Programming Language Techniques for Natural Language Applications

It is easy to imagine machines that can communicate in natural language. Constructing such machines is more difficult. The aim of this thesis is to demonstrate how declarative grammar formalisms that distinguish between abstract and concrete syntax make it easier to develop natural language applications. We describe how the type-theorectical grammar formalism Grammatical Framework (GF) can be used as a high-level language for natural language applications. By taking advantage of techniques from the field of programming language implementation, we can use GF grammars to perform portable and efficient parsing and linearization, generate speech recognition language models, implement multimodal fusion and fission, generate support code for abstract syntax transformations, generate dialogue managers, and implement speech translators and web-based syntax-aware editors. By generating application components from a declarative grammar, we can reduce duplicated work, ensure consistency, make it easier to build multilingual systems, improve linguistic quality, enable re-use across system domains, and make systems more portable

A Bi-Directional Refinement Algorithm for the Calculus of (Co)Inductive Constructions

The paper describes the refinement algorithm for the Calculus of (Co)Inductive Constructions (CIC) implemented in the interactive theorem prover Matita. The refinement algorithm is in charge of giving a meaning to the terms, types and proof terms directly written by the user or generated by using tactics, decision procedures or general automation. The terms are written in an "external syntax" meant to be user friendly that allows omission of information, untyped binders and a certain liberal use of user defined sub-typing. The refiner modifies the terms to obtain related well typed terms in the internal syntax understood by the kernel of the ITP. In particular, it acts as a type inference algorithm when all the binders are untyped. The proposed algorithm is bi-directional: given a term in external syntax and a type expected for the term, it propagates as much typing information as possible towards the leaves of the term. Traditional mono-directional algorithms, instead, proceed in a bottom-up way by inferring the type of a sub-term and comparing (unifying) it with the type expected by its context only at the end. We propose some novel bi-directional rules for CIC that are particularly effective. Among the benefits of bi-directionality we have better error message reporting and better inference of dependent types. Moreover, thanks to bi-directionality, the coercion system for sub-typing is more effective and type inference generates simpler unification problems that are more likely to be solved by the inherently incomplete higher order unification algorithms implemented. Finally we introduce in the external syntax the notion of vector of placeholders that enables to omit at once an arbitrary number of arguments. Vectors of placeholders allow a trivial implementation of implicit arguments and greatly simplify the implementation of primitive and simple tactics