BasePrelude.DataTypes

The character type Char represents Unicode codespace and its elements are code points as in definitions D9 and D10 of the Unicode Standard.

Character literals in Haskell are single-quoted: 'Q', 'Я' or 'Ω'. To represent a single quote itself use '\'', and to represent a backslash use '\\'. The full grammar can be found in the section 2.6 of the Haskell 2010 Language Report.

To specify a character by its code point one can use decimal, hexadecimal or octal notation: '\65', '\x41' and '\o101' are all alternative forms of 'A'. The largest code point is '\x10ffff'.

There is a special escape syntax for ASCII control characters:

Data.Char provides utilities to work with 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.

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>>> sLeft "foo">>> let n = Right 3 :: Either String Int>>> nRight 3>>> :type ss :: Either String Int>>> :type nn :: 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) sLeft "foo">>> fmap (*2) nRight 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)>>> :}

>>> parseMultipleRight 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)>>> :}

>>> parseMultipleLeft "parse error"

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.

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 (i.e., fits into an Int), the IS constructor is used. Otherwise IP and IN constructors are used to store a BigNat representing the positive or the negative value magnitude, respectively.

Invariant: IP and IN are used iff the value does not fit in IS.

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.

String is an alias for a list of characters.

String constants in Haskell are values of type String. That means if you write a string literal like "hello world", it will have the type [Char], which is the same as String.

Note: You can ask the compiler to automatically infer different types with the -XOverloadedStrings language extension, for example "hello world" :: Text. See IsString for more information.

Because String is just a list of characters, you can use normal list functions to do basic string manipulation. See Data.List for operations on lists.

Performance considerations

[Char] is a relatively memory-inefficient type. It is a linked list of boxed word-size characters, internally it looks something like:

╭─────┬───┬──╮  ╭─────┬───┬──╮  ╭─────┬───┬──╮  ╭────╮
│ (:) │   │ ─┼─>│ (:) │   │ ─┼─>│ (:) │   │ ─┼─>│ [] │
╰─────┴─┼─┴──╯  ╰─────┴─┼─┴──╯  ╰─────┴─┼─┴──╯  ╰────╯
        v               v               v
       'a'             'b'             'c'

The String "abc" will use 5*3+1 = 16 (in general 5n+1) words of space in memory.

Furthermore, operations like (++) (string concatenation) are O(n) (in the left argument).

For historical reasons, the base library uses String in a lot of places for the conceptual simplicity, but library code dealing with user-data should use the text package for Unicode text, or the the bytestring package for binary data.

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 Prelude.minBound and Prelude.maxBound from the Prelude.Bounded class.

8-bit signed integer type

16-bit signed integer type

32-bit signed integer type

64-bit signed integer type

A Word is an unsigned integral type, with the same size as Int.

8-bit unsigned integer type

16-bit unsigned integer type

32-bit unsigned integer type

64-bit unsigned integer type

A data type representing complex numbers.

You can read about complex numbers on wikipedia.

In haskell, complex numbers are represented as a :+ b which can be thought of as representing a + bi. For a complex number z, abs z is a number with the magnitude of z, but oriented in the positive real direction, whereas signum z has the phase of z, but unit magnitude. Apart from the loss of precision due to IEEE754 floating point numbers, it holds that z == abs z * signum z.

Note that Complex's instances inherit the deficiencies from the type parameter's. For example, Complex Float's Ord instance has similar problems to Float's.

As can be seen in the examples, the Foldable and Traversable instances traverse the real part first.

Examples

>>> (5.0 :+ 2.5) + 6.511.5 :+ 2.5

>>> abs (1.0 :+ 1.0) - sqrt 2.00.0 :+ 0.0

>>> abs (signum (4.0 :+ 3.0))1.0 :+ 0.0

>>> foldr (:) [] (1 :+ 2)[1,2]

>>> mapM print (1 :+ 2)12

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

Natural number

Invariant: numbers <= 0xffffffffffffffff use the NS constructor

Non-empty (and non-strict) list type.