Definition:Formal Language/Alphabet

This page is about alphabet in the context of formal languages. For other uses, see alphabet.

Definition

Let $\LL$ be a formal language.

The alphabet $\AA$ of $\LL$ is a set of symbols from which collations in $\LL$ may be constructed.

An alphabet consists of the following parts:

Depending on the specific nature of any particular formal language, these too may be subcategorized.

A letter of a formal language is a more or less arbitrary symbol whose interpretation depends on the specific context.

In building a formal language, letters are considered to be the undefined terms of said language.

An important part of assigning semantics to a formal language is to provide an interpretation for its letters.

A sign of a formal language $\LL$ is a symbol whose primary purpose is to structure $\LL$.

In building a formal language, signs form the hooks allowing the formal grammar to define the well-formed formulae of the formal language.

Common examples of signs are parentheses, "(" and ")", and the comma, ",".

Signs form part of the alphabet of $\LL$.

Unlike the letters, they must be the same for each signature for $\LL$.

Let $\AA$ be the alphabet of a formal language $\LL$.

The symbols which comprise $\AA$ are called the primitive symbols of $\AA$.

Some sources use $\Sigma$ to denote an arbitrary alphabet.

Results about alphabets in the context of formal languages can be found here.