A regular tree grammar defines a regular tree language. Regular tree grammars are widely applied as tools in formal reasoning, but in practice the basic formalism is hidden in languages designed at human users. The **RTG** language is a little language that just contains the constructs of the clean formalism. The language is probably best introduced by a tiny example:

regular tree grammar start Exp productions Var -> Var (<string>) Exp -> Int (<int>) | Times (Exp, Exp) | Plus (Exp, Exp) | Call (Var, ExpList) ExpList -> <cons> (Exp, ExpList) | <nil> ()

A regular tree grammar consists of a list of start non-terminals and a list of productions. The list of start non-terminals defines what non-terminals are allowed at the root of tree in the language defined by this RTG. The productions specify the terms that can be produced for a certain non-terminal. The left-hand-side of a production is non-terminal, the right hand side is a term that can contain non-terminals.

Formally, a regular tree grammar consists of:

- An unranked alphabet of non-terminals: N
- A ranked alphabet of terminals: T
- A set of start symbols S, which is a subset of N
- A set of productions of the form N -> t, where t is an element of the set of ground terms over T union N.

For more formal discussion on tree grammars and tree languages see Tree Automata Techniques and Applications^{?} or Connecting XML Processing and Term Rewriting with Tree Grammars.

Notice that the regular tree grammar shown above contains a few constructs between angle brackets: `<cons>`

, `<nil>`

, `<string>`

, and `<int>`

. The first two are built-in *terminals* for representing lists. The last two are built-in non-terminals for strings and integers.

[Under construction -- MartinBravenboer - 25 Apr 2004]

Revision: r1.2 - 25 Apr 2004 - 19:27 - MartinBravenboer

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