# How do you call alternatives in the grammatical productions?

I have encountered a question, which asks what is a syntactic form. This motivated me to ask myself, what is the anatomy of the grammatic rule,

     S ::= A | B | C


Anatomy established that S is called LHS whereas A | B | C is called expectedly RHS. But, how do you call the individual alternatives within the RHS? Is it related to your syntactic forms?

• Um... "alternatives"? – Raphael Jun 19 '16 at 15:24

1. how do you call the individual alternatives within the RHS?

As @Rafael mentioned, they are called alternatives.

Parsing Techinques: A Practical Guide, 2nd ed. (2008) by D. Grune and C.J.H. Jacobs, page 15:

There is a more compact notation, in which several right-hand sides for one and the same left-hand side are grouped together and then separated by vertical bars, |. This bar belongs to the formalism, just as the arrow $\to$, and can be read “or else”. The right-hand sides separated by vertical bars are also called alternatives.

1. Is it related to your syntactic forms?

From the same source (p. 13):

Non-terminals [S, A, B, C in the example] are called (grammar) variables or syntactic categories in linguistic contexts.

It seems the terms syntactic form and syntactic category are used somewhat interchangeably. So, if an alternative is a variable, then it represents a syntactic form, but if it has more complex structure (it can contain terminals, or several non-terminals), then we might say that from the point of view of the grammar's author the alternative does not represent a syntactic form. But someone else can always turn it into one by defining a new non-terminal with an appropriate RHS.

Since B.C. Pierce's syntactic forms include terminals (true, false, 0), I agree with the accepted answer that the term syntactic form is used somewhat informally and is not defined precisely.

• Should they have different syntactic forms? – Little Alien Jun 19 '16 at 16:43
• I'm not sure I completely understand your question (especially the meaning of the word "have" here). I'd say the alternatives define (normally different) syntactic forms. Does it make anything clearer? – Anton Trunov Jun 19 '16 at 16:51
• If we turn to the TAPL example from the first link, then it says, that a term (t) is either true (syntactic category consisting of only 1 element), or false, or anif-expression (syntactic category of infinite number of elements), etc. – Anton Trunov Jun 19 '16 at 16:54
• Does it mean that syntactic forms and alternatives are the same things, syntactic form is what the alternative defines? – Little Alien Jun 19 '16 at 17:06
• I've updated the answer, trying to clarify that part. – Anton Trunov Jun 19 '16 at 17:30