WolframLang: Pattern Syntax

By Xah Lee. Date: . Last updated: .

Here's a list of all pattern syntax. 〔see Pattern Matching〕

Literal Expression

Literal expression matches itself. For example: symbol a, number 3, string "abc", all match themselves, and arbitrary expression f[a,b,c] matches itself. 

ReplaceAll[ {3,4}, 4 -> x]
(* {3, x} *)

ReplaceAll[ {a, f[3], f[9]}, f[9] -> g[9]]
(* {a, f[3], g[9]} *)

ReplaceAll[ {2/3, {4, 8}, {c}}, 2/3 -> 1/3]
(* {1/3, {4, 8}, {c}} *)

Blank Pattern

_

match any Expression

same as Blank[]

Blank 

ReplaceAll[ {3,4}, _ -> x]
(* x *)

ReplaceAll[ {a, f[3], f[9]}, f[_] -> g ]
(* {a, g, g} *)

ReplaceAll[ {a, f[3], g[4], f[5]}, _[_] -> g]
(* {a, g, g, g} *)

ReplaceAll[ {{2}, {4, 8}, {c}}, {_ , _} -> xpair]
(* {{2}, xpair, {c}} *)

for ReplaceAll usage, see WolframLang: Change Expression by Pattern

_h

any expression with Head h

same as Blank[h]

Blank 

Cases[ {3, 4.5, 5/6, {x, y}}, _Integer, {1} ]
(* {3} *)

Cases[ {3, 4.5, 5/6, {x, y}}, _Rational, {1} ]
(* {5/6} *)

Cases[ {3, 4.5, 5/6, {x, y}}, _Real, {1} ]
(* {4.5} *)

Cases[ {3, 4.5, 5/6, {x, y}}, _List, {1} ]
(* {{x, y}} *)

Cases[ {3, f[a], f[b]} , _f , {1}]
(* {f[a], f[b]} *)

Basic Named Pattern

x_

any expression, giving it a name x

same as Pattern[x, Blank[]]

Pattern 
ReplaceAll[ {3,4}, x_ -> x+y ]
(* {3 + y, 4 + y} *)
x_h

any expression with Head h, giving it a name x

same as Pattern[x, Blank[h]] 

ReplaceAll[ {3, {5,6}}, x_List -> f[x] ]
(* f[{3, {5, 6}}] *)

ReplaceAll[ {3, f[a]}, x_f -> y ]
(* {3, y} *)

Repetition, One or More, Zero or More

__

any sequence of one or more expressions. (2 LOW LINE characters)

BlankSequence 

Cases[ {3, {}, {5, 6}, {7, f, 9}}, {__}, {1} ]
(* {{5, 6}, {7, f, 9}} *)
___

any sequence of zero or more expressions (3 LOW LINE characters)

BlankNullSequence 

Cases[ {3, {}, {5, 6}, {7, f, 9}}, {___}, {1} ]
(* {{}, {5, 6}, {7, f, 9}} *)
__h and ___h

sequences of expressions, each with Head h

same as BlankSequence[h] or BlankNullSequence[h]

x__ and x___

sequences of expressions, giving it a name x

same as Pattern[x, BlankSequence[]] or Pattern[x, BlankNullSequence[]]

x__h and x___h

sequences of expressions with Head h, giving it a name x

same as Pattern[x, BlankSequence[h]] or Pattern[x, BlankNullSequence[h]]

Repeated Pattern

pattern..

a pattern repeated one or more times

Repeated

pattern...

a pattern repeated zero or more times

Repeated[pattern, spec]

a pattern repeated according to spec

Conditional Patterns

pattern?test

a pattern that yields True when test is applied to its value

PatternTest

pattern/;cond

a pattern for which cond evaluates to True

Condition

alternatives

p1|p2|etc

a pattern that matches at least one of the pattern.

same as Alternatives[p1, p2, etc]

Alternatives

Literal Pattern

HoldPattern[pattern]

a pattern not evaluated

Verbatim[expr]

an expression to be matched verbatim

Naming a Generic Pattern

x:pattern

a pattern, giving it a name x

same as Pattern[x, Blank[]]

Pattern Negation

Except[c]

any expression except one that matches c

Except[c, pattern]

any expression matching pattern, except one that matches c

Advanced Patterns

PatternSequence[p1, p2, etc]

a sequence of patterns

OrderlessPatternSequence[p1, p2, etc]

an orderless sequence of patterns

KeyValuePattern[{‹key1› → ‹val1›, etc}]

an orderless sequence of key → val pairs

x_:v

an expression with default value v

Optional

x_h:v

an expression with Head h and default value v

x_.

an expression with a globally defined default value

Optional[x_h]

an expression that must have Head h, and has a globally defined default value

OptionsPattern[]

a sequence of options

〔see WolframLang: Define Function with Optional Parameters〕

More Advanced Patterns

Longest[pattern]

the longest sequence consistent with pattern

Shortest[pattern]

the shortest sequence consistent with pattern

Reference

PatternsAndTransformationRules

Pattern Matching