Expressivity and Complexity of the Grammatical Framework
Doctoral thesis, 2004
This thesis investigates the expressive power and parsing complexity of the Grammatical Framework (GF), a formalism originally designed for displaying formal propositions and proofs in natural language. This is done by relating GF with two more well-known grammar formalisms; Generalized Context-Free Grammar (GCFG), best seen as a framework for describing various grammar formalisms; and Parallel Multiple Context-Free Grammar (PMCFG), an instance of GCFG.
Since GF is a fairly new theory, some questions about expressivity and parsing complexity have until now not been answered; and these questions are the main
focus of this thesis. The main result is that the important subclass context-free GF is equivalent to PMCFG, which has polynomial parsing complexity, and whose expressive power is fairly well known.
Furthermore, we give a number of tabular parsing algorithms for PMCFG with polynomial complexity, by extending existing algorithms for context-free grammars. We suggest three possible extensions of GF/PMCFG, and discuss how the
expressive power and parsing complexity are influenced. Finally, we discuss the parsing problem for unrestricted GF grammars, which is undecidable in general.
We nevertheless describe a procedure for parsing grammars containing higher-order functions and dependent types.
context-free rewriting systems
multiple context-free grammar
generalized context-free grammar