Grammatical Framework (GF) is a special-purpose functional language for defining grammars. It uses a Logical Framework (LF) for a description of abstract syntax, and adds to this a notation for defining concrete syntax. GF grammars themselves are purely declarative, but can be used both for linearizing syntax trees and parsing strings. GF can describe both formal and natural languages. The key notion of this description is a grammatical object, which is not just a string, but a record that contains all information on inflection and inherent grammatical features such as number and gender in natural languages, or precedence in formal languages. Grammatical objects have a type system, which helps to eliminate run-time errors in language processing. In the same way as a LF, GF uses dependent types in abstract syntax to express semantic conditions, such as well-typedness and proof obligations. Multilingual grammars, where one abstract syntax has many parallel concrete syntaxes, can be used for reliable and meaning-preserving translation. They can also be used in authoring systems, where syntax trees are constructed in an interactive editor similar to proof editors based on LF. While being edited, the trees can simultaneously be viewed in different languages. This paper starts with a gradual introduction to GF, going through a sequence of simpler formalisms till the full power is reached. The introduction is followed by a systematic presentation of the GF formalism and outlines of the main algorithms: partial evaluation and parser generation. The paper concludes by brief discussions of the Haskell implementation of GF, existing applications, and related work.
