Formal grammar in the context of "Attribute grammar"

In logic, mathematics, computer science, and linguistics, a formal language is a set of strings whose symbols are taken from a set called "alphabet".

The alphabet of a formal language consists of symbols that concatenate into strings (also called "words"). Words that belong to a particular formal language are sometimes called well-formed words. A formal language is often defined by means of a formal grammar such as a regular grammar or context-free grammar.

In theoretical computer science and formal language theory, a regular grammar is a grammar that is right-regular or left-regular.While their exact definition varies from textbook to textbook, they all require that

• all production rules have at most one non-terminal symbol;
• that symbol is either always at the end or always at the start of the rule's right-hand side.

Every regular grammar describes a regular language.

In formal language theory, a context-free grammar (CFG) is a formal grammar whose production rules can be applied to a nonterminal symbol regardless of its context.In particular, in a context-free grammar, each production rule is of the form

with ${\displaystyle A}$ a single nonterminal symbol, and ${\displaystyle \alpha }$ a string of terminals and/or nonterminals (${\displaystyle \alpha }$ can be empty). Regardless of which symbols surround it, the single nonterminal ${\displaystyle A}$ on the left hand side can always be replaced by ${\displaystyle \alpha }$ on the right hand side. This distinguishes it from a context-sensitive grammar, which can have production rules in the form ${\displaystyle \alpha A\beta \rightarrow \alpha \gamma \beta }$ with ${\displaystyle A}$ a nonterminal symbol and ${\displaystyle \alpha }$, ${\displaystyle \beta }$, and ${\displaystyle \gamma }$ strings of terminal and/or nonterminal symbols.

An L-system or Lindenmayer system is a parallel rewriting system and a type of formal grammar. An L-system consists of an alphabet of symbols that can be used to make strings, a collection of production rules that expand each symbol into some larger string of symbols, an initial "axiom" string from which to begin construction, and a mechanism for translating the generated strings into geometric structures. L-systems were introduced and developed in 1968 by Aristid Lindenmayer, a Hungarian theoretical biologist and botanist at the University of Utrecht. Lindenmayer used L-systems to describe the behaviour of plant cells and to model the growth processes of plant development. L-systems have also been used to model the morphology of a variety of organisms and can be used to generate self-similar fractals.

The Chomsky hierarchy in the fields of formal language theory, computer science, and linguistics, is a containment hierarchy of classes of formal grammars. A formal grammar describes how to form strings from a formal language's alphabet that are valid according to the language's syntax. The linguist Noam Chomsky theorized that four different classes of formal grammars existed that could generate increasingly complex languages. Each class can also completely generate the language of all inferior classes (set inclusive).

In formal languages, terminal and nonterminal symbols are parts of the vocabulary under a formal grammar. Vocabulary is a finite, nonempty set of symbols. Terminal symbols are symbols that cannot be replaced by other symbols of the vocabulary. Nonterminal symbols are symbols that can be replaced by other symbols of the vocabulary by the production rules under the same formal grammar.

A formal grammar defines a formal language over the vocabulary of the grammar.