What does a double colon followed by an equals sign (::=) mean in programming documentation?

Question

What does ::= mean in programming documentation?
For example in the Lua documentation: or in Python documentation.

soulcheck · Accepted Answer · 2012-02-08T15:40:24.793

63

It symbolizes 'symbol derivation rule' in Backus–Naur Form

Meaning that in:

<symbol> ::= __expression__

nonterminal <symbol> consists of (is defined as, is constructed from, derives from) __expression__

It's used to describe language grammars.

Notice that both examples are in Extended Backus–Naur Form, but using a traditional BNF symbol-expression separator (::=).

edited Feb 08 '12 at 15:40

answered Feb 08 '12 at 15:17

soulcheck

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Is there any difference between used in your answer and "identifier" used in m0skit0's answer? It looks like both are names i.e. ways of identifying or referring to data. – Charles Holbrow Feb 08 '12 at 15:29
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@AudiOishi no, the `<` and `>` are used only to mark the difference between terminals and nonterminals. It's normal to omit them in EBNF, as terminals are quoted. In BNF terminals didn't have to be quoted so there had to be some way to differentiate them from non-terminals. – soulcheck Feb 08 '12 at 15:33
We also sometimes see a single colon followed by an equals sign (e.g. http://www.ietf.org/rfc/rfc1806.txt). Is that the same meaning? – Shaun Luttin Oct 27 '15 at 15:33
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@ShaunLuttin yes, though it might create confusion with assignment operator. – soulcheck Oct 27 '15 at 15:39

score 21 · Answer 2 · edited Oct 04 '12 at 15:20

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This is Backus-Naur Form (BNF) notation describing the language. ::= in this context means is defined as.

For example, in the Python language documentation you refer to, an identifier is defined as a letter or an underscore, followed by a letter, a digit or an underscore. The notation then goes on to describe what a letter and a digit is defined as, and so on.

edited Oct 04 '12 at 15:20

Andreas Louv

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answered Feb 08 '12 at 15:23

martineg

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Is there an explanation for why `::=` means "is defined as"? Like the way symbols like `+=` and `<>` make sense? – Kyle Delaney Nov 19 '16 at 00:51

score 7 · Answer 3 · answered Feb 08 '12 at 15:25

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As others have already said, it's part of the BNF notation. Wikipedia has an explanation and some examples, which I won't repeat here.

The history and evolution of the ::= symbol itself is explained in The History of the ALGOL Effort (p29 onwards).

answered Feb 08 '12 at 15:25

NPE

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score 5 · Answer 4 · answered Feb 08 '12 at 15:19

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The given element syntax. For example:

identifier ::=  (letter|"_") (letter | digit | "_")*

Means all identifiers must conform to the given syntax rule.

answered Feb 08 '12 at 15:19

m0skit0

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What does a double colon followed by an equals sign (::=) mean in programming documentation?

4 Answers4

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