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.. 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 option flags 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`).


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

    .. include:: what_glasgow_exts_does.gen.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.
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.. _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.html>`. (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
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you need the :ghc-flag:`-XMagicHash` extension (:ref:`magic-hash`).
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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.
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(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.)
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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
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object. Examples include ``Array#``, the type of primitive arrays. Thus,
``Array#`` is an unlifted, boxed type. A
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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:
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no unevaluated thunks, no indirections. Nothing can be at the other end
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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.

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Unboxed type kinds
------------------
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Because unboxed types are represented without the use of pointers, we
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cannot store them in use a polymorphic datatype at an unboxed type.
For example, the ``Just`` node
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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 ``*`` is the kind of ordinary datatypes,
such as ``Int``. Furthermore, type constructors can have kinds with arrows;
for example, ``Maybe`` has kind ``* -> *``. 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
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floating point. In constrast, the kind ``*`` is actually just a synonym
for ``TYPE 'PtrRepLifted``. More details of the ``TYPE`` mechanisms appear in
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the `section on runtime representation polymorphism <#runtime-rep>`__.

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Given that ``Int#``'s kind is not ``*``, it then it follows that
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``Maybe Int#`` is disallowed. Similarly, because type variables tend
to be of kind ``*`` (for example, in ``(.) :: (b -> c) -> (a -> b) -> a -> c``,
all the type variables have kind ``*``), 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:
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-  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. 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
--------------

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.. ghc-flag:: -XUnboxedTuples
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    Enable the use of unboxed tuple syntax.

Unboxed tuples aren't really exported by ``GHC.Exts``; they are a
syntactic extension enabled by the language flag :ghc-flag:`-XUnboxedTuples`. An
unboxed tuple looks like this: ::
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    (# 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:

-  Values of unboxed tuple types are subject to the same restrictions as
   other unboxed types; i.e. they may not be stored in polymorphic data
   structures or passed to polymorphic functions.

-  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.

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.. _unboxed-sums:

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

.. ghc-flag:: -XUnboxedSums

    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 tuple
and sums).

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

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

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

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

    (# | True #) -- second alternative

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. Code generator tries to generate as compact layout as possible.
In the best case, size of an unboxed sum is size of its biggest alternative +
one word (for tag). The algorithm for generating 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. E.g. say two alternatives have these fields: ::

    Word32, String, Float#
    Float#, Float#, Maybe Int

  Final layout will be something like ::

    Int32, Float32, Float32, Word32, Pointer

  First `Int32` is for the tag. It has 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, and second alternative
  needs two `Float32` fields. `Word32` field is for the `Word32` in the first
  alternative. `Pointer` field is shared between `String` and `Maybe Int` values
  of the alternatives.

  In the case of enumeration types (like `Bool`), the unboxed sum layout only
  has an `Int32` field (i.e. the whole thing is represented by an integer).

In the example above, a value of this type is thus represented as 5 values. As
an another example, this is the layout for unboxed version of `Maybe a` type: ::

    Int32, Pointer

The `Pointer` field is not used when tag says that it's `Nothing`. Otherwise
`Pointer` points to the value in `Just`.

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.. _syntax-extns:

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

.. _unicode-syntax:

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

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.. ghc-flag:: -XUnicodeSyntax

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

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

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+--------------+---------------+-------------+-----------------------------------------+
| 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 |
+--------------+---------------+-------------+-----------------------------------------+
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.. _magic-hash:

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

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.. ghc-flag:: -XMagicHash

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

The language extension :ghc-flag:`-XMagicHash` allows ``#`` as a postfix modifier
to identifiers. Thus, ``x#`` is a valid variable, and ``T#`` is a valid type
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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
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variables. Nor does the :ghc-flag:`-XMagicHash` extension bring anything into
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scope. For example, to bring ``Int#`` into scope you must import
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``GHC.Prim`` (see :ref:`primitives`); the :ghc-flag:`-XMagicHash` extension then
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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``.

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The :ghc-flag:`-XMagicHash` also enables some new forms of literals (see
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: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
-----------------

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.. ghc-flag:: -XNegativeLiterals

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    :since: 7.8.1

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    Enable the use of un-parenthesized negative numeric literals.

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

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.. ghc-flag:: -XNumDecimals

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    :since: 7.8.1

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

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

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

.. _binary-literals:

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

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.. ghc-flag:: -XBinaryLiterals

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    :since: 7.10.1

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    Allow the use of binary notation in integer literals.

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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``).

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The language extension :ghc-flag:`-XBinaryLiterals` 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 :ghc-flag:`-XBinaryLiterals` is enabled.
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.. _pattern-guards:

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

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.. ghc-flag:: -XNoPatternGuards
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    :implied by: :ghc-flag:`-XHaskell98`
    :since: 6.8.1

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

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

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.. ghc-flag:: -XViewPatterns

    Allow use of view pattern syntax.

View patterns are enabled by the flag :ghc-flag:`-XViewPatterns`. More
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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
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language as follows: ::
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    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).
Rik Steenkamp's avatar
Rik Steenkamp committed
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Without view patterns, using this signature is a little inconvenient: ::
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    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
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matching against the result: ::
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    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
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   :ref:`pattern-guards` can be written using view patterns as follows: ::
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       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
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      view pattern expression are in scope. For example: ::
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          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
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      in later arguments: ::
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          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
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      allowed: ::
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          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
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   Report <http://www.haskell.org/onlinereport/>`__, add the following: ::
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       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.

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.. _n-k-patterns:
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n+k patterns
------------
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.. ghc-flag:: -XNPlusKPatterns
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    :implied by: :ghc-flag:`-XHaskell98`
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    :since: 6.12

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    Enable use of ``n+k`` patterns.
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.. _recursive-do-notation:
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The recursive do-notation
-------------------------
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.. ghc-flag:: -XRecursiveDo
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    Allow the use of recursive ``do`` notation.
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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.
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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: ::
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    class Monad m => MonadFix m where
       mfix :: (a -> m a) -> m a
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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.
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For monads that do belong to the ``MonadFix`` class, GHC provides an
extended version of the do-notation that allows recursive bindings. The
:ghc-flag:`-XRecursiveDo` (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*.
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Here is a simple (albeit contrived) example:
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::
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    {-# LANGUAGE RecursiveDo #-}
    justOnes = mdo { xs <- Just (1:xs)
                   ; return (map negate xs) }
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or equivalently
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::
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    {-# LANGUAGE RecursiveDo #-}
    justOnes = do { rec { xs <- Just (1:xs) }
                  ; return (map negate xs) }
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As you can guess ``justOnes`` will evaluate to ``Just [-1,-1,-1,...``.
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GHC's implementation the mdo-notation closely follows the original
translation as described in the paper `A recursive do for
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Haskell <http://leventerkok.github.io/papers/recdo.pdf>`__, which
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in turn is based on the work `Value Recursion in Monadic
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Computations <http://leventerkok.github.io/papers/erkok-thesis.pdf>`__.
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Furthermore, GHC extends the syntax described in the former paper with a
lower level syntax flagged by the ``rec`` keyword, as we describe next.
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Recursive binding groups
~~~~~~~~~~~~~~~~~~~~~~~~
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The flag :ghc-flag:`-XRecursiveDo` 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
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::
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        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) }
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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.)
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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:
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::

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

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    vs <- mfix (\ ~vs -> do { ss; return vs })
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where ``vs`` is a tuple of the variables bound by ``ss``.
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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.
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The ``mdo`` notation
~~~~~~~~~~~~~~~~~~~~
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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
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Haskell <http://leventerkok.github.io/papers/recdo.pdf>`__.
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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
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Computations <http://leventerkok.github.io/papers/erkok-thesis.pdf>`__.)
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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.
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The definition is syntactic:
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-  A generator ⟨g⟩ *depends* on a textually following generator ⟨g'⟩, if
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   -  ⟨g'⟩ defines a variable that is used by ⟨g⟩, or
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   -  ⟨g'⟩ textually appears between ⟨g⟩ and ⟨g''⟩, where ⟨g⟩ depends on
      ⟨g''⟩.
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-  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.
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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.
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Here is an example ``mdo``-expression, and its translation to ``rec``
blocks:
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::
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    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 }
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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.
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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.
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Here are some other important points in using the recursive-do notation:
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-  It is enabled with the flag :ghc-flag:`-XRecursiveDo`, or the
   ``LANGUAGE RecursiveDo`` pragma. (The same flag enables both
   ``mdo``-notation, and the use of ``rec`` blocks inside ``do``
   expressions.)
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-  ``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.
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-  If recursive bindings are required for a monad, then that monad must
   be declared an instance of the ``MonadFix`` class.
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-  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).
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-  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.)
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.. _applicative-do:
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Applicative do-notation
-----------------------
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.. index::
   single: Applicative do-notation
   single: do-notation; Applicative
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.. ghc-flag:: -XApplicativeDo
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    :since: 8.0.1
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    Allow use of ``Applicative`` ``do`` notation.
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The language option :ghc-flag:`-XApplicativeDo` enables an alternative translation for
the do-notation, which uses the operators ``<$>``, ``<*>``, along with ``join``
as far as possible. There are two main reasons for wanting to do this:
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-  We can use do-notation with types that are an instance of ``Applicative`` and
   ``Functor``, but not ``Monad``
-  In some monads, using the applicative operators is more efficient than monadic
   bind. For example, it may enable more parallelism.
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Applicative do-notation desugaring preserves the original semantics, provided
that the ``Applicative`` instance satisfies ``<*> = ap`` and ``pure = return``
(these are true of all the common monadic types). Thus, you can normally turn on
:ghc-flag:`-XApplicativeDo` without fear of breaking your program. There is one pitfall
to watch out for; see :ref:`applicative-do-pitfall`.
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There are no syntactic changes with :ghc-flag:`-XApplicativeDo`. The only way it shows
up at the source level is that you can have a ``do`` expression that doesn't
require a ``Monad`` constraint. For example, in GHCi: ::
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    Prelude> :set -XApplicativeDo
    Prelude> :t \m -> do { x <- m; return (not x) }
    \m -> do { x <- m; return (not x) }
      :: Functor f => f Bool -> f Bool
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This example only requires ``Functor``, because it is translated into ``(\x ->
not x) <$> m``. A more complex example requires ``Applicative``, ::
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    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
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Here GHC has translated the expression into ::
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    (\x y -> x || y) <$> m 'a' <*> m 'b'
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It is possible to see the actual translation by using :ghc-flag:`-ddump-ds`, but be
warned, the output is quite verbose.
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Note that if the expression can't be translated into uses of ``<$>``, ``<*>``
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: ::
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    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
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Here, ``m x`` depends on the value of ``x`` produced by the first statement, so
the expression cannot be translated using ``<*>``.
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In general, the rule for when a ``do`` statement incurs a ``Monad`` constraint
is as follows. If the do-expression has the following form: ::
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    do p1 <- E1; ...; pn <- En; return E
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where none of the variables defined by ``p1...pn`` are mentioned in ``E1...En``,
then the expression will only require ``Applicative``. Otherwise, the expression
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will require ``Monad``. The block may return a pure expression ``E`` depending
upon the results ``p1...pn`` with either ``return`` or ``pure``.
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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.
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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

    :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)``.
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.. _applicative-do-pitfall:
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Things to watch out for
~~~~~~~~~~~~~~~~~~~~~~~
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Your code should just work as before when :ghc-flag:`-XApplicativeDo` 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: ::
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    instance Functor MyType where
        fmap f m = do x <- m; return (f x)
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Then applicative desugaring will turn it into ::
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    instance Functor MyType where
        fmap f m = fmap (\x -> f x) m
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And the program will loop at runtime. Similarly, an ``Applicative`` instance
like this ::
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    instance Applicative MyType where
        pure = return
        x <*> y = do f <- x; a <- y; return (f a)
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will result in an infinte loop when ``<*>`` is called.
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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. ::
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    instance Functor MyType where
        fmap f m = m >>= return . f
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    instance Applicative MyType where
        pure = return
        (<*>) = ap
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.. _parallel-list-comprehensions:
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Parallel List Comprehensions
----------------------------
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.. index::
   single: list comprehensions; parallel
   single: parallel list comprehensions
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.. ghc-flag:: -XParallelListComp
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    Allow parallel list comprehension syntax.
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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.
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A parallel list comprehension has multiple independent branches of
qualifier lists, each separated by a ``|`` symbol. For example, the
following zips together two lists: ::
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       [ (x, y) | x <- xs | y <- ys ]
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The behaviour of parallel list comprehensions follows that of zip, in
that the resulting list will have the same length as the shortest
branch.
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We can define parallel list comprehensions by translation to regular
comprehensions. Here's the basic idea:
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Given a parallel comprehension of the form: ::
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       [ e | p1 <- e11, p2 <- e12, ...
           | q1 <- e21, q2 <- e22, ...
           ...
       ]
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This will be translated to: ::
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       [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
                                             [(q1,q2) | q1 <- e21, q2 <- e22, ...]
                                             ...
       ]
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where ``zipN`` is the appropriate zip for the given number of branches.
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.. _generalised-list-comprehensions:
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Generalised (SQL-like) List Comprehensions
------------------------------------------
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.. index::
   single: list comprehensions; generalised
   single: extended list comprehensions
   single: group
   single: SQL
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.. ghc-flag:: -XTransformListComp
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    Allow use of generalised list (SQL-like) comprehension syntax. This
    introduces the ``group``, ``by``, and ``using`` keywords.
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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" <http://research.microsoft.com/~simonpj/papers/list-comp>`__,
except that the syntax we use differs slightly from the paper.
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The extension is enabled with the flag :ghc-flag:`-XTransformListComp`.
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Here is an example:
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::
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    employees = [ ("Simon", "MS", 80)
                , ("Erik", "MS", 100)
                , ("Phil", "Ed", 40)
                , ("Gordon", "Ed", 45)
                , ("Paul", "Yale", 60) ]
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    output = [ (the dept, sum salary)
             | (name, dept, salary) <- employees
             , then group by dept using groupWith
             , then sortWith by (sum salary)
             , then take 5 ]
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In this example, the list ``output`` would take on the value:
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::
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    [("Yale", 60), ("Ed", 85), ("MS", 180)]
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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``.)
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There are five new forms of comprehension qualifier, all introduced by
the (existing) keyword ``then``:
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-  ::
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       then f
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   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
   .
-  ::
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       then f by e
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   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.
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   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.
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-  ::
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       then group by e using f
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   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:
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   ::
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       -- 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)
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       output = [ (the x, y)
       | x <- ([1..3] ++ [1..2])
       , y <- [4..6]
       , then group by x using groupRuns ]
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   This results in the variable ``output`` taking on the value below:
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   ::
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       [(1, [4, 5, 6]), (2, [4, 5, 6]), (3, [4, 5, 6]), (1, [4, 5, 6]), (2, [4, 5, 6])]
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   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.
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