Regular Expression Precedence

You might be tempted to read the following regular expression as third or fifth row:

'fifth row'.match /third|fifth row/ #=> #<MatchData "fifth row">
'third row'.match /third|fifth row/ #=> #<MatchData "third">

But unfortunately, as you can see, it’s more like either third (only) or else fifth row. This is due to something called order of operations or operator precedence. The invisible operator for concatenation has higher precedence than the alternation operator |.

To oil these wheels, we now add parentheses to our three operators. In a regular expression, the sub expression enclosed in parentheses get the highest priority:

'fifth row'.match /(third|fifth) row/ #=> #<MatchData "fifth row">
'third row'.match /(third|fifth) row/ #=> #<MatchData "third row">

Note that the parentheses are meta-characters, not literals. They won’t match anything in the subject string. And of course it’s possible to nest parentheses:

'third row'.match /(third|(four|fif)th) row/ #=> #<MatchData "third row">
'fourth row'.match /(third|(four|fif)th) row/ #=> #<MatchData "fourth row">
'fifth row'.match /(third|(four|fif)th) row/ #=> #<MatchData "fifth row">

There are three things we need to remember, to know in what order and with what operands the regular expression engine will execute the operators:

  • Operator precedence is an ordered list that tells you if one operator should be executed before another operator in a regular expression. Several operators can have the same priority. In mathematics, the terms inside the parentheses have the highest priority. Multiplication and division have a lower priority. Addition and subtraction have the lowest. This is why 6+6/(2+1) = 8.
  • Operator position indicates where the operands are located in relation to the operator. The position can be prefix, infix, or postfix. If the operator is prefix, then the operand resides to the right of the operator, as the unary minus sign e.g. -3. An infix operator has an operand on each side, as in addition 1+2. A postfix operator stands to the right of its operand, as the exclamation point that represents the faculty operator in 5!.
  • Operator associativity tells us how to group two operators on the same precedence level. An infix operator can be right-associative, left-associative or non-associative. In mathematics, the infix operations addition and subtraction have the same precedence. Since both are left-associative the following equation holds: 1-2+3 = (1-2)+3 = 2. Prefix or postfix operators are either associative or non-associative. If they are associative, we start with the operator that is closest to the operand. An operator that is non-associative can’t compete with operators of same precedence.

Here goes the table for the operators we have studied so far. Later on, there’s a complete table of all regex operators.

Operator Symbol Precedence Position Associativity
Kleene star * 1 Postfix Associative
Concatenation N/A 2 Infix Left-associative
Alternation | 3 Infix Left-associative

If you think this is hard to remember, then try to memorize the mnemonic SCA. It stands for Star-Concat-Alter, i.e. the order of precedence in regular expressions.

Pomodoro Technique Illustrated -- New book from The Pragmatic Programmers, LLC

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