prelude-compat-0.0.0.1: Provide Prelude and Data.List with fixed content across GHC versions

Prelude2010

Synopsis

# Documentation

(\$!) :: (a -> b) -> a -> b infixr 0

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.

catch :: IO a -> (IOError -> IO a) -> IO a Source

gcd :: Integral a => a -> a -> a

`gcd x y` is the non-negative factor of both `x` and `y` of which every common factor of `x` and `y` is also a factor; for example `gcd 4 2 = 2`, `gcd (-4) 6 = 2`, `gcd 0 4` = `4`. `gcd 0 0` = `0`. (That is, the common divisor that is "greatest" in the divisibility preordering.)

Note: Since for signed fixed-width integer types, `abs minBound < 0`, the result may be negative if one of the arguments is `minBound` (and necessarily is if the other is `0` or `minBound`) for such types.

(\$) :: (a -> b) -> a -> b infixr 0

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`.

(&&) :: Bool -> Bool -> Bool infixr 3

Boolean "and"

(.) :: (b -> c) -> (a -> b) -> a -> c infixr 9

Function composition.

(=<<) :: Monad m => (a -> m b) -> m a -> m b infixr 1

Same as `>>=`, but with the arguments interchanged.

data Bool :: *

Constructors

 False True

Instances

class Bounded a where

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`.

Methods

minBound :: a

maxBound :: a

Instances

 Bounded () (Bounded a, Bounded b) => Bounded (a, b) Bounded (Proxy k s) (Bounded a, Bounded b, Bounded c) => Bounded (a, b, c) (~) k a b => Bounded ((:~:) k a b) (Bounded a, Bounded b, Bounded c, Bounded d) => Bounded (a, b, c, d) (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e) => Bounded (a, b, c, d, e) (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f) => Bounded (a, b, c, d, e, f) (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g) => Bounded (a, b, c, d, e, f, g) (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h) => Bounded (a, b, c, d, e, f, g, h) (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i) => Bounded (a, b, c, d, e, f, g, h, i) (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j) => Bounded (a, b, c, d, e, f, g, h, i, j) (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k) => Bounded (a, b, c, d, e, f, g, h, i, j, k) (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l) (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l, Bounded m) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l, m) (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l, Bounded m, Bounded n) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l, m, n) (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l, Bounded m, Bounded n, Bounded o) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o)

data Char :: *

The character type `Char` is an enumeration whose values represent Unicode (or equivalently ISO/IEC 10646) characters (see http://www.unicode.org/ for details). This set extends the ISO 8859-1 (Latin-1) character set (the first 256 characters), which is itself an extension of the ASCII character set (the first 128 characters). A character literal in Haskell has type `Char`.

To convert a `Char` to or from the corresponding `Int` value defined by Unicode, use `toEnum` and `fromEnum` from the `Enum` class respectively (or equivalently `ord` and `chr`).

Instances

 type Rep Char = D1 D_Char (C1 C_Char (S1 NoSelector (Rec0 Char)))

data Double :: *

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.

Instances

 type Rep Double = D1 D_Double (C1 C_Double (S1 NoSelector (Rec0 Double)))

data Either a b :: * -> * -> *

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 `String`s, and the `Right` constructor can be used only on `Int`s:

````>>> ````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 `Int`s.

````>>> ````:{
```    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"
```

Constructors

 Left a Right b

Instances

 Monad (Either e) (Eq a, Eq b) => Eq (Either a b) (Ord a, Ord b) => Ord (Either a b) (Read a, Read b) => Read (Either a b) (Show a, Show b) => Show (Either a b) Generic (Either a b) type Rep1 (Either a) = D1 D1Either ((:+:) (C1 C1_0Either (S1 NoSelector (Rec0 a))) (C1 C1_1Either (S1 NoSelector Par1))) type Rep (Either a b) = D1 D1Either ((:+:) (C1 C1_0Either (S1 NoSelector (Rec0 a))) (C1 C1_1Either (S1 NoSelector (Rec0 b)))) type (==) (Either k k1) a b = EqEither k k1 a b

class Enum a where

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:

• The calls `succ maxBound` and `pred minBound` should result in a runtime error.
• `fromEnum` and `toEnum` should give a runtime error if the result value is not representable in the result type. For example, `toEnum 7 :: Bool` is an error.
• `enumFrom` and `enumFromThen` should be defined with an implicit bound, thus:
```   enumFrom     x   = enumFromTo     x maxBound
enumFromThen x y = enumFromThenTo x y bound
where
| otherwise                = minBound```

Minimal complete definition

Methods

succ :: a -> a

the successor of a value. For numeric types, `succ` adds 1.

pred :: a -> a

the predecessor of a value. For numeric types, `pred` subtracts 1.

toEnum :: Int -> a

Convert from an `Int`.

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`.

enumFrom :: a -> [a]

Used in Haskell's translation of `[n..]`.

enumFromThen :: a -> a -> [a]

Used in Haskell's translation of `[n,n'..]`.

enumFromTo :: a -> a -> [a]

Used in Haskell's translation of `[n..m]`.

enumFromThenTo :: a -> a -> a -> [a]

Used in Haskell's translation of `[n,n'..m]`.

Instances

 Enum () Integral a => Enum (Ratio a) Enum (Proxy k s) (~) k a b => Enum ((:~:) k a b)

class Eq a where

The `Eq` class defines equality (`==`) and inequality (`/=`). All the basic datatypes exported by the Prelude are instances of `Eq`, and `Eq` may be derived for any datatype whose constituents are also instances of `Eq`.

Minimal complete definition: either `==` or `/=`.

Minimal complete definition

Methods

(==) :: a -> a -> Bool infix 4

(/=) :: a -> a -> Bool infix 4

Instances

 Eq () Eq a => Eq [a] Eq a => Eq (Ratio a) Eq (U1 p) Eq p => Eq (Par1 p) Eq a => Eq (ZipList a) Eq a => Eq (Maybe a) (Eq a, Eq b) => Eq (Either a b) Eq (f p) => Eq (Rec1 f p) (Eq a, Eq b) => Eq (a, b) (Ix i, Eq e) => Eq (Array i e) Eq a => Eq (Const a b) Eq (Proxy k s) Eq c => Eq (K1 i c p) (Eq (f p), Eq (g p)) => Eq ((:+:) f g p) (Eq (f p), Eq (g p)) => Eq ((:*:) f g p) Eq (f (g p)) => Eq ((:.:) f g p) (Eq a, Eq b, Eq c) => Eq (a, b, c) Eq (STArray s i e) Eq ((:~:) k a b) Eq (f p) => Eq (M1 i c f p) (Eq a, Eq b, Eq c, Eq d) => Eq (a, b, c, d) (Eq a, Eq b, Eq c, Eq d, Eq e) => Eq (a, b, c, d, e) (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f) => Eq (a, b, c, d, e, f) (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g) => Eq (a, b, c, d, e, f, g) (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h) => Eq (a, b, c, d, e, f, g, h) (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i) => Eq (a, b, c, d, e, f, g, h, i) (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j) => Eq (a, b, c, d, e, f, g, h, i, j) (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k) => Eq (a, b, c, d, e, f, g, h, i, j, k) (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l) => Eq (a, b, c, d, e, f, g, h, i, j, k, l) (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m) (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m, Eq n) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m, n) (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m, Eq n, Eq o) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o)

type FilePath = 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.

data Float :: *

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.

Instances

 type Rep Float = D1 D_Float (C1 C_Float (S1 NoSelector (Rec0 Float)))

class Fractional a => Floating a where

Trigonometric and hyperbolic functions and related functions.

Minimal complete definition

Methods

pi :: a

exp :: a -> a

log :: a -> a

sqrt :: a -> a

(**) :: a -> a -> a infixr 8

logBase :: a -> a -> a

sin :: a -> a

cos :: a -> a

tan :: a -> a

asin :: a -> a

acos :: a -> a

atan :: a -> a

sinh :: a -> a

cosh :: a -> a

tanh :: a -> a

asinh :: a -> a

acosh :: a -> a

atanh :: a -> a

Instances

class Num a => Fractional a where

Fractional numbers, supporting real division.

Minimal complete definition

fromRational, (recip | (/))

Methods

(/) :: a -> a -> a infixl 7

fractional division

recip :: a -> a

reciprocal fraction

fromRational :: Rational -> 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`.

Instances

 Integral a => Fractional (Ratio a)

class Functor f where

The `Functor` class is used for types that can be mapped over. Instances of `Functor` should satisfy the following laws:

```fmap id  ==  id
fmap (f . g)  ==  fmap f . fmap g```

The instances of `Functor` for lists, `Maybe` and `IO` satisfy these laws.

Methods

fmap :: (a -> b) -> f a -> f b

Instances

 Functor [] Functor Id Functor ((->) r) Functor ((,) a) Functor (StateL s) Functor (StateR s) Ix i => Functor (Array i) Functor (Const m) Monad m => Functor (WrappedMonad m) Functor (Proxy *) Arrow a => Functor (WrappedArrow a b)

data IO 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.

Instances

type IOError = IOException

The Haskell 2010 type for exceptions in the `IO` monad. Any I/O operation may raise an `IOError` instead of returning a result. For a more general type of exception, including also those that arise in pure code, see Control.Exception.Exception.

In Haskell 2010, this is an opaque type.

data Int :: *

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.

Instances

 type Rep Int = D1 D_Int (C1 C_Int (S1 NoSelector (Rec0 Int)))

data Integer :: *

Invariant: `Jn#` and `Jp#` are used iff value doesn't fit in `S#`

Useful properties resulting from the invariants:

• `abs (`S#` _) <= abs (`Jp#` _)`
• `abs (`S#` _) <  abs (`Jn#` _)`

Instances

class (Real a, Enum a) => Integral a where

Integral numbers, supporting integer division.

Minimal complete definition

Methods

quot :: a -> a -> a infixl 7

integer division truncated toward zero

rem :: a -> a -> a infixl 7

integer remainder, satisfying

`(x `quot` y)*y + (x `rem` y) == x`

div :: a -> a -> a infixl 7

integer division truncated toward negative infinity

mod :: a -> a -> a infixl 7

integer modulus, satisfying

`(x `div` y)*y + (x `mod` y) == x`

quotRem :: a -> a -> (a, a)

simultaneous `quot` and `rem`

divMod :: a -> a -> (a, a)

simultaneous `div` and `mod`

toInteger :: a -> Integer

conversion to `Integer`

Instances

data Maybe a :: * -> *

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.

Constructors

 Nothing Just a

Instances

 Eq a => Eq (Maybe a) Ord a => Ord (Maybe a) Read a => Read (Maybe a) Show a => Show (Maybe a) Generic (Maybe a) Monoid a => Monoid (Maybe a) Lift a semigroup into `Maybe` forming a `Monoid` according to http://en.wikipedia.org/wiki/Monoid: "Any semigroup `S` may be turned into a monoid simply by adjoining an element `e` not in `S` and defining `e*e = e` and `e*s = s = s*e` for all `s ∈ S`." Since there is no "Semigroup" typeclass providing just `mappend`, we use `Monoid` instead. type Rep1 Maybe = D1 D1Maybe ((:+:) (C1 C1_0Maybe U1) (C1 C1_1Maybe (S1 NoSelector Par1))) type Rep (Maybe a) = D1 D1Maybe ((:+:) (C1 C1_0Maybe U1) (C1 C1_1Maybe (S1 NoSelector (Rec0 a)))) type (==) (Maybe k) a b = EqMaybe k a b

class Applicative m => Monad m where

The `Monad` class defines the basic operations over a monad, a concept from a branch of mathematics known as category theory. From the perspective of a Haskell programmer, however, it is best to think of a monad as an abstract datatype of actions. Haskell's `do` expressions provide a convenient syntax for writing monadic expressions.

Instances of `Monad` should satisfy the following laws:

• ``return` a `>>=` k  =  k a`
• `m `>>=` `return`  =  m`
• `m `>>=` (x -> k x `>>=` h)  =  (m `>>=` k) `>>=` h`

Furthermore, the `Monad` and `Applicative` operations should relate as follows:

• ``pure` = `return``
• `(`<*>`) = `ap``

The above laws imply:

• ``fmap` f xs  =  xs `>>=` `return` . f`
• `(`>>`) = (`*>`)`

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.

Minimal complete definition

(>>=)

Methods

(>>=) :: m a -> (a -> m b) -> m b infixl 1

Sequentially compose two actions, passing any value produced by the first as an argument to the second.

(>>) :: m a -> m b -> m b infixl 1

Sequentially compose two actions, discarding any value produced by the first, like sequencing operators (such as the semicolon) in imperative languages.

return :: a -> m a

Inject a value into the monadic type.

fail :: String -> m a

Fail with a message. This operation is not part of the mathematical definition of a monad, but is invoked on pattern-match failure in a `do` expression.

Instances

class Num a where

Basic numeric class.

Minimal complete definition

(+), (*), abs, signum, fromInteger, (negate | (-))

Methods

(+) :: a -> a -> a infixl 6

(-) :: a -> a -> a infixl 6

(*) :: a -> a -> a infixl 7

negate :: a -> a

Unary negation.

abs :: a -> a

Absolute value.

signum :: 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).

fromInteger :: Integer -> 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`.

Instances

 Integral a => Num (Ratio a)

class Eq a => Ord a where

The `Ord` class is used for totally ordered datatypes.

Instances of `Ord` can be derived for any user-defined datatype whose constituent types are in `Ord`. The declared order of the constructors in the data declaration determines the ordering in derived `Ord` instances. The `Ordering` datatype allows a single comparison to determine the precise ordering of two objects.

Minimal complete definition: either `compare` or `<=`. Using `compare` can be more efficient for complex types.

Minimal complete definition

Methods

compare :: a -> a -> Ordering

(<) :: a -> a -> Bool infix 4

(<=) :: a -> a -> Bool infix 4

(>) :: a -> a -> Bool infix 4

(>=) :: a -> a -> Bool infix 4

max :: a -> a -> a

min :: a -> a -> a

Instances

 Ord () Ord a => Ord [a] Integral a => Ord (Ratio a) Ord (U1 p) Ord p => Ord (Par1 p) Ord a => Ord (ZipList a) Ord a => Ord (Maybe a) (Ord a, Ord b) => Ord (Either a b) Ord (f p) => Ord (Rec1 f p) (Ord a, Ord b) => Ord (a, b) (Ix i, Ord e) => Ord (Array i e) Ord a => Ord (Const a b) Ord (Proxy k s) Ord c => Ord (K1 i c p) (Ord (f p), Ord (g p)) => Ord ((:+:) f g p) (Ord (f p), Ord (g p)) => Ord ((:*:) f g p) Ord (f (g p)) => Ord ((:.:) f g p) (Ord a, Ord b, Ord c) => Ord (a, b, c) Ord ((:~:) k a b) Ord (f p) => Ord (M1 i c f p) (Ord a, Ord b, Ord c, Ord d) => Ord (a, b, c, d) (Ord a, Ord b, Ord c, Ord d, Ord e) => Ord (a, b, c, d, e) (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f) => Ord (a, b, c, d, e, f) (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g) => Ord (a, b, c, d, e, f, g) (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h) => Ord (a, b, c, d, e, f, g, h) (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i) => Ord (a, b, c, d, e, f, g, h, i) (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j) => Ord (a, b, c, d, e, f, g, h, i, j) (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k) => Ord (a, b, c, d, e, f, g, h, i, j, k) (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l) => Ord (a, b, c, d, e, f, g, h, i, j, k, l) (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l, Ord m) => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m) (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l, Ord m, Ord n) => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m, n) (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l, Ord m, Ord n, Ord o) => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o)

data Ordering :: *

Constructors

 LT EQ GT

Instances

 type Rep Ordering = D1 D1Ordering ((:+:) (C1 C1_0Ordering U1) ((:+:) (C1 C1_1Ordering U1) (C1 C1_2Ordering U1))) type (==) Ordering a b = EqOrdering a b

type Rational = Ratio Integer

Arbitrary-precision rational numbers, represented as a ratio of two `Integer` values. A rational number may be constructed using the `%` operator.

Parsing of `String`s, 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

(\r -> [(Leaf m,t) |
("Leaf",s) <- lex r,
(m,t) <- readsPrec (app_prec+1) s]) r

(\r -> [(u:^:v,w) |
(":^:",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
return (Leaf m))

+++ (prec up_prec \$ do
Symbol ":^:" <- lexP
return (u :^: v))

where app_prec = 10
up_prec = 5

Minimal complete definition

Methods

Arguments

 :: Int the operator precedence of the enclosing context (a number from `0` to `11`). Function application has precedence `10`. -> ReadS a

attempts to parse a value from the front of the string, returning a list of (parsed value, remaining string) pairs. If there is no successful parse, the returned list is empty.

Derived instances of `Read` and `Show` satisfy the following:

• `(x,"")` is an element of `(readsPrec d (showsPrec d x ""))`.

That is, `readsPrec` parses the string produced by `showsPrec`, and delivers the value that `showsPrec` started with.

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.

Instances

type ReadS a = String -> [(a, 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`).

class (Num a, Ord a) => Real a where

Methods

toRational :: a -> Rational

the rational equivalent of its real argument with full precision

Instances

 Integral a => Real (Ratio a)

class (RealFrac a, Floating a) => RealFloat a where

Minimal complete definition

Methods

a constant function, returning the radix of the representation (often `2`)

floatDigits :: a -> Int

a constant function, returning the number of digits of `floatRadix` in the significand

floatRange :: a -> (Int, Int)

a constant function, returning the lowest and highest values the exponent may assume

decodeFloat :: a -> (Integer, 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`.

encodeFloat :: Integer -> Int -> a

`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.

exponent :: a -> Int

`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.

significand :: a -> a

The first component of `decodeFloat`, scaled to lie in the open interval (`-1`,`1`), either `0.0` or of absolute value `>= 1/b`, where `b` is the floating-point radix. The behaviour is unspecified on infinite or `NaN` values.

scaleFloat :: Int -> a -> a

multiplies a floating-point number by an integer power of the radix

isNaN :: a -> Bool

`True` if the argument is an IEEE "not-a-number" (NaN) value

isInfinite :: a -> Bool

`True` if the argument is an IEEE infinity or negative infinity

isDenormalized :: a -> Bool

`True` if the argument is too small to be represented in normalized format

isNegativeZero :: a -> Bool

`True` if the argument is an IEEE negative zero

isIEEE :: a -> Bool

`True` if the argument is an IEEE floating point number

atan2 :: a -> a -> a

a version of arctangent taking two real floating-point arguments. For real floating `x` and `y`, `atan2 y x` computes the angle (from the positive x-axis) of the vector from the origin to the point `(x,y)`. `atan2 y x` returns a value in the range [`-pi`, `pi`]. It follows the Common Lisp semantics for the origin when signed zeroes are supported. `atan2 y 1`, with `y` in a type that is `RealFloat`, should return the same value as `atan y`. A default definition of `atan2` is provided, but implementors can provide a more accurate implementation.

Instances

class (Real a, Fractional a) => RealFrac a where

Extracting components of fractions.

Minimal complete definition

properFraction

Methods

properFraction :: Integral b => a -> (b, 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`.

truncate :: Integral b => a -> b

`truncate x` returns the integer nearest `x` between zero and `x`

round :: Integral b => a -> b

`round x` returns the nearest integer to `x`; the even integer if `x` is equidistant between two integers

ceiling :: Integral b => a -> b

`ceiling x` returns the least integer not less than `x`

floor :: Integral b => a -> b

`floor x` returns the greatest integer not greater than `x`

Instances

 Integral a => RealFrac (Ratio a)

class Show a where

Conversion of values to readable `String`s.

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)"`.

Minimal complete definition

Methods

showsPrec

Arguments

 :: Int the operator precedence of the enclosing context (a number from `0` to `11`). Function application has precedence `10`. -> a the value to be converted to a `String` -> ShowS

Convert a value to a readable `String`.

`showsPrec` should satisfy the law

`showsPrec d x r ++ s  ==  showsPrec d x (r ++ s)`

Derived instances of `Read` and `Show` satisfy the following:

• `(x,"")` is an element of `(readsPrec d (showsPrec d x ""))`.

That is, `readsPrec` parses the string produced by `showsPrec`, and delivers the value that `showsPrec` started with.

show :: a -> String

A specialised variant of `showsPrec`, using precedence context zero, and returning an ordinary `String`.

showList :: [a] -> ShowS

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.

Instances

 Show () Show a => Show [a] (Integral a, Show a) => Show (Ratio a) Show (U1 p) Show p => Show (Par1 p) Show a => Show (ZipList a) Show a => Show (Maybe a) (Show a, Show b) => Show (Either a b) Show (f p) => Show (Rec1 f p) (Show a, Show b) => Show (a, b) (Ix a, Show a, Show b) => Show (Array a b) Show a => Show (Const a b) Show (Proxy k s) Show c => Show (K1 i c p) (Show (f p), Show (g p)) => Show ((:+:) f g p) (Show (f p), Show (g p)) => Show ((:*:) f g p) Show (f (g p)) => Show ((:.:) f g p) (Show a, Show b, Show c) => Show (a, b, c) Show ((:~:) k a b) Show (f p) => Show (M1 i c f p) (Show a, Show b, Show c, Show d) => Show (a, b, c, d) (Show a, Show b, Show c, Show d, Show e) => Show (a, b, c, d, e) (Show a, Show b, Show c, Show d, Show e, Show f) => Show (a, b, c, d, e, f) (Show a, Show b, Show c, Show d, Show e, Show f, Show g) => Show (a, b, c, d, e, f, g) (Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h) => Show (a, b, c, d, e, f, g, h) (Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i) => Show (a, b, c, d, e, f, g, h, i) (Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j) => Show (a, b, c, d, e, f, g, h, i, j) (Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k) => Show (a, b, c, d, e, f, g, h, i, j, k) (Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k, Show l) => Show (a, b, c, d, e, f, g, h, i, j, k, l) (Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k, Show l, Show m) => Show (a, b, c, d, e, f, g, h, i, j, k, l, m) (Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k, Show l, Show m, Show n) => Show (a, b, c, d, e, f, g, h, i, j, k, l, m, n) (Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k, Show l, Show m, Show n, Show o) => Show (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o)

type ShowS = String -> String

The `shows` functions return a function that prepends the output `String` to an existing `String`. This allows constant-time concatenation of results using function composition.

type String = [Char]

A `String` is a list of characters. String constants in Haskell are values of type `String`.

(^) :: (Num a, Integral b) => a -> b -> a infixr 8

raise a number to a non-negative integral power

(^^) :: (Fractional a, Integral b) => a -> b -> a infixr 8

raise a number to an integral power

appendFile :: FilePath -> String -> IO ()

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]])`

asTypeOf :: 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.

const :: a -> b -> a

Constant function.

curry :: ((a, b) -> c) -> a -> b -> c

`curry` converts an uncurried function to a curried function.

either :: (a -> c) -> (b -> c) -> Either a b -> c

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
```

error :: [Char] -> a

`error` stops execution and displays an error message.

even :: Integral a => a -> Bool

flip :: (a -> b -> c) -> b -> a -> c

`flip f` takes its (first) two arguments in the reverse order of `f`.

fromIntegral :: (Integral a, Num b) => a -> b

general coercion from integral types

fst :: (a, b) -> a

Extract the first component of a pair.

Read a character from the standard input device (same as `hGetChar` `stdin`).

The `getContents` operation returns all user input as a single string, which is read lazily as it is needed (same as `hGetContents` `stdin`).

Read a line from the standard input device (same as `hGetLine` `stdin`).

id :: a -> a

Identity function.

interact :: (String -> String) -> IO ()

The `interact` function takes a function of type `String->String` as its argument. The entire input from the standard input device is passed to this function as its argument, and the resulting string is output on the standard output device.

ioError :: IOError -> IO a

Raise an `IOError` in the `IO` monad.

lcm :: Integral a => a -> a -> a

`lcm x y` is the smallest positive integer that both `x` and `y` divide.

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

lines :: String -> [String]

`lines` breaks a string up into a list of strings at newline characters. The resulting strings do not contain newlines.

mapM :: Traversable t => forall a m b. Monad m => (a -> m b) -> t a -> m (t b)

Map each element of a structure to a monadic action, evaluate these actions from left to right, and collect the results. For a version that ignores the results see `mapM_`.

mapM_ :: (Foldable t, Monad m) => (a -> m b) -> t a -> m ()

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`.

As of base 4.8.0.0, `mapM_` is just `traverse_`, specialized to `Monad`.

maximum :: Foldable t => forall a. Ord a => t a -> a

The largest element of a non-empty structure.

maybe :: b -> (a -> b) -> Maybe a -> b

The `maybe` function takes a default value, a function, and a `Maybe` value. If the `Maybe` value is `Nothing`, the function returns the default value. Otherwise, it applies the function to the value inside the `Just` and returns the result.

#### 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
```""
```

minimum :: Foldable t => forall a. Ord a => t a -> a

The least element of a non-empty structure.

not :: Bool -> Bool

Boolean "not"

odd :: Integral a => a -> Bool

`otherwise` is defined as the value `True`. It helps to make guards more readable. eg.

``` f x | x < 0     = ...
| otherwise = ...```

print :: Show a => a -> IO ()

The `print` function outputs a value of any printable type to the standard output device. Printable types are those that are instances of class `Show`; `print` converts values to strings for output using the `show` operation and adds a newline.

For example, a program to print the first 20 integers and their powers of 2 could be written as:

`main = print ([(n, 2^n) | n <- [0..19]])`

product :: Foldable t => forall a. Num a => t a -> a

The `product` function computes the product of the numbers of a structure.

putChar :: Char -> IO ()

Write a character to the standard output device (same as `hPutChar` `stdout`).

putStr :: String -> IO ()

Write a string to the standard output device (same as `hPutStr` `stdout`).

putStrLn :: String -> IO ()

The same as `putStr`, but adds a newline character.

The `read` function reads input from a string, which must be completely consumed by the input process.

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`.

The `readIO` function is similar to `read` except that it signals parse failure to the `IO` monad instead of terminating the program.

The `readLn` function combines `getLine` and `readIO`.

`readParen True p` parses what `p` parses, but surrounded with parentheses.

`readParen False p` parses what `p` parses, but optionally surrounded with parentheses.

equivalent to `readsPrec` with a precedence of 0.

realToFrac :: (Real a, Fractional b) => a -> b

general coercion to fractional types

seq :: a -> b -> b

The value of `seq a b` is bottom if `a` is bottom, and otherwise equal to `b`. `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.

sequence :: Traversable t => forall m a. Monad m => t (m a) -> m (t a)

Evaluate each monadic action in the structure from left to right, and collect the results. For a version that ignores the results see `sequence_`.

sequence_ :: (Foldable t, Monad m) => t (m a) -> m ()

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`.

As of base 4.8.0.0, `sequence_` is just `sequenceA_`, specialized to `Monad`.

utility function converting a `Char` to a show function that simply prepends the character unchanged.

showParen :: Bool -> ShowS -> ShowS

utility function that surrounds the inner show function with parentheses when the `Bool` parameter is `True`.

utility function converting a `String` to a show function that simply prepends the string unchanged.

shows :: Show a => a -> ShowS

equivalent to `showsPrec` with a precedence of 0.

snd :: (a, b) -> b

Extract the second component of a pair.

subtract :: Num a => 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.

sum :: Foldable t => forall a. Num a => t a -> a

The `sum` function computes the sum of the numbers of a structure.

uncurry :: (a -> b -> c) -> (a, b) -> c

`uncurry` converts a curried function to a function on pairs.

undefined :: 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.

unlines :: [String] -> String

`unlines` is an inverse operation to `lines`. It joins lines, after appending a terminating newline to each.

until :: (a -> Bool) -> (a -> a) -> a -> a

`until p f` yields the result of applying `f` until `p` holds.

Construct an `IOError` value with a string describing the error. The `fail` method of the `IO` instance of the `Monad` class raises a `userError`, thus:

```instance Monad IO where
...
fail s = ioError (userError s)```

writeFile :: FilePath -> String -> IO ()

The computation `writeFile` `file str` function writes the string `str`, to the file `file`.

(||) :: Bool -> Bool -> Bool infixr 2

Boolean "or"

(!!) :: [a] -> Int -> a Source

(++) :: [a] -> [a] -> [a] infixr 5 Source

all :: (a -> Bool) -> [a] -> Bool Source

any :: (a -> Bool) -> [a] -> Bool Source

break :: (a -> Bool) -> [a] -> ([a], [a]) Source

concat :: [[a]] -> [a] Source

concatMap :: (a -> [b]) -> [a] -> [b] Source

cycle :: [a] -> [a] Source

drop :: Int -> [a] -> [a] Source

dropWhile :: (a -> Bool) -> [a] -> [a] Source

elem :: Eq a => a -> [a] -> Bool Source

filter :: (a -> Bool) -> [a] -> [a] Source

foldl :: (a -> b -> a) -> a -> [b] -> a Source

foldl1 :: (a -> a -> a) -> [a] -> a Source

foldr :: (a -> b -> b) -> b -> [a] -> b Source

foldr1 :: (a -> a -> a) -> [a] -> a Source

head :: [a] -> a Source

init :: [a] -> [a] Source

iterate :: (a -> a) -> a -> [a] Source

last :: [a] -> a Source

length :: [a] -> Int Source

lookup :: Eq a => a -> [(a, b)] -> Maybe b Source

map :: (a -> b) -> [a] -> [b] Source

notElem :: Eq a => a -> [a] -> Bool Source

null :: [a] -> Bool Source

or :: [Bool] -> Bool Source

repeat :: a -> [a] Source

replicate :: Int -> a -> [a] Source

reverse :: [a] -> [a] Source

scanl :: (a -> b -> a) -> a -> [b] -> [a] Source

scanl1 :: (a -> a -> a) -> [a] -> [a] Source

scanr :: (a -> b -> b) -> b -> [a] -> [b] Source

scanr1 :: (a -> a -> a) -> [a] -> [a] Source

span :: (a -> Bool) -> [a] -> ([a], [a]) Source

splitAt :: Int -> [a] -> ([a], [a]) Source

tail :: [a] -> [a] Source

take :: Int -> [a] -> [a] Source

takeWhile :: (a -> Bool) -> [a] -> [a] Source

unzip :: [(a, b)] -> ([a], [b]) Source

unzip3 :: [(a, b, c)] -> ([a], [b], [c]) Source

zip :: [a] -> [b] -> [(a, b)] Source

zip3 :: [a] -> [b] -> [c] -> [(a, b, c)] Source

zipWith :: (a -> b -> c) -> [a] -> [b] -> [c] Source

zipWith3 :: (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d] Source