This is the abstract of talk that I gave in Chalmers.

Title: GF as functional-logic language

Abstract

~~~~~~

Grammatical Framework (GF) is a domain specific language for describing
natural language grammars. Despite that GF is language with very
specific application domain, it is also Turing complete and could be
used to solve nontrivial tasks in a surprising way. The design of the
language has a lot of common with other functional and logic programming
languages, most notably: Agda, Haskell, Curry and Lambda Prolog. Curry
is an interesting language which combines in a neat way the functional
and the logical paradigms but still from type theoretic point of view
this is not satisfactory because it doesn't exploit the Curry-Howard
isomorphism. Thanks to the dependent types of GF, which relates it to
Agda, and thanks to some other specifics in the type system, GF could
also be classified as functional-logic language but the two paradigms in
GF are combined in the expected way. The execution model of GF also has
a lot of common with Lambda Prolog but to cover the full semantics of GF
the virtual machine should work in two modes: narrowing and residuation.
The residuation mode is something that could be seen in the virtual
machine of Curry but not in Lambda Prolog.

In this seminar I will talk about my work in progress on a virtual
machine for running GF applications. Not everything is in place yet but
the pieces are starting to stick together. As a demo I will show how to
solve the classical n-queens problem in GF. From the logical programming
paradigm I use backtracking and from the functional paradigm I use
efficient deterministic computations. From type theoretical point of
view I define the type of all n-queens puzzles.

URL: www.grammaticalframework.org/doc/gf-fp.pdf