- after traversing the entire input string.
--
--
-- >>> foldl (\acc c -> c : acc) "abcd" "efgh"
-- "hgfeabcd"
--
--
-- A left fold of a structure that is infinite on the right cannot
-- terminate, even when for any finite input the fold just returns the
-- initial accumulator:
--
--
-- >>> foldl (\a _ -> a) 0 $ repeat 1
-- * Hangs forever *
--
--
-- WARNING: When it comes to lists, you always want to use either
-- foldl' or foldr instead.
foldl :: Foldable t => (b -> a -> b) -> b -> t a -> b
-- | A variant of foldr that has no base case, and thus may only be
-- applied to non-empty structures.
--
-- This function is non-total and will raise a runtime exception if the
-- structure happens to be empty.
--
-- Examples
--
-- Basic usage:
--
--
-- >>> foldr1 (+) [1..4]
-- 10
--
--
--
-- >>> foldr1 (+) []
-- Exception: Prelude.foldr1: empty list
--
--
--
-- >>> foldr1 (+) Nothing
-- *** Exception: foldr1: empty structure
--
--
--
-- >>> foldr1 (-) [1..4]
-- -2
--
--
--
-- >>> foldr1 (&&) [True, False, True, True]
-- False
--
--
--
-- >>> foldr1 (||) [False, False, True, True]
-- True
--
--
--
-- >>> foldr1 (+) [1..]
-- * Hangs forever *
--
foldr1 :: Foldable t => (a -> a -> a) -> t a -> a
-- | A variant of foldl that has no base case, and thus may only be
-- applied to non-empty structures.
--
-- This function is non-total and will raise a runtime exception if the
-- structure happens to be empty.
--
--
-- foldl1 f = foldl1 f . toList
--
--
-- Examples
--
-- Basic usage:
--
--
-- >>> foldl1 (+) [1..4]
-- 10
--
--
--
-- >>> foldl1 (+) []
-- *** Exception: Prelude.foldl1: empty list
--
--
--
-- >>> foldl1 (+) Nothing
-- *** Exception: foldl1: empty structure
--
--
--
-- >>> foldl1 (-) [1..4]
-- -8
--
--
--
-- >>> foldl1 (&&) [True, False, True, True]
-- False
--
--
--
-- >>> foldl1 (||) [False, False, True, True]
-- True
--
--
--
-- >>> foldl1 (+) [1..]
-- * Hangs forever *
--
foldl1 :: Foldable t => (a -> a -> a) -> t a -> a
-- | Test whether the structure is empty. The default implementation is
-- Left-associative and lazy in both the initial element and the
-- accumulator. Thus optimised for structures where the first element can
-- be accessed in constant time. Structures where this is not the case
-- should have a non-default implementation.
--
-- Examples
--
-- Basic usage:
--
--
-- >>> null []
-- True
--
--
--
-- >>> null [1]
-- False
--
--
-- null is expected to terminate even for infinite structures. The
-- default implementation terminates provided the structure is bounded on
-- the left (there is a leftmost element).
--
--
-- >>> null [1..]
-- False
--
null :: Foldable t => t a -> Bool
-- | Returns the size/length of a finite structure as an Int. The
-- default implementation just counts elements starting with the
-- leftmost. Instances for structures that can compute the element count
-- faster than via element-by-element counting, should provide a
-- specialised implementation.
--
-- Examples
--
-- Basic usage:
--
--
-- >>> length []
-- 0
--
--
--
-- >>> length ['a', 'b', 'c']
-- 3
--
-- >>> length [1..]
-- * Hangs forever *
--
length :: Foldable t => t a -> Int
-- | Does the element occur in the structure?
--
-- Note: elem is often used in infix form.
--
-- Examples
--
-- Basic usage:
--
--
-- >>> 3 `elem` []
-- False
--
--
--
-- >>> 3 `elem` [1,2]
-- False
--
--
--
-- >>> 3 `elem` [1,2,3,4,5]
-- True
--
--
-- For infinite structures, the default implementation of elem
-- terminates if the sought-after value exists at a finite distance from
-- the left side of the structure:
--
--
-- >>> 3 `elem` [1..]
-- True
--
--
--
-- >>> 3 `elem` ([4..] ++ [3])
-- * Hangs forever *
--
elem :: (Foldable t, Eq a) => a -> t a -> Bool
-- | The largest element of a non-empty structure.
--
-- This function is non-total and will raise a runtime exception if the
-- structure happens to be empty. A structure that supports random access
-- and maintains its elements in order should provide a specialised
-- implementation to return the maximum in faster than linear time.
--
-- Examples
--
-- Basic usage:
--
--
-- >>> maximum [1..10]
-- 10
--
--
--
-- >>> maximum []
-- *** Exception: Prelude.maximum: empty list
--
--
--
-- >>> maximum Nothing
-- *** Exception: maximum: empty structure
--
--
-- WARNING: This function is partial for possibly-empty structures like
-- lists.
maximum :: (Foldable t, Ord a) => t a -> a
-- | The least element of a non-empty structure.
--
-- This function is non-total and will raise a runtime exception if the
-- structure happens to be empty. A structure that supports random access
-- and maintains its elements in order should provide a specialised
-- implementation to return the minimum in faster than linear time.
--
-- Examples
--
-- Basic usage:
--
--
-- >>> minimum [1..10]
-- 1
--
--
--
-- >>> minimum []
-- *** Exception: Prelude.minimum: empty list
--
--
--
-- >>> minimum Nothing
-- *** Exception: minimum: empty structure
--
--
-- WARNING: This function is partial for possibly-empty structures like
-- lists.
minimum :: (Foldable t, Ord a) => t a -> a
-- | The sum function computes the sum of the numbers of a
-- structure.
--
-- Examples
--
-- Basic usage:
--
--
-- >>> sum []
-- 0
--
--
--
-- >>> sum [42]
-- 42
--
--
--
-- >>> sum [1..10]
-- 55
--
--
--
-- >>> sum [4.1, 2.0, 1.7]
-- 7.8
--
--
--
-- >>> sum [1..]
-- * Hangs forever *
--
sum :: (Foldable t, Num a) => t a -> a
-- | The product function computes the product of the numbers of a
-- structure.
--
-- Examples
--
-- Basic usage:
--
--
-- >>> product []
-- 1
--
--
--
-- >>> product [42]
-- 42
--
--
--
-- >>> product [1..10]
-- 3628800
--
--
--
-- >>> product [4.1, 2.0, 1.7]
-- 13.939999999999998
--
--
--
-- >>> product [1..]
-- * Hangs forever *
--
product :: (Foldable t, Num a) => t a -> a
infix 4 `elem`
-- | 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
--
--
-- fail s should be an action that runs in the monad itself, not
-- an exception (except in instances of MonadIO). In particular,
-- fail should not be implemented in terms of error.
class Monad m => MonadFail (m :: Type -> Type)
fail :: MonadFail m => String -> m a
-- | Functors representing data structures that can be transformed to
-- structures of the same shape by performing an
-- Applicative (or, therefore, Monad) action on each
-- element from left to right.
--
-- A more detailed description of what same shape means, the
-- various methods, how traversals are constructed, and example advanced
-- use-cases can be found in the Overview section of
-- Data.Traversable#overview.
--
-- For the class laws see the Laws section of
-- Data.Traversable#laws.
class (Functor t, Foldable t) => Traversable (t :: Type -> Type)
-- | Map each element of a structure to an action, evaluate these actions
-- from left to right, and collect the results. For a version that
-- ignores the results see traverse_.
--
-- Examples
--
-- Basic usage:
--
-- In the first two examples we show each evaluated action mapping to the
-- output structure.
--
--
-- >>> traverse Just [1,2,3,4]
-- Just [1,2,3,4]
--
--
--
-- >>> traverse id [Right 1, Right 2, Right 3, Right 4]
-- Right [1,2,3,4]
--
--
-- In the next examples, we show that Nothing and Left
-- values short circuit the created structure.
--
--
-- >>> traverse (const Nothing) [1,2,3,4]
-- Nothing
--
--
--
-- >>> traverse (\x -> if odd x then Just x else Nothing) [1,2,3,4]
-- Nothing
--
--
--
-- >>> traverse id [Right 1, Right 2, Right 3, Right 4, Left 0]
-- Left 0
--
traverse :: (Traversable t, Applicative f) => (a -> f b) -> t a -> f (t b)
-- | Evaluate each action in the structure from left to right, and collect
-- the results. For a version that ignores the results see
-- sequenceA_.
--
-- Examples
--
-- Basic usage:
--
-- For the first two examples we show sequenceA fully evaluating a a
-- structure and collecting the results.
--
--
-- >>> sequenceA [Just 1, Just 2, Just 3]
-- Just [1,2,3]
--
--
--
-- >>> sequenceA [Right 1, Right 2, Right 3]
-- Right [1,2,3]
--
--
-- The next two example show Nothing and Just will short
-- circuit the resulting structure if present in the input. For more
-- context, check the Traversable instances for Either and
-- Maybe.
--
--
-- >>> sequenceA [Just 1, Just 2, Just 3, Nothing]
-- Nothing
--
--
--
-- >>> sequenceA [Right 1, Right 2, Right 3, Left 4]
-- Left 4
--
sequenceA :: (Traversable t, Applicative f) => t (f a) -> f (t a)
-- | Map each element of a structure to a monadic action, evaluate these
-- actions from left to right, and collect the results. For a version
-- that ignores the results see mapM_.
--
-- Examples
--
-- mapM is literally a traverse with a type signature
-- restricted to Monad. Its implementation may be more efficient
-- due to additional power of Monad.
mapM :: (Traversable t, Monad m) => (a -> m b) -> t a -> m (t b)
-- | Evaluate each monadic action in the structure from left to right, and
-- collect the results. For a version that ignores the results see
-- sequence_.
--
-- Examples
--
-- Basic usage:
--
-- The first two examples are instances where the input and and output of
-- sequence are isomorphic.
--
--
-- >>> sequence $ Right [1,2,3,4]
-- [Right 1,Right 2,Right 3,Right 4]
--
--
--
-- >>> sequence $ [Right 1,Right 2,Right 3,Right 4]
-- Right [1,2,3,4]
--
--
-- The following examples demonstrate short circuit behavior for
-- sequence.
--
--
-- >>> sequence $ Left [1,2,3,4]
-- Left [1,2,3,4]
--
--
--
-- >>> sequence $ [Left 0, Right 1,Right 2,Right 3,Right 4]
-- Left 0
--
sequence :: (Traversable t, Monad m) => t (m a) -> m (t a)
-- | 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
-- | The Haskell 2010 type for exceptions in the IO monad. Any I/O
-- operation may raise an IOException instead of returning a
-- result. For a more general type of exception, including also those
-- that arise in pure code, see Exception.
--
-- In Haskell 2010, this is an opaque type.
type IOError = IOException
-- | 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. This allows us to run IO
-- computations in any monadic stack, so long as it supports these kinds
-- of operations (i.e. IO is the base monad for the stack).
--
-- Example
--
--
-- import Control.Monad.Trans.State -- from the "transformers" library
--
-- printState :: Show s => StateT s IO ()
-- printState = do
-- state <- get
-- liftIO $ print state
--
--
-- Had we omitted liftIO, we would have ended up with
-- this error:
--
--
-- • Couldn't match type ‘IO’ with ‘StateT s IO’
-- Expected type: StateT s IO ()
-- Actual type: IO ()
--
--
-- The important part here is the mismatch between StateT s IO
-- () and IO ().
--
-- Luckily, we know of a function that takes an IO a and
-- returns an (m a): liftIO, enabling us to run
-- the program and see the expected results:
--
--
-- > evalStateT printState "hello"
-- "hello"
--
-- > evalStateT printState 3
-- 3
--
liftIO :: MonadIO m => IO a -> m a
-- | Trigonometric and hyperbolic functions and related functions.
--
-- The Haskell Report defines no laws for Floating. However,
-- (+), (*) and exp are
-- customarily expected to define an exponential field and have the
-- following properties:
--
--
-- - exp (a + b) = exp a * exp b
-- - exp (fromInteger 0) = fromInteger 1
--
class Fractional a => Floating a
pi :: Floating a => a
log :: Floating a => a -> a
sqrt :: Floating a => a -> a
(**) :: Floating a => a -> a -> a
logBase :: Floating a => a -> a -> a
sin :: Floating a => a -> a
cos :: Floating a => a -> a
tan :: Floating a => a -> a
asin :: Floating a => a -> a
acos :: Floating a => a -> a
atan :: Floating a => a -> a
sinh :: Floating a => a -> a
cosh :: Floating a => a -> a
tanh :: Floating a => a -> a
asinh :: Floating a => a -> a
acosh :: Floating a => a -> a
atanh :: Floating a => a -> a
infixr 8 **
-- | Basic numeric class.
--
-- The Haskell Report defines no laws for Num. However,
-- (+) and (*) are customarily expected
-- to define a ring and have the following properties:
--
--
-- - Associativity of (+) (x + y) +
-- z = x + (y + z)
-- - Commutativity of (+) x + y
-- = y + x
-- - fromInteger 0 is the additive
-- identity x + fromInteger 0 = x
-- - negate gives the additive inverse x +
-- negate x = fromInteger 0
-- - Associativity of (*) (x * y) *
-- z = x * (y * z)
-- - fromInteger 1 is the multiplicative
-- identity x * fromInteger 1 = x and
-- fromInteger 1 * x = x
-- - Distributivity of (*) with respect to
-- (+) a * (b + c) = (a * b) + (a *
-- c) and (b + c) * a = (b * a) + (c * a)
-- - Coherence with toInteger if the type also
-- implements Integral, then fromInteger is a left inverse
-- for toInteger, i.e. fromInteger (toInteger i) ==
-- i
--
--
-- 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 6 +
infixl 7 *
-- | Efficient, machine-independent access to the components of a
-- floating-point number.
class (RealFrac a, Floating a) => RealFloat a
-- | a constant function, returning the radix of the representation (often
-- 2)
floatRadix :: RealFloat a => a -> Integer
-- | a constant function, returning the number of digits of
-- floatRadix in the significand
floatDigits :: RealFloat a => a -> Int
-- | a constant function, returning the lowest and highest values the
-- exponent may assume
floatRange :: RealFloat a => a -> (Int, Int)
-- | The function decodeFloat applied to a real floating-point
-- number returns the significand expressed as an Integer and an
-- appropriately scaled exponent (an Int). If
-- decodeFloat x yields (m,n), then x
-- is equal in value to m*b^^n, where b is the
-- floating-point radix, and furthermore, either m and
-- n are both zero or else b^(d-1) <= abs m <
-- b^d, where d is the value of floatDigits
-- x. In particular, decodeFloat 0 = (0,0). If the
-- type contains a negative zero, also decodeFloat (-0.0) =
-- (0,0). The result of decodeFloat x is
-- unspecified if either of isNaN x or
-- isInfinite x is True.
decodeFloat :: RealFloat a => a -> (Integer, Int)
-- | encodeFloat performs the inverse of decodeFloat in the
-- sense that for finite x with the exception of -0.0,
-- uncurry encodeFloat (decodeFloat x) = x.
-- encodeFloat m n is one of the two closest
-- representable floating-point numbers to m*b^^n (or
-- ±Infinity if overflow occurs); usually the closer, but if
-- m contains too many bits, the result may be rounded in the
-- wrong direction.
encodeFloat :: RealFloat a => Integer -> Int -> a
-- | exponent corresponds to the second component of
-- decodeFloat. exponent 0 = 0 and for finite
-- nonzero x, exponent x = snd (decodeFloat x)
-- + floatDigits x. If x is a finite floating-point
-- number, it is equal in value to significand x * b ^^
-- exponent x, where b is the floating-point radix.
-- The behaviour is unspecified on infinite or NaN values.
exponent :: RealFloat a => a -> Int
-- | The first component of decodeFloat, scaled to lie in the open
-- interval (-1,1), either 0.0 or of absolute
-- value >= 1/b, where b is the floating-point
-- radix. The behaviour is unspecified on infinite or NaN
-- values.
significand :: RealFloat a => a -> a
-- | multiplies a floating-point number by an integer power of the radix
scaleFloat :: RealFloat a => Int -> a -> a
-- | True if the argument is an IEEE "not-a-number" (NaN) value
isNaN :: RealFloat a => a -> Bool
-- | True if the argument is an IEEE infinity or negative infinity
isInfinite :: RealFloat a => a -> Bool
-- | True if the argument is too small to be represented in
-- normalized format
isDenormalized :: RealFloat a => a -> Bool
-- | True if the argument is an IEEE negative zero
isNegativeZero :: RealFloat a => a -> Bool
-- | True if the argument is an IEEE floating point number
isIEEE :: RealFloat a => a -> Bool
-- | a version of arctangent taking two real floating-point arguments. For
-- real floating x and y, atan2 y x
-- computes the angle (from the positive x-axis) of the vector from the
-- origin to the point (x,y). atan2 y x returns
-- a value in the range [-pi, pi]. It follows the
-- Common Lisp semantics for the origin when signed zeroes are supported.
-- atan2 y 1, with y in a type that is
-- RealFloat, should return the same value as atan
-- y. A default definition of atan2 is provided, but
-- implementors can provide a more accurate implementation.
atan2 :: RealFloat a => a -> a -> a
-- | The shows functions return a function that prepends the
-- output String to an existing String. This allows
-- constant-time concatenation of results using function composition.
type ShowS = String -> String
-- | A parser for a type a, represented as a function that takes a
-- String and returns a list of possible parses as
-- (a,String) pairs.
--
-- Note that this kind of backtracking parser is very inefficient;
-- reading a large structure may be quite slow (cf ReadP).
type ReadS a = String -> [(a, String)]
-- | 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
-- | A file path.
data () => File
-- | An absolute path.
data () => Abs
-- | A relative path; one without a root. Note that a .. path
-- component to represent the parent directory is not allowed by this
-- library.
data () => Rel
-- | A directory path.
data () => Dir
-- | General coercion to Fractional types.
--
-- WARNING: This function goes through the Rational type, which
-- does not have values for NaN for example. This means it does
-- not round-trip.
--
-- For Double it also behaves differently with or without -O0:
--
--
-- Prelude> realToFrac nan -- With -O0
-- -Infinity
-- Prelude> realToFrac nan
-- NaN
--
realToFrac :: (Real a, Fractional b) => a -> b
-- | General coercion from Integral types.
--
-- WARNING: This function performs silent truncation if the result type
-- is not at least as big as the argument's type.
fromIntegral :: (Integral a, Num b) => a -> b
-- | 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 representation-polymorphic in its
-- result type, so that foo $ True where foo :: Bool
-- -> Int# is well-typed.
($) :: forall (r :: RuntimeRep) a (b :: TYPE r). (a -> b) -> a -> b
infixr 0 $
-- | otherwise is defined as the value True. It helps to make
-- guards more readable. eg.
--
--
-- f x | x < 0 = ...
-- | otherwise = ...
--
otherwise :: Bool
-- | 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.
--
-- WARNING: This function takes linear time in the number of elements of
-- the first list.
(++) :: [a] -> [a] -> [a]
infixr 5 ++
-- | <math>. map f xs is the list obtained by
-- applying f to each element of xs, i.e.,
--
--
-- map f [x1, x2, ..., xn] == [f x1, f x2, ..., f xn]
-- map f [x1, x2, ...] == [f x1, f x2, ...]
--
--
--
-- >>> map (+1) [1, 2, 3]
-- [2,3,4]
--
map :: (a -> b) -> [a] -> [b]
-- | 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
-- | Identity function.
--
--
-- id x = x
--
id :: a -> a
-- | Extract the first component of a pair.
fst :: (a, b) -> a
-- | Extract the second component of a pair.
snd :: (a, b) -> b
-- | <math>. lookup key assocs looks up a key in an
-- association list. For the result to be Nothing, the list must
-- be finite.
--
--
-- >>> lookup 2 []
-- Nothing
--
-- >>> lookup 2 [(1, "first")]
-- Nothing
--
-- >>> lookup 2 [(1, "first"), (2, "second"), (3, "third")]
-- Just "second"
--
lookup :: Eq a => a -> [(a, b)] -> Maybe b
-- | <math>. filter, applied to a predicate and a list,
-- returns the list of those elements that satisfy the predicate; i.e.,
--
--
-- filter p xs = [ x | x <- xs, p x]
--
--
--
-- >>> filter odd [1, 2, 3]
-- [1,3]
--
filter :: (a -> Bool) -> [a] -> [a]
-- | 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 ()
-- | The reverse of when.
unless :: Applicative f => Bool -> f () -> f ()
-- | 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 <$>
-- | The value of seq a b is bottom if a is
-- bottom, and otherwise equal to b. In other words, it
-- evaluates the first argument a to weak head normal form
-- (WHNF). seq is usually introduced to improve performance by
-- avoiding unneeded laziness.
--
-- A note on evaluation order: the expression seq a b
-- does not guarantee that a will be evaluated before
-- b. The only guarantee given by seq is that the both
-- a and b will be evaluated before seq returns
-- a value. In particular, this means that b may be evaluated
-- before a. If you need to guarantee a specific order of
-- evaluation, you must use the function pseq from the
-- "parallel" package.
seq :: forall {r :: RuntimeRep} a (b :: TYPE r). a -> b -> b
infixr 0 `seq`
-- | Map each element of a structure to a monadic action, evaluate these
-- actions from left to right, and ignore the results. For a version that
-- doesn't ignore the results see mapM.
--
-- mapM_ is just like traverse_, but specialised to monadic
-- actions.
mapM_ :: (Foldable t, Monad m) => (a -> m b) -> t a -> m ()
-- | takeWhile, applied to a predicate p and a list
-- xs, returns the longest prefix (possibly empty) of
-- xs of elements that satisfy p.
--
--
-- >>> takeWhile (< 3) [1,2,3,4,1,2,3,4]
-- [1,2]
--
-- >>> takeWhile (< 9) [1,2,3]
-- [1,2,3]
--
-- >>> takeWhile (< 0) [1,2,3]
-- []
--
takeWhile :: (a -> Bool) -> [a] -> [a]
-- | take n, applied to a list xs, returns the
-- prefix of xs of length n, or xs itself if
-- n >= length xs.
--
--
-- >>> take 5 "Hello World!"
-- "Hello"
--
-- >>> take 3 [1,2,3,4,5]
-- [1,2,3]
--
-- >>> take 3 [1,2]
-- [1,2]
--
-- >>> take 3 []
-- []
--
-- >>> take (-1) [1,2]
-- []
--
-- >>> take 0 [1,2]
-- []
--
--
-- It is an instance of the more general genericTake, in which
-- n may be of any integral type.
take :: Int -> [a] -> [a]
-- | The read function reads input from a string, which must be
-- completely consumed by the input process. read fails with an
-- error if the parse is unsuccessful, and it is therefore
-- discouraged from being used in real applications. Use readMaybe
-- or readEither for safe alternatives.
--
--
-- >>> read "123" :: Int
-- 123
--
--
--
-- >>> read "hello" :: Int
-- *** Exception: Prelude.read: no parse
--
read :: Read a => String -> a
-- | Function composition.
(.) :: (b -> c) -> (a -> b) -> a -> c
infixr 9 .
-- | const x y always evaluates to x, ignoring its second
-- argument.
--
--
-- >>> const 42 "hello"
-- 42
--
--
--
-- >>> map (const 42) [0..3]
-- [42,42,42,42]
--
const :: a -> b -> a
-- | error stops execution and displays an error message.
error :: forall (r :: RuntimeRep) (a :: TYPE r). HasCallStack => [Char] -> a
-- | <math>. zipWith generalises zip by zipping with
-- the function given as the first argument, instead of a tupling
-- function.
--
--
-- zipWith (,) xs ys == zip xs ys
-- zipWith f [x1,x2,x3..] [y1,y2,y3..] == [f x1 y1, f x2 y2, f x3 y3..]
--
--
-- For example, zipWith (+) is applied to two lists to
-- produce the list of corresponding sums:
--
--
-- >>> zipWith (+) [1, 2, 3] [4, 5, 6]
-- [5,7,9]
--
--
-- zipWith is right-lazy:
--
--
-- >>> let f = undefined
--
-- >>> zipWith f [] undefined
-- []
--
--
-- zipWith is capable of list fusion, but it is restricted to its
-- first list argument and its resulting list.
zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
even :: Integral a => a -> Bool
-- | 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
-- | <math>. Extract the first element of a list, which must be
-- non-empty.
--
--
-- >>> head [1, 2, 3]
-- 1
--
-- >>> head [1..]
-- 1
--
-- >>> head []
-- *** Exception: Prelude.head: empty list
--
--
-- WARNING: This function is partial. You can use case-matching,
-- uncons or listToMaybe instead.
head :: HasCallStack => [a] -> a
-- | Synchronously throw the given exception.
--
-- Note that, if you provide an exception value which is of an
-- asynchronous type, it will be wrapped up in
-- SyncExceptionWrapper. See toSyncException.
throwIO :: (MonadIO m, Exception e) => e -> m a
-- | The computation writeFile file str function writes the
-- string str, to the file file.
writeFile :: FilePath -> String -> IO ()
-- | Read a line from the standard input device (same as hGetLine
-- stdin).
getLine :: IO String
-- | The same as putStr, but adds a newline character.
putStrLn :: String -> IO ()
-- | cycle ties a finite list into a circular one, or equivalently,
-- the infinite repetition of the original list. It is the identity on
-- infinite lists.
--
--
-- >>> cycle []
-- *** Exception: Prelude.cycle: empty list
--
-- >>> cycle [42]
-- [42,42,42,42,42,42,42,42,42,42...
--
-- >>> cycle [2, 5, 7]
-- [2,5,7,2,5,7,2,5,7,2,5,7...
--
cycle :: HasCallStack => [a] -> [a]
-- | The concatenation of all the elements of a container of lists.
--
-- Examples
--
-- Basic usage:
--
--
-- >>> concat (Just [1, 2, 3])
-- [1,2,3]
--
--
--
-- >>> concat (Left 42)
-- []
--
--
--
-- >>> concat [[1, 2, 3], [4, 5], [6], []]
-- [1,2,3,4,5,6]
--
concat :: Foldable t => t [a] -> [a]
-- | <math>. zip takes two lists and returns a list of
-- corresponding pairs.
--
--
-- >>> zip [1, 2] ['a', 'b']
-- [(1,'a'),(2,'b')]
--
--
-- If one input list is shorter than the other, excess elements of the
-- longer list are discarded, even if one of the lists is infinite:
--
--
-- >>> zip [1] ['a', 'b']
-- [(1,'a')]
--
-- >>> zip [1, 2] ['a']
-- [(1,'a')]
--
-- >>> zip [] [1..]
-- []
--
-- >>> zip [1..] []
-- []
--
--
-- zip is right-lazy:
--
--
-- >>> zip [] undefined
-- []
--
-- >>> zip undefined []
-- *** Exception: Prelude.undefined
-- ...
--
--
-- zip is capable of list fusion, but it is restricted to its
-- first list argument and its resulting list.
zip :: [a] -> [b] -> [(a, b)]
-- | The print function outputs a value of any printable type to the
-- standard output device. Printable types are those that are instances
-- of class Show; print converts values to strings for
-- output using the show operation and adds a newline.
--
-- For example, a program to print the first 20 integers and their powers
-- of 2 could be written as:
--
--
-- main = print ([(n, 2^n) | n <- [0..19]])
--
print :: Show a => a -> IO ()
-- | raise a number to a non-negative integral power
(^) :: (Num a, Integral b) => a -> b -> a
infixr 8 ^
-- | Boolean "and", lazy in the second argument
(&&) :: Bool -> Bool -> Bool
infixr 3 &&
-- | Boolean "or", lazy in the second argument
(||) :: Bool -> Bool -> Bool
infixr 2 ||
-- | Boolean "not"
not :: Bool -> Bool
-- | A variant of error that does not produce a stack trace.
errorWithoutStackTrace :: forall (r :: RuntimeRep) (a :: TYPE r). [Char] -> a
-- | A special case of error. It is expected that compilers will
-- recognize this and insert error messages which are more appropriate to
-- the context in which undefined appears.
undefined :: forall (r :: RuntimeRep) (a :: TYPE r). HasCallStack => a
-- | Same as >>=, but with the arguments interchanged.
(=<<) :: Monad m => (a -> m b) -> m a -> m b
infixr 1 =<<
-- | flip f takes its (first) two arguments in the reverse
-- order of f.
--
--
-- >>> flip (++) "hello" "world"
-- "worldhello"
--
flip :: (a -> b -> c) -> b -> a -> c
-- | Strict (call-by-value) application operator. It takes a function and
-- an argument, evaluates the argument to weak head normal form (WHNF),
-- then calls the function with that value.
($!) :: forall (r :: RuntimeRep) a (b :: TYPE r). (a -> b) -> a -> b
infixr 0 $!
-- | until p f yields the result of applying f
-- until p holds.
until :: (a -> Bool) -> (a -> a) -> a -> a
-- | 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
-- | the same as flip (-).
--
-- Because - is treated specially in the Haskell grammar,
-- (- e) is not a section, but an application of
-- prefix negation. However, (subtract
-- exp) is equivalent to the disallowed section.
subtract :: Num a => a -> a -> a
-- | The 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
-- | <math>. Extract the elements after the head of a list, which
-- must be non-empty.
--
--
-- >>> tail [1, 2, 3]
-- [2,3]
--
-- >>> tail [1]
-- []
--
-- >>> tail []
-- *** Exception: Prelude.tail: empty list
--
--
-- WARNING: This function is partial. You can use case-matching or
-- uncons instead.
tail :: HasCallStack => [a] -> [a]
-- | <math>. Extract the last element of a list, which must be finite
-- and non-empty.
--
--
-- >>> last [1, 2, 3]
-- 3
--
-- >>> last [1..]
-- * Hangs forever *
--
-- >>> last []
-- *** Exception: Prelude.last: empty list
--
--
-- WARNING: This function is partial. You can use reverse with
-- case-matching, uncons or listToMaybe instead.
last :: HasCallStack => [a] -> a
-- | <math>. Return all the elements of a list except the last one.
-- The list must be non-empty.
--
--
-- >>> init [1, 2, 3]
-- [1,2]
--
-- >>> init [1]
-- []
--
-- >>> init []
-- *** Exception: Prelude.init: empty list
--
--
-- WARNING: This function is partial. You can use reverse with
-- case-matching or uncons instead.
init :: HasCallStack => [a] -> [a]
-- | <math>. scanl is similar to foldl, but returns a
-- list of successive reduced values from the left:
--
--
-- scanl f z [x1, x2, ...] == [z, z `f` x1, (z `f` x1) `f` x2, ...]
--
--
-- Note that
--
--
-- last (scanl f z xs) == foldl f z xs
--
--
--
-- >>> scanl (+) 0 [1..4]
-- [0,1,3,6,10]
--
-- >>> scanl (+) 42 []
-- [42]
--
-- >>> scanl (-) 100 [1..4]
-- [100,99,97,94,90]
--
-- >>> scanl (\reversedString nextChar -> nextChar : reversedString) "foo" ['a', 'b', 'c', 'd']
-- ["foo","afoo","bafoo","cbafoo","dcbafoo"]
--
-- >>> scanl (+) 0 [1..]
-- * Hangs forever *
--
scanl :: (b -> a -> b) -> b -> [a] -> [b]
-- | <math>. scanl1 is a variant of scanl that has no
-- starting value argument:
--
--
-- scanl1 f [x1, x2, ...] == [x1, x1 `f` x2, ...]
--
--
--
-- >>> scanl1 (+) [1..4]
-- [1,3,6,10]
--
-- >>> scanl1 (+) []
-- []
--
-- >>> scanl1 (-) [1..4]
-- [1,-1,-4,-8]
--
-- >>> scanl1 (&&) [True, False, True, True]
-- [True,False,False,False]
--
-- >>> scanl1 (||) [False, False, True, True]
-- [False,False,True,True]
--
-- >>> scanl1 (+) [1..]
-- * Hangs forever *
--
scanl1 :: (a -> a -> a) -> [a] -> [a]
-- | <math>. scanr is the right-to-left dual of scanl.
-- Note that the order of parameters on the accumulating function are
-- reversed compared to scanl. Also note that
--
--
-- head (scanr f z xs) == foldr f z xs.
--
--
--
-- >>> scanr (+) 0 [1..4]
-- [10,9,7,4,0]
--
-- >>> scanr (+) 42 []
-- [42]
--
-- >>> scanr (-) 100 [1..4]
-- [98,-97,99,-96,100]
--
-- >>> scanr (\nextChar reversedString -> nextChar : reversedString) "foo" ['a', 'b', 'c', 'd']
-- ["abcdfoo","bcdfoo","cdfoo","dfoo","foo"]
--
-- >>> force $ scanr (+) 0 [1..]
-- *** Exception: stack overflow
--
scanr :: (a -> b -> b) -> b -> [a] -> [b]
-- | <math>. scanr1 is a variant of scanr that has no
-- starting value argument.
--
--
-- >>> scanr1 (+) [1..4]
-- [10,9,7,4]
--
-- >>> scanr1 (+) []
-- []
--
-- >>> scanr1 (-) [1..4]
-- [-2,3,-1,4]
--
-- >>> scanr1 (&&) [True, False, True, True]
-- [False,False,True,True]
--
-- >>> scanr1 (||) [True, True, False, False]
-- [True,True,False,False]
--
-- >>> force $ scanr1 (+) [1..]
-- *** Exception: stack overflow
--
scanr1 :: (a -> a -> a) -> [a] -> [a]
-- | iterate f x returns an infinite list of repeated
-- applications of f to x:
--
--
-- iterate f x == [x, f x, f (f x), ...]
--
--
-- Note that iterate is lazy, potentially leading to thunk
-- build-up if the consumer doesn't force each iterate. See
-- iterate' for a strict variant of this function.
--
--
-- >>> take 10 $ iterate not True
-- [True,False,True,False...
--
-- >>> take 10 $ iterate (+3) 42
-- [42,45,48,51,54,57,60,63...
--
iterate :: (a -> a) -> a -> [a]
-- | repeat x is an infinite list, with x the
-- value of every element.
--
--
-- >>> repeat 17
-- [17,17,17,17,17,17,17,17,17...
--
repeat :: a -> [a]
-- | replicate n x is a list of length n with
-- x the value of every element. It is an instance of the more
-- general genericReplicate, in which n may be of any
-- integral type.
--
--
-- >>> replicate 0 True
-- []
--
-- >>> replicate (-1) True
-- []
--
-- >>> replicate 4 True
-- [True,True,True,True]
--
replicate :: 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]
-- | 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]
-- | splitAt n xs returns a tuple where first element is
-- xs prefix of length n and second element is the
-- remainder of the list:
--
--
-- >>> splitAt 6 "Hello World!"
-- ("Hello ","World!")
--
-- >>> splitAt 3 [1,2,3,4,5]
-- ([1,2,3],[4,5])
--
-- >>> splitAt 1 [1,2,3]
-- ([1],[2,3])
--
-- >>> splitAt 3 [1,2,3]
-- ([1,2,3],[])
--
-- >>> splitAt 4 [1,2,3]
-- ([1,2,3],[])
--
-- >>> splitAt 0 [1,2,3]
-- ([],[1,2,3])
--
-- >>> splitAt (-1) [1,2,3]
-- ([],[1,2,3])
--
--
-- It is equivalent to (take n xs, drop n xs) when
-- n is not _|_ (splitAt _|_ xs = _|_).
-- splitAt is an instance of the more general
-- genericSplitAt, in which n may be of any integral
-- type.
splitAt :: Int -> [a] -> ([a], [a])
-- | span, applied to a predicate p and a list xs,
-- returns a tuple where first element is longest prefix (possibly empty)
-- of xs of elements that satisfy p and second element
-- is the remainder of the list:
--
--
-- >>> span (< 3) [1,2,3,4,1,2,3,4]
-- ([1,2],[3,4,1,2,3,4])
--
-- >>> span (< 9) [1,2,3]
-- ([1,2,3],[])
--
-- >>> span (< 0) [1,2,3]
-- ([],[1,2,3])
--
--
-- span p xs is equivalent to (takeWhile p xs,
-- dropWhile p xs)
span :: (a -> Bool) -> [a] -> ([a], [a])
-- | 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])
-- | reverse xs returns the elements of xs in
-- reverse order. xs must be finite.
--
--
-- >>> reverse []
-- []
--
-- >>> reverse [42]
-- [42]
--
-- >>> reverse [2,5,7]
-- [7,5,2]
--
-- >>> reverse [1..]
-- * Hangs forever *
--
reverse :: [a] -> [a]
-- | and returns the conjunction of a container of Bools. For the
-- result to be True, the container must be finite; False,
-- however, results from a False value finitely far from the left
-- end.
--
-- Examples
--
-- Basic usage:
--
--
-- >>> and []
-- True
--
--
--
-- >>> and [True]
-- True
--
--
--
-- >>> and [False]
-- False
--
--
--
-- >>> and [True, True, False]
-- False
--
--
--
-- >>> and (False : repeat True) -- Infinite list [False,True,True,True,...
-- False
--
--
--
-- >>> and (repeat True)
-- * Hangs forever *
--
and :: Foldable t => t Bool -> Bool
-- | or returns the disjunction of a container of Bools. For the
-- result to be False, the container must be finite; True,
-- however, results from a True value finitely far from the left
-- end.
--
-- Examples
--
-- Basic usage:
--
--
-- >>> or []
-- False
--
--
--
-- >>> or [True]
-- True
--
--
--
-- >>> or [False]
-- False
--
--
--
-- >>> or [True, True, False]
-- True
--
--
--
-- >>> or (True : repeat False) -- Infinite list [True,False,False,False,...
-- True
--
--
--
-- >>> or (repeat False)
-- * Hangs forever *
--
or :: Foldable t => t Bool -> Bool
-- | Determines whether any element of the structure satisfies the
-- predicate.
--
-- Examples
--
-- Basic usage:
--
--
-- >>> any (> 3) []
-- False
--
--
--
-- >>> any (> 3) [1,2]
-- False
--
--
--
-- >>> any (> 3) [1,2,3,4,5]
-- True
--
--
--
-- >>> any (> 3) [1..]
-- True
--
--
--
-- >>> any (> 3) [0, -1..]
-- * Hangs forever *
--
any :: Foldable t => (a -> Bool) -> t a -> Bool
-- | Determines whether all elements of the structure satisfy the
-- predicate.
--
-- Examples
--
-- Basic usage:
--
--
-- >>> all (> 3) []
-- True
--
--
--
-- >>> all (> 3) [1,2]
-- False
--
--
--
-- >>> all (> 3) [1,2,3,4,5]
-- False
--
--
--
-- >>> all (> 3) [1..]
-- False
--
--
--
-- >>> all (> 3) [4..]
-- * Hangs forever *
--
all :: Foldable t => (a -> Bool) -> t a -> Bool
-- | notElem is the negation of elem.
--
-- Examples
--
-- Basic usage:
--
--
-- >>> 3 `notElem` []
-- True
--
--
--
-- >>> 3 `notElem` [1,2]
-- True
--
--
--
-- >>> 3 `notElem` [1,2,3,4,5]
-- False
--
--
-- For infinite structures, notElem terminates if the value exists
-- at a finite distance from the left side of the structure:
--
--
-- >>> 3 `notElem` [1..]
-- False
--
--
--
-- >>> 3 `notElem` ([4..] ++ [3])
-- * Hangs forever *
--
notElem :: (Foldable t, Eq a) => a -> t a -> Bool
infix 4 `notElem`
-- | Map a function over all the elements of a container and concatenate
-- the resulting lists.
--
-- Examples
--
-- Basic usage:
--
--
-- >>> concatMap (take 3) [[1..], [10..], [100..], [1000..]]
-- [1,2,3,10,11,12,100,101,102,1000,1001,1002]
--
--
--
-- >>> concatMap (take 3) (Just [1..])
-- [1,2,3]
--
concatMap :: Foldable t => (a -> [b]) -> t a -> [b]
-- | List index (subscript) operator, starting from 0. It is an instance of
-- the more general genericIndex, which takes an index of any
-- integral type.
--
--
-- >>> ['a', 'b', 'c'] !! 0
-- 'a'
--
-- >>> ['a', 'b', 'c'] !! 2
-- 'c'
--
-- >>> ['a', 'b', 'c'] !! 3
-- *** Exception: Prelude.!!: index too large
--
-- >>> ['a', 'b', 'c'] !! (-1)
-- *** Exception: Prelude.!!: negative index
--
--
-- WARNING: This function is partial. You can use atMay instead.
(!!) :: HasCallStack => [a] -> Int -> a
infixl 9 !!
-- | zip3 takes three lists and returns a list of triples, analogous
-- to zip. It is capable of list fusion, but it is restricted to
-- its first list argument and its resulting list.
zip3 :: [a] -> [b] -> [c] -> [(a, b, c)]
-- | The zipWith3 function takes a function which combines three
-- elements, as well as three lists and returns a list of the function
-- applied to corresponding elements, analogous to zipWith. It is
-- capable of list fusion, but it is restricted to its first list
-- argument and its resulting list.
--
--
-- zipWith3 (,,) xs ys zs == zip3 xs ys zs
-- zipWith3 f [x1,x2,x3..] [y1,y2,y3..] [z1,z2,z3..] == [f x1 y1 z1, f x2 y2 z2, f x3 y3 z3..]
--
zipWith3 :: (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d]
-- | unzip transforms a list of pairs into a list of first
-- components and a list of second components.
--
--
-- >>> unzip []
-- ([],[])
--
-- >>> unzip [(1, 'a'), (2, 'b')]
-- ([1,2],"ab")
--
unzip :: [(a, b)] -> ([a], [b])
-- | The unzip3 function takes a list of triples and returns three
-- lists, analogous to unzip.
--
--
-- >>> unzip3 []
-- ([],[],[])
--
-- >>> unzip3 [(1, 'a', True), (2, 'b', False)]
-- ([1,2],"ab",[True,False])
--
unzip3 :: [(a, b, c)] -> ([a], [b], [c])
-- | equivalent to showsPrec with a precedence of 0.
shows :: Show a => a -> ShowS
-- | utility function converting a Char to a show function that
-- simply prepends the character unchanged.
showChar :: Char -> ShowS
-- | utility function converting a String to a show function that
-- simply prepends the string unchanged.
showString :: String -> ShowS
-- | utility function that surrounds the inner show function with
-- parentheses when the Bool parameter is True.
showParen :: Bool -> ShowS -> ShowS
odd :: Integral a => a -> Bool
-- | raise a number to an integral power
(^^) :: (Fractional a, Integral b) => a -> b -> a
infixr 8 ^^
-- | gcd x y is the non-negative factor of both x
-- and y of which every common factor of x and
-- y is also a factor; for example gcd 4 2 = 2,
-- gcd (-4) 6 = 2, gcd 0 4 = 4.
-- gcd 0 0 = 0. (That is, the common divisor
-- that is "greatest" in the divisibility preordering.)
--
-- Note: Since for signed fixed-width integer types, abs
-- minBound < 0, the result may be negative if one of the
-- arguments is minBound (and necessarily is if the other
-- is 0 or minBound) for such types.
gcd :: Integral a => a -> a -> a
-- | lcm x y is the smallest positive integer that both
-- x and y divide.
lcm :: Integral a => a -> a -> a
-- | curry converts an uncurried function to a curried function.
--
-- Examples
--
--
-- >>> curry fst 1 2
-- 1
--
curry :: ((a, b) -> c) -> a -> b -> c
-- | The lex function reads a single lexeme from the input,
-- discarding initial white space, and returning the characters that
-- constitute the lexeme. If the input string contains only white space,
-- lex returns a single successful `lexeme' consisting of the
-- empty string. (Thus lex "" = [("","")].) If there is
-- no legal lexeme at the beginning of the input string, lex fails
-- (i.e. returns []).
--
-- This lexer is not completely faithful to the Haskell lexical syntax in
-- the following respects:
--
--
-- - Qualified names are not handled properly
-- - Octal and hexadecimal numerics are not recognized as a single
-- token
-- - Comments are not treated properly
--
lex :: ReadS String
-- | readParen True p parses what p parses,
-- but surrounded with parentheses.
--
-- readParen False p parses what p
-- parses, but optionally surrounded with parentheses.
readParen :: Bool -> ReadS a -> ReadS a
-- | equivalent to readsPrec with a precedence of 0.
reads :: Read a => ReadS a
-- | Evaluate each monadic action in the structure from left to right, and
-- ignore the results. For a version that doesn't ignore the results see
-- sequence.
--
-- sequence_ is just like sequenceA_, but specialised to
-- monadic actions.
sequence_ :: (Foldable t, Monad m) => t (m a) -> m ()
-- | Splits the argument into a list of lines stripped of their
-- terminating \n characters. The \n terminator is
-- optional in a final non-empty line of the argument string.
--
-- For example:
--
--
-- >>> lines "" -- empty input contains no lines
-- []
--
-- >>> lines "\n" -- single empty line
-- [""]
--
-- >>> lines "one" -- single unterminated line
-- ["one"]
--
-- >>> lines "one\n" -- single non-empty line
-- ["one"]
--
-- >>> lines "one\n\n" -- second line is empty
-- ["one",""]
--
-- >>> lines "one\ntwo" -- second line is unterminated
-- ["one","two"]
--
-- >>> lines "one\ntwo\n" -- two non-empty lines
-- ["one","two"]
--
--
-- When the argument string is empty, or ends in a \n character,
-- it can be recovered by passing the result of lines to the
-- unlines function. Otherwise, unlines appends the missing
-- terminating \n. This makes unlines . lines
-- idempotent:
--
--
-- (unlines . lines) . (unlines . lines) = (unlines . lines)
--
lines :: String -> [String]
-- | Appends a \n character to each input string, then
-- concatenates the results. Equivalent to foldMap (s ->
-- s ++ "\n").
--
--
-- >>> unlines ["Hello", "World", "!"]
-- "Hello\nWorld\n!\n"
--
--
-- Note that unlines . lines /=
-- id when the input is not \n-terminated:
--
--
-- >>> unlines . lines $ "foo\nbar"
-- "foo\nbar\n"
--
unlines :: [String] -> String
-- | words breaks a string up into a list of words, which were
-- delimited by white space (as defined by isSpace). This function
-- trims any white spaces at the beginning and at the end.
--
--
-- >>> words "Lorem ipsum\ndolor"
-- ["Lorem","ipsum","dolor"]
--
-- >>> words " foo bar "
-- ["foo","bar"]
--
words :: String -> [String]
-- | unwords joins words with separating spaces (U+0020 SPACE).
--
--
-- >>> unwords ["Lorem", "ipsum", "dolor"]
-- "Lorem ipsum dolor"
--
--
-- unwords is neither left nor right inverse of words:
--
--
-- >>> words (unwords [" "])
-- []
--
-- >>> unwords (words "foo\nbar")
-- "foo bar"
--
unwords :: [String] -> String
-- | Construct an IOException value with a string describing the
-- error. The fail method of the IO instance of the
-- Monad class raises a userError, thus:
--
--
-- instance Monad IO where
-- ...
-- fail s = ioError (userError s)
--
userError :: String -> IOError
-- | Raise an IOException in the IO monad.
ioError :: IOError -> IO a
-- | Write a character to the standard output device (same as
-- hPutChar stdout).
putChar :: Char -> IO ()
-- | Write a string to the standard output device (same as hPutStr
-- stdout).
putStr :: String -> IO ()
-- | Read a character from the standard input device (same as
-- hGetChar stdin).
getChar :: IO Char
-- | The getContents operation returns all user input as a single
-- string, which is read lazily as it is needed (same as
-- hGetContents stdin).
getContents :: IO String
-- | The interact function takes a function of type
-- String->String as its argument. The entire input from the
-- standard input device is passed to this function as its argument, and
-- the resulting string is output on the standard output device.
interact :: (String -> String) -> IO ()
-- | The readFile function reads a file and returns the contents of
-- the file as a string. The file is read lazily, on demand, as with
-- getContents.
readFile :: FilePath -> IO String
-- | The computation appendFile file str function appends
-- the string str, to the file file.
--
-- Note that writeFile and appendFile write a literal
-- string to a file. To write a value of any printable type, as with
-- print, use the show function to convert the value to a
-- string first.
--
--
-- main = appendFile "squares" (show [(x,x*x) | x <- [0,0.1..2]])
--
appendFile :: FilePath -> String -> IO ()
-- | The readLn function combines getLine and readIO.
readLn :: Read a => IO a
-- | The readIO function is similar to read except that it
-- signals parse failure to the IO monad instead of terminating
-- the program.
readIO :: Read a => String -> IO a
-- | O(n) Convert a String into a Text. Performs
-- replacement on invalid scalar values, so unpack .
-- pack is not id:
--
--
-- >>> Data.Text.unpack (pack "\55555")
-- "\65533"
--
pack :: String -> Text
-- | O(n) Convert a Text into a String.
unpack :: Text -> String
-- | Convert to a FilePath type.
--
-- All directories have a trailing slash, so if you want no trailing
-- slash, you can use dropTrailingPathSeparator from the filepath
-- package.
toFilePath :: Path b t -> FilePath
-- | Type-safe implementation for requesting AccessToken
-- permissions
--
--
-- https://docs.github.com/en/rest/apps/apps?apiVersion=2022-11-28#create-an-installation-access-token-for-an-app
--
-- Usage:
--
--
-- - Use a constructor function for a specific permission, each of
-- which only accepts appropriate values (e.g. you can't ask for
-- admin on a permission that only allows read or
-- write).
-- - Combine these using Permissions Semigroup
-- instance.
--
--
-- For example:
--
--
-- let permissions = actions Read <> checks Write
--
-- generateInstallationTokenScoped mempty {permissions} creds installationId
--
--
-- Supplying the same permission more than once will take the higher:
--
--
-- checks Read <> checks Write == checks Write
--
module GitHub.App.Token.Permissions
data Permissions
data Read
Read :: Read
data Write
Write :: Write
data Admin
Admin :: Admin
actions :: AsReadWrite a => a -> Permissions
administration :: AsReadWrite a => a -> Permissions
checks :: AsReadWrite a => a -> Permissions
codespaces :: AsReadWrite a => a -> Permissions
contents :: AsReadWrite a => a -> Permissions
dependabot_secrets :: AsReadWrite a => a -> Permissions
deployments :: AsReadWrite a => a -> Permissions
environments :: AsReadWrite a => a -> Permissions
issues :: AsReadWrite a => a -> Permissions
metadata :: AsReadWrite a => a -> Permissions
packages :: AsReadWrite a => a -> Permissions
pages :: AsReadWrite a => a -> Permissions
pull_requests :: AsReadWrite a => a -> Permissions
repository_custom_properties :: AsReadWrite a => a -> Permissions
repository_hooks :: AsReadWrite a => a -> Permissions
repository_projects :: AsReadWriteAdmin a => a -> Permissions
secret_scanning_alerts :: AsReadWrite p => p -> Permissions
secrets :: AsReadWrite p => p -> Permissions
security_events :: AsReadWrite p => p -> Permissions
single_file :: AsReadWrite p => p -> Permissions
statuses :: AsReadWrite p => p -> Permissions
vulnerability_alerts :: AsReadWrite p => p -> Permissions
-- | Only supported permission is Write
workflows :: Permissions
members :: AsReadWrite p => p -> Permissions
organization_administration :: AsReadWrite p => p -> Permissions
organization_custom_roles :: AsReadWrite p => p -> Permissions
organization_custom_org_roles :: AsReadWrite p => p -> Permissions
organization_custom_properties :: AsReadWriteAdmin p => p -> Permissions
-- | Only supported permission is Write
organization_copilot_seat_management :: Permissions
organization_announcement_banners :: AsReadWrite p => p -> Permissions
-- | Only supported permission is Read
organization_events :: Permissions
organization_hooks :: AsReadWrite p => p -> Permissions
organization_personal_access_tokens :: AsReadWrite p => p -> Permissions
organization_personal_access_token_requests :: AsReadWrite p => p -> Permissions
-- | Only supported permission is Read
organization_plan :: Permissions
organization_projects :: AsReadWriteAdmin p => p -> Permissions
organization_packages :: AsReadWrite p => p -> Permissions
organization_secrets :: AsReadWrite p => p -> Permissions
organization_self_hosted_runners :: AsReadWrite p => p -> Permissions
organization_user_blocking :: AsReadWrite p => p -> Permissions
team_discussions :: AsReadWrite p => p -> Permissions
email_addresses :: AsReadWrite p => p -> Permissions
followers :: AsReadWrite p => p -> Permissions
git_ssh_keys :: AsReadWrite p => p -> Permissions
gpg_keys :: AsReadWrite p => p -> Permissions
interaction_limits :: AsReadWrite p => p -> Permissions
-- | Only supported permission is Write
profile :: Permissions
starring :: AsReadWrite p => p -> Permissions
instance GHC.Base.Semigroup GitHub.App.Token.Permissions.Permission
instance GHC.Show.Show GitHub.App.Token.Permissions.Permission
instance GHC.Classes.Ord GitHub.App.Token.Permissions.Permission
instance GHC.Classes.Eq GitHub.App.Token.Permissions.Permission
instance Data.Aeson.Types.ToJSON.ToJSON GitHub.App.Token.Permissions.Permissions
instance GHC.Base.Monoid GitHub.App.Token.Permissions.Permissions
instance GHC.Base.Semigroup GitHub.App.Token.Permissions.Permissions
instance GHC.Show.Show GitHub.App.Token.Permissions.Permissions
instance GHC.Classes.Eq GitHub.App.Token.Permissions.Permissions
instance GitHub.App.Token.Permissions.AsReadWriteAdmin GitHub.App.Token.Permissions.Admin
instance GitHub.App.Token.Permissions.AsReadWrite GitHub.App.Token.Permissions.Write
instance GitHub.App.Token.Permissions.AsReadWriteAdmin GitHub.App.Token.Permissions.Write
instance GitHub.App.Token.Permissions.AsReadWrite GitHub.App.Token.Permissions.Read
instance GitHub.App.Token.Permissions.AsReadWriteAdmin GitHub.App.Token.Permissions.Read
instance Data.Aeson.Types.ToJSON.ToJSON GitHub.App.Token.Permissions.Permission
module GitHub.App.Token.JWT
signJWT :: MonadIO m => ExpirationTime -> Issuer -> PrivateKey -> m ByteString
newtype ExpirationTime
ExpirationTime :: NominalDiffTime -> ExpirationTime
[$sel:unwrap:ExpirationTime] :: ExpirationTime -> NominalDiffTime
newtype Issuer
Issuer :: Text -> Issuer
[$sel:unwrap:Issuer] :: Issuer -> Text
newtype PrivateKey
PrivateKey :: ByteString -> PrivateKey
[$sel:unwrap:PrivateKey] :: PrivateKey -> ByteString
newtype InvalidPrivateKey
InvalidPrivateKey :: PrivateKey -> InvalidPrivateKey
data InvalidDate
InvalidDate :: String -> UTCTime -> InvalidDate
[$sel:field:InvalidDate] :: InvalidDate -> String
[$sel:date:InvalidDate] :: InvalidDate -> UTCTime
newtype InvalidIssuer
InvalidIssuer :: Issuer -> InvalidIssuer
instance GHC.Show.Show GitHub.App.Token.JWT.Issuer
instance GHC.Show.Show GitHub.App.Token.JWT.PrivateKey
instance GHC.Exception.Type.Exception GitHub.App.Token.JWT.InvalidPrivateKey
instance GHC.Show.Show GitHub.App.Token.JWT.InvalidPrivateKey
instance GHC.Exception.Type.Exception GitHub.App.Token.JWT.InvalidDate
instance GHC.Show.Show GitHub.App.Token.JWT.InvalidDate
instance GHC.Exception.Type.Exception GitHub.App.Token.JWT.InvalidIssuer
instance GHC.Show.Show GitHub.App.Token.JWT.InvalidIssuer
module GitHub.App.Token.AppCredentials
data AppCredentials
AppCredentials :: AppId -> PrivateKey -> AppCredentials
[$sel:appId:AppCredentials] :: AppCredentials -> AppId
[$sel:privateKey:AppCredentials] :: AppCredentials -> PrivateKey
newtype AppId
AppId :: Int -> AppId
[$sel:unwrap:AppId] :: AppId -> Int
newtype PrivateKey
PrivateKey :: ByteString -> PrivateKey
[$sel:unwrap:PrivateKey] :: PrivateKey -> ByteString
module GitHub.App.Token.Generate
newtype InstallationId
InstallationId :: Int -> InstallationId
[$sel:unwrap:InstallationId] :: InstallationId -> Int
data AccessToken
AccessToken :: Text -> UTCTime -> AccessToken
[$sel:token:AccessToken] :: AccessToken -> Text
[$sel:expires_at:AccessToken] :: AccessToken -> UTCTime
-- | Generate a token for all repositories and the installation's
-- permissions
--
-- See generateInstallationTokenScoped for changing either of
-- these.
generateInstallationToken :: MonadIO m => AppCredentials -> InstallationId -> m AccessToken
data Owner
Org :: Text -> Owner
User :: Text -> Owner
generateOwnerToken :: MonadIO m => AppCredentials -> Owner -> m AccessToken
-- |
-- https://docs.github.com/en/rest/apps/apps?apiVersion=2022-11-28#create-an-installation-access-token-for-an-app
data CreateAccessToken
CreateAccessToken :: [Text] -> [Int] -> Permissions -> CreateAccessToken
-- | List of {owner}/{name} values
[$sel:repositories:CreateAccessToken] :: CreateAccessToken -> [Text]
[$sel:repository_ids:CreateAccessToken] :: CreateAccessToken -> [Int]
[$sel:permissions:CreateAccessToken] :: CreateAccessToken -> Permissions
generateInstallationTokenScoped :: MonadIO m => CreateAccessToken -> AppCredentials -> InstallationId -> m AccessToken
generateOwnerTokenScoped :: MonadIO m => CreateAccessToken -> AppCredentials -> Owner -> m AccessToken
newtype InvalidPrivateKey
InvalidPrivateKey :: PrivateKey -> InvalidPrivateKey
data InvalidDate
InvalidDate :: String -> UTCTime -> InvalidDate
[$sel:field:InvalidDate] :: InvalidDate -> String
[$sel:date:InvalidDate] :: InvalidDate -> UTCTime
newtype InvalidIssuer
InvalidIssuer :: Issuer -> InvalidIssuer
data AccessTokenHttpError
AccessTokenHttpError :: Status -> ByteString -> AccessTokenHttpError
[$sel:status:AccessTokenHttpError] :: AccessTokenHttpError -> Status
[$sel:body:AccessTokenHttpError] :: AccessTokenHttpError -> ByteString
data AccessTokenJsonDecodeError
AccessTokenJsonDecodeError :: ByteString -> String -> AccessTokenJsonDecodeError
[$sel:body:AccessTokenJsonDecodeError] :: AccessTokenJsonDecodeError -> ByteString
[$sel:message:AccessTokenJsonDecodeError] :: AccessTokenJsonDecodeError -> String
data GetInstallationHttpError
GetInstallationHttpError :: Status -> ByteString -> GetInstallationHttpError
[$sel:status:GetInstallationHttpError] :: GetInstallationHttpError -> Status
[$sel:body:GetInstallationHttpError] :: GetInstallationHttpError -> ByteString
data GetInstallationJsonDecodeError
GetInstallationJsonDecodeError :: ByteString -> String -> GetInstallationJsonDecodeError
[$sel:body:GetInstallationJsonDecodeError] :: GetInstallationJsonDecodeError -> ByteString
[$sel:message:GetInstallationJsonDecodeError] :: GetInstallationJsonDecodeError -> String
instance Data.Aeson.Types.FromJSON.FromJSON GitHub.App.Token.Generate.InstallationId
instance Data.Aeson.Types.FromJSON.FromJSON GitHub.App.Token.Generate.AccessToken
instance GHC.Generics.Generic GitHub.App.Token.Generate.AccessToken
instance GHC.Show.Show GitHub.App.Token.Generate.AccessToken
instance GHC.Exception.Type.Exception GitHub.App.Token.Generate.AccessTokenHttpError
instance GHC.Show.Show GitHub.App.Token.Generate.AccessTokenHttpError
instance GHC.Exception.Type.Exception GitHub.App.Token.Generate.AccessTokenJsonDecodeError
instance GHC.Show.Show GitHub.App.Token.Generate.AccessTokenJsonDecodeError
instance GHC.Base.Monoid GitHub.App.Token.Generate.CreateAccessToken
instance GHC.Base.Semigroup GitHub.App.Token.Generate.CreateAccessToken
instance Data.Aeson.Types.ToJSON.ToJSON GitHub.App.Token.Generate.CreateAccessToken
instance GHC.Generics.Generic GitHub.App.Token.Generate.CreateAccessToken
instance GHC.Classes.Eq GitHub.App.Token.Generate.CreateAccessToken
instance Data.Aeson.Types.FromJSON.FromJSON GitHub.App.Token.Generate.Installation
instance GHC.Generics.Generic GitHub.App.Token.Generate.Installation
instance GHC.Exception.Type.Exception GitHub.App.Token.Generate.GetInstallationHttpError
instance GHC.Show.Show GitHub.App.Token.Generate.GetInstallationHttpError
instance GHC.Exception.Type.Exception GitHub.App.Token.Generate.GetInstallationJsonDecodeError
instance GHC.Show.Show GitHub.App.Token.Generate.GetInstallationJsonDecodeError
module GitHub.App.Token
-- | Generate a token for all repositories and the installation's
-- permissions
--
-- See generateInstallationTokenScoped for changing either of
-- these.
generateInstallationToken :: MonadIO m => AppCredentials -> InstallationId -> m AccessToken
data AppCredentials
AppCredentials :: AppId -> PrivateKey -> AppCredentials
[$sel:appId:AppCredentials] :: AppCredentials -> AppId
[$sel:privateKey:AppCredentials] :: AppCredentials -> PrivateKey
newtype AppId
AppId :: Int -> AppId
[$sel:unwrap:AppId] :: AppId -> Int
newtype PrivateKey
PrivateKey :: ByteString -> PrivateKey
[$sel:unwrap:PrivateKey] :: PrivateKey -> ByteString
newtype InstallationId
InstallationId :: Int -> InstallationId
[$sel:unwrap:InstallationId] :: InstallationId -> Int
data AccessToken
AccessToken :: Text -> UTCTime -> AccessToken
[$sel:token:AccessToken] :: AccessToken -> Text
[$sel:expires_at:AccessToken] :: AccessToken -> UTCTime
-- |
-- https://docs.github.com/en/rest/apps/apps?apiVersion=2022-11-28#create-an-installation-access-token-for-an-app
data CreateAccessToken
CreateAccessToken :: [Text] -> [Int] -> Permissions -> CreateAccessToken
-- | List of {owner}/{name} values
[$sel:repositories:CreateAccessToken] :: CreateAccessToken -> [Text]
[$sel:repository_ids:CreateAccessToken] :: CreateAccessToken -> [Int]
[$sel:permissions:CreateAccessToken] :: CreateAccessToken -> Permissions
generateInstallationTokenScoped :: MonadIO m => CreateAccessToken -> AppCredentials -> InstallationId -> m AccessToken
data Owner
Org :: Text -> Owner
User :: Text -> Owner
generateOwnerToken :: MonadIO m => AppCredentials -> Owner -> m AccessToken
generateOwnerTokenScoped :: MonadIO m => CreateAccessToken -> AppCredentials -> Owner -> m AccessToken
module GitHub.App.Token.Refresh
class HasExpiresAt a
expiresAt :: HasExpiresAt a => a -> UTCTime
data Refresh a
-- | Run an action to (e.g.) generate a token and create a thread to
-- refresh it
--
-- refreshing will create an initial token and a thread that
-- checks its expires_at on a loop. When it has expired, the
-- action is used again to replace the token.
--
--
-- ref <- refreshing $ generateInstallationToken creds installationId
--
--
-- Use getRefresh to access the (possibly) updated token.
--
--
-- for_ repos $ repo -> do
-- token <- getRefresh
-- makeSomeRequest token repo
--
--
-- If you can't rely on program exit to clean up this background thread,
-- you can manually cancel it:
--
--
-- cancelRefresh ref
--
refreshing :: (MonadUnliftIO m, HasExpiresAt a) => m a -> m (Refresh a)
getRefresh :: MonadIO m => Refresh a -> m a
cancelRefresh :: MonadIO m => Refresh a -> m ()
instance GitHub.App.Token.Refresh.HasExpiresAt GitHub.App.Token.Generate.AccessToken