7.3. Syntactic extensions
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## 7.3. Syntactic extensions

### 7.3.1. Unicode syntax

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

ASCII | Unicode alternative | Code point | Name
--- | --- | --- | ---
`::` | :: | 0x2237 | PROPORTION
`=>` | ⇒ | 0x21D2 | RIGHTWARDS DOUBLE ARROW
`forall` | ∀ | 0x2200 | FOR ALL
`->` | → | 0x2192 | RIGHTWARDS ARROW
`<-` | ← | 0x2190 | LEFTWARDS ARROW
-< | ↢ | 0x2919 | LEFTWARDS ARROW-TAIL
>- | ↣ | 0x291A | RIGHTWARDS ARROW-TAIL
-<< |  | 0x291B | LEFTWARDS DOUBLE ARROW-TAIL
>>- |  | 0x291C | RIGHTWARDS DOUBLE ARROW-TAIL
* | ★ | 0x2605 | BLACK STAR

### 7.3.2. The magic hash

The language extension `-XMagicHash` 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 `-XMagicHash` extension bring anything into scope. For example, to bring `Int#` into scope you must import `GHC.Prim` (see Section 7.2, “Unboxed types and primitive operations”); the `-XMagicHash` 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 `-XMagicHash` also enables some new forms of literals (see Section 7.2.1, “Unboxed types”):

- `'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#`

### 7.3.3. Negative literals

The literal `-123` is, according to Haskell98 and Haskell 2010, desugared as `negate (fromInteger 123)`. The language extension `-XNegativeLiterals` 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.

### 7.3.4. Fractional looking integer literals

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

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

### 7.3.5. Hierarchical Modules

GHC supports a small extension to the syntax of module names: a module name is allowed to contain a dot `‘.’`. This is also known as the “hierarchical module namespace” extension, because it extends the normally flat Haskell module namespace into a more flexible hierarchy of modules.

This extension has very little impact on the language itself; modules names are always fully qualified, so you can just think of the fully qualified module name as “the module name”. In particular, this means that the full module name must be given after the `module` keyword at the beginning of the module; for example, the module `A.B.C` must begin

    module A.B.C

It is a common strategy to use the `as` keyword to save some typing when using qualified names with hierarchical modules. For example:

    import qualified Control.Monad.ST.Strict as ST

For details on how GHC searches for source and interface files in the presence of hierarchical modules, see Section 4.7.3, “The search path”.

GHC comes with a large collection of libraries arranged hierarchically; see the accompanying library documentation. More libraries to install are available from HackageDB.

### 7.3.6. Pattern guards

The discussion that follows is an abbreviated version of Simon Peyton Jones's original proposal. (Note that the proposal was written before pattern guards were implemented, so refers to them as unimplemented.)

Suppose we have an abstract data type of finite maps, with a lookup operation:

    lookup :: FiniteMap -> Int -> Maybe Int

The lookup returns `Nothing` if the supplied key is not in the domain of the mapping, and `(Just v)` otherwise, where `v` is the value that the key maps to. Now consider the following definition:

    clunky env var1 var2 | ok1 && ok2 = val1 + val2
    | otherwise  = var1 + var2
    where
      m1 = lookup env var1
      m2 = lookup env var2
      ok1 = maybeToBool m1
      ok2 = maybeToBool m2
      val1 = expectJust m1
      val2 = expectJust m2

The auxiliary functions are

    maybeToBool :: Maybe a -> Bool
    maybeToBool (Just x) = True
    maybeToBool Nothing  = False

    expectJust :: Maybe a -> a
    expectJust (Just x) = x
    expectJust Nothing  = error "Unexpected Nothing"

What is `clunky` doing? The guard `ok1 && ok2` checks that both lookups succeed, using `maybeToBool` to convert the `Maybe` types to booleans. The (lazily evaluated) `expectJust` calls extract the values from the results of the lookups, and binds the returned values to `val1` and `val2` respectively. If either lookup fails, then clunky takes the `otherwise` case and returns the sum of its arguments.

This is certainly legal Haskell, but it is a tremendously verbose and un-obvious way to achieve the desired effect. Arguably, a more direct way to write clunky would be to use case expressions:

    clunky env var1 var2 = case lookup env var1 of
      Nothing -> fail
      Just val1 -> case lookup env var2 of
        Nothing -> fail
        Just val2 -> val1 + val2
    where
      fail = var1 + var2

This is a bit shorter, but hardly better. Of course, we can rewrite any set of pattern-matching, guarded equations as case expressions; that is precisely what the compiler does when compiling equations! The reason that Haskell provides guarded equations is because they allow us to write down the cases we want to consider, one at a time, independently of each other. This structure is hidden in the case version. Two of the right-hand sides are really the same (`fail`), and the whole expression tends to become more and more indented.

Here is how I would write clunky:

    clunky env var1 var2
      | Just val1 <- lookup env var1
      , Just val2 <- lookup env var2
      = val1 + val2
    ...other equations for clunky...

The semantics should be clear enough. The qualifiers are matched in order. For a `<-` qualifier, which I call a pattern guard, the right hand side is evaluated and matched against the pattern on the left. If the match fails then the whole guard fails and the next equation is tried. If it succeeds, then the appropriate binding takes place, and the next qualifier is matched, in the augmented environment. Unlike list comprehensions, however, the type of the expression to the right of the `<-` is the same as the type of the pattern to its left. The bindings introduced by pattern guards scope over all the remaining guard qualifiers, and over the right hand side of the equation.

Just as with list comprehensions, boolean expressions can be freely mixed with among the pattern guards. For example:

    f x | [y] <- x
        , y > 3
        , Just z <- h y
        = ...

Haskell's current guards therefore emerge as a special case, in which the qualifier list has just one element, a boolean expression.

### 7.3.7. View patterns

View patterns are enabled by the flag `-XViewPatterns`. More information and examples of view patterns can be found on the Wiki page.

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 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 Section 7.3.6, “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 Trac #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, 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. 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.

### 7.3.8. Pattern synonyms

Pattern synonyms are enabled by the flag `-XPatternSynonyms`, which is required for both defining them and using them. More information and examples of view patterns can be found on the Wiki page.

Pattern synonyms enable giving names to parametrized pattern schemes. They can also be thought of as abstract constructors that don't have a bearing on data representation. For example, in a programming language implementation, we might represent types of the language as follows:

    data Type = App String [Type]

Here are some examples of using said representation. Consider a few types of the `Type` universe encoded like this:

      App "->" [t1, t2]          -- t1 -> t2
      App "Int" []               -- Int
      App "Maybe" [App "Int" []] -- Maybe Int

This representation is very generic in that no types are given special treatment. However, some functions might need to handle some known types specially, for example the following two functions collect all argument types of (nested) arrow types, and recognize the `Int` type, respectively:

      collectArgs :: Type -> [Type]
      collectArgs (App "->" [t1, t2]) = t1 : collectArgs t2
      collectArgs _                   = []

      isInt :: Type -> Bool
      isInt (App "Int" []) = True
      isInt _              = False

Matching on `App` directly is both hard to read and error prone to write. And the situation is even worse when the matching is nested:

      isIntEndo :: Type -> Bool
      isIntEndo (App "->" [App "Int" [], App "Int" []]) = True
      isIntEndo _                                       = False

Pattern synonyms permit abstracting from the representation to expose matchers that behave in a constructor-like manner with respect to pattern matching. We can create pattern synonyms for the known types we care about, without committing the representation to them (note that these don't have to be defined in the same module as the `Type` type):

      pattern Arrow t1 t2 = App "->"    [t1, t2]
      pattern Int         = App "Int"   []
      pattern Maybe t     = App "Maybe" [t]

Which enables us to rewrite our functions in a much cleaner style:

      collectArgs :: Type -> [Type]
      collectArgs (Arrow t1 t2) = t1 : collectArgs t2
      collectArgs _             = []

      isInt :: Type -> Bool
      isInt Int = True
      isInt _   = False

      isIntEndo :: Type -> Bool
      isIntEndo (Arrow Int Int) = True
      isIntEndo _               = False

Note that in this example, the pattern synonyms `Int` and `Arrow` can also be used as expressions (they are bidirectional). This is not necessarily the case: unidirectional pattern synonyms can also be declared with the following syntax:

      pattern Head x <- x:xs

In this case, `Head` `x` cannot be used in expressions, only patterns, since it wouldn't specify a value for the `xs` on the right-hand side.

The semantics of a unidirectional pattern synonym declaration and usage are as follows:

- Syntax:

  A pattern synonym declaration can be either unidirectional or bidirectional. The syntax for unidirectional pattern synonyms is:

        pattern Name args <- pat

  and the syntax for bidirectional pattern synonyms is:

        pattern Name args = pat

  Pattern synonym declarations can only occur in the top level of a module. In particular, they are not allowed as local definitions. Currently, they also don't work in GHCi, but that is a technical restriction that will be lifted in later versions.

  The name of the pattern synonym itself is in the same namespace as proper data constructors. Either prefix or infix syntax can be used. In export/import specifications, you have to prefix pattern names with the `pattern` keyword, e.g.:

        module Example (pattern Single) where
        pattern Single x = [x]

- Scoping:

  The variables in the left-hand side of the definition are bound by the pattern on the right-hand side. For bidirectional pattern synonyms, all the variables of the right-hand side must also occur on the left-hand side; also, wildcard patterns and view patterns are not allowed. For unidirectional pattern synonyms, there is no restriction on the right-hand side pattern.

  Pattern synonyms cannot be defined recursively.

- Typing:

  Given a pattern synonym definition of the form

        pattern P var1 var2 ... varN <- pat

  it is assigned a pattern type of the form

        pattern CProv => P t1 t2 ... tN :: CReq => t

  where `CProv` and `CReq` are type contexts, and `t1`, `t2`, ..., `tN` and `t` are types.

  A pattern synonym of this type can be used in a pattern if the instatiated (monomorphic) type satisfies the constraints of `CReq`. In this case, it extends the context available in the right-hand side of the match with `CProv`, just like how an existentially-typed data constructor can extend the context.

  For example, in the following program:

      {-# LANGUAGE PatternSynonyms, GADTs #-}
      module ShouldCompile where

      data T a where
      	MkT :: (Show b) => a -> b -> T a

      pattern ExNumPat x = MkT 42 x

  the pattern type of `ExNumPat` is

      pattern (Show b) => ExNumPat b :: (Num a, Eq a) => T a

  and so can be used in a function definition like the following:

        f :: (Num t, Eq t) => T t -> String
        f (ExNumPat x) = show x

  For bidirectional pattern synonyms, uses as expressions have the type

        (CProv, CReq) => t1 -> t2 -> ... -> tN -> t

  So in the previous example, `ExNumPat`, when used in an expression, has type

        ExNumPat :: (Show b, Num a, Eq a) => b -> T t

- Matching:

  A pattern synonym occurrence in a pattern is evaluated by first matching against the pattern synonym itself, and then on the argument patterns. For example, in the following program, `f` and `f'` are equivalent:

      pattern Pair x y <- [x, y]

      f (Pair True True) = True
      f _                = False

      f' [x, y] | True <- x, True <- y = True
      f' _                                   = False

  Note that the strictness of `f` differs from that of `g` defined below:

      g [True, True] = True
      g _            = False

      *Main> f (False:undefined)
      *** Exception: Prelude.undefined
      *Main> g (False:undefined)
      False

### 7.3.9. n+k patterns

`n+k` pattern support is disabled by default. To enable it, you can use the `-XNPlusKPatterns` flag.

### 7.3.10. Traditional record syntax

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

### 7.3.11. The 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 `-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.

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, which in turn is based on the work Value Recursion in Monadic Computations. Furthermore, GHC extends the syntax described in the former paper with a lower level syntax flagged by the `rec` keyword, as we describe next.

#### 7.3.11.1. Recursive binding groups

The 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

        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.

#### 7.3.11.2. 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 Secton 3.2 of A recursive do for Haskell. 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.)

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 flag `-XRecursiveDo`, or the `LANGUAGE RecursiveDo` pragma. (The same flag 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.)

### 7.3.12. Parallel List Comprehensions

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.

### 7.3.13. Generalised (SQL-Like) List Comprehensions

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", except that the syntax we use differs slightly from the paper.

The extension is enabled with the flag `-XTransformListComp`.

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",...]

### 7.3.14. Monad comprehensions

Monad comprehensions generalise the list comprehension notation, including parallel comprehensions (Section 7.3.12, “Parallel List Comprehensions”) and transform comprehensions (Section 7.3.13, “Generalised (SQL-Like) 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 `-XTransformListComp`):

      [ 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 `-XTransformListComp`):

      [ 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 `-XParallelListComp`):

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

  Parallel statements are translated using the `mzip` function, which requires a `MonadZip` instance defined in `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 `MonadComprehensions` extension is enabled. The types and more detailed examples on how to use comprehensions are explained in the previous chapters Section 7.3.13, “Generalised (SQL-Like) List Comprehensions” and Section 7.3.12, “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 `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]`:

    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.

Monad comprehensions support rebindable syntax (Section 7.3.15, “Rebindable syntax and the implicit Prelude import”). 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.

### 7.3.15. Rebindable syntax and the implicit Prelude import

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.)

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 `-XRebindableSyntax` flag 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 handed in just the same way, except that the translation is `fromRational (3.68::Rational)`.

- 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 (Section 7.3.11, “The recursive do-notation ”), and parallel array comprehensions, are unaffected.

- Arrow notation (see Section 7.17, “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!

`-XRebindableSyntax` implies `-XNoImplicitPrelude`.

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.

### 7.3.16. Postfix operators

The `-XPostfixOperators` flag 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.

### 7.3.17. Tuple sections

The `-XTupleSections` flag enables Python-style 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 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.

### 7.3.18. Lambda-case

The `-XLambdaCase` flag 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

### 7.3.19. Empty case alternatives

The `-XEmptyCase` flag 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 Trac). 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 should be able to compile with `-fwarn-incomplete-patterns`. (Though the pattern match checking is not yet clever enough to do that.) On the other hand (A) looks dangerous, and GHC doesn't check to make sure that, in fact, the function can never get called.

### 7.3.20. Multi-way if-expressions

With `-XMultiWayIf` flag 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.

### 7.3.21. Record field disambiguation

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 `-XDisambiguateRecordFields` flag, 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 Section 7.3.22, “Record puns ”). For example:

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

- With `-XDisambiguateRecordFields` 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.)

### 7.3.22. Record puns

Record puns are enabled by the flag `-XNamedFieldPuns`.

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.)

### 7.3.23. Record wildcards

Record wildcards are enabled by the flag `-XRecordWildCards`. This flag implies `-XDisambiguateRecordFields`.

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:

- Wildcards can be mixed with other patterns, including puns (Section 7.3.22, “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 expressions, writing, 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.

- 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).

  - In the case of expressions (but not patterns), the variable `f` is in scope unqualified, apart from the binding of the record selector itself.

  For example

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

  The `R{..}` expands to `R{M.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).

### 7.3.24. 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 (Section 7.3.11, “The 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 flag is necessary to enable them.

### 7.3.25. Package-qualified imports

With the `-XPackageImports` flag, 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.

### 7.3.26. Safe imports

With the `-XSafe`, `-XTrustworthy` and `-XUnsafe` 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 Section 7.27, “Safe Haskell”

### 7.3.27. Explicit namespaces in import/export

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 (Section 7.4.4, “Type operators”) it becomes possible to declare `(++)` as a type constructor. In that case, how would you export or import it?

The `-XExplicitNamespaces` 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 `-XExplicitNamespaces` is implied by `-XTypeOperators` and (for some reason) by `-XTypeFamilies`.

### 7.3.28. 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`

  Stolen (in types) by: `-XExplicitForAll`, and hence by `-XScopedTypeVariables`, `-XLiberalTypeSynonyms`, `-XRankNTypes`, `-XExistentialQuantification`

`mdo`

  Stolen by: `-XRecursiveDo`

`foreign`

  Stolen by: `-XForeignFunctionInterface`

`rec`, `proc`, `-<`, `>-`, `-<<`, `>>-`, and `(|`, `|)` brackets

  Stolen by: `-XArrows`

`?`varid``

  Stolen by: `-XImplicitParams`

`[|`, `[e|`, `[p|`, `[d|`, `[t|`, `$(`, `$$(`, `[||`, `[e||`, `$`varid``, `$$`varid``

  Stolen by: `-XTemplateHaskell`

`[`varid`|`

  Stolen by: `-XQuasiQuotes`

`varid`{`#`}, `char``#`, `string``#`, `integer``#`, `float``#`, `float``##`

  Stolen by: `-XMagicHash`

`(#`, `#)`

  Stolen by: `-XUnboxedTuples`

`varid``!``varid`

  Stolen by: `-XBangPatterns`

`pattern`

  Stolen by: `-XPatternSynonyms`

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