6.6  Patterns

See also the following language extensions: lazy patterns, local opens, first-class modules, attributes, extension nodes and exception cases in pattern matching.

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

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 , … ,  pattern_n ) matches all variants whose constructor is equal to constr, and whose arguments match pattern₁ …  pattern_n. 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 ; … ;  pattern_n ] matches lists of length n whose elements match pattern₁ …pattern_n, respectively. This pattern behaves like pattern₁ :: … ::  pattern_n :: [].

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-name<sub>1</sub>  typexpr<sub>1</sub> | … | ` tag-name_n  typexpr_n] is defined, then the pattern #typeconstr is a shorthand for the following or-pattern: ( `tag-name<sub>1</sub>(_ :  typexpr<sub>1</sub>) | … | ` tag-name_n(_ :  typexpr_n)). It matches all values of type [< typeconstr ].

Tuple patterns

The pattern pattern₁ , … ,  pattern_n matches n-tuples whose components match the patterns pattern₁ through pattern_n. That is, the pattern matches the tuple values (v₁, …, v_n) such that pattern_i matches v_i for i = 1,… , n.

Record patterns

The pattern { field₁ =  pattern₁ ; … ;  field_n =  pattern_n } matches records that define at least the fields field₁ through field_n, and such that the value associated to field_i matches the pattern pattern_i, for i = 1,… , n. The record value can define more fields than field₁ …field_n; the values associated to these extra fields are not taken into account for matching. Optional type constraints can be added field by field with { field₁ :  typexpr₁ =  pattern₁ ;… ; field_n :  typexpr_n =  pattern_n } to force the type of field_k to be compatible with typexpr_k.

Array patterns

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

Range patterns

The pattern ' c ' .. ' d ' is a shorthand for the pattern

where c₁, c₂, …, c_n are the characters that occur between c and d in the ASCII character set. For instance, the pattern '0'..'9' matches all characters that are digits.