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351 lines
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HTML
351 lines
8.4 KiB
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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
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<META NAME="generator" CONTENT="http://txt2tags.sf.net">
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<TITLE>A Birds-Eye View of GF as a Grammar Formalism</TITLE>
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</HEAD><BODY BGCOLOR="white" TEXT="black">
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<P ALIGN="center"><CENTER><H1>A Birds-Eye View of GF as a Grammar Formalism</H1>
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<FONT SIZE="4">
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<I>Author: Aarne Ranta</I><BR>
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Last update: Thu Feb 2 14:16:01 2006
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</FONT></CENTER>
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<P></P>
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<HR NOSHADE SIZE=1>
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<P></P>
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<UL>
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<LI><A HREF="#toc1">GF in a few words</A>
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<LI><A HREF="#toc2">History of GF</A>
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<LI><A HREF="#toc3">Some key ingredients of GF in other grammar formalisms</A>
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<LI><A HREF="#toc4">Examples of descriptions in each formalism</A>
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<LI><A HREF="#toc5">Lambda terms and records</A>
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<LI><A HREF="#toc6">The structure of GF formalisms</A>
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<LI><A HREF="#toc7">The expressivity of GF</A>
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<LI><A HREF="#toc8">Grammars and parsing</A>
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<LI><A HREF="#toc9">Grammars as software libraries</A>
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<LI><A HREF="#toc10">Multilinguality</A>
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<LI><A HREF="#toc11">Parametrized modules</A>
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</UL>
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<P></P>
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<HR NOSHADE SIZE=1>
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<P></P>
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<P>
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<IMG ALIGN="middle" SRC="Logos/gf0.png" BORDER="0" ALT="">
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</P>
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<P>
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<I>Abstract. This document gives a general description of the</I>
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<I>Grammatical Framework (GF), with comparisons to other grammar</I>
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<I>formalisms such as CG, ACG, HPSG, and LFG.</I>
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</P>
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<P>
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<!-- NEW -->
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</P>
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<A NAME="toc1"></A>
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<H2>GF in a few words</H2>
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<P>
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Grammatical Framework (GF) is a grammar formalism
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based on <B>constructive type theory</B>.
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</P>
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<P>
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GF makes a distinction between <B>abstract syntax</B> and <B>concrete syntax</B>.
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</P>
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<P>
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The abstract syntax part of GF is a <B>logical framework</B>, with
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dependent types and higher-order functions.
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</P>
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<P>
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The concrete syntax is a system of <B>records</B> containing strings and features.
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</P>
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<P>
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A GF grammar defines a <B>reversible homomorphism</B> from an abstract syntax to a
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concrete syntax.
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</P>
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<P>
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A <B>multilingual GF grammar</B> is a set of concrete syntaxes associated with
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one abstract syntax.
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</P>
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<P>
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GF grammars are written in a high-level <B>functional programming language</B>,
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which is compiled into a <B>core language</B> (GFC).
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</P>
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<P>
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GF grammars can be used as <B>resources</B>, i.e. as libraries for writing
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new grammars; these are compiled and optimized by the method of
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<B>grammar composition</B>.
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</P>
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<P>
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GF has a <B>module system</B> that supports grammar engineering and separate
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compilation.
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</P>
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<P>
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<!-- NEW -->
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</P>
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<A NAME="toc2"></A>
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<H2>History of GF</H2>
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<P>
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1988. Intuitionistic Categorial Grammar; type theory as abstract syntax,
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playing the role of Montague's analysis trees. Grammars implemented in Prolog.
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</P>
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<P>
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1994. Type-Theoretical Grammar. Abstract syntax organized as a system of
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combinators. Grammars implemented in ALF.
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</P>
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<P>
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1996. Multilingual Type-Theoretical Grammar. Rules for generating six
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languages from the same abstract syntax. Grammars implemented in ALF, ML, and
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Haskell.
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</P>
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<P>
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1998. The first implementation of GF as a language of its own.
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</P>
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<P>
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2000. New version of GF: high-level functional source language, records used
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for concrete syntax.
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</P>
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<P>
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2003. The module system.
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</P>
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<P>
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2004. Ljunglöf's thesis <I>Expressivity and Complexity of GF</I>.
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</P>
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<P>
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<!-- NEW -->
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</P>
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<A NAME="toc3"></A>
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<H2>Some key ingredients of GF in other grammar formalisms</H2>
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<UL>
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<LI>[GF ]: Grammatical Framework
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<LI>[CG ]: categorial grammar
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<LI>[ACG ]: abstract categorial grammar
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<LI>[HPSG ]: head-driven phrase structure grammar
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<LI>[LFG ]: lexical functional grammar
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</UL>
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<TABLE CELLPADDING="4" BORDER="1">
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<TR>
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<TD ALIGN="center">/</TD>
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<TD>GF</TD>
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<TD>ACG</TD>
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<TD>LFG</TD>
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<TD>HPSG</TD>
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<TD>CG</TD>
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</TR>
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<TR>
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<TD>abstract vs concrete syntax</TD>
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<TD>X</TD>
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<TD>X</TD>
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<TD>?</TD>
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<TD>-</TD>
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<TD>-</TD>
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</TR>
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<TR>
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<TD>type theory</TD>
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<TD>X</TD>
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<TD>X</TD>
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<TD>-</TD>
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<TD>-</TD>
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<TD>X</TD>
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</TR>
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<TR>
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<TD>records and features</TD>
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<TD>X</TD>
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<TD>-</TD>
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<TD>X</TD>
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<TD>X</TD>
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<TD>-</TD>
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</TR>
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</TABLE>
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<P></P>
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<P>
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<!-- NEW -->
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</P>
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<A NAME="toc4"></A>
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<H2>Examples of descriptions in each formalism</H2>
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<P>
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To be written...
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</P>
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<P>
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<!-- NEW -->
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</P>
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<A NAME="toc5"></A>
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<H2>Lambda terms and records</H2>
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<P>
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In CS, abstract syntax is trees and concrete syntax is strings.
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This works more or less for programming languages.
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</P>
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<P>
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In CG, all syntax is lambda terms.
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</P>
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<P>
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In Montague grammar, abstract syntax is lambda terms and
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concrete syntax is trees. Abstract syntax as lambda terms
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can be considered well-established.
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</P>
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<P>
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In PATR and HPSG, concrete syntax it records. This can be considered
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well-established for natural languages.
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</P>
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<P>
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In ACG, both are lambda terms. This is more general than GF,
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but reversibility requires linearity restriction, which can be
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unnatural for grammar writing.
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</P>
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<P>
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In GF, linearization from lambda terms to records is reversible,
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and grammar writing is not restricted to linear terms.
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</P>
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<P>
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Grammar composition in ACG is just function composition. In GF,
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it is more restricted...
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</P>
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<P>
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<!-- NEW -->
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</P>
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<A NAME="toc6"></A>
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<H2>The structure of GF formalisms</H2>
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<P>
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The following diagram (to be drawn properly!) describes the
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levels.
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</P>
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<PRE>
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| programming language design
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V
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GF source language
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| type-directed partial evaluation
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V
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GFC assembly language
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| Ljunglöf's translation
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V
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MCFG parser
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</PRE>
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<P>
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The last two phases are nontrivial mathematica properties.
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</P>
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<P>
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In most grammar formalisms, grammarians have to work on the GFC
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(or MCFG) level.
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</P>
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<P>
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Maybe they use macros - they are therefore like macro assemblers. But there
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are no separately compiled library modules, no type checking, etc.
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</P>
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<P>
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<!-- NEW -->
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</P>
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<A NAME="toc7"></A>
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<H2>The expressivity of GF</H2>
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<P>
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Parsing complexity is the same as MCFG: polynomial, with
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unrestricted exponent depending on grammar.
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This is between TAG and HPSG.
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</P>
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<P>
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If semantic well-formedness (type theory) is taken into account,
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then arbitrary logic can be expressed. The well-formedness of
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abstract syntax is decidable, but the well-formedness of a
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concrete-syntax string can require an arbitrary proof construction
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and is therefore undecidable.
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</P>
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<P>
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Separability between AS and CS: like TAG (Tree Adjoining Grammar), GF
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has the goal of assigning intended trees for strings. This is
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generalized to shared trees for different languages.
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</P>
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<P>
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The high-level language strives after the properties of
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writability and readability (programming language notions).
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</P>
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<P>
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<!-- NEW -->
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</P>
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<A NAME="toc8"></A>
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<H2>Grammars and parsing</H2>
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<P>
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In many projects, a grammar is just seen as a <B>declarative parsing program</B>.
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</P>
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<P>
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For GF, a grammar is primarily the <B>definition of a language</B>.
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</P>
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<P>
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Detaching grammars from parsers is a good idea, giving
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</P>
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<UL>
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<LI>more efficient and robust parsing (statistical etc)
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<LI>cleaner grammars
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</UL>
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<P>
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Separating abstract from concrete syntax is a prerequisite for this:
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we want parsers to return abstract syntax objects, and these must exist
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independently of parse trees.
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</P>
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<P>
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A possible radical approach to parsing:
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use a grammar to generate a treebank and machine-learn
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a statistical parser from this.
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</P>
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<P>
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Comparison: Steedman in CCG has done something like this.
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</P>
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<P>
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<!-- NEW -->
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</P>
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<A NAME="toc9"></A>
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<H2>Grammars as software libraries</H2>
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<P>
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Reuse for different purposes.
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</P>
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<P>
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Grammar composition.
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</P>
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<P>
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<!-- NEW -->
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</P>
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<A NAME="toc10"></A>
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<H2>Multilinguality</H2>
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<P>
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In <B>application grammars</B>, the AS is a semantic
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model, and a CS covers domain terminology and idioms.
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</P>
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<P>
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This can give publication-quality translation on
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limited domains (e.g. the WebALT project).
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</P>
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<P>
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Resource grammars with grammar composition lead to
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<B>compile-time transfer</B>.
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</P>
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<P>
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When is <B>run-time transfer</B> necessary?
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</P>
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<P>
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Cf. CLE (Core Language Engine).
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</P>
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<P>
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<!-- NEW -->
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</P>
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<A NAME="toc11"></A>
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<H2>Parametrized modules</H2>
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<P>
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This notion comes from the ML language in the 1980's.
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</P>
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<P>
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It can be used for sharing even more code between languages
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than their AS.
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</P>
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<P>
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Especially, for related languages (Scandinavian, Romance).
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</P>
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<P>
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Cf. grammar porting in CLE: what they do with untyped
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macro packages GF does with typable interfaces.
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</P>
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