This paper presents a methodology for implementing natural language morphology in the functional language Haskell. The main idea behind is simple: instead of working with untyped regular expressions, which is the state of the art of morphology in computational linguistics, we use finite functions over hereditarily finite algebraic datatypes. The definitions of these datatypes and functions are the language-dependent part of the morphology. The languageindependent part consists of an untyped dictionary format which is used for synthesis of word forms, and a decorated trie, which is used for analysis. Functional Morphology builds on ideas introduced by Huet in his computational linguistics toolkit Zen, which he has used to implement the morphology of Sanskrit. The goal has been to make it easy for linguists, who are not trained as functional programmers, to apply the ideas to new languages. As a proof of the productivity of the

Abstract. This paper reports on refinements and extensions to the MathLang framework that add substantial support for natural language text. We show how the extended framework supports multiple views of mathematical texts, including natural language views using the exact text that the mathematician wants to use. Thus, MathLang now supports the ability to capture the essential mathematical structure of mathematics written using natural language text. We show examples of how arbitrary mathematical text can be encoded in MathLang without needing to change any of the words or symbols of the texts or their order. In particular, we show the encoding of a theorem and its proof that has been used by Wiedijk for comparing many theorem prover representations of mathematics, namely the irrationality of √ 2 (originally due to Pythagoras). We encode a 1960 version by Hardy and Wright, and a more recent version by Barendregt. 1 On the way to a mathematical vernacular for computers Mathematicians now use computer software for a variety of tasks: typing mathematical texts, performing calculation, analyzing theories, verifying proofs. Software tools like

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Abstract. We describe a system for automatically translating formal software specifications to natural language. The system produces natural language which is acceptable to a human reader, and it supports byhand optimization by users who are not experts of our system. The translation system is implemented using the Grammatical Framework, a grammar formalism based on Martin-Löf’s type theory. We show that this grammar-based approach scales well enough to handle a non-trivial case study: translating the Object Constraint Language specifications of the Java Card API into English. 1

The GF Resource Grammar Library is a set of natural language grammars implemented in GF (Grammatical Framework). These grammars are in a strong sense parallel: they are built upon a common abstract syntax, i.e. a common tree structure. Individual languages are obtained via compositional mappings from abstract syntax trees to feature structures specific to each language. The grammar defines, for each language, a complete set of morphological paradigms and a syntax fragment comparable to CLE (Core Language Engine). It is available as open-source software under the GNU LGPL License.

Abstract. Unlike computer algebra systems, automated theorem provers have not yet achieved considerable recognition and relevance in mathematical practice. A significant shortcoming of mathematical proof assistance systems is that they require the fully formal representation of mathematical content, whereas in mathematical practice an informal, natural-language-like representation where obvious parts are omitted is common. We aim to support mathematical paper writing by integrating a scientific text editor and mathematical assistance systems such that mathematical derivations authored by human beings in a mathematical document can be automatically checked. To this end, we first define a calculus-independent representation language for formal mathematics that allows for underspecified parts. Then we provide two systems of rules that check if a proof is correct and at an acceptable level of granularity. These checks are done by decomposing the proof into basic steps that are then passed on to proof assistance systems for formal verification. We illustrate our approach using an example textbook proof. 1

In this paper, we explore statistical language modelling for a speech-enabled MP3 player application by generating a corpus from the interpretation grammar written for the application with the Grammatical Framework (GF) (Ranta, 2004).

Mathematical notation has the characteristic of being ambiguous: operators can be overloaded and information that can be deduced is often omitted. Mathematicians are used to this ambiguity and can easily disambiguate a formula making use of the context and of their ability to find the right interpretation. Software applications that have to deal with formulae usually avoid these issues by fixing an unambiguous input notation. This solution is annoying for mathematicians because of the resulting tricky syntaxes and becomes a show stopper to the simultaneous adoption of tools characterized by different input languages. In this paper we present an efficient algorithm suitable for ambiguous parsing of mathematical formulae. The only requirement of the algorithm is the existence of a “validity” predicate over abstract syntax trees of incomplete formulae with placeholders. This requirement can be easily fulfilled in the applicative area of interactive proof assistants, and in several other areas of Mathematical Knowledge Management.

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We demonstrate a new development environment for "Information State Update" dialogue systems which allows non-expert developers to produce complete spoken dialogue systems based only on a Business Process Model (BPM) describing their application (e.g. banking, cinema booking, shopping, restaurant information). The environment includes automatic generation of Grammatical Framework (GF) grammars for robust interpretation of spontaneous speech, and uses application databases to generate lexical entries and grammar rules. The GF grammar is compiled to an ATK or Nuance language model for speech recognition. The demonstration system allows users to create and modify spoken dialogue systems, starting with a definition of a Business Process Model and ending with a working system. This paper describes the environment, its main components, and some of the research issues involved in its development.