Enable rebindable fail with overloaded strings

[ghc.git] / docs / users_guide / glasgow_exts.rst

.. index::
   single: language, GHC extensions

As with all known Haskell systems, GHC implements some extensions to the
standard Haskell language. They can all be enabled or disabled by command line
flags or language pragmas. By default GHC understands the most recent Haskell
version it supports, plus a handful of extensions.

Some of the Glasgow extensions serve to give you access to the
underlying facilities with which we implement Haskell. Thus, you can get
at the Raw Iron, if you are willing to write some non-portable code at a
more primitive level. You need not be “stuck” on performance because of
the implementation costs of Haskell's "high-level" features—you can
always code "under" them. In an extreme case, you can write all your
time-critical code in C, and then just glue it together with Haskell!

Before you get too carried away working at the lowest level (e.g.,
sloshing ``MutableByteArray#``\ s around your program), you may wish to
check if there are libraries that provide a "Haskellised veneer" over
the features you want. The separate
`libraries documentation <../libraries/index.html>`__ describes all the
libraries that come with GHC.

.. _options-language:

Language options
================

.. index::
   single: language; option
   single: options; language
   single: extensions; options controlling

The language extensions control what variation of the language are
permitted.

Language options can be controlled in two ways:

-  Every language option can switched on by a command-line flag
   "``-X...``" (e.g. ``-XTemplateHaskell``), and switched off by the
   flag "``-XNo...``"; (e.g. ``-XNoTemplateHaskell``).

-  Language options recognised by Cabal can also be enabled using the
   ``LANGUAGE`` pragma, thus ``{-# LANGUAGE TemplateHaskell #-}`` (see
   :ref:`language-pragma`).

GHC supports these language options:

.. extension-print::
    :type: table

Although not recommended, the deprecated :ghc-flag:`-fglasgow-exts` flag enables
a large swath of the extensions supported by GHC at once.

.. ghc-flag:: -fglasgow-exts
    :shortdesc: Deprecated. Enable most language extensions;
        see :ref:`options-language` for exactly which ones.
    :type: dynamic
    :reverse: -fno-glasgow-exts
    :category: misc

    The flag ``-fglasgow-exts`` is equivalent to enabling the following extensions:

    .. include:: what_glasgow_exts_does.rst

    Enabling these options is the *only* effect of ``-fglasgow-exts``. We are trying
    to move away from this portmanteau flag, and towards enabling features
    individually.

.. _primitives:

Unboxed types and primitive operations
======================================

GHC is built on a raft of primitive data types and operations;
"primitive" in the sense that they cannot be defined in Haskell itself.
While you really can use this stuff to write fast code, we generally
find it a lot less painful, and more satisfying in the long run, to use
higher-level language features and libraries. With any luck, the code
you write will be optimised to the efficient unboxed version in any
case. And if it isn't, we'd like to know about it.

All these primitive data types and operations are exported by the
library ``GHC.Prim``, for which there is
:ghc-prim-ref:`detailed online documentation <GHC.Prim.>`. (This
documentation is generated from the file ``compiler/prelude/primops.txt.pp``.)

If you want to mention any of the primitive data types or operations in
your program, you must first import ``GHC.Prim`` to bring them into
scope. Many of them have names ending in ``#``, and to mention such names
you need the :extension:`MagicHash` extension.

The primops make extensive use of `unboxed types <#glasgow-unboxed>`__
and `unboxed tuples <#unboxed-tuples>`__, which we briefly summarise
here.

.. _glasgow-unboxed:

Unboxed types
-------------

Most types in GHC are boxed, which means that values of that type are
represented by a pointer to a heap object. The representation of a
Haskell ``Int``, for example, is a two-word heap object. An unboxed
type, however, is represented by the value itself, no pointers or heap
allocation are involved.

Unboxed types correspond to the “raw machine” types you would use in C:
``Int#`` (long int), ``Double#`` (double), ``Addr#`` (void \*), etc. The
*primitive operations* (PrimOps) on these types are what you might
expect; e.g., ``(+#)`` is addition on ``Int#``\ s, and is the
machine-addition that we all know and love—usually one instruction.

Primitive (unboxed) types cannot be defined in Haskell, and are
therefore built into the language and compiler. Primitive types are
always unlifted; that is, a value of a primitive type cannot be bottom.
(Note: a "boxed" type means that a value is represented by a pointer to a heap
object; a "lifted" type means that terms of that type may be bottom. See
the next paragraph for an example.)
We use the convention (but it is only a convention) that primitive
types, values, and operations have a ``#`` suffix (see
:ref:`magic-hash`). For some primitive types we have special syntax for
literals, also described in the `same section <#magic-hash>`__.

Primitive values are often represented by a simple bit-pattern, such as
``Int#``, ``Float#``, ``Double#``. But this is not necessarily the case:
a primitive value might be represented by a pointer to a heap-allocated
object. Examples include ``Array#``, the type of primitive arrays. Thus,
``Array#`` is an unlifted, boxed type. A
primitive array is heap-allocated because it is too big a value to fit
in a register, and would be too expensive to copy around; in a sense, it
is accidental that it is represented by a pointer. If a pointer
represents a primitive value, then it really does point to that value:
no unevaluated thunks, no indirections. Nothing can be at the other end
of the pointer than the primitive value. A numerically-intensive program
using unboxed types can go a *lot* faster than its “standard”
counterpart—we saw a threefold speedup on one example.

Unboxed type kinds
------------------

Because unboxed types are represented without the use of pointers, we
cannot store them in use a polymorphic datatype at an unboxed type.
For example, the ``Just`` node
of ``Just 42#`` would have to be different from the ``Just`` node of
``Just 42``; the former stores an integer directly, while the latter
stores a pointer. GHC currently does not support this variety of ``Just``
nodes (nor for any other datatype). Accordingly, the *kind* of an unboxed
type is different from the kind of a boxed type.

The Haskell Report describes that ``*`` (spelled ``Type`` and imported from
``Data.Kind`` in the GHC dialect of Haskell) is the kind of ordinary datatypes,
such as ``Int``. Furthermore, type constructors can have kinds with arrows; for
example, ``Maybe`` has kind ``Type -> Type``. Unboxed types have a kind that
specifies their runtime representation. For example, the type ``Int#`` has kind
``TYPE 'IntRep`` and ``Double#`` has kind ``TYPE 'DoubleRep``. These kinds say
that the runtime representation of an ``Int#`` is a machine integer, and the
runtime representation of a ``Double#`` is a machine double-precision floating
point. In contrast, the kind ``Type`` is actually just a synonym for ``TYPE
'LiftedRep``. More details of the ``TYPE`` mechanisms appear in the `section
on runtime representation polymorphism <#runtime-rep>`__.

Given that ``Int#``'s kind is not ``Type``, it then it follows that ``Maybe
Int#`` is disallowed. Similarly, because type variables tend to be of kind
``Type`` (for example, in ``(.) :: (b -> c) -> (a -> b) -> a -> c``, all the
type variables have kind ``Type``), polymorphism tends not to work over
primitive types. Stepping back, this makes some sense, because a polymorphic
function needs to manipulate the pointers to its data, and most primitive types
are unboxed.

There are some restrictions on the use of primitive types:

-  You cannot define a newtype whose representation type (the argument
   type of the data constructor) is an unboxed type. Thus, this is
   illegal:

   ::

         newtype A = MkA Int#

-  You cannot bind a variable with an unboxed type in a *top-level*
   binding.

-  You cannot bind a variable with an unboxed type in a *recursive*
   binding.

-  You may bind unboxed variables in a (non-recursive, non-top-level)
   pattern binding, but you must make any such pattern-match strict.
   (Failing to do so emits a warning :ghc-flag:`-Wunbanged-strict-patterns`.)
   For example, rather than:

   ::

         data Foo = Foo Int Int#

         f x = let (Foo a b, w) = ..rhs.. in ..body..

   you must write:

   ::

         data Foo = Foo Int Int#

         f x = let !(Foo a b, w) = ..rhs.. in ..body..

   since ``b`` has type ``Int#``.

.. _unboxed-tuples:

Unboxed tuples
--------------

.. extension:: UnboxedTuples
    :shortdesc: Enable the use of unboxed tuple syntax.

    :since: 6.8.1


Unboxed tuples aren't really exported by ``GHC.Exts``; they are a
syntactic extension (:extension:`UnboxedTuples`). An
unboxed tuple looks like this: ::

    (# e_1, ..., e_n #)

where ``e_1..e_n`` are expressions of any type (primitive or
non-primitive). The type of an unboxed tuple looks the same.

Note that when unboxed tuples are enabled, ``(#`` is a single lexeme, so
for example when using operators like ``#`` and ``#-`` you need to write
``( # )`` and ``( #- )`` rather than ``(#)`` and ``(#-)``.

Unboxed tuples are used for functions that need to return multiple
values, but they avoid the heap allocation normally associated with
using fully-fledged tuples. When an unboxed tuple is returned, the
components are put directly into registers or on the stack; the unboxed
tuple itself does not have a composite representation. Many of the
primitive operations listed in ``primops.txt.pp`` return unboxed tuples.
In particular, the ``IO`` and ``ST`` monads use unboxed tuples to avoid
unnecessary allocation during sequences of operations.

There are some restrictions on the use of unboxed tuples:

-  The typical use of unboxed tuples is simply to return multiple
   values, binding those multiple results with a ``case`` expression,
   thus:

   ::

         f x y = (# x+1, y-1 #)
         g x = case f x x of { (# a, b #) -> a + b }

   You can have an unboxed tuple in a pattern binding, thus

   ::

         f x = let (# p,q #) = h x in ..body..

   If the types of ``p`` and ``q`` are not unboxed, the resulting
   binding is lazy like any other Haskell pattern binding. The above
   example desugars like this:

   ::

         f x = let t = case h x of { (# p,q #) -> (p,q) }
                   p = fst t
                   q = snd t
               in ..body..

   Indeed, the bindings can even be recursive.

.. _unboxed-sums:

Unboxed sums
------------

.. extension:: UnboxedSums
    :shortdesc: Enable unboxed sums.

    :since: 8.2.1

    Enable the use of unboxed sum syntax.

`-XUnboxedSums` enables new syntax for anonymous, unboxed sum types. The syntax
for an unboxed sum type with N alternatives is ::

    (# t_1 | t_2 | ... | t_N #)

where ``t_1`` ... ``t_N`` are types (which can be unlifted, including unboxed
tuples and sums).

Unboxed tuples can be used for multi-arity alternatives. For example: ::

    (# (# Int, String #) | Bool #)

The term level syntax is similar. Leading and preceding bars (`|`) indicate which
alternative it is. Here are two terms of the type shown above: ::

    (# (# 1, "foo" #) | #) -- first alternative

    (# | True #) -- second alternative

The pattern syntax reflects the term syntax: ::

    case x of
      (# (# i, str #) | #) -> ...
      (# | bool #) -> ...

Unboxed sums are "unboxed" in the sense that, instead of allocating sums in the
heap and representing values as pointers, unboxed sums are represented as their
components, just like unboxed tuples. These "components" depend on alternatives
of a sum type. Like unboxed tuples, unboxed sums are lazy in their lifted
components.

The code generator tries to generate as compact layout as possible for each
unboxed sum. In the best case, size of an unboxed sum is size of its biggest
alternative plus one word (for a tag). The algorithm for generating the memory
layout for a sum type works like this:

- All types are classified as one of these classes: 32bit word, 64bit word,
  32bit float, 64bit float, pointer.

- For each alternative of the sum type, a layout that consists of these fields
  is generated. For example, if an alternative has ``Int``, ``Float#`` and
  ``String`` fields, the layout will have an 32bit word, 32bit float and
  pointer fields.

- Layout fields are then overlapped so that the final layout will be as compact
  as possible. For example, suppose we have the unboxed sum: ::

    (# (# Word32#, String, Float# #)
    |  (# Float#, Float#, Maybe Int #) #)

  The final layout will be something like ::

    Int32, Float32, Float32, Word32, Pointer

  The first ``Int32`` is for the tag. There are two ``Float32`` fields because
  floating point types can't overlap with other types, because of limitations of
  the code generator that we're hoping to overcome in the future. The second
  alternative needs two ``Float32`` fields: The ``Word32`` field is for the
  ``Word32#`` in the first alternative. The ``Pointer`` field is shared between
  ``String`` and ``Maybe Int`` values of the alternatives.

  As another example, this is the layout for the unboxed version of ``Maybe a``
  type, ``(# (# #) | a #)``: ::

    Int32, Pointer

  The ``Pointer`` field is not used when tag says that it's ``Nothing``.
  Otherwise ``Pointer`` points to the value in ``Just``. As mentioned
  above, this type is lazy in its lifted field. Therefore, the type ::

    data Maybe' a = Maybe' (# (# #) | a #)

  is *precisely* isomorphic to the type ``Maybe a``, although its memory
  representation is different.

  In the degenerate case where all the alternatives have zero width, such
  as the ``Bool``-like ``(# (# #) | (# #) #)``, the unboxed sum layout only
  has an ``Int32`` tag field (i.e., the whole thing is represented by an integer).

.. _syntax-extns:

Syntactic extensions
====================

.. _unicode-syntax:

Unicode syntax
--------------

.. extension:: UnicodeSyntax
    :shortdesc: Enable unicode syntax.

    :since: 6.8.1

    Enable the use of Unicode characters in place of their equivalent ASCII
    sequences.

The language extension :extension:`UnicodeSyntax` enables
Unicode characters to be used to stand for certain ASCII character
sequences. The following alternatives are provided:

+--------------+---------------+-------------+-----------------------------------------+
| ASCII        | Unicode       | Code point  | Name                                    |
|              | alternative   |             |                                         |
+==============+===============+=============+=========================================+
| ``::``       | ∷             | 0x2237      | PROPORTION                              |
+--------------+---------------+-------------+-----------------------------------------+
| ``=>``       | ⇒             | 0x21D2      | RIGHTWARDS DOUBLE ARROW                 |
+--------------+---------------+-------------+-----------------------------------------+
| ``->``       | →             | 0x2192      | RIGHTWARDS ARROW                        |
+--------------+---------------+-------------+-----------------------------------------+
| ``<-``       | ←             | 0x2190      | LEFTWARDS ARROW                         |
+--------------+---------------+-------------+-----------------------------------------+
| ``>-``       | ⤚             | 0x291a      | RIGHTWARDS ARROW-TAIL                   |
+--------------+---------------+-------------+-----------------------------------------+
| ``-<``       | ⤙             | 0x2919      | LEFTWARDS ARROW-TAIL                    |
+--------------+---------------+-------------+-----------------------------------------+
| ``>>-``      | ⤜             | 0x291C      | RIGHTWARDS DOUBLE ARROW-TAIL            |
+--------------+---------------+-------------+-----------------------------------------+
| ``-<<``      | ⤛             | 0x291B      | LEFTWARDS DOUBLE ARROW-TAIL             |
+--------------+---------------+-------------+-----------------------------------------+
| ``*``        | ★             | 0x2605      | BLACK STAR                              |
+--------------+---------------+-------------+-----------------------------------------+
| ``forall``   | ∀             | 0x2200      | FOR ALL                                 |
+--------------+---------------+-------------+-----------------------------------------+
| ``(|``       | ⦇             | 0x2987      | Z NOTATION LEFT IMAGE BRACKET           |
+--------------+---------------+-------------+-----------------------------------------+
| ``|)``       | ⦈             | 0x2988      | Z NOTATION RIGHT IMAGE BRACKET          |
+--------------+---------------+-------------+-----------------------------------------+
| ``[|``       | ⟦             | 0x27E6      | MATHEMATICAL LEFT WHITE SQUARE BRACKET  |
+--------------+---------------+-------------+-----------------------------------------+
| ``|]``       | ⟧             | 0x27E7      | MATHEMATICAL RIGHT WHITE SQUARE BRACKET |
+--------------+---------------+-------------+-----------------------------------------+

.. _magic-hash:

The magic hash
--------------

.. extension:: MagicHash
    :shortdesc: Allow ``#`` as a postfix modifier on identifiers.

    :since: 6.8.1

    Enables the use of the hash character (``#``) as an identifier suffix.

The language extension :extension:`MagicHash` allows ``#`` as a postfix modifier
to identifiers. Thus, ``x#`` is a valid variable, and ``T#`` is a valid type
constructor or data constructor.

The hash sign does not change semantics at all. We tend to use variable
names ending in "#" for unboxed values or types (e.g. ``Int#``), but
there is no requirement to do so; they are just plain ordinary
variables. Nor does the :extension:`MagicHash` extension bring anything into
scope. For example, to bring ``Int#`` into scope you must import
``GHC.Prim`` (see :ref:`primitives`); the :extension:`MagicHash` extension then
allows you to *refer* to the ``Int#`` that is now in scope. Note that
with this option, the meaning of ``x#y = 0`` is changed: it defines a
function ``x#`` taking a single argument ``y``; to define the operator
``#``, put a space: ``x # y = 0``.

The :extension:`MagicHash` also enables some new forms of literals (see
:ref:`glasgow-unboxed`):

-  ``'x'#`` has type ``Char#``

-  ``"foo"#`` has type ``Addr#``

-  ``3#`` has type ``Int#``. In general, any Haskell integer lexeme
   followed by a ``#`` is an ``Int#`` literal, e.g. ``-0x3A#`` as well as
   ``32#``.

-  ``3##`` has type ``Word#``. In general, any non-negative Haskell
   integer lexeme followed by ``##`` is a ``Word#``.

-  ``3.2#`` has type ``Float#``.

-  ``3.2##`` has type ``Double#``

.. _negative-literals:

Negative literals
-----------------

.. extension:: NegativeLiterals
    :shortdesc: Enable support for negative literals.

    :since: 7.8.1

    Enable the use of un-parenthesized negative numeric literals.

The literal ``-123`` is, according to Haskell98 and Haskell 2010,
desugared as ``negate (fromInteger 123)``. The language extension
:extension:`NegativeLiterals` means that it is instead desugared as
``fromInteger (-123)``.

This can make a difference when the positive and negative range of a
numeric data type don't match up. For example, in 8-bit arithmetic -128
is representable, but +128 is not. So ``negate (fromInteger 128)`` will
elicit an unexpected integer-literal-overflow message.

.. _num-decimals:

Fractional looking integer literals
-----------------------------------

.. extension:: NumDecimals
    :shortdesc: Enable support for 'fractional' integer literals.

    :since: 7.8.1

    Allow the use of floating-point literal syntax for integral types.

Haskell 2010 and Haskell 98 define floating literals with the syntax
``1.2e6``. These literals have the type ``Fractional a => a``.

The language extension :extension:`NumDecimals` allows you to also use the
floating literal syntax for instances of ``Integral``, and have values
like ``(1.2e6 :: Num a => a)``

.. _binary-literals:

Binary integer literals
-----------------------

.. extension:: BinaryLiterals
    :shortdesc: Enable support for binary literals.

    :since: 7.10.1

    Allow the use of binary notation in integer literals.

Haskell 2010 and Haskell 98 allows for integer literals to be given in
decimal, octal (prefixed by ``0o`` or ``0O``), or hexadecimal notation
(prefixed by ``0x`` or ``0X``).

The language extension :extension:`BinaryLiterals` adds support for expressing
integer literals in binary notation with the prefix ``0b`` or ``0B``. For
instance, the binary integer literal ``0b11001001`` will be desugared into
``fromInteger 201`` when :extension:`BinaryLiterals` is enabled.

.. _hex-float-literals:

Hexadecimal floating point literals
-----------------------------------

.. extension:: HexFloatLiterals
    :shortdesc: Enable support for :ref:`hexadecimal floating point literals <hex-float-literals>`.

    :since: 8.4.1

    Allow writing floating point literals using hexadecimal notation.

The hexadecimal notation for floating point literals is useful when you
need to specify floating point constants precisely, as the literal notation
corresponds closely to the underlying bit-encoding of the number.

In this notation floating point numbers are written using hexadecimal digits,
and so the digits are interpreted using base 16, rather then the usual 10.
This means that digits left of the decimal point correspond to positive
powers of 16, while the ones to the right correspond to negative ones.

You may also write an explicit exponent, which is similar to the exponent
in decimal notation with the following differences:
- the exponent begins with ``p`` instead of ``e``
- the exponent is written in base ``10`` (**not** 16)
- the base of the exponent is ``2`` (**not** 16).

In terms of the underlying bit encoding, each hexadecimal digit corresponds
to 4 bits, and you may think of the exponent as "moving" the floating point
by one bit left (negative) or right (positive).  Here are some examples:

-  ``0x0.1``     is the same as ``1/16``
-  ``0x0.01``    is the same as ``1/256``
-  ``0xF.FF``    is the same as ``15 + 15/16 + 15/256``
-  ``0x0.1p4``   is the same as ``1``
-  ``0x0.1p-4``  is the same as ``1/256``
-  ``0x0.1p12``  is the same as ``256``




.. _numeric-underscores:

Numeric underscores
-------------------

.. extension:: NumericUnderscores
    :shortdesc: Enable support for :ref:`numeric underscores <numeric-underscores>`.

    :since: 8.6.1

    Allow the use of underscores in numeric literals.

GHC allows for numeric literals to be given in decimal, octal, hexadecimal,
binary, or float notation.

The language extension :extension:`NumericUnderscores` adds support for expressing
underscores in numeric literals.
For instance, the numeric literal ``1_000_000`` will be parsed into
``1000000`` when :extension:`NumericUnderscores` is enabled.
That is, underscores in numeric literals are ignored when
:extension:`NumericUnderscores` is enabled.
See also :ghc-ticket:`14473`.

For example:

.. code-block:: none

    -- decimal
    million    = 1_000_000
    billion    = 1_000_000_000
    lightspeed = 299_792_458
    version    = 8_04_1
    date       = 2017_12_31

    -- hexadecimal
    red_mask = 0xff_00_00
    size1G   = 0x3fff_ffff

    -- binary
    bit8th   = 0b01_0000_0000
    packbits = 0b1_11_01_0000_0_111
    bigbits  = 0b1100_1011__1110_1111__0101_0011

    -- float
    pi       = 3.141_592_653_589_793
    faraday  = 96_485.332_89
    avogadro = 6.022_140_857e+23

    -- function
    isUnderMillion = (< 1_000_000)

    clip64M x
        | x > 0x3ff_ffff = 0x3ff_ffff
        | otherwise = x

    test8bit x = (0b01_0000_0000 .&. x) /= 0

About validity:

.. code-block:: none

    x0 = 1_000_000   -- valid
    x1 = 1__000000   -- valid
    x2 = 1000000_    -- invalid
    x3 = _1000000    -- invalid

    e0 = 0.0001      -- valid
    e1 = 0.000_1     -- valid
    e2 = 0_.0001     -- invalid
    e3 = _0.0001     -- invalid
    e4 = 0._0001     -- invalid
    e5 = 0.0001_     -- invalid

    f0 = 1e+23       -- valid
    f1 = 1_e+23      -- valid
    f2 = 1__e+23     -- valid
    f3 = 1e_+23      -- invalid

    g0 = 1e+23       -- valid
    g1 = 1e+_23      -- invalid
    g2 = 1e+23_      -- invalid

    h0 = 0xffff      -- valid
    h1 = 0xff_ff     -- valid
    h2 = 0x_ffff     -- valid
    h3 = 0x__ffff    -- valid
    h4 = _0xffff     -- invalid

.. _pattern-guards:

Pattern guards
--------------

.. extension:: NoPatternGuards
    :shortdesc: Disable pattern guards.
        Implied by :extension:`Haskell98`.

    :implied by: :extension:`Haskell98`
    :since: 6.8.1

Disable `pattern guards
<http://www.haskell.org/onlinereport/haskell2010/haskellch3.html#x8-460003.13>`__.

.. _view-patterns:

View patterns
-------------

.. extension:: ViewPatterns
    :shortdesc: Enable view patterns.

    :since: 6.10.1

    Allow use of view pattern syntax.

View patterns are enabled by the language extension :extension:`ViewPatterns`. More
information and examples of view patterns can be found on the
:ghc-wiki:`Wiki page <ViewPatterns>`.

View patterns are somewhat like pattern guards that can be nested inside
of other patterns. They are a convenient way of pattern-matching against
values of abstract types. For example, in a programming language
implementation, we might represent the syntax of the types of the
language as follows: ::

    type Typ

    data TypView = Unit
                 | Arrow Typ Typ

    view :: Typ -> TypView

    -- additional operations for constructing Typ's ...

The representation of Typ is held abstract, permitting implementations
to use a fancy representation (e.g., hash-consing to manage sharing).
Without view patterns, using this signature is a little inconvenient: ::

    size :: Typ -> Integer
    size t = case view t of
      Unit -> 1
      Arrow t1 t2 -> size t1 + size t2

It is necessary to iterate the case, rather than using an equational
function definition. And the situation is even worse when the matching
against ``t`` is buried deep inside another pattern.

View patterns permit calling the view function inside the pattern and
matching against the result: ::

    size (view -> Unit) = 1
    size (view -> Arrow t1 t2) = size t1 + size t2

That is, we add a new form of pattern, written ⟨expression⟩ ``->``
⟨pattern⟩ that means "apply the expression to whatever we're trying to
match against, and then match the result of that application against the
pattern". The expression can be any Haskell expression of function type,
and view patterns can be used wherever patterns are used.

The semantics of a pattern ``(`` ⟨exp⟩ ``->`` ⟨pat⟩ ``)`` are as
follows:

-  Scoping:
   The variables bound by the view pattern are the variables bound by
   ⟨pat⟩.

   Any variables in ⟨exp⟩ are bound occurrences, but variables bound "to
   the left" in a pattern are in scope. This feature permits, for
   example, one argument to a function to be used in the view of another
   argument. For example, the function ``clunky`` from
   :ref:`pattern-guards` can be written using view patterns as follows: ::

       clunky env (lookup env -> Just val1) (lookup env -> Just val2) = val1 + val2
       ...other equations for clunky...

   More precisely, the scoping rules are:

   -  In a single pattern, variables bound by patterns to the left of a
      view pattern expression are in scope. For example: ::

          example :: Maybe ((String -> Integer,Integer), String) -> Bool
          example (Just ((f,_), f -> 4)) = True

      Additionally, in function definitions, variables bound by matching
      earlier curried arguments may be used in view pattern expressions
      in later arguments: ::

          example :: (String -> Integer) -> String -> Bool
          example f (f -> 4) = True

      That is, the scoping is the same as it would be if the curried
      arguments were collected into a tuple.

   -  In mutually recursive bindings, such as ``let``, ``where``, or the
      top level, view patterns in one declaration may not mention
      variables bound by other declarations. That is, each declaration
      must be self-contained. For example, the following program is not
      allowed: ::

          let {(x -> y) = e1 ;
               (y -> x) = e2 } in x

   (For some amplification on this design choice see :ghc-ticket:`4061`.

-  Typing: If ⟨exp⟩ has type ⟨T1⟩ ``->`` ⟨T2⟩ and ⟨pat⟩ matches a ⟨T2⟩,
   then the whole view pattern matches a ⟨T1⟩.

-  Matching: To the equations in Section 3.17.3 of the `Haskell 98
   Report <http://www.haskell.org/onlinereport/>`__, add the following: ::

       case v of { (e -> p) -> e1 ; _ -> e2 }
        =
       case (e v) of { p -> e1 ; _ -> e2 }

   That is, to match a variable ⟨v⟩ against a pattern ``(`` ⟨exp⟩ ``->``
   ⟨pat⟩ ``)``, evaluate ``(`` ⟨exp⟩ ⟨v⟩ ``)`` and match the result
   against ⟨pat⟩.

-  Efficiency: When the same view function is applied in multiple
   branches of a function definition or a case expression (e.g., in
   ``size`` above), GHC makes an attempt to collect these applications
   into a single nested case expression, so that the view function is
   only applied once. Pattern compilation in GHC follows the matrix
   algorithm described in Chapter 4 of `The Implementation of Functional
   Programming
   Languages <http://research.microsoft.com/~simonpj/Papers/slpj-book-1987/>`__.
   When the top rows of the first column of a matrix are all view
   patterns with the "same" expression, these patterns are transformed
   into a single nested case. This includes, for example, adjacent view
   patterns that line up in a tuple, as in

   ::

       f ((view -> A, p1), p2) = e1
       f ((view -> B, p3), p4) = e2

   The current notion of when two view pattern expressions are "the
   same" is very restricted: it is not even full syntactic equality.
   However, it does include variables, literals, applications, and
   tuples; e.g., two instances of ``view ("hi", "there")`` will be
   collected. However, the current implementation does not compare up to
   alpha-equivalence, so two instances of ``(x, view x -> y)`` will not
   be coalesced.

.. _n-k-patterns:

n+k patterns
------------

.. extension:: NPlusKPatterns
    :shortdesc: Enable support for ``n+k`` patterns.
        Implied by :extension:`Haskell98`.

    :implied by: :extension:`Haskell98`
    :since: 6.12.1

    Enable use of ``n+k`` patterns.

.. _recursive-do-notation:

The recursive do-notation
-------------------------

.. extension:: RecursiveDo
    :shortdesc: Enable recursive do (mdo) notation.

    :since: 6.8.1

    Allow the use of recursive ``do`` notation.

The do-notation of Haskell 98 does not allow *recursive bindings*, that
is, the variables bound in a do-expression are visible only in the
textually following code block. Compare this to a let-expression, where
bound variables are visible in the entire binding group.

It turns out that such recursive bindings do indeed make sense for a
variety of monads, but not all. In particular, recursion in this sense
requires a fixed-point operator for the underlying monad, captured by
the ``mfix`` method of the ``MonadFix`` class, defined in
``Control.Monad.Fix`` as follows: ::

    class Monad m => MonadFix m where
       mfix :: (a -> m a) -> m a

Haskell's ``Maybe``, ``[]`` (list), ``ST`` (both strict and lazy
versions), ``IO``, and many other monads have ``MonadFix`` instances. On
the negative side, the continuation monad, with the signature
``(a -> r) -> r``, does not.

For monads that do belong to the ``MonadFix`` class, GHC provides an
extended version of the do-notation that allows recursive bindings. The
:extension:`RecursiveDo` (language pragma: ``RecursiveDo``) provides the
necessary syntactic support, introducing the keywords ``mdo`` and
``rec`` for higher and lower levels of the notation respectively. Unlike
bindings in a ``do`` expression, those introduced by ``mdo`` and ``rec``
are recursively defined, much like in an ordinary let-expression. Due to
the new keyword ``mdo``, we also call this notation the *mdo-notation*.

Here is a simple (albeit contrived) example:

::

    {-# LANGUAGE RecursiveDo #-}
    justOnes = mdo { xs <- Just (1:xs)
                   ; return (map negate xs) }

or equivalently

::

    {-# LANGUAGE RecursiveDo #-}
    justOnes = do { rec { xs <- Just (1:xs) }
                  ; return (map negate xs) }

As you can guess ``justOnes`` will evaluate to ``Just [-1,-1,-1,...``.

GHC's implementation the mdo-notation closely follows the original
translation as described in the paper `A recursive do for
Haskell <http://leventerkok.github.io/papers/recdo.pdf>`__, which
in turn is based on the work `Value Recursion in Monadic
Computations <http://leventerkok.github.io/papers/erkok-thesis.pdf>`__.
Furthermore, GHC extends the syntax described in the former paper with a
lower level syntax flagged by the ``rec`` keyword, as we describe next.

Recursive binding groups
~~~~~~~~~~~~~~~~~~~~~~~~

The extension :extension:`RecursiveDo` also introduces a new keyword ``rec``, which
wraps a mutually-recursive group of monadic statements inside a ``do``
expression, producing a single statement. Similar to a ``let`` statement
inside a ``do``, variables bound in the ``rec`` are visible throughout
the ``rec`` group, and below it. For example, compare

::

        do { a <- getChar            do { a <- getChar
           ; let { r1 = f a r2          ; rec { r1 <- f a r2
           ;     ; r2 = g r1 }          ;     ; r2 <- g r1 }
           ; return (r1 ++ r2) }        ; return (r1 ++ r2) }

In both cases, ``r1`` and ``r2`` are available both throughout the
``let`` or ``rec`` block, and in the statements that follow it. The
difference is that ``let`` is non-monadic, while ``rec`` is monadic. (In
Haskell ``let`` is really ``letrec``, of course.)

The semantics of ``rec`` is fairly straightforward. Whenever GHC finds a
``rec`` group, it will compute its set of bound variables, and will
introduce an appropriate call to the underlying monadic value-recursion
operator ``mfix``, belonging to the ``MonadFix`` class. Here is an
example:

::

    rec { b <- f a c     ===>    (b,c) <- mfix (\ ~(b,c) -> do { b <- f a c
        ; c <- f b a }                                         ; c <- f b a
                                                               ; return (b,c) })

As usual, the meta-variables ``b``, ``c`` etc., can be arbitrary
patterns. In general, the statement ``rec ss`` is desugared to the
statement

::

    vs <- mfix (\ ~vs -> do { ss; return vs })

where ``vs`` is a tuple of the variables bound by ``ss``.

Note in particular that the translation for a ``rec`` block only
involves wrapping a call to ``mfix``: it performs no other analysis on
the bindings. The latter is the task for the ``mdo`` notation, which is
described next.

The ``mdo`` notation
~~~~~~~~~~~~~~~~~~~~

A ``rec``-block tells the compiler where precisely the recursive knot
should be tied. It turns out that the placement of the recursive knots
can be rather delicate: in particular, we would like the knots to be
wrapped around as minimal groups as possible. This process is known as
*segmentation*, and is described in detail in Section 3.2 of `A
recursive do for
Haskell <http://leventerkok.github.io/papers/recdo.pdf>`__.
Segmentation improves polymorphism and reduces the size of the recursive
knot. Most importantly, it avoids unnecessary interference caused by a
fundamental issue with the so-called *right-shrinking* axiom for monadic
recursion. In brief, most monads of interest (IO, strict state, etc.) do
*not* have recursion operators that satisfy this axiom, and thus not
performing segmentation can cause unnecessary interference, changing the
termination behavior of the resulting translation. (Details can be found
in Sections 3.1 and 7.2.2 of `Value Recursion in Monadic
Computations <http://leventerkok.github.io/papers/erkok-thesis.pdf>`__.)

The ``mdo`` notation removes the burden of placing explicit ``rec``
blocks in the code. Unlike an ordinary ``do`` expression, in which
variables bound by statements are only in scope for later statements,
variables bound in an ``mdo`` expression are in scope for all statements
of the expression. The compiler then automatically identifies minimal
mutually recursively dependent segments of statements, treating them as
if the user had wrapped a ``rec`` qualifier around them.

The definition is syntactic:

-  A generator ⟨g⟩ *depends* on a textually following generator ⟨g'⟩, if

   -  ⟨g'⟩ defines a variable that is used by ⟨g⟩, or

   -  ⟨g'⟩ textually appears between ⟨g⟩ and ⟨g''⟩, where ⟨g⟩ depends on
      ⟨g''⟩.

-  A *segment* of a given ``mdo``-expression is a minimal sequence of
   generators such that no generator of the sequence depends on an
   outside generator. As a special case, although it is not a generator,
   the final expression in an ``mdo``-expression is considered to form a
   segment by itself.

Segments in this sense are related to *strongly-connected components*
analysis, with the exception that bindings in a segment cannot be
reordered and must be contiguous.

Here is an example ``mdo``-expression, and its translation to ``rec``
blocks:

::

    mdo { a <- getChar      ===> do { a <- getChar
        ; b <- f a c                ; rec { b <- f a c
        ; c <- f b a                ;     ; c <- f b a }
        ; z <- h a b                ; z <- h a b
        ; d <- g d e                ; rec { d <- g d e
        ; e <- g a z                ;     ; e <- g a z }
        ; putChar c }               ; putChar c }

Note that a given ``mdo`` expression can cause the creation of multiple
``rec`` blocks. If there are no recursive dependencies, ``mdo`` will
introduce no ``rec`` blocks. In this latter case an ``mdo`` expression
is precisely the same as a ``do`` expression, as one would expect.

In summary, given an ``mdo`` expression, GHC first performs
segmentation, introducing ``rec`` blocks to wrap over minimal recursive
groups. Then, each resulting ``rec`` is desugared, using a call to
``Control.Monad.Fix.mfix`` as described in the previous section. The
original ``mdo``-expression typechecks exactly when the desugared
version would do so.

Here are some other important points in using the recursive-do notation:

-  It is enabled with the extension :extension:`RecursiveDo`, or the
   ``LANGUAGE RecursiveDo`` pragma. (The same extension enables both
   ``mdo``-notation, and the use of ``rec`` blocks inside ``do``
   expressions.)

-  ``rec`` blocks can also be used inside ``mdo``-expressions, which
   will be treated as a single statement. However, it is good style to
   either use ``mdo`` or ``rec`` blocks in a single expression.

-  If recursive bindings are required for a monad, then that monad must
   be declared an instance of the ``MonadFix`` class.

-  The following instances of ``MonadFix`` are automatically provided:
   List, Maybe, IO. Furthermore, the ``Control.Monad.ST`` and
   ``Control.Monad.ST.Lazy`` modules provide the instances of the
   ``MonadFix`` class for Haskell's internal state monad (strict and
   lazy, respectively).

-  Like ``let`` and ``where`` bindings, name shadowing is not allowed
   within an ``mdo``-expression or a ``rec``-block; that is, all the
   names bound in a single ``rec`` must be distinct. (GHC will complain
   if this is not the case.)

.. _applicative-do:

Applicative do-notation
-----------------------

.. index::
   single: Applicative do-notation
   single: do-notation; Applicative

.. extension:: ApplicativeDo
    :shortdesc: Enable Applicative do-notation desugaring

    :since: 8.0.1

    Allow use of ``Applicative`` ``do`` notation.

The language option :extension:`ApplicativeDo` enables an alternative translation for
the do-notation, which uses the operators ``<$>``, ``<*>``, along with ``join``
as far as possible. There are two main reasons for wanting to do this:

-  We can use do-notation with types that are an instance of ``Applicative`` and
   ``Functor``, but not ``Monad``
-  In some monads, using the applicative operators is more efficient than monadic
   bind. For example, it may enable more parallelism.

Applicative do-notation desugaring preserves the original semantics, provided
that the ``Applicative`` instance satisfies ``<*> = ap`` and ``pure = return``
(these are true of all the common monadic types). Thus, you can normally turn on
:extension:`ApplicativeDo` without fear of breaking your program. There is one pitfall
to watch out for; see :ref:`applicative-do-pitfall`.

There are no syntactic changes with :extension:`ApplicativeDo`. The only way it shows
up at the source level is that you can have a ``do`` expression that doesn't
require a ``Monad`` constraint. For example, in GHCi: ::

    Prelude> :set -XApplicativeDo
    Prelude> :t \m -> do { x <- m; return (not x) }
    \m -> do { x <- m; return (not x) }
      :: Functor f => f Bool -> f Bool

This example only requires ``Functor``, because it is translated into ``(\x ->
not x) <$> m``. A more complex example requires ``Applicative``, ::

    Prelude> :t \m -> do { x <- m 'a'; y <- m 'b'; return (x || y) }
    \m -> do { x <- m 'a'; y <- m 'b'; return (x || y) }
      :: Applicative f => (Char -> f Bool) -> f Bool

Here GHC has translated the expression into ::

    (\x y -> x || y) <$> m 'a' <*> m 'b'

It is possible to see the actual translation by using :ghc-flag:`-ddump-ds`, but be
warned, the output is quite verbose.

Note that if the expression can't be translated into uses of ``<$>``, ``<*>``
only, then it will incur a ``Monad`` constraint as usual. This happens when
there is a dependency on a value produced by an earlier statement in the
``do``-block: ::

    Prelude> :t \m -> do { x <- m True; y <- m x; return (x || y) }
    \m -> do { x <- m True; y <- m x; return (x || y) }
      :: Monad m => (Bool -> m Bool) -> m Bool

Here, ``m x`` depends on the value of ``x`` produced by the first statement, so
the expression cannot be translated using ``<*>``.

In general, the rule for when a ``do`` statement incurs a ``Monad`` constraint
is as follows. If the do-expression has the following form: ::

    do p1 <- E1; ...; pn <- En; return E

where none of the variables defined by ``p1...pn`` are mentioned in ``E1...En``,
and ``p1...pn`` are all variables or lazy patterns,
then the expression will only require ``Applicative``. Otherwise, the expression
will require ``Monad``. The block may return a pure expression ``E`` depending
upon the results ``p1...pn`` with either ``return`` or ``pure``.

Note: the final statement must match one of these patterns exactly:

- ``return E``
- ``return $ E``
- ``pure E``
- ``pure $ E``

otherwise GHC cannot recognise it as a ``return`` statement, and the
transformation to use ``<$>`` that we saw above does not apply.  In
particular, slight variations such as ``return . Just $ x`` or ``let x
= e in return x`` would not be recognised.

If the final statement is not of one of these forms, GHC falls back to
standard ``do`` desugaring, and the expression will require a
``Monad`` constraint.

When the statements of a ``do`` expression have dependencies between
them, and ``ApplicativeDo`` cannot infer an ``Applicative`` type, it
uses a heuristic algorithm to try to use ``<*>`` as much as possible.
This algorithm usually finds the best solution, but in rare complex
cases it might miss an opportunity.  There is an algorithm that finds
the optimal solution, provided as an option:

.. ghc-flag:: -foptimal-applicative-do
    :shortdesc: Use a slower but better algorithm for ApplicativeDo
    :type: dynamic
    :reverse: -fno-optimal-applicative-do
    :category: optimization

    :since: 8.0.1

    Enables an alternative algorithm for choosing where to use ``<*>``
    in conjunction with the ``ApplicativeDo`` language extension.
    This algorithm always finds the optimal solution, but it is
    expensive: ``O(n^3)``, so this option can lead to long compile
    times when there are very large ``do`` expressions (over 100
    statements).  The default ``ApplicativeDo`` algorithm is ``O(n^2)``.


.. _applicative-do-strict:

Strict patterns
~~~~~~~~~~~~~~~


A strict pattern match in a bind statement prevents
``ApplicativeDo`` from transforming that statement to use
``Applicative``.  This is because the transformation would change the
semantics by making the expression lazier.

For example, this code will require a ``Monad`` constraint::

    > :t \m -> do { (x:xs) <- m; return x }
    \m -> do { (x:xs) <- m; return x } :: Monad m => m [b] -> m b

but making the pattern match lazy allows it to have a ``Functor`` constraint::

    > :t \m -> do { ~(x:xs) <- m; return x }
    \m -> do { ~(x:xs) <- m; return x } :: Functor f => f [b] -> f b

A "strict pattern match" is any pattern match that can fail.  For
example, ``()``, ``(x:xs)``, ``!z``, and ``C x`` are strict patterns,
but ``x`` and ``~(1,2)`` are not.  For the purposes of
``ApplicativeDo``, a pattern match against a ``newtype`` constructor
is considered strict.

When there's a strict pattern match in a sequence of statements,
``ApplicativeDo`` places a ``>>=`` between that statement and the one
that follows it.  The sequence may be transformed to use ``<*>``
elsewhere, but the strict pattern match and the following statement
will always be connected with ``>>=``, to retain the same strictness
semantics as the standard do-notation.  If you don't want this, simply
put a ``~`` on the pattern match to make it lazy.

.. _applicative-do-pitfall:

Things to watch out for
~~~~~~~~~~~~~~~~~~~~~~~

Your code should just work as before when :extension:`ApplicativeDo` is enabled,
provided you use conventional ``Applicative`` instances. However, if you define
a ``Functor`` or ``Applicative`` instance using do-notation, then it will likely
get turned into an infinite loop by GHC. For example, if you do this: ::

    instance Functor MyType where
        fmap f m = do x <- m; return (f x)

Then applicative desugaring will turn it into ::

    instance Functor MyType where
        fmap f m = fmap (\x -> f x) m

And the program will loop at runtime. Similarly, an ``Applicative`` instance
like this ::

    instance Applicative MyType where
        pure = return
        x <*> y = do f <- x; a <- y; return (f a)

will result in an infinte loop when ``<*>`` is called.

Just as you wouldn't define a ``Monad`` instance using the do-notation, you
shouldn't define ``Functor`` or ``Applicative`` instance using do-notation (when
using ``ApplicativeDo``) either. The correct way to define these instances in
terms of ``Monad`` is to use the ``Monad`` operations directly, e.g. ::

    instance Functor MyType where
        fmap f m = m >>= return . f

    instance Applicative MyType where
        pure = return
        (<*>) = ap


.. _parallel-list-comprehensions:

Parallel List Comprehensions
----------------------------

.. index::
   single: list comprehensions; parallel
   single: parallel list comprehensions

.. extension:: ParallelListComp
    :shortdesc: Enable parallel list comprehensions.

    :since: 6.8.1

    Allow parallel list comprehension syntax.

Parallel list comprehensions are a natural extension to list
comprehensions. List comprehensions can be thought of as a nice syntax
for writing maps and filters. Parallel comprehensions extend this to
include the ``zipWith`` family.

A parallel list comprehension has multiple independent branches of
qualifier lists, each separated by a ``|`` symbol. For example, the
following zips together two lists: ::

       [ (x, y) | x <- xs | y <- ys ]

The behaviour of parallel list comprehensions follows that of zip, in
that the resulting list will have the same length as the shortest
branch.

We can define parallel list comprehensions by translation to regular
comprehensions. Here's the basic idea:

Given a parallel comprehension of the form: ::

       [ e | p1 <- e11, p2 <- e12, ...
           | q1 <- e21, q2 <- e22, ...
           ...
       ]

This will be translated to: ::

       [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
                                             [(q1,q2) | q1 <- e21, q2 <- e22, ...]
                                             ...
       ]

where ``zipN`` is the appropriate zip for the given number of branches.

.. _generalised-list-comprehensions:

Generalised (SQL-like) List Comprehensions
------------------------------------------

.. index::
   single: list comprehensions; generalised
   single: extended list comprehensions
   single: group
   single: SQL

.. extension:: TransformListComp
    :shortdesc: Enable generalised list comprehensions.

    :since: 6.10.1

    Allow use of generalised list (SQL-like) comprehension syntax. This
    introduces the ``group``, ``by``, and ``using`` keywords.

Generalised list comprehensions are a further enhancement to the list
comprehension syntactic sugar to allow operations such as sorting and
grouping which are familiar from SQL. They are fully described in the
paper `Comprehensive comprehensions: comprehensions with "order by" and
"group by" <https://www.microsoft.com/en-us/research/wp-content/uploads/2007/09/list-comp.pdf>`__,
except that the syntax we use differs slightly from the paper.

The extension is enabled with the extension :extension:`TransformListComp`.

Here is an example:

::

    employees = [ ("Simon", "MS", 80)
                , ("Erik", "MS", 100)
                , ("Phil", "Ed", 40)
                , ("Gordon", "Ed", 45)
                , ("Paul", "Yale", 60) ]

    output = [ (the dept, sum salary)
             | (name, dept, salary) <- employees
             , then group by dept using groupWith
             , then sortWith by (sum salary)
             , then take 5 ]

In this example, the list ``output`` would take on the value:

::

    [("Yale", 60), ("Ed", 85), ("MS", 180)]

There are three new keywords: ``group``, ``by``, and ``using``. (The
functions ``sortWith`` and ``groupWith`` are not keywords; they are
ordinary functions that are exported by ``GHC.Exts``.)

There are five new forms of comprehension qualifier, all introduced by
the (existing) keyword ``then``:

-  ::

       then f

   This statement requires that
   f
   have the type
   forall a. [a] -> [a]
   . You can see an example of its use in the motivating example, as
   this form is used to apply
   take 5
   .
-  ::

       then f by e

   This form is similar to the previous one, but allows you to create a
   function which will be passed as the first argument to f. As a
   consequence f must have the type
   ``forall a. (a -> t) -> [a] -> [a]``. As you can see from the type,
   this function lets f "project out" some information from the elements
   of the list it is transforming.

   An example is shown in the opening example, where ``sortWith`` is
   supplied with a function that lets it find out the ``sum salary`` for
   any item in the list comprehension it transforms.

-  ::

       then group by e using f

   This is the most general of the grouping-type statements. In this
   form, f is required to have type
   ``forall a. (a -> t) -> [a] -> [[a]]``. As with the ``then f by e``
   case above, the first argument is a function supplied to f by the
   compiler which lets it compute e on every element of the list being
   transformed. However, unlike the non-grouping case, f additionally
   partitions the list into a number of sublists: this means that at
   every point after this statement, binders occurring before it in the
   comprehension refer to *lists* of possible values, not single values.
   To help understand this, let's look at an example:

   ::

       -- This works similarly to groupWith in GHC.Exts, but doesn't sort its input first
       groupRuns :: Eq b => (a -> b) -> [a] -> [[a]]
       groupRuns f = groupBy (\x y -> f x == f y)

       output = [ (the x, y)
       | x <- ([1..3] ++ [1..2])
       , y <- [4..6]
       , then group by x using groupRuns ]

   This results in the variable ``output`` taking on the value below:

   ::

       [(1, [4, 5, 6]), (2, [4, 5, 6]), (3, [4, 5, 6]), (1, [4, 5, 6]), (2, [4, 5, 6])]

   Note that we have used the ``the`` function to change the type of x
   from a list to its original numeric type. The variable y, in
   contrast, is left unchanged from the list form introduced by the
   grouping.

-  ::

       then group using f

   With this form of the group statement, f is required to simply have
   the type ``forall a. [a] -> [[a]]``, which will be used to group up
   the comprehension so far directly. An example of this form is as
   follows:

   ::

       output = [ x
       | y <- [1..5]
       , x <- "hello"
       , then group using inits]

   This will yield a list containing every prefix of the word "hello"
   written out 5 times:

   ::

       ["","h","he","hel","hell","hello","helloh","hellohe","hellohel","hellohell","hellohello","hellohelloh",...]

.. _monad-comprehensions:

Monad comprehensions
--------------------

.. index::
   single: monad comprehensions

.. extension:: MonadComprehensions
    :shortdesc: Enable monad comprehensions.

    :since: 7.2.1

    Enable list comprehension syntax for arbitrary monads.

Monad comprehensions generalise the list comprehension notation,
including parallel comprehensions (:ref:`parallel-list-comprehensions`)
and transform comprehensions (:ref:`generalised-list-comprehensions`) to
work for any monad.

Monad comprehensions support:

-  Bindings: ::

       [ x + y | x <- Just 1, y <- Just 2 ]

   Bindings are translated with the ``(>>=)`` and ``return`` functions
   to the usual do-notation: ::

       do x <- Just 1
          y <- Just 2
          return (x+y)

-  Guards: ::

       [ x | x <- [1..10], x <= 5 ]

   Guards are translated with the ``guard`` function, which requires a
   ``MonadPlus`` instance: ::

       do x <- [1..10]
          guard (x <= 5)
          return x

-  Transform statements (as with :extension:`TransformListComp`): ::

       [ x+y | x <- [1..10], y <- [1..x], then take 2 ]

   This translates to: ::

       do (x,y) <- take 2 (do x <- [1..10]
                              y <- [1..x]
                              return (x,y))
          return (x+y)

-  Group statements (as with :extension:`TransformListComp`):

   ::

       [ x | x <- [1,1,2,2,3], then group by x using GHC.Exts.groupWith ]
       [ x | x <- [1,1,2,2,3], then group using myGroup ]

-  Parallel statements (as with :extension:`ParallelListComp`):

   ::

       [ (x+y) | x <- [1..10]
               | y <- [11..20]
               ]

   Parallel statements are translated using the ``mzip`` function, which
   requires a ``MonadZip`` instance defined in
   :base-ref:`Control.Monad.Zip.`:

   ::

       do (x,y) <- mzip (do x <- [1..10]
                            return x)
                        (do y <- [11..20]
                            return y)
          return (x+y)

All these features are enabled by default if the :extension:`MonadComprehensions`
extension is enabled. The types and more detailed examples on how to use
comprehensions are explained in the previous chapters
:ref:`generalised-list-comprehensions` and
:ref:`parallel-list-comprehensions`. In general you just have to replace
the type ``[a]`` with the type ``Monad m => m a`` for monad
comprehensions.

.. note::
    Even though most of these examples are using the list monad, monad
    comprehensions work for any monad. The ``base`` package offers all
    necessary instances for lists, which make :extension:`MonadComprehensions`
    backward compatible to built-in, transform and parallel list
    comprehensions.

More formally, the desugaring is as follows. We write ``D[ e | Q]`` to
mean the desugaring of the monad comprehension ``[ e | Q]``:

.. code-block:: none

    Expressions: e
    Declarations: d
    Lists of qualifiers: Q,R,S

    -- Basic forms
    D[ e | ]               = return e
    D[ e | p <- e, Q ]  = e >>= \p -> D[ e | Q ]
    D[ e | e, Q ]          = guard e >> \p -> D[ e | Q ]
    D[ e | let d, Q ]      = let d in D[ e | Q ]

    -- Parallel comprehensions (iterate for multiple parallel branches)
    D[ e | (Q | R), S ]    = mzip D[ Qv | Q ] D[ Rv | R ] >>= \(Qv,Rv) -> D[ e | S ]

    -- Transform comprehensions
    D[ e | Q then f, R ]                  = f D[ Qv | Q ] >>= \Qv -> D[ e | R ]

    D[ e | Q then f by b, R ]             = f (\Qv -> b) D[ Qv | Q ] >>= \Qv -> D[ e | R ]

    D[ e | Q then group using f, R ]      = f D[ Qv | Q ] >>= \ys ->
                                            case (fmap selQv1 ys, ..., fmap selQvn ys) of
                                             Qv -> D[ e | R ]

    D[ e | Q then group by b using f, R ] = f (\Qv -> b) D[ Qv | Q ] >>= \ys ->
                                            case (fmap selQv1 ys, ..., fmap selQvn ys) of
                                               Qv -> D[ e | R ]

    where  Qv is the tuple of variables bound by Q (and used subsequently)
           selQvi is a selector mapping Qv to the ith component of Qv

    Operator     Standard binding       Expected type
    --------------------------------------------------------------------
    return       GHC.Base               t1 -> m t2
    (>>=)        GHC.Base               m1 t1 -> (t2 -> m2 t3) -> m3 t3
    (>>)         GHC.Base               m1 t1 -> m2 t2         -> m3 t3
    guard        Control.Monad          t1 -> m t2
    fmap         GHC.Base               forall a b. (a->b) -> n a -> n b
    mzip         Control.Monad.Zip      forall a b. m a -> m b -> m (a,b)

The comprehension should typecheck when its desugaring would typecheck,
except that (as discussed in :ref:`generalised-list-comprehensions`) in the
"then ``f``" and "then group using ``f``" clauses, when the "by ``b``" qualifier
is omitted, argument ``f`` should have a polymorphic type. In particular, "then
``Data.List.sort``" and "then group using ``Data.List.group``" are
insufficiently polymorphic.

Monad comprehensions support rebindable syntax
(:ref:`rebindable-syntax`). Without rebindable syntax, the operators
from the "standard binding" module are used; with rebindable syntax, the
operators are looked up in the current lexical scope. For example,
parallel comprehensions will be typechecked and desugared using whatever
"``mzip``" is in scope.

The rebindable operators must have the "Expected type" given in the
table above. These types are surprisingly general. For example, you can
use a bind operator with the type

::

    (>>=) :: T x y a -> (a -> T y z b) -> T x z b

In the case of transform comprehensions, notice that the groups are
parameterised over some arbitrary type ``n`` (provided it has an
``fmap``, as well as the comprehension being over an arbitrary monad.

.. _monadfail-desugaring:

New monadic failure desugaring mechanism
----------------------------------------

.. extension:: MonadFailDesugaring
    :shortdesc: Enable monadfail desugaring.

    :since: 8.0.1

    Use the ``MonadFail.fail`` instead of the legacy ``Monad.fail`` function
    when desugaring refutable patterns in ``do`` blocks.

The ``-XMonadFailDesugaring`` extension switches the desugaring of
``do``-blocks to use ``MonadFail.fail`` instead of ``Monad.fail``.

This extension is enabled by default since GHC 8.6.1, under the
`MonadFail Proposal (MFP)
<https://prime.haskell.org/wiki/Libraries/Proposals/MonadFail>`__.

This extension is temporary, and will be deprecated in a future release.

.. _rebindable-syntax:

Rebindable syntax and the implicit Prelude import
-------------------------------------------------

.. extension:: NoImplicitPrelude
    :shortdesc: Don't implicitly ``import Prelude``.
        Implied by :extension:`RebindableSyntax`.

    :since: 6.8.1

    Don't import ``Prelude`` by default.

GHC normally imports ``Prelude.hi`` files for
you. If you'd rather it didn't, then give it a ``-XNoImplicitPrelude``
option. The idea is that you can then import a Prelude of your own. (But
don't call it ``Prelude``; the Haskell module namespace is flat, and you
must not conflict with any Prelude module.)

.. extension:: RebindableSyntax
    :shortdesc: Employ rebindable syntax.
        Implies :extension:`NoImplicitPrelude`.

    :implies: :extension:`NoImplicitPrelude`
    :since: 7.0.1

    Enable rebinding of a variety of usually-built-in operations.

Suppose you are importing a Prelude of your own in order to define your
own numeric class hierarchy. It completely defeats that purpose if the
literal "1" means "``Prelude.fromInteger 1``", which is what the Haskell
Report specifies. So the :extension:`RebindableSyntax` extension causes the
following pieces of built-in syntax to refer to *whatever is in scope*,
not the Prelude versions:

-  An integer literal ``368`` means "``fromInteger (368::Integer)``",
   rather than "``Prelude.fromInteger (368::Integer)``".

-  Fractional literals are handled in just the same way, except that the
   translation is ``fromRational (3.68::Rational)``.

-  String literals are also handled the same way, except that the
   translation is ``fromString ("368"::String)``.

-  The equality test in an overloaded numeric pattern uses whatever
   ``(==)`` is in scope.

-  The subtraction operation, and the greater-than-or-equal test, in
   ``n+k`` patterns use whatever ``(-)`` and ``(>=)`` are in scope.

-  Negation (e.g. "``- (f x)``") means "``negate (f x)``", both in
   numeric patterns, and expressions.

-  Conditionals (e.g. "``if`` e1 ``then`` e2 ``else`` e3") means
   "``ifThenElse`` e1 e2 e3". However ``case`` expressions are
   unaffected.

-  "Do" notation is translated using whatever functions ``(>>=)``,
   ``(>>)``, and ``fail``, are in scope (not the Prelude versions). List
   comprehensions, ``mdo`` (:ref:`recursive-do-notation`), and parallel
   array comprehensions, are unaffected.

-  Arrow notation (see :ref:`arrow-notation`) uses whatever ``arr``,
   ``(>>>)``, ``first``, ``app``, ``(|||)`` and ``loop`` functions are
   in scope. But unlike the other constructs, the types of these
   functions must match the Prelude types very closely. Details are in
   flux; if you want to use this, ask!

-  List notation, such as ``[x,y]`` or ``[m..n]`` can also be treated
   via rebindable syntax if you use `-XOverloadedLists`;
   see :ref:`overloaded-lists`.

-  An overloaded label "``#foo``" means "``fromLabel @"foo"``", rather than
   "``GHC.OverloadedLabels.fromLabel @"foo"``" (see :ref:`overloaded-labels`).

:extension:`RebindableSyntax` implies :extension:`NoImplicitPrelude`.

In all cases (apart from arrow notation), the static semantics should be
that of the desugared form, even if that is a little unexpected. For
example, the static semantics of the literal ``368`` is exactly that of
``fromInteger (368::Integer)``; it's fine for ``fromInteger`` to have
any of the types: ::

    fromInteger :: Integer -> Integer
    fromInteger :: forall a. Foo a => Integer -> a
    fromInteger :: Num a => a -> Integer
    fromInteger :: Integer -> Bool -> Bool

Be warned: this is an experimental facility, with fewer checks than
usual. Use ``-dcore-lint`` to typecheck the desugared program. If Core
Lint is happy you should be all right.

Things unaffected by :extension:`RebindableSyntax`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

:extension:`RebindableSyntax` does not apply to any code generated from a
``deriving`` clause or declaration. To see why, consider the following code: ::

    {-# LANGUAGE RebindableSyntax, OverloadedStrings #-}
    newtype Text = Text String

    fromString :: String -> Text
    fromString = Text

    data Foo = Foo deriving Show

This will generate code to the effect of: ::

    instance Show Foo where
      showsPrec _ Foo = showString "Foo"

But because :extension:`RebindableSyntax` and :extension:`OverloadedStrings`
are enabled, the ``"Foo"`` string literal would now be of type ``Text``, not
``String``, which ``showString`` doesn't accept! This causes the generated
``Show`` instance to fail to typecheck. It's hard to imagine any scenario where
it would be desirable have :extension:`RebindableSyntax` behavior within
derived code, so GHC simply ignores :extension:`RebindableSyntax` entirely
when checking derived code.

.. _postfix-operators:

Postfix operators
-----------------

.. extension:: PostfixOperators
    :shortdesc: Enable postfix operators.

    :since: 7.10.1

    Allow the use of post-fix operators

The :extension:`PostfixOperators` extension enables a small extension to the syntax
of left operator sections, which allows you to define postfix operators.
The extension is this: the left section ::

      (e !)

is equivalent (from the point of view of both type checking and
execution) to the expression ::

      ((!) e)

(for any expression ``e`` and operator ``(!)``. The strict Haskell 98
interpretation is that the section is equivalent to ::

      (\y -> (!) e y)

That is, the operator must be a function of two arguments. GHC allows it
to take only one argument, and that in turn allows you to write the
function postfix.

The extension does not extend to the left-hand side of function
definitions; you must define such a function in prefix form.

.. _tuple-sections:

Tuple sections
--------------

.. extension:: TupleSections
    :shortdesc: Enable tuple sections.

    :since: 6.12

    Allow the use of tuple section syntax

The :extension:`TupleSections` extension enables partially applied
tuple constructors. For example, the following program ::

      (, True)

is considered to be an alternative notation for the more unwieldy
alternative ::

      \x -> (x, True)

You can omit any combination of arguments to the tuple, as in the
following ::

      (, "I", , , "Love", , 1337)

which translates to ::

      \a b c d -> (a, "I", b, c, "Love", d, 1337)

If you have `unboxed tuples <#unboxed-tuples>`__ enabled, tuple sections
will also be available for them, like so ::

      (# , True #)

Because there is no unboxed unit tuple, the following expression ::

      (# #)

continues to stand for the unboxed singleton tuple data constructor.

.. _lambda-case:

Lambda-case
-----------

.. extension:: LambdaCase
    :shortdesc: Enable lambda-case expressions.

    :since: 7.6.1

    Allow the use of lambda-case syntax.

The :extension:`LambdaCase` extension enables expressions of the form ::

      \case { p1 -> e1; ...; pN -> eN }

which is equivalent to ::

      \freshName -> case freshName of { p1 -> e1; ...; pN -> eN }

Note that ``\case`` starts a layout, so you can write ::

      \case
        p1 -> e1
        ...
        pN -> eN

.. _empty-case:

Empty case alternatives
-----------------------

.. extension:: EmptyCase
    :shortdesc: Allow empty case alternatives.

    :since: 7.8.1

    Allow empty case expressions.

The :extension:`EmptyCase` extension enables case expressions, or lambda-case
expressions, that have no alternatives, thus: ::

    case e of { }   -- No alternatives

or ::

    \case { }       -- -XLambdaCase is also required

This can be useful when you know that the expression being scrutinised
has no non-bottom values. For example:

::

      data Void
      f :: Void -> Int
      f x = case x of { }

With dependently-typed features it is more useful (see :ghc-ticket:`2431`). For
example, consider these two candidate definitions of ``absurd``:

::

    data a :~: b where
      Refl :: a :~: a

    absurd :: True :~: False -> a
    absurd x = error "absurd"    -- (A)
    absurd x = case x of {}      -- (B)

We much prefer (B). Why? Because GHC can figure out that
``(True :~: False)`` is an empty type. So (B) has no partiality and GHC
is able to compile with :ghc-flag:`-Wincomplete-patterns` and
:ghc-flag:`-Werror`. On the other hand (A) looks dangerous, and GHC doesn't
check to make sure that, in fact, the function can never get called.

.. _multi-way-if:

Multi-way if-expressions
------------------------

.. extension:: MultiWayIf
    :shortdesc: Enable multi-way if-expressions.

    :since: 7.6.1

    Allow the use of multi-way-``if`` syntax.

With :extension:`MultiWayIf` extension GHC accepts conditional expressions with
multiple branches: ::

      if | guard1 -> expr1
         | ...
         | guardN -> exprN

which is roughly equivalent to ::

      case () of
        _ | guard1 -> expr1
        ...
        _ | guardN -> exprN

Multi-way if expressions introduce a new layout context. So the example
above is equivalent to: ::

      if { | guard1 -> expr1
         ; | ...
         ; | guardN -> exprN
         }

The following behaves as expected: ::

      if | guard1 -> if | guard2 -> expr2
                        | guard3 -> expr3
         | guard4 -> expr4

because layout translates it as ::

      if { | guard1 -> if { | guard2 -> expr2
                          ; | guard3 -> expr3
                          }
         ; | guard4 -> expr4
         }

Layout with multi-way if works in the same way as other layout contexts,
except that the semi-colons between guards in a multi-way if are
optional. So it is not necessary to line up all the guards at the same
column; this is consistent with the way guards work in function
definitions and case expressions.

.. _local-fixity-declarations:

Local Fixity Declarations
-------------------------

A careful reading of the Haskell 98 Report reveals that fixity
declarations (``infix``, ``infixl``, and ``infixr``) are permitted to
appear inside local bindings such those introduced by ``let`` and
``where``. However, the Haskell Report does not specify the semantics of
such bindings very precisely.

In GHC, a fixity declaration may accompany a local binding: ::

    let f = ...
        infixr 3 `f`
    in
        ...

and the fixity declaration applies wherever the binding is in scope. For
example, in a ``let``, it applies in the right-hand sides of other
``let``-bindings and the body of the ``let``\ C. Or, in recursive ``do``
expressions (:ref:`recursive-do-notation`), the local fixity
declarations of a ``let`` statement scope over other statements in the
group, just as the bound name does.

Moreover, a local fixity declaration *must* accompany a local binding
of that name: it is not possible to revise the fixity of name bound
elsewhere, as in ::

    let infixr 9 $ in ...

Because local fixity declarations are technically Haskell 98, no extension is
necessary to enable them.

.. _package-imports:

Import and export extensions
----------------------------

Hiding things the imported module doesn't export
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Technically in Haskell 2010 this is illegal: ::

    module A( f ) where
      f = True

    module B where
      import A hiding( g )  -- A does not export g
      g = f

The ``import A hiding( g )`` in module ``B`` is technically an error
(`Haskell Report,
5.3.1 <http://www.haskell.org/onlinereport/haskell2010/haskellch5.html#x11-1020005.3.1>`__)
because ``A`` does not export ``g``. However GHC allows it, in the
interests of supporting backward compatibility; for example, a newer
version of ``A`` might export ``g``, and you want ``B`` to work in
either case.

The warning :ghc-flag:`-Wdodgy-imports`, which is off by default but included
with :ghc-flag:`-W`, warns if you hide something that the imported module does
not export.

.. _package-qualified-imports:

Package-qualified imports
~~~~~~~~~~~~~~~~~~~~~~~~~

.. extension:: PackageImports
    :shortdesc: Enable package-qualified imports.

    :since: 6.10.1

    Allow the use of package-qualified ``import`` syntax.

With the :extension:`PackageImports` extension, GHC allows import declarations to be
qualified by the package name that the module is intended to be imported
from. For example: ::

    import "network" Network.Socket

would import the module ``Network.Socket`` from the package ``network``
(any version). This may be used to disambiguate an import when the same
module is available from multiple packages, or is present in both the
current package being built and an external package.

The special package name ``this`` can be used to refer to the current
package being built.

.. note::
   You probably don't need to use this feature, it was added mainly so that we
   can build backwards-compatible versions of packages when APIs change. It can
   lead to fragile dependencies in the common case: modules occasionally move
   from one package to another, rendering any package-qualified imports broken.
   See also :ref:`package-thinning-and-renaming` for an alternative way of
   disambiguating between module names.

.. _safe-imports-ext:

Safe imports
~~~~~~~~~~~~

.. extension:: Safe
    :shortdesc: Enable the :ref:`Safe Haskell <safe-haskell>` Safe mode.
    :noindex:

    :since: 7.2.1

    Declare the Safe Haskell state of the current module.

.. extension:: Trustworthy
    :shortdesc: Enable the :ref:`Safe Haskell <safe-haskell>` Trustworthy mode.
    :noindex:

    :since: 7.2.1

    Declare the Safe Haskell state of the current module.

.. extension:: Unsafe
    :shortdesc: Enable Safe Haskell Unsafe mode.
    :noindex:

    :since: 7.4.1

    Declare the Safe Haskell state of the current module.

With the :extension:`Safe`, :extension:`Trustworthy` and :extension:`Unsafe`
language flags, GHC extends the import declaration syntax to take an optional
``safe`` keyword after the ``import`` keyword. This feature is part of the Safe
Haskell GHC extension. For example: ::

    import safe qualified Network.Socket as NS

would import the module ``Network.Socket`` with compilation only
succeeding if ``Network.Socket`` can be safely imported. For a description of
when a import is considered safe see :ref:`safe-haskell`.

.. _explicit-namespaces:

Explicit namespaces in import/export
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. extension:: ExplicitNamespaces
    :shortdesc: Enable using the keyword ``type`` to specify the namespace of
        entries in imports and exports (:ref:`explicit-namespaces`).
        Implied by :extension:`TypeOperators` and :extension:`TypeFamilies`.

    :since: 7.6.1

    Enable use of explicit namespaces in module export lists.

In an import or export list, such as ::

      module M( f, (++) ) where ...
        import N( f, (++) )
        ...

the entities ``f`` and ``(++)`` are *values*. However, with type
operators (:ref:`type-operators`) it becomes possible to declare
``(++)`` as a *type constructor*. In that case, how would you export or
import it?

The :extension:`ExplicitNamespaces` extension allows you to prefix the name of
a type constructor in an import or export list with "``type``" to
disambiguate this case, thus: ::

      module M( f, type (++) ) where ...
        import N( f, type (++) )
        ...
      module N( f, type (++) ) where
        data family a ++ b = L a | R b

The extension :extension:`ExplicitNamespaces` is implied by
:extension:`TypeOperators` and (for some reason) by :extension:`TypeFamilies`.

In addition, with :extension:`PatternSynonyms` you can prefix the name of a
data constructor in an import or export list with the keyword
``pattern``, to allow the import or export of a data constructor without
its parent type constructor (see :ref:`patsyn-impexp`).

.. _block-arguments:

More liberal syntax for function arguments
------------------------------------------

.. extension:: BlockArguments
    :shortdesc: Allow ``do`` blocks and other constructs as function arguments.

    :since: 8.6.1

    Allow ``do`` expressions, lambda expressions, etc. to be directly used as
    a function argument.

In Haskell 2010, certain kinds of expressions can be used without parentheses
as an argument to an operator, but not as an argument to a function.
They include ``do``, lambda, ``if``, ``case``, and ``let``
expressions. Some GHC extensions also define language constructs of this type:
``mdo`` (:ref:`recursive-do-notation`), ``\case`` (:ref:`lambda-case`), and
``proc`` (:ref:`arrow-notation`).

The :extension:`BlockArguments` extension allows these constructs to be directly
used as a function argument. For example::

    when (x > 0) do
      print x
      exitFailure

will be parsed as::

    when (x > 0) (do
      print x
      exitFailure)

and

::

    withForeignPtr fptr \ptr -> c_memcpy buf ptr size

will be parsed as::

    withForeignPtr fptr (\ptr -> c_memcpy buf ptr size)

Changes to the grammar
~~~~~~~~~~~~~~~~~~~~~~

The Haskell report `defines
<https://www.haskell.org/onlinereport/haskell2010/haskellch3.html#x8-220003>`_
the ``lexp`` nonterminal thus (``*`` indicates a rule of interest)::

    lexp  →  \ apat1 … apatn -> exp            (lambda abstraction, n ≥ 1)  *
          |  let decls in exp                  (let expression)             *
          |  if exp [;] then exp [;] else exp  (conditional)                *
          |  case exp of { alts }              (case expression)            *
          |  do { stmts }                      (do expression)              *
          |  fexp

    fexp  →  [fexp] aexp                       (function application)

    aexp  →  qvar                              (variable)
          |  gcon                              (general constructor)
          |  literal
          |  ( exp )                           (parenthesized expression)
          |  qcon { fbind1 … fbindn }          (labeled construction)
          |  aexp { fbind1 … fbindn }          (labelled update)
          |  …

The :extension:`BlockArguments` extension moves these production rules under
``aexp``::

    lexp  →  fexp

    fexp  →  [fexp] aexp                       (function application)

    aexp  →  qvar                              (variable)
          |  gcon                              (general constructor)
          |  literal
          |  ( exp )                           (parenthesized expression)
          |  qcon { fbind1 … fbindn }          (labeled construction)
          |  aexp { fbind1 … fbindn }          (labelled update)
          |  \ apat1 … apatn -> exp            (lambda abstraction, n ≥ 1)  *
          |  let decls in exp                  (let expression)             *
          |  if exp [;] then exp [;] else exp  (conditional)                *
          |  case exp of { alts }              (case expression)            *
          |  do { stmts }                      (do expression)              *
          |  …

Now the ``lexp`` nonterminal is redundant and can be dropped from the grammar.

Note that this change relies on an existing meta-rule to resolve ambiguities:

    The grammar is ambiguous regarding the extent of lambda abstractions, let
    expressions, and conditionals. The ambiguity is resolved by the meta-rule
    that each of these constructs extends as far to the right as possible.

For example, ``f \a -> a b`` will be parsed as ``f (\a -> a b)``, not as ``f
(\a -> a) b``.

.. _syntax-stolen:

Summary of stolen syntax
------------------------

Turning on an option that enables special syntax *might* cause working
Haskell 98 code to fail to compile, perhaps because it uses a variable
name which has become a reserved word. This section lists the syntax
that is "stolen" by language extensions. We use notation and nonterminal
names from the Haskell 98 lexical syntax (see the Haskell 98 Report). We
only list syntax changes here that might affect existing working
programs (i.e. "stolen" syntax). Many of these extensions will also
enable new context-free syntax, but in all cases programs written to use
the new syntax would not be compilable without the option enabled.

There are two classes of special syntax:

-  New reserved words and symbols: character sequences which are no
   longer available for use as identifiers in the program.

-  Other special syntax: sequences of characters that have a different
   meaning when this particular option is turned on.

The following syntax is stolen:

``forall``
    .. index::
       single: forall

    Stolen (in types) by: :extension:`ExplicitForAll`, and hence by
    :extension:`ScopedTypeVariables`, :extension:`LiberalTypeSynonyms`,
    :extension:`RankNTypes`, :extension:`ExistentialQuantification`

``mdo``
    .. index::
       single: mdo

    Stolen by: :extension:`RecursiveDo`

``foreign``
    .. index::
       single: foreign

    Stolen by: :extension:`ForeignFunctionInterface`

``rec``, ``proc``, ``-<``, ``>-``, ``-<<``, ``>>-``, ``(|``, ``|)``
    .. index::
       single: proc

    Stolen by: :extension:`Arrows`

``?varid``
    .. index::
       single: implicit parameters

    Stolen by: :extension:`ImplicitParams`

``[|``, ``[e|``, ``[p|``, ``[d|``, ``[t|``, ``[||``, ``[e||``
    .. index::
       single: Quasi-quotes

    Stolen by: :extension:`QuasiQuotes`. Moreover, this introduces an ambiguity
    with list comprehension syntax. See the
    :ref:`discussion on quasi-quoting <quasi-quotes-list-comprehension-ambiguity>`
    for details.

``$(``, ``$$(``, ``$varid``, ``$$varid``
    .. index::
       single: Template Haskell

    Stolen by: :extension:`TemplateHaskell`

``[varid|``
    .. index::
       single: quasi-quotation

    Stolen by: :extension:`QuasiQuotes`

⟨varid⟩, ``#``\ ⟨char⟩, ``#``, ⟨string⟩, ``#``, ⟨integer⟩, ``#``, ⟨float⟩, ``#``, ⟨float⟩, ``##``
    Stolen by: :extension:`MagicHash`

``(#``, ``#)``
    Stolen by: :extension:`UnboxedTuples`

⟨varid⟩, ``!``, ⟨varid⟩
    Stolen by: :extension:`BangPatterns`

``pattern``
    Stolen by: :extension:`PatternSynonyms`

``static``
    Stolen by: :extension:`StaticPointers`

.. _data-type-extensions:

Extensions to data types and type synonyms
==========================================

.. _nullary-types:

Data types with no constructors
-------------------------------

.. extension:: EmptyDataDecls
    :shortdesc: Allow definition of empty ``data`` types.

    :since: 6.8.1

    Allow definition of empty ``data`` types.

With the :extension:`EmptyDataDecls` extension, GHC lets you declare a
data type with no constructors.

You only need to enable this extension if the language you're using
is Haskell 98, in which a data type must have at least one constructor.
Haskell 2010 relaxed this rule to allow data types with no constructors,
and thus :extension:`EmptyDataDecls` is enabled by default when the
language is Haskell 2010.

For example: ::

      data S      -- S :: Type
      data T a    -- T :: Type -> Type

Syntactically, the declaration lacks the "= constrs" part. The type can be
parameterised over types of any kind, but if the kind is not ``Type`` then an
explicit kind annotation must be used (see :ref:`kinding`).

Such data types have only one value, namely bottom. Nevertheless, they
can be useful when defining "phantom types".

In conjunction with the :ghc-flag:`-XEmptyDataDeriving` extension, empty data
declarations can also derive instances of standard type classes
(see :ref:`empty-data-deriving`).

.. _datatype-contexts:

Data type contexts
------------------

.. extension:: DatatypeContexts
    :shortdesc: Allow contexts on ``data`` types.

    :since: 7.0.1

    Allow contexts on ``data`` types.

Haskell allows datatypes to be given contexts, e.g. ::

    data Eq a => Set a = NilSet | ConsSet a (Set a)

give constructors with types: ::

    NilSet :: Set a
    ConsSet :: Eq a => a -> Set a -> Set a

This is widely considered a misfeature, and is going to be removed from
the language. In GHC, it is controlled by the deprecated extension
``DatatypeContexts``.

.. _infix-tycons:

Infix type constructors, classes, and type variables
----------------------------------------------------

GHC allows type constructors, classes, and type variables to be
operators, and to be written infix, very much like expressions. More
specifically:

-  A type constructor or class can be any non-reserved operator.
   Symbols used in types are always like capitalized identifiers; they
   are never variables. Note that this is different from the lexical
   syntax of data constructors, which are required to begin with a
   ``:``.

-  Data type and type-synonym declarations can be written infix,
   parenthesised if you want further arguments. E.g. ::

         data a :*: b = Foo a b
         type a :+: b = Either a b
         class a :=: b where ...

         data (a :**: b) x = Baz a b x
         type (a :++: b) y = Either (a,b) y

-  Types, and class constraints, can be written infix. For example ::

         x :: Int :*: Bool
         f :: (a :=: b) => a -> b

-  Back-quotes work as for expressions, both for type constructors and
   type variables; e.g. ``Int `Either` Bool``, or ``Int `a` Bool``.
   Similarly, parentheses work the same; e.g. ``(:*:) Int Bool``.

-  Fixities may be declared for type constructors, or classes, just as
   for data constructors. However, one cannot distinguish between the
   two in a fixity declaration; a fixity declaration sets the fixity for
   a data constructor and the corresponding type constructor. For
   example: ::

         infixl 7 T, :*:

   sets the fixity for both type constructor ``T`` and data constructor
   ``T``, and similarly for ``:*:``. ``Int `a` Bool``.

-  The function arrow ``->`` is ``infixr`` with fixity -1.

.. _type-operators:

Type operators
--------------

.. extension:: TypeOperators
    :shortdesc: Enable type operators.
        Implies :extension:`ExplicitNamespaces`.

    :implies: :extension:`ExplicitNamespaces`
    :since: 6.8.1

    Allow the use and definition of types with operator names.

In types, an operator symbol like ``(+)`` is normally treated as a type
*variable*, just like ``a``. Thus in Haskell 98 you can say

::

    type T (+) = ((+), (+))
    -- Just like: type T a = (a,a)

    f :: T Int -> Int
    f (x,y)= x

As you can see, using operators in this way is not very useful, and
Haskell 98 does not even allow you to write them infix.

The language :extension:`TypeOperators` changes this behaviour:

-  Operator symbols become type *constructors* rather than type
   *variables*.

-  Operator symbols in types can be written infix, both in definitions
   and uses. For example: ::

       data a + b = Plus a b
       type Foo = Int + Bool

-  There is now some potential ambiguity in import and export lists; for
   example if you write ``import M( (+) )`` do you mean the *function*
   ``(+)`` or the *type constructor* ``(+)``? The default is the former,
   but with :extension:`ExplicitNamespaces` (which is implied by
   :extension:`TypeOperators`) GHC allows you to specify the latter by
   preceding it with the keyword ``type``, thus: ::

       import M( type (+) )

   See :ref:`explicit-namespaces`.

-  The fixity of a type operator may be set using the usual fixity
   declarations but, as in :ref:`infix-tycons`, the function and type
   constructor share a single fixity.

.. _type-synonyms:

Liberalised type synonyms
-------------------------

.. extension:: LiberalTypeSynonyms
    :shortdesc: Enable liberalised type synonyms.

    :implies: :extension:`ExplicitForAll`
    :since: 6.8.1

    Relax many of the Haskell 98 rules on type synonym definitions.

Type synonyms are like macros at the type level, but Haskell 98 imposes
many rules on individual synonym declarations. With the
:extension:`LiberalTypeSynonyms` extension, GHC does validity checking on types
*only after expanding type synonyms*. That means that GHC can be very
much more liberal about type synonyms than Haskell 98.

-  You can write a ``forall`` (including overloading) in a type synonym,
   thus: ::

         type Discard a = forall b. Show b => a -> b -> (a, String)

         f :: Discard a
         f x y = (x, show y)

         g :: Discard Int -> (Int,String)    -- A rank-2 type
         g f = f 3 True

-  If you also use :extension:`UnboxedTuples`, you can write an unboxed tuple
   in a type synonym: ::

         type Pr = (# Int, Int #)

         h :: Int -> Pr
         h x = (# x, x #)

-  You can apply a type synonym to a forall type: ::

         type Foo a = a -> a -> Bool

         f :: Foo (forall b. b->b)

   After expanding the synonym, ``f`` has the legal (in GHC) type: ::

         f :: (forall b. b->b) -> (forall b. b->b) -> Bool

-  You can apply a type synonym to a partially applied type synonym: ::

         type Generic i o = forall x. i x -> o x
         type Id x = x

         foo :: Generic Id []

   After expanding the synonym, ``foo`` has the legal (in GHC) type: ::

         foo :: forall x. x -> [x]

GHC currently does kind checking before expanding synonyms (though even
that could be changed).

After expanding type synonyms, GHC does validity checking on types,
looking for the following malformedness which isn't detected simply by
kind checking:

-  Type constructor applied to a type involving for-alls (if
   :extension:`ImpredicativeTypes` is off)

-  Partially-applied type synonym.

So, for example, this will be rejected: ::

      type Pr = forall a. a

      h :: [Pr]
      h = ...

because GHC does not allow type constructors applied to for-all types.

.. _existential-quantification:

Existentially quantified data constructors
------------------------------------------

.. extension:: ExistentialQuantification
    :shortdesc: Enable liberalised type synonyms.

    :implies: :extension:`ExplicitForAll`
    :since: 6.8.1

    Allow existentially quantified type variables in types.

The idea of using existential quantification in data type declarations
was suggested by Perry, and implemented in Hope+ (Nigel Perry, *The
Implementation of Practical Functional Programming Languages*, PhD
Thesis, University of London, 1991). It was later formalised by Laufer
and Odersky (*Polymorphic type inference and abstract data types*,
TOPLAS, 16(5), pp. 1411-1430, 1994). It's been in Lennart Augustsson's
``hbc`` Haskell compiler for several years, and proved very useful.
Here's the idea. Consider the declaration: ::

      data Foo = forall a. MkFoo a (a -> Bool)
               | Nil

The data type ``Foo`` has two constructors with types: ::

      MkFoo :: forall a. a -> (a -> Bool) -> Foo
      Nil   :: Foo

Notice that the type variable ``a`` in the type of ``MkFoo`` does not
appear in the data type itself, which is plain ``Foo``. For example, the
following expression is fine: ::

      [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]

Here, ``(MkFoo 3 even)`` packages an integer with a function ``even``
that maps an integer to ``Bool``; and ``MkFoo 'c'
isUpper`` packages a character with a compatible function. These two
things are each of type ``Foo`` and can be put in a list.

What can we do with a value of type ``Foo``? In particular, what
happens when we pattern-match on ``MkFoo``? ::

      f (MkFoo val fn) = ???

Since all we know about ``val`` and ``fn`` is that they are compatible,
the only (useful) thing we can do with them is to apply ``fn`` to
``val`` to get a boolean. For example: ::

      f :: Foo -> Bool
      f (MkFoo val fn) = fn val

What this allows us to do is to package heterogeneous values together
with a bunch of functions that manipulate them, and then treat that
collection of packages in a uniform manner. You can express quite a bit
of object-oriented-like programming this way.

.. _existential:

Why existential?
~~~~~~~~~~~~~~~~

What has this to do with *existential* quantification? Simply that
``MkFoo`` has the (nearly) isomorphic type ::

      MkFoo :: (exists a . (a, a -> Bool)) -> Foo

But Haskell programmers can safely think of the ordinary *universally*
quantified type given above, thereby avoiding adding a new existential
quantification construct.

.. _existential-with-context:

Existentials and type classes
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

An easy extension is to allow arbitrary contexts before the constructor.
For example: ::

    data Baz = forall a. Eq a => Baz1 a a
             | forall b. Show b => Baz2 b (b -> b)

The two constructors have the types you'd expect: ::

    Baz1 :: forall a. Eq a => a -> a -> Baz
    Baz2 :: forall b. Show b => b -> (b -> b) -> Baz

But when pattern matching on ``Baz1`` the matched values can be compared
for equality, and when pattern matching on ``Baz2`` the first matched
value can be converted to a string (as well as applying the function to
it). So this program is legal: ::

      f :: Baz -> String
      f (Baz1 p q) | p == q    = "Yes"
                   | otherwise = "No"
      f (Baz2 v fn)            = show (fn v)

Operationally, in a dictionary-passing implementation, the constructors
``Baz1`` and ``Baz2`` must store the dictionaries for ``Eq`` and
``Show`` respectively, and extract it on pattern matching.

.. _existential-records:

Record Constructors
~~~~~~~~~~~~~~~~~~~

GHC allows existentials to be used with records syntax as well. For
example: ::

    data Counter a = forall self. NewCounter
        { _this    :: self
        , _inc     :: self -> self
        , _display :: self -> IO ()
        , tag      :: a
        }

Here ``tag`` is a public field, with a well-typed selector function
``tag :: Counter a -> a``. The ``self`` type is hidden from the outside;
any attempt to apply ``_this``, ``_inc`` or ``_display`` as functions
will raise a compile-time error. In other words, *GHC defines a record
selector function only for fields whose type does not mention the
existentially-quantified variables*. (This example used an underscore in
the fields for which record selectors will not be defined, but that is
only programming style; GHC ignores them.)

To make use of these hidden fields, we need to create some helper
functions: ::

    inc :: Counter a -> Counter a
    inc (NewCounter x i d t) = NewCounter
        { _this = i x, _inc = i, _display = d, tag = t }

    display :: Counter a -> IO ()
    display NewCounter{ _this = x, _display = d } = d x

Now we can define counters with different underlying implementations: ::

    counterA :: Counter String
    counterA = NewCounter
        { _this = 0, _inc = (1+), _display = print, tag = "A" }

    counterB :: Counter String
    counterB = NewCounter
        { _this = "", _inc = ('#':), _display = putStrLn, tag = "B" }

    main = do
        display (inc counterA)         -- prints "1"
        display (inc (inc counterB))   -- prints "##"

Record update syntax is supported for existentials (and GADTs): ::

    setTag :: Counter a -> a -> Counter a
    setTag obj t = obj{ tag = t }

The rule for record update is this:

    the types of the updated fields may mention only the universally-quantified
    type variables of the data constructor. For GADTs, the field may mention
    only types that appear as a simple type-variable argument in the
    constructor's result type.

For example: ::

    data T a b where { T1 { f1::a, f2::b, f3::(b,c) } :: T a b } -- c is existential
    upd1 t x = t { f1=x }   -- OK:   upd1 :: T a b -> a' -> T a' b
    upd2 t x = t { f3=x }   -- BAD   (f3's type mentions c, which is
                            --        existentially quantified)

    data G a b where { G1 { g1::a, g2::c } :: G a [c] }
    upd3 g x = g { g1=x }   -- OK:   upd3 :: G a b -> c -> G c b
    upd4 g x = g { g2=x }   -- BAD (f2's type mentions c, which is not a simple
                            --      type-variable argument in G1's result type)

Restrictions
~~~~~~~~~~~~

There are several restrictions on the ways in which existentially-quantified
constructors can be used.

-  When pattern matching, each pattern match introduces a new, distinct,
   type for each existential type variable. These types cannot be
   unified with any other type, nor can they escape from the scope of
   the pattern match. For example, these fragments are incorrect: ::

       f1 (MkFoo a f) = a

   Here, the type bound by ``MkFoo`` "escapes", because ``a`` is the
   result of ``f1``. One way to see why this is wrong is to ask what
   type ``f1`` has: ::

         f1 :: Foo -> a             -- Weird!

   What is this "``a``" in the result type? Clearly we don't mean this: ::

         f1 :: forall a. Foo -> a   -- Wrong!

   The original program is just plain wrong. Here's another sort of
   error ::

         f2 (Baz1 a b) (Baz1 p q) = a==q

   It's ok to say ``a==b`` or ``p==q``, but ``a==q`` is wrong because it
   equates the two distinct types arising from the two ``Baz1``
   constructors.

-  You can't pattern-match on an existentially quantified constructor in
   a ``let`` or ``where`` group of bindings. So this is illegal: ::

         f3 x = a==b where { Baz1 a b = x }

   Instead, use a ``case`` expression: ::

         f3 x = case x of Baz1 a b -> a==b

   In general, you can only pattern-match on an existentially-quantified
   constructor in a ``case`` expression or in the patterns of a function
   definition. The reason for this restriction is really an
   implementation one. Type-checking binding groups is already a
   nightmare without existentials complicating the picture. Also an
   existential pattern binding at the top level of a module doesn't make
   sense, because it's not clear how to prevent the
   existentially-quantified type "escaping". So for now, there's a
   simple-to-state restriction. We'll see how annoying it is.

-  You can't use existential quantification for ``newtype``
   declarations. So this is illegal: ::

         newtype T = forall a. Ord a => MkT a

   Reason: a value of type ``T`` must be represented as a pair of a
   dictionary for ``Ord t`` and a value of type ``t``. That contradicts
   the idea that ``newtype`` should have no concrete representation. You
   can get just the same efficiency and effect by using ``data`` instead
   of ``newtype``. If there is no overloading involved, then there is
   more of a case for allowing an existentially-quantified ``newtype``,
   because the ``data`` version does carry an implementation cost, but
   single-field existentially quantified constructors aren't much use.
   So the simple restriction (no existential stuff on ``newtype``)
   stands, unless there are convincing reasons to change it.

-  You can't use ``deriving`` to define instances of a data type with
   existentially quantified data constructors. Reason: in most cases it
   would not make sense. For example:; ::

       data T = forall a. MkT [a] deriving( Eq )

   To derive ``Eq`` in the standard way we would need to have equality
   between the single component of two ``MkT`` constructors: ::

       instance Eq T where
         (MkT a) == (MkT b) = ???

   But ``a`` and ``b`` have distinct types, and so can't be compared.
   It's just about possible to imagine examples in which the derived
   instance would make sense, but it seems altogether simpler simply to
   prohibit such declarations. Define your own instances!

.. _gadt-style:

Declaring data types with explicit constructor signatures
---------------------------------------------------------

.. extension:: GADTSyntax
    :shortdesc: Enable generalised algebraic data type syntax.

    :since: 7.2.1

    Allow the use of GADT syntax in data type definitions (but not GADTs
    themselves; for this see :extension:`GADTs`)

When the ``GADTSyntax`` extension is enabled, GHC allows you to declare
an algebraic data type by giving the type signatures of constructors
explicitly. For example: ::

      data Maybe a where
          Nothing :: Maybe a
          Just    :: a -> Maybe a

The form is called a "GADT-style declaration" because Generalised
Algebraic Data Types, described in :ref:`gadt`, can only be declared
using this form.

Notice that GADT-style syntax generalises existential types
(:ref:`existential-quantification`). For example, these two declarations
are equivalent: ::

      data Foo = forall a. MkFoo a (a -> Bool)
      data Foo' where { MKFoo :: a -> (a->Bool) -> Foo' }

Any data type that can be declared in standard Haskell 98 syntax can
also be declared using GADT-style syntax. The choice is largely
stylistic, but GADT-style declarations differ in one important respect:
they treat class constraints on the data constructors differently.
Specifically, if the constructor is given a type-class context, that
context is made available by pattern matching. For example: ::

      data Set a where
        MkSet :: Eq a => [a] -> Set a

      makeSet :: Eq a => [a] -> Set a
      makeSet xs = MkSet (nub xs)

      insert :: a -> Set a -> Set a
      insert a (MkSet as) | a `elem` as = MkSet as
                          | otherwise   = MkSet (a:as)

A use of ``MkSet`` as a constructor (e.g. in the definition of
``makeSet``) gives rise to a ``(Eq a)`` constraint, as you would expect.
The new feature is that pattern-matching on ``MkSet`` (as in the
definition of ``insert``) makes *available* an ``(Eq a)`` context. In
implementation terms, the ``MkSet`` constructor has a hidden field that
stores the ``(Eq a)`` dictionary that is passed to ``MkSet``; so when
pattern-matching that dictionary becomes available for the right-hand
side of the match. In the example, the equality dictionary is used to
satisfy the equality constraint generated by the call to ``elem``, so
that the type of ``insert`` itself has no ``Eq`` constraint.

For example, one possible application is to reify dictionaries: ::

       data NumInst a where
         MkNumInst :: Num a => NumInst a

       intInst :: NumInst Int
       intInst = MkNumInst

       plus :: NumInst a -> a -> a -> a
       plus MkNumInst p q = p + q

Here, a value of type ``NumInst a`` is equivalent to an explicit
``(Num a)`` dictionary.

All this applies to constructors declared using the syntax of
:ref:`existential-with-context`. For example, the ``NumInst`` data type
above could equivalently be declared like this: ::

       data NumInst a
          = Num a => MkNumInst (NumInst a)

Notice that, unlike the situation when declaring an existential, there
is no ``forall``, because the ``Num`` constrains the data type's
universally quantified type variable ``a``. A constructor may have both
universal and existential type variables: for example, the following two
declarations are equivalent: ::

       data T1 a
        = forall b. (Num a, Eq b) => MkT1 a b
       data T2 a where
        MkT2 :: (Num a, Eq b) => a -> b -> T2 a

All this behaviour contrasts with Haskell 98's peculiar treatment of
contexts on a data type declaration (Section 4.2.1 of the Haskell 98
Report). In Haskell 98 the definition ::

      data Eq a => Set' a = MkSet' [a]

gives ``MkSet'`` the same type as ``MkSet`` above. But instead of
*making available* an ``(Eq a)`` constraint, pattern-matching on
``MkSet'`` *requires* an ``(Eq a)`` constraint! GHC faithfully
implements this behaviour, odd though it is. But for GADT-style
declarations, GHC's behaviour is much more useful, as well as much more
intuitive.

The rest of this section gives further details about GADT-style data
type declarations.

-  The result type of each data constructor must begin with the type
   constructor being defined. If the result type of all constructors has
   the form ``T a1 ... an``, where ``a1 ... an`` are distinct type
   variables, then the data type is *ordinary*; otherwise is a
   *generalised* data type (:ref:`gadt`).

-  As with other type signatures, you can give a single signature for
   several data constructors. In this example we give a single signature
   for ``T1`` and ``T2``: ::

         data T a where
           T1,T2 :: a -> T a
           T3 :: T a

-  The type signature of each constructor is independent, and is
   implicitly universally quantified as usual. In particular, the type
   variable(s) in the "``data T a where``" header have no scope, and
   different constructors may have different universally-quantified type
   variables: ::

         data T a where        -- The 'a' has no scope
           T1,T2 :: b -> T b   -- Means forall b. b -> T b
           T3 :: T a           -- Means forall a. T a

-  A constructor signature may mention type class constraints, which can
   differ for different constructors. For example, this is fine: ::

         data T a where
           T1 :: Eq b => b -> b -> T b
           T2 :: (Show c, Ix c) => c -> [c] -> T c

   When pattern matching, these constraints are made available to
   discharge constraints in the body of the match. For example: ::

         f :: T a -> String
         f (T1 x y) | x==y      = "yes"
                    | otherwise = "no"
         f (T2 a b)             = show a

   Note that ``f`` is not overloaded; the ``Eq`` constraint arising from
   the use of ``==`` is discharged by the pattern match on ``T1`` and
   similarly the ``Show`` constraint arising from the use of ``show``.

-  Unlike a Haskell-98-style data type declaration, the type variable(s)
   in the "``data Set a where``" header have no scope. Indeed, one can
   write a kind signature instead: ::

         data Set :: Type -> Type where ...

   or even a mixture of the two: ::

         data Bar a :: (Type -> Type) -> Type where ...

   The type variables (if given) may be explicitly kinded, so we could
   also write the header for ``Foo`` like this: ::

         data Bar a (b :: Type -> Type) where ...

-  You can use strictness annotations, in the obvious places in the
   constructor type: ::

         data Term a where
             Lit    :: !Int -> Term Int
             If     :: Term Bool -> !(Term a) -> !(Term a) -> Term a
             Pair   :: Term a -> Term b -> Term (a,b)

-  You can use a ``deriving`` clause on a GADT-style data type
   declaration. For example, these two declarations are equivalent ::

         data Maybe1 a where {
             Nothing1 :: Maybe1 a ;
             Just1    :: a -> Maybe1 a
           } deriving( Eq, Ord )

         data Maybe2 a = Nothing2 | Just2 a
              deriving( Eq, Ord )

-  The type signature may have quantified type variables that do not
   appear in the result type: ::

         data Foo where
            MkFoo :: a -> (a->Bool) -> Foo
            Nil   :: Foo

   Here the type variable ``a`` does not appear in the result type of
   either constructor. Although it is universally quantified in the type
   of the constructor, such a type variable is often called
   "existential". Indeed, the above declaration declares precisely the
   same type as the ``data Foo`` in :ref:`existential-quantification`.

   The type may contain a class context too, of course: ::

         data Showable where
           MkShowable :: Show a => a -> Showable

-  You can use record syntax on a GADT-style data type declaration: ::

         data Person where
             Adult :: { name :: String, children :: [Person] } -> Person
             Child :: Show a => { name :: !String, funny :: a } -> Person

   As usual, for every constructor that has a field ``f``, the type of
   field ``f`` must be the same (modulo alpha conversion). The ``Child``
   constructor above shows that the signature may have a context,
   existentially-quantified variables, and strictness annotations, just
   as in the non-record case. (NB: the "type" that follows the
   double-colon is not really a type, because of the record syntax and
   strictness annotations. A "type" of this form can appear only in a
   constructor signature.)

-  Record updates are allowed with GADT-style declarations, only fields
   that have the following property: the type of the field mentions no
   existential type variables.

-  As in the case of existentials declared using the Haskell-98-like
   record syntax (:ref:`existential-records`), record-selector functions
   are generated only for those fields that have well-typed selectors.
   Here is the example of that section, in GADT-style syntax: ::

       data Counter a where
           NewCounter :: { _this    :: self
                         , _inc     :: self -> self
                         , _display :: self -> IO ()
                         , tag      :: a
                         } -> Counter a

   As before, only one selector function is generated here, that for
   ``tag``. Nevertheless, you can still use all the field names in
   pattern matching and record construction.

-  In a GADT-style data type declaration there is no obvious way to
   specify that a data constructor should be infix, which makes a
   difference if you derive ``Show`` for the type. (Data constructors
   declared infix are displayed infix by the derived ``show``.) So GHC
   implements the following design: a data constructor declared in a
   GADT-style data type declaration is displayed infix by ``Show`` iff
   (a) it is an operator symbol, (b) it has two arguments, (c) it has a
   programmer-supplied fixity declaration. For example

   ::

          infix 6 (:--:)
          data T a where
            (:--:) :: Int -> Bool -> T Int

.. _gadt:

Generalised Algebraic Data Types (GADTs)
----------------------------------------

.. extension:: GADTs
    :shortdesc: Enable generalised algebraic data types.
        Implies :extension:`GADTSyntax` and :extension:`MonoLocalBinds`.

    :implies: :extension:`MonoLocalBinds`, :extension:`GADTSyntax`
    :since: 6.8.1

    Allow use of Generalised Algebraic Data Types (GADTs).

Generalised Algebraic Data Types generalise ordinary algebraic data
types by allowing constructors to have richer return types. Here is an
example: ::

      data Term a where
          Lit    :: Int -> Term Int
          Succ   :: Term Int -> Term Int
          IsZero :: Term Int -> Term Bool
          If     :: Term Bool -> Term a -> Term a -> Term a
          Pair   :: Term a -> Term b -> Term (a,b)

Notice that the return type of the constructors is not always
``Term a``, as is the case with ordinary data types. This generality
allows us to write a well-typed ``eval`` function for these ``Terms``: ::

      eval :: Term a -> a
      eval (Lit i)      = i
      eval (Succ t)     = 1 + eval t
      eval (IsZero t)   = eval t == 0
      eval (If b e1 e2) = if eval b then eval e1 else eval e2
      eval (Pair e1 e2) = (eval e1, eval e2)

The key point about GADTs is that *pattern matching causes type
refinement*. For example, in the right hand side of the equation ::

      eval :: Term a -> a
      eval (Lit i) =  ...

the type ``a`` is refined to ``Int``. That's the whole point! A precise
specification of the type rules is beyond what this user manual aspires
to, but the design closely follows that described in the paper `Simple
unification-based type inference for
GADTs <http://research.microsoft.com/%7Esimonpj/papers/gadt/>`__, (ICFP
2006). The general principle is this: *type refinement is only carried
out based on user-supplied type annotations*. So if no type signature is
supplied for ``eval``, no type refinement happens, and lots of obscure
error messages will occur. However, the refinement is quite general. For
example, if we had: ::

      eval :: Term a -> a -> a
      eval (Lit i) j =  i+j

the pattern match causes the type ``a`` to be refined to ``Int``
(because of the type of the constructor ``Lit``), and that refinement
also applies to the type of ``j``, and the result type of the ``case``
expression. Hence the addition ``i+j`` is legal.

These and many other examples are given in papers by Hongwei Xi, and Tim
Sheard. There is a longer introduction `on the
wiki <http://www.haskell.org/haskellwiki/GADT>`__, and Ralf Hinze's `Fun
with phantom
types <http://www.cs.ox.ac.uk/ralf.hinze/publications/With.pdf>`__ also
has a number of examples. Note that papers may use different notation to
that implemented in GHC.

The rest of this section outlines the extensions to GHC that support
GADTs. The extension is enabled with :extension:`GADTs`. The :extension:`GADTs` extension
also sets :extension:`GADTSyntax` and :extension:`MonoLocalBinds`.

-  A GADT can only be declared using GADT-style syntax
   (:ref:`gadt-style`); the old Haskell 98 syntax for data declarations
   always declares an ordinary data type. The result type of each
   constructor must begin with the type constructor being defined, but
   for a GADT the arguments to the type constructor can be arbitrary
   monotypes. For example, in the ``Term`` data type above, the type of
   each constructor must end with ``Term ty``, but the ``ty`` need not
   be a type variable (e.g. the ``Lit`` constructor).

-  It is permitted to declare an ordinary algebraic data type using
   GADT-style syntax. What makes a GADT into a GADT is not the syntax,
   but rather the presence of data constructors whose result type is not
   just ``T a b``.

-  You cannot use a ``deriving`` clause for a GADT; only for an ordinary
   data type.

-  As mentioned in :ref:`gadt-style`, record syntax is supported. For
   example:

   ::

         data Term a where
             Lit    :: { val  :: Int }      -> Term Int
             Succ   :: { num  :: Term Int } -> Term Int
             Pred   :: { num  :: Term Int } -> Term Int
             IsZero :: { arg  :: Term Int } -> Term Bool
             Pair   :: { arg1 :: Term a
                       , arg2 :: Term b
                       }                    -> Term (a,b)
             If     :: { cnd  :: Term Bool
                       , tru  :: Term a
                       , fls  :: Term a
                       }                    -> Term a

   However, for GADTs there is the following additional constraint:
   every constructor that has a field ``f`` must have the same result
   type (modulo alpha conversion) Hence, in the above example, we cannot
   merge the ``num`` and ``arg`` fields above into a single name.
   Although their field types are both ``Term Int``, their selector
   functions actually have different types:

   ::

         num :: Term Int -> Term Int
         arg :: Term Bool -> Term Int

-  When pattern-matching against data constructors drawn from a GADT,
   for example in a ``case`` expression, the following rules apply:

   -  The type of the scrutinee must be rigid.

   -  The type of the entire ``case`` expression must be rigid.

   -  The type of any free variable mentioned in any of the ``case``
      alternatives must be rigid.

   A type is "rigid" if it is completely known to the compiler at its
   binding site. The easiest way to ensure that a variable a rigid type
   is to give it a type signature. For more precise details see `Simple
   unification-based type inference for
   GADTs <http://research.microsoft.com/%7Esimonpj/papers/gadt/>`__. The
   criteria implemented by GHC are given in the Appendix.

.. _record-system-extensions:

Extensions to the record system
===============================

.. _traditional-record-syntax:

Traditional record syntax
-------------------------

.. extension:: NoTraditionalRecordSyntax
    :shortdesc: Disable support for traditional record syntax
        (as supported by Haskell 98) ``C {f = x}``

    :since: 7.4.1

    Disallow use of record syntax.

Traditional record syntax, such as ``C {f = x}``, is enabled by default.
To disable it, you can use the :extension:`NoTraditionalRecordSyntax` extension.

.. _disambiguate-fields:

Record field disambiguation
---------------------------

.. extension:: DisambiguateRecordFields
    :shortdesc: Enable record field disambiguation.
        Implied by :extension:`RecordWildCards`.

    :since: 6.8.1

    Allow the compiler to automatically choose between identically-named
    record selectors based on type (if the choice is unambiguous).

In record construction and record pattern matching it is entirely
unambiguous which field is referred to, even if there are two different
data types in scope with a common field name. For example:

::

    module M where
      data S = MkS { x :: Int, y :: Bool }

    module Foo where
      import M

      data T = MkT { x :: Int }

      ok1 (MkS { x = n }) = n+1   -- Unambiguous
      ok2 n = MkT { x = n+1 }     -- Unambiguous

      bad1 k = k { x = 3 }        -- Ambiguous
      bad2 k = x k                -- Ambiguous

Even though there are two ``x``'s in scope, it is clear that the ``x``
in the pattern in the definition of ``ok1`` can only mean the field
``x`` from type ``S``. Similarly for the function ``ok2``. However, in
the record update in ``bad1`` and the record selection in ``bad2`` it is
not clear which of the two types is intended.

Haskell 98 regards all four as ambiguous, but with the
:extension:`DisambiguateRecordFields` extension, GHC will accept the former two. The
rules are precisely the same as those for instance declarations in
Haskell 98, where the method names on the left-hand side of the method
bindings in an instance declaration refer unambiguously to the method of
that class (provided they are in scope at all), even if there are other
variables in scope with the same name. This reduces the clutter of
qualified names when you import two records from different modules that
use the same field name.

Some details:

-  Field disambiguation can be combined with punning (see
   :ref:`record-puns`). For example: ::

       module Foo where
         import M
         x=True
         ok3 (MkS { x }) = x+1   -- Uses both disambiguation and punning

-  With :extension:`DisambiguateRecordFields` you can use *unqualified* field
   names even if the corresponding selector is only in scope *qualified*
   For example, assuming the same module ``M`` as in our earlier
   example, this is legal: ::

       module Foo where
         import qualified M    -- Note qualified

         ok4 (M.MkS { x = n }) = n+1   -- Unambiguous

   Since the constructor ``MkS`` is only in scope qualified, you must
   name it ``M.MkS``, but the field ``x`` does not need to be qualified
   even though ``M.x`` is in scope but ``x`` is not (In effect, it is
   qualified by the constructor).

.. _duplicate-record-fields:

Duplicate record fields
-----------------------

.. extension:: DuplicateRecordFields
    :shortdesc: Allow definition of record types with identically-named fields.

    :implies: :extension:`DisambiguateRecordFields`
    :since: 8.0.1

    Allow definition of record types with identically-named fields.

Going beyond :extension:`DisambiguateRecordFields` (see :ref:`disambiguate-fields`),
the :extension:`DuplicateRecordFields` extension allows multiple datatypes to be
declared using the same field names in a single module. For example, it allows
this: ::

    module M where
      data S = MkS { x :: Int }
      data T = MkT { x :: Bool }

Uses of fields that are always unambiguous because they mention the constructor,
including construction and pattern-matching, may freely use duplicated field
names. For example, the following are permitted (just as with
:extension:`DisambiguateRecordFields`): ::

    s = MkS { x = 3 }

    f (MkT { x = b }) = b

Field names used as selector functions or in record updates must be unambiguous,
either because there is only one such field in scope, or because a type
signature is supplied, as described in the following sections.

Selector functions
~~~~~~~~~~~~~~~~~~

Fields may be used as selector functions only if they are unambiguous, so this
is still not allowed if both ``S(x)`` and ``T(x)`` are in scope: ::

    bad r = x r

An ambiguous selector may be disambiguated by the type being "pushed down" to
the occurrence of the selector (see :ref:`higher-rank-type-inference` for more
details on what "pushed down" means). For example, the following are permitted: ::

    ok1 = x :: S -> Int

    ok2 :: S -> Int
    ok2 = x

    ok3 = k x -- assuming we already have k :: (S -> Int) -> _

In addition, the datatype that is meant may be given as a type signature on the
argument to the selector: ::

    ok4 s = x (s :: S)

However, we do not infer the type of the argument to determine the datatype, or
have any way of deferring the choice to the constraint solver. Thus the
following is ambiguous: ::

    bad :: S -> Int
    bad s = x s

Even though a field label is duplicated in its defining module, it may be
possible to use the selector unambiguously elsewhere. For example, another
module could import ``S(x)`` but not ``T(x)``, and then use ``x`` unambiguously.

Record updates
~~~~~~~~~~~~~~

In a record update such as ``e { x = 1 }``, if there are multiple ``x`` fields
in scope, then the type of the context must fix which record datatype is
intended, or a type annotation must be supplied. Consider the following
definitions: ::

    data S = MkS { foo :: Int }
    data T = MkT { foo :: Int, bar :: Int }
    data U = MkU { bar :: Int, baz :: Int }

Without :extension:`DuplicateRecordFields`, an update mentioning ``foo`` will always be
ambiguous if all these definitions were in scope. When the extension is enabled,
there are several options for disambiguating updates:

- Check for types that have all the fields being updated. For example: ::

      f x = x { foo = 3, bar = 2 }

  Here ``f`` must be updating ``T`` because neither ``S`` nor ``U`` have both
  fields.

- Use the type being pushed in to the record update, as in the following: ::

      g1 :: T -> T
      g1 x = x { foo = 3 }

      g2 x = x { foo = 3 } :: T

      g3 = k (x { foo = 3 }) -- assuming we already have k :: T -> _

- Use an explicit type signature on the record expression, as in: ::

      h x = (x :: T) { foo = 3 }

The type of the expression being updated will not be inferred, and no
constraint-solving will be performed, so the following will be rejected as
ambiguous: ::

    let x :: T
        x = blah
    in x { foo = 3 }

    \x -> [x { foo = 3 },  blah :: T ]

    \ (x :: T) -> x { foo = 3 }

Import and export of record fields
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

When :extension:`DuplicateRecordFields` is enabled, an ambiguous field must be exported
as part of its datatype, rather than at the top level. For example, the
following is legal: ::

    module M (S(x), T(..)) where
      data S = MkS { x :: Int }
      data T = MkT { x :: Bool }

However, this would not be permitted, because ``x`` is ambiguous: ::

    module M (x) where ...

Similar restrictions apply on import.

.. _record-puns:

Record puns
-----------

.. extension:: NamedFieldPuns
    :shortdesc: Enable record puns.

    :since: 6.10.1

    Allow use of record puns.

Record puns are enabled by the language extension :extension:`NamedFieldPuns`.

When using records, it is common to write a pattern that binds a
variable with the same name as a record field, such as: ::

    data C = C {a :: Int}
    f (C {a = a}) = a

Record punning permits the variable name to be elided, so one can simply
write ::

    f (C {a}) = a

to mean the same pattern as above. That is, in a record pattern, the
pattern ``a`` expands into the pattern ``a = a`` for the same name
``a``.

Note that:

-  Record punning can also be used in an expression, writing, for
   example, ::

       let a = 1 in C {a}

   instead of ::

       let a = 1 in C {a = a}

   The expansion is purely syntactic, so the expanded right-hand side
   expression refers to the nearest enclosing variable that is spelled
   the same as the field name.

-  Puns and other patterns can be mixed in the same record: ::

       data C = C {a :: Int, b :: Int}
       f (C {a, b = 4}) = a

-  Puns can be used wherever record patterns occur (e.g. in ``let``
   bindings or at the top-level).

-  A pun on a qualified field name is expanded by stripping off the
   module qualifier. For example: ::

       f (C {M.a}) = a

   means ::

       f (M.C {M.a = a}) = a

   (This is useful if the field selector ``a`` for constructor ``M.C``
   is only in scope in qualified form.)

.. _record-wildcards:

Record wildcards
----------------

.. extension:: RecordWildCards
    :shortdesc: Enable record wildcards.
        Implies :extension:`DisambiguateRecordFields`.

    :implies: :extension:`DisambiguateRecordFields`.
    :since: 6.8.1

    Allow the use of wildcards in record construction and pattern matching.

Record wildcards are enabled by the language extension :extension:`RecordWildCards`. This
exension implies :extension:`DisambiguateRecordFields`.

For records with many fields, it can be tiresome to write out each field
individually in a record pattern, as in ::

    data C = C {a :: Int, b :: Int, c :: Int, d :: Int}
    f (C {a = 1, b = b, c = c, d = d}) = b + c + d

Record wildcard syntax permits a "``..``" in a record pattern, where
each elided field ``f`` is replaced by the pattern ``f = f``. For
example, the above pattern can be written as ::

    f (C {a = 1, ..}) = b + c + d

More details:

-  Record wildcards in patterns can be mixed with other patterns,
   including puns (:ref:`record-puns`); for example, in a pattern
   ``(C {a = 1, b, ..})``. Additionally, record wildcards can be used
   wherever record patterns occur, including in ``let`` bindings and at
   the top-level. For example, the top-level binding ::

       C {a = 1, ..} = e

   defines ``b``, ``c``, and ``d``.

-  Record wildcards can also be used in an expression, when constructing
   a record. For example, ::

       let {a = 1; b = 2; c = 3; d = 4} in C {..}

   in place of ::

       let {a = 1; b = 2; c = 3; d = 4} in C {a=a, b=b, c=c, d=d}

   The expansion is purely syntactic, so the record wildcard expression
   refers to the nearest enclosing variables that are spelled the same
   as the omitted field names.

-  For both pattern and expression wildcards, the "``..``" expands to
   the missing *in-scope* record fields. Specifically the expansion of
   "``C {..}``" includes ``f`` if and only if:

   -  ``f`` is a record field of constructor ``C``.

   -  The record field ``f`` is in scope somehow (either qualified or
      unqualified).

   These rules restrict record wildcards to the situations in which the
   user could have written the expanded version. For example ::

       module M where
         data R = R { a,b,c :: Int }
       module X where
         import M( R(R,a,c) )
         f a b = R { .. }

   The ``R{..}`` expands to ``R{a=a}``, omitting ``b`` since the
   record field is not in scope, and omitting ``c`` since the variable
   ``c`` is not in scope (apart from the binding of the record selector
   ``c``, of course).

-  When record wildcards are use in record construction, a field ``f``
   is initialised only if ``f`` is in scope,
   and is not imported or bound at top level.
   For example, ``f`` can be bound by an enclosing pattern match or
   let/where-binding. For example ::

        module M where
          import A( a )

          data R = R { a,b,c,d :: Int }

          c = 3 :: Int

          f b = R { .. }  -- Expands to R { b = b, d = d }
            where
              d = b+1

   Here, ``a`` is imported, and ``c`` is bound at top level, so neither
   contribute to the expansion of the "``..``".
   The motivation here is that it should be
   easy for the reader to figure out what the "``..``" expands to.

-  Record wildcards cannot be used (a) in a record update construct, and
   (b) for data constructors that are not declared with record fields.
   For example: ::

       f x = x { v=True, .. }   -- Illegal (a)

       data T = MkT Int Bool
       g = MkT { .. }           -- Illegal (b)
       h (MkT { .. }) = True    -- Illegal (b)


.. _record-field-selector-polymorphism:

Record field selector polymorphism
----------------------------------

The module :base-ref:`GHC.Records.` defines the following: ::

  class HasField (x :: k) r a | x r -> a where
    getField :: r -> a

A ``HasField x r a`` constraint represents the fact that ``x`` is a
field of type ``a`` belonging to a record type ``r``.  The
``getField`` method gives the record selector function.

This allows definitions that are polymorphic over record types with a specified
field.  For example, the following works with any record type that has a field
``name :: String``: ::

  foo :: HasField "name" r String => r -> String
  foo r = reverse (getField @"name" r)

``HasField`` is a magic built-in typeclass (similar to ``Coercible``, for
example).  It is given special treatment by the constraint solver (see
:ref:`solving-hasfield-constraints`).  Users may define their own instances of
``HasField`` also (see :ref:`virtual-record-fields`).

.. _solving-hasfield-constraints:

Solving HasField constraints
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

If the constraint solver encounters a constraint ``HasField x r a``
where ``r`` is a concrete datatype with a field ``x`` in scope, it
will automatically solve the constraint using the field selector as
the dictionary, unifying ``a`` with the type of the field if
necessary.  This happens irrespective of which extensions are enabled.

For example, if the following datatype is in scope ::

  data Person = Person { name :: String }

the end result is rather like having an instance ::

  instance HasField "name" Person String where
    getField = name

except that this instance is not actually generated anywhere, rather
the constraint is solved directly by the constraint solver.

A field must be in scope for the corresponding ``HasField`` constraint
to be solved.  This retains the existing representation hiding
mechanism, whereby a module may choose not to export a field,
preventing client modules from accessing or updating it directly.

Solving ``HasField`` constraints depends on the field selector functions that
are generated for each datatype definition:

-  If a record field does not have a selector function because its type would allow
   an existential variable to escape, the corresponding ``HasField`` constraint
   will not be solved.  For example, ::

     {-# LANGUAGE ExistentialQuantification #-}
     data Exists t = forall x . MkExists { unExists :: t x }

   does not give rise to a selector ``unExists :: Exists t -> t x`` and we will not
   solve ``HasField "unExists" (Exists t) a`` automatically.

-  If a record field has a polymorphic type (and hence the selector function is
   higher-rank), the corresponding ``HasField`` constraint will not be solved,
   because doing so would violate the functional dependency on ``HasField`` and/or
   require impredicativity.  For example, ::

     {-# LANGUAGE RankNTypes #-}
     data Higher = MkHigher { unHigher :: forall t . t -> t }

   gives rise to a selector ``unHigher :: Higher -> (forall t . t -> t)`` but does
   not lead to solution of the constraint ``HasField "unHigher" Higher a``.

-  A record GADT may have a restricted type for a selector function, which may lead
   to additional unification when solving ``HasField`` constraints.  For example, ::

     {-# LANGUAGE GADTs #-}
     data Gadt t where
       MkGadt :: { unGadt :: Maybe v } -> Gadt [v]

   gives rise to a selector ``unGadt :: Gadt [v] -> Maybe v``, so the solver will reduce
   the constraint ``HasField "unGadt" (Gadt t) b`` by unifying ``t ~ [v]`` and
   ``b ~ Maybe v`` for some fresh metavariable ``v``, rather as if we had an instance ::

     instance (t ~ [v], b ~ Maybe v) => HasField "unGadt" (Gadt t) b

-  If a record type has an old-fashioned datatype context, the ``HasField``
   constraint will be reduced to solving the constraints from the context.
   For example, ::

     {-# LANGUAGE DatatypeContexts #-}
     data Eq a => Silly a = MkSilly { unSilly :: a }

   gives rise to a selector ``unSilly :: Eq a => Silly a -> a``, so
   the solver will reduce the constraint ``HasField "unSilly" (Silly a) b`` to
   ``Eq a`` (and unify ``a`` with ``b``), rather as if we had an instance ::

     instance (Eq a, a ~ b) => HasField "unSilly" (Silly a) b

.. _virtual-record-fields:

Virtual record fields
~~~~~~~~~~~~~~~~~~~~~

Users may define their own instances of ``HasField``, provided they do
not conflict with the built-in constraint solving behaviour.  This
allows "virtual" record fields to be defined for datatypes that do not
otherwise have them.

For example, this instance would make the ``name`` field of ``Person``
accessible using ``#fullname`` as well: ::

  instance HasField "fullname" Person String where
    getField = name

More substantially, an anonymous records library could provide
``HasField`` instances for its anonymous records, and thus be
compatible with the polymorphic record selectors introduced by this
proposal.  For example, something like this makes it possible to use
``getField`` to access ``Record`` values with the appropriate
string in the type-level list of fields: ::

  data Record (xs :: [(k, Type)]) where
    Nil  :: Record '[]
    Cons :: Proxy x -> a -> Record xs -> Record ('(x, a) ': xs)

  instance HasField x (Record ('(x, a) ': xs)) a where
    getField (Cons _ v _) = v
  instance HasField x (Record xs) a => HasField x (Record ('(y, b) ': xs)) a where
    getField (Cons _ _ r) = getField @x r

  r :: Record '[ '("name", String) ]
  r = Cons Proxy "R" Nil)

  x = getField @"name" r

Since representations such as this can support field labels with kinds other
than ``Symbol``, the ``HasField`` class is poly-kinded (even though the built-in
constraint solving works only at kind ``Symbol``).  In particular, this allows
users to declare scoped field labels such as in the following example: ::

  data PersonFields = Name

  s :: Record '[ '(Name, String) ]
  s = Cons Proxy "S" Nil

  y = getField @Name s

In order to avoid conflicting with the built-in constraint solving,
the following user-defined ``HasField`` instances are prohibited (in
addition to the usual rules, such as the prohibition on type
families appearing in instance heads):

-  ``HasField _ r _`` where ``r`` is a variable;

-  ``HasField _ (T ...) _`` if ``T`` is a data family (because it
   might have fields introduced later, using data instance declarations);

-  ``HasField x (T ...) _`` if ``x`` is a variable and ``T`` has any
   fields at all (but this instance is permitted if ``T`` has no fields);

-  ``HasField "foo" (T ...) _`` if ``T`` has a field ``foo`` (but this
   instance is permitted if it does not).

If a field has a higher-rank or existential type, the corresponding ``HasField``
constraint will not be solved automatically (as described above), but in the
interests of simplicity we do not permit users to define their own instances
either.  If a field is not in scope, the corresponding instance is still
prohibited, to avoid conflicts in downstream modules.


.. _deriving:

Extensions to the "deriving" mechanism
======================================

Haskell 98 allows the programmer to add a deriving clause to a data type
declaration, to generate a standard instance declaration for specified class.
GHC extends this mechanism along several axes:

* The derivation mechanism can be used separtely from the data type
  declaration, using the `standalone deriving mechanism
  <#stand-alone-deriving>`__.

* In Haskell 98, the only derivable classes are ``Eq``,
  ``Ord``, ``Enum``, ``Ix``, ``Bounded``, ``Read``, and ``Show``. `Various
  language extensions <#deriving-extra>`__ extend this list.

* Besides the stock approach to deriving instances by generating all method
  definitions, GHC supports two additional deriving strategies, which can
  derive arbitrary classes:

  * `Generalised newtype deriving <#newtype-deriving>`__ for newtypes and
  * `deriving any class <#derive-any-class>`__ using an empty instance
    declaration.

  The user can optionally declare the desired `deriving strategy
  <#deriving-stragies>`__, especially if the compiler chooses the wrong
  one `by default <#default-deriving-strategy>`__.

.. _empty-data-deriving:

Deriving instances for empty data types
---------------------------------------

.. ghc-flag:: -XEmptyDataDeriving
    :shortdesc: Allow deriving instances of standard type classes for
                empty data types.
    :type: dynamic
    :reverse: -XNoEmptyDataDeriving
    :category:

    :since: 8.4.1

    Allow deriving instances of standard type classes for empty data types.

One can write data types with no constructors using the
:ghc-flag:`-XEmptyDataDecls` flag (see :ref:`nullary-types`), which is on by
default in Haskell 2010. What is not on by default is the ability to derive
type class instances for these types. This ability is enabled through use of
the :ghc-flag:`-XEmptyDataDeriving` flag. For instance, this lets one write: ::

    data Empty deriving (Eq, Ord, Read, Show)

This would generate the following instances: ::

    instance Eq Empty where
      _ == _ = True

    instance Ord Empty where
      compare _ _ = EQ

    instance Read Empty where
      readPrec = pfail

    instance Show Empty where
      showsPrec _ x = case x of {}

The :ghc-flag:`-XEmptyDataDeriving` flag is only required to enable deriving
of these four "standard" type classes (which are mentioned in the Haskell
Report). Other extensions to the ``deriving`` mechanism, which are explained
below in greater detail, do not require :ghc-flag:`-XEmptyDataDeriving` to be
used in conjunction with empty data types. These include:

* :ghc-flag:`-XStandaloneDeriving` (see :ref:`stand-alone-deriving`)
* Type classes which require their own extensions to be enabled to be derived,
  such as :ghc-flag:`-XDeriveFunctor` (see :ref:`deriving-extra`)
* :ghc-flag:`-XDeriveAnyClass` (see :ref:`derive-any-class`)

.. _deriving-inferred:

Inferred context for deriving clauses
-------------------------------------

The Haskell Report is vague about exactly when a ``deriving`` clause is
legal. For example: ::

      data T0 f a = MkT0 a         deriving( Eq )
      data T1 f a = MkT1 (f a)     deriving( Eq )
      data T2 f a = MkT2 (f (f a)) deriving( Eq )

The natural generated ``Eq`` code would result in these instance
declarations: ::

      instance Eq a         => Eq (T0 f a) where ...
      instance Eq (f a)     => Eq (T1 f a) where ...
      instance Eq (f (f a)) => Eq (T2 f a) where ...

The first of these is obviously fine. The second is still fine, although
less obviously. The third is not Haskell 98, and risks losing
termination of instances.

GHC takes a conservative position: it accepts the first two, but not the
third. The rule is this: each constraint in the inferred instance
context must consist only of type variables, with no repetitions.

This rule is applied regardless of flags. If you want a more exotic
context, you can write it yourself, using the `standalone deriving
mechanism <#stand-alone-deriving>`__.

.. _stand-alone-deriving:

Stand-alone deriving declarations
---------------------------------

.. extension:: StandaloneDeriving
    :shortdesc: Enable standalone deriving.

    :since: 6.8.1

    Allow the use of stand-alone ``deriving`` declarations.

GHC allows stand-alone ``deriving`` declarations, enabled by
:extension:`StandaloneDeriving`: ::

      data Foo a = Bar a | Baz String

      deriving instance Eq a => Eq (Foo a)

The syntax is identical to that of an ordinary instance declaration
apart from (a) the keyword ``deriving``, and (b) the absence of the
``where`` part.

However, standalone deriving differs from a ``deriving`` clause in a
number of important ways:

-  The standalone deriving declaration does not need to be in the same
   module as the data type declaration. (But be aware of the dangers of
   orphan instances (:ref:`orphan-modules`).

-  In most cases, you must supply an explicit context (in the example the
   context is ``(Eq a)``), exactly as you would in an ordinary instance
   declaration. (In contrast, in a ``deriving`` clause attached to a
   data type declaration, the context is inferred.)

   The exception to this rule is that the context of a standalone deriving
   declaration can infer its context when a single, extra-wildcards constraint
   is used as the context, such as in: ::

         deriving instance _ => Eq (Foo a)

   This is essentially the same as if you had written ``deriving Foo`` after
   the declaration for ``data Foo a``. Using this feature requires the use of
   :extension:`PartialTypeSignatures` (:ref:`partial-type-signatures`).

-  Unlike a ``deriving`` declaration attached to a ``data`` declaration,
   the instance can be more specific than the data type (assuming you
   also use :extension:`FlexibleInstances`, :ref:`instance-rules`). Consider
   for example ::

         data Foo a = Bar a | Baz String

         deriving instance Eq a => Eq (Foo [a])
         deriving instance Eq a => Eq (Foo (Maybe a))

   This will generate a derived instance for ``(Foo [a])`` and
   ``(Foo (Maybe a))``, but other types such as ``(Foo (Int,Bool))``
   will not be an instance of ``Eq``.

-  Unlike a ``deriving`` declaration attached to a ``data`` declaration,
   GHC does not restrict the form of the data type. Instead, GHC simply
   generates the appropriate boilerplate code for the specified class,
   and typechecks it. If there is a type error, it is your problem. (GHC
   will show you the offending code if it has a type error.)

   The merit of this is that you can derive instances for GADTs and
   other exotic data types, providing only that the boilerplate code
   does indeed typecheck. For example: ::

         data T a where
            T1 :: T Int
            T2 :: T Bool

         deriving instance Show (T a)

   In this example, you cannot say ``... deriving( Show )`` on the data
   type declaration for ``T``, because ``T`` is a GADT, but you *can*
   generate the instance declaration using stand-alone deriving.

   The down-side is that, if the boilerplate code fails to typecheck,
   you will get an error message about that code, which you did not
   write. Whereas, with a ``deriving`` clause the side-conditions are
   necessarily more conservative, but any error message may be more
   comprehensible.

-  Under most circumstances, you cannot use standalone deriving to create an
   instance for a data type whose constructors are not all in scope. This is
   because the derived instance would generate code that uses the constructors
   behind the scenes, which would break abstraction.

   The one exception to this rule is :extension:`DeriveAnyClass`, since
   deriving an instance via :extension:`DeriveAnyClass` simply generates
   an empty instance declaration, which does not require the use of any
   constructors. See the `deriving any class <#derive-any-class>`__ section
   for more details.

In other ways, however, a standalone deriving obeys the same rules as
ordinary deriving:

-  A ``deriving instance`` declaration must obey the same rules
   concerning form and termination as ordinary instance declarations,
   controlled by the same flags; see :ref:`instance-decls`.

-  The stand-alone syntax is generalised for newtypes in exactly the
   same way that ordinary ``deriving`` clauses are generalised
   (:ref:`newtype-deriving`). For example: ::

         newtype Foo a = MkFoo (State Int a)

         deriving instance MonadState Int Foo

   GHC always treats the *last* parameter of the instance (``Foo`` in
   this example) as the type whose instance is being derived.

.. _deriving-extra:

Deriving instances of extra classes (``Data``, etc.)
----------------------------------------------------

Haskell 98 allows the programmer to add "``deriving( Eq, Ord )``" to a
data type declaration, to generate a standard instance declaration for
classes specified in the ``deriving`` clause. In Haskell 98, the only
classes that may appear in the ``deriving`` clause are the standard
classes ``Eq``, ``Ord``, ``Enum``, ``Ix``, ``Bounded``, ``Read``, and
``Show``.

GHC extends this list with several more classes that may be
automatically derived:

-  With :extension:`DeriveGeneric`, you can derive instances of the classes
   ``Generic`` and ``Generic1``, defined in ``GHC.Generics``. You can
   use these to define generic functions, as described in
   :ref:`generic-programming`.

-  With :extension:`DeriveFunctor`, you can derive instances of the class
   ``Functor``, defined in ``GHC.Base``.

-  With :extension:`DeriveDataTypeable`, you can derive instances of the class
   ``Data``, defined in ``Data.Data``.

-  With :extension:`DeriveFoldable`, you can derive instances of the class
   ``Foldable``, defined in ``Data.Foldable``.

-  With :extension:`DeriveTraversable`, you can derive instances of the class
   ``Traversable``, defined in ``Data.Traversable``. Since the
   ``Traversable`` instance dictates the instances of ``Functor`` and
   ``Foldable``, you'll probably want to derive them too, so
   :extension:`DeriveTraversable` implies :extension:`DeriveFunctor` and
   :extension:`DeriveFoldable`.

-  With :extension:`DeriveLift`, you can derive instances of the class ``Lift``,
   defined in the ``Language.Haskell.TH.Syntax`` module of the
   ``template-haskell`` package.

You can also use a standalone deriving declaration instead (see
:ref:`stand-alone-deriving`).

In each case the appropriate class must be in scope before it can be
mentioned in the ``deriving`` clause.

.. _deriving-functor:

Deriving ``Functor`` instances
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. extension:: DeriveFunctor
    :shortdesc: Enable deriving for the Functor class.
        Implied by :extension:`DeriveTraversable`.

    :since: 7.10.1

    Allow automatic deriving of instances for the ``Functor`` typeclass.


With :extension:`DeriveFunctor`, one can derive ``Functor`` instances for data types
of kind ``Type -> Type``. For example, this declaration::

    data Example a = Ex a Char (Example a) (Example Char)
      deriving Functor

would generate the following instance: ::

    instance Functor Example where
      fmap f (Ex a1 a2 a3 a4) = Ex (f a1) a2 (fmap f a3) a4

The basic algorithm for :extension:`DeriveFunctor` walks the arguments of each
constructor of a data type, applying a mapping function depending on the type
of each argument. If a plain type variable is found that is syntactically
equivalent to the last type parameter of the data type (``a`` in the above
example), then we apply the function ``f`` directly to it. If a type is
encountered that is not syntactically equivalent to the last type parameter
*but does mention* the last type parameter somewhere in it, then a recursive
call to ``fmap`` is made. If a type is found which doesn't mention the last
type parameter at all, then it is left alone.

The second of those cases, in which a type is unequal to the type parameter but
does contain the type parameter, can be surprisingly tricky. For example, the
following example compiles::

    newtype Right a = Right (Either Int a) deriving Functor

Modifying the code slightly, however, produces code which will not compile::

    newtype Wrong a = Wrong (Either a Int) deriving Functor

The difference involves the placement of the last type parameter, ``a``. In the
``Right`` case, ``a`` occurs within the type ``Either Int a``, and moreover, it
appears as the last type argument of ``Either``. In the ``Wrong`` case,
however, ``a`` is not the last type argument to ``Either``; rather, ``Int`` is.

This distinction is important because of the way :extension:`DeriveFunctor` works. The
derived ``Functor Right`` instance would be::

    instance Functor Right where
      fmap f (Right a) = Right (fmap f a)

Given a value of type ``Right a``, GHC must produce a value of type
``Right b``. Since the argument to the ``Right`` constructor has type
``Either Int a``, the code recursively calls ``fmap`` on it to produce a value
of type ``Either Int b``, which is used in turn to construct a final value of
type ``Right b``.

The generated code for the ``Functor Wrong`` instance would look exactly the
same, except with ``Wrong`` replacing every occurrence of ``Right``. The
problem is now that ``fmap`` is being applied recursively to a value of type
``Either a Int``. This cannot possibly produce a value of type
``Either b Int``, as ``fmap`` can only change the last type parameter! This
causes the generated code to be ill-typed.

As a general rule, if a data type has a derived ``Functor`` instance and its
last type parameter occurs on the right-hand side of the data declaration, then
either it must (1) occur bare (e.g., ``newtype Id a = Id a``), or (2) occur as the
last argument of a type constructor (as in ``Right`` above).

There are two exceptions to this rule:

#. Tuple types. When a non-unit tuple is used on the right-hand side of a data
   declaration, :extension:`DeriveFunctor` treats it as a product of distinct types.
   In other words, the following code::

       new