Patterns

## 6.6 Patterns

pattern | ::= | value-name
| ∣ | _
| ∣ | constant
| ∣ | pattern as value-name
| ∣ | ( pattern )
| ∣ | ( pattern : typexpr )
| ∣ | pattern | pattern
| ∣ | constr pattern
| ∣ | `tag-name pattern
| ∣ | #typeconstr
| ∣ | pattern { , pattern }+
| ∣ | { field = pattern { ; field = pattern } [ ; ] }
| ∣ | [ pattern { ; pattern } [ ; ] ]
| ∣ | pattern :: pattern
| ∣ | [| pattern { ; pattern } [ ; ] |]

The table below shows the relative precedences and associativity of operators and non-closed pattern constructions. The constructions with higher precedences come first.

Operator | Associativity
.. (see section 7.4) | –
lazy (see section 7.6) | –
Constructor application, Tag application | right
:: | right
, | –
| | left
as | –

Patterns are templates that allow selecting data structures of a given shape, and binding identifiers to components of the data structure. This selection operation is called pattern matching; its outcome is either “this value does not match this pattern”, or “this value matches this pattern, resulting in the following bindings of names to values”.

#### Variable patterns

A pattern that consists in a value name matches any value, binding the name to the value. The pattern _ also matches any value, but does not bind any name.

Patterns are linear: a variable cannot be bound several times by a given pattern. In particular, there is no way to test for equality between two parts of a data structure using only a pattern (but when guards can be used for this purpose).

#### Constant patterns

A pattern consisting in a constant matches the values that are equal to this constant.

#### Alias patterns

The pattern pattern1 as value-name matches the same values as pattern1. If the matching against pattern1 is successful, the name value-name is bound to the matched value, in addition to the bindings performed by the matching against pattern1.

#### Parenthesized patterns

The pattern ( pattern1 ) matches the same values as pattern1. A type constraint can appear in a parenthesized pattern, as in ( pattern1 : typexpr ). This constraint forces the type of pattern1 to be compatible with typexpr.

#### “Or” patterns

The pattern pattern1 | pattern2 represents the logical “or” of the two patterns pattern1 and pattern2. A value matches pattern1 | pattern2 if it matches pattern1 or pattern2. The two sub-patterns pattern1 and pattern2 must bind exactly the same identifiers to values having the same types. Matching is performed from left to right. More precisely, in case some value v matches pattern1 | pattern2, the bindings performed are those of pattern1 when v matches pattern1. Otherwise, value v matches pattern2 whose bindings are performed.

#### Variant patterns

The pattern constr ( pattern1 , … , patternn ) matches all variants whose constructor is equal to constr, and whose arguments match pattern1 … patternn. It is a type error if n is not the number of arguments expected by the constructor.

The pattern constr _ matches all variants whose constructor is constr.

The pattern pattern1 :: pattern2 matches non-empty lists whose heads match pattern1, and whose tails match pattern2.

The pattern [ pattern1 ; … ; patternn ] matches lists of length n whose elements match pattern1 …patternn, respectively. This pattern behaves like pattern1 :: … :: patternn :: [].

#### Polymorphic variant patterns

The pattern `tag-name pattern1 matches all polymorphic variants whose tag is equal to tag-name, and whose argument matches pattern1.

#### Polymorphic variant abbreviation patterns

If the type [('a,'b,…)] typeconstr = [ ` tag-name1 typexpr1 | … | ` tag-namen typexprn] is defined, then the pattern #typeconstr is a shorthand for the following or-pattern: ( `tag-name1(_ : typexpr1) | … | ` tag-namen(_ : typexprn)). It matches all values of type [< typeconstr ].

#### Tuple patterns

The pattern pattern1 , … , patternn matches n-tuples whose components match the patterns pattern1 through patternn. That is, the pattern matches the tuple values (v1, …, vn) such that patterni matches vi for i = 1,… , n.

#### Record patterns

The pattern { field1 = pattern1 ; … ; fieldn = patternn } matches records that define at least the fields field1 through fieldn, and such that the value associated to fieldi matches the pattern patterni, for i = 1,… , n. The record value can define more fields than field1 …fieldn; the values associated to these extra fields are not taken into account for matching.

#### Array patterns

The pattern [| pattern1 ; … ; patternn |] matches arrays of length n such that the i-th array element matches the pattern patterni, for i = 1,… , n.