7.3. Syntactic extensions
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## 7.3. Syntactic extensions

### 7.3.1. 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 4.6.3, “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.

### 7.3.2. 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.

### 7.3.3. The recursive do-notation

The recursive do-notation (also known as mdo-notation) is implemented as described in "A recursive do for Haskell", Levent Erkok, John Launchbury", Haskell Workshop 2002, pages: 29-37. Pittsburgh, Pennsylvania.

The do-notation of Haskell 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 several applications can benefit from recursive bindings in the do-notation, and this extension provides the necessary syntactic support.

Here is a simple (yet contrived) example:

    import Control.Monad.Fix

    justOnes = mdo xs <- Just (1:xs)
                   return xs

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

The Control.Monad.Fix library introduces the `MonadFix` class. It's definition is:

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

The function `mfix` dictates how the required recursion operation should be performed. If recursive bindings are required for a monad, then that monad must be declared an instance of the `MonadFix` class. For details, see the above mentioned reference.

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).

There are three important points in using the recursive-do notation:

- The recursive version of the do-notation uses the keyword `mdo` (rather than `do`).

- You should `import Control.Monad.Fix`. (Note: Strictly speaking, this import is required only when you need to refer to the name `MonadFix` in your program, but the import is always safe, and the programmers are encouraged to always import this module when using the mdo-notation.)

- As with other extensions, ghc should be given the flag `-fglasgow-exts`

The web page: http://www.cse.ogi.edu/PacSoft/projects/rmb contains up to date information on recursive monadic bindings.

Historical note: The old implementation of the mdo-notation (and most of the existing documents) used the name `MonadRec` for the class and the corresponding library. This name is not supported by GHC.

### 7.3.4. 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 behavior 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.

### 7.3.5. Rebindable syntax

GHC allows most kinds of built-in syntax to be rebound by the user, to facilitate replacing the `Prelude` with a home-grown version, for example.

You may want 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 `-fno-implicit-prelude` 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.

- "Do" notation is translated using whatever functions `(>>=)`, `(>>)`, and `fail`, are in scope (not the Prelude versions). List comprehensions, mdo (Section 7.3.3, “The recursive do-notation ”), and parallel array comprehensions, are unaffected.

- Arrow notation (see Section 7.7, “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!

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 emample, 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.

### 7.3.6. Postfix operators

GHC allows 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.

Since this extension goes beyond Haskell 98, it should really be enabled by a flag; but in fact it is enabled all the time. (No Haskell 98 programs change their behaviour, of course.)

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

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