6.7.2. View patterns

ViewPatterns
Since

6.10.1

Allow use of view pattern syntax.

View patterns are enabled by the language extension ViewPatterns. 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 is a little inconvenient:

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

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

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

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

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

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

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

    Any variables in ⟨exp⟩ are bound occurrences, but variables bound “to the left” in a pattern are in scope. This feature permits, for example, one argument to a function to be used in the view of another argument. For example, the function clunky from 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 #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.