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Functional morphology
 Proceedings of the Ninth ACM SIGPLAN International Conference of Functional Programming, Snowbird
, 2004
"... 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 ov ..."
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Cited by 28 (13 self)
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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 languagedependent 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
Flexible encoding of mathematics on the computer
 In MKM 2004, volume 3119 of LNCS
, 2004
"... 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 ..."
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Cited by 23 (13 self)
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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
Translating formal software specifications to natural language/a grammar based approach
 In Proceedings of Logical Aspects of Computational Linguistics (LACL’05
, 2005
"... 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 imple ..."
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Cited by 16 (1 self)
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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 MartinLöf’s type theory. We show that this grammarbased approach scales well enough to handle a nontrivial case study: translating the Object Constraint Language specifications of the Java Card API into English. 1
The GF Resource grammar library
 August
, 2002
"... 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 fro ..."
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Cited by 15 (4 self)
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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 opensource software under the GNU LGPL License.
Multilingual Syntax Editing in GF
 In Proceedings of the 4th International Conference on Intelligent Text Processing and Computational Linguistics (CICLing’03
, 2003
"... ..."
Implementing Controlled Languages in GF
"... Abstract. The paper introduces GF, Grammatical Framework, as a tool for implementing controlled languages. GF provides a highlevel grammar formalism and a resource grammar library that make it easy to write grammars that cover similar fragments in several natural languages at the same time. Authori ..."
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Cited by 7 (2 self)
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Abstract. The paper introduces GF, Grammatical Framework, as a tool for implementing controlled languages. GF provides a highlevel grammar formalism and a resource grammar library that make it easy to write grammars that cover similar fragments in several natural languages at the same time. Authoring help tools and automatic translation are provided for all grammars. As an example, a grammar of Attempto Controlled English is implemented and then ported to French, German, and Swedish. 1
Textbook proofs meet formal logic  the problem of underspecification and granularity
 Proceedings of MKM’05, volume 3863 of LNAI, IUB
, 2006
"... 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, ..."
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Cited by 7 (3 self)
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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, naturallanguagelike 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 calculusindependent 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
PLATΩ: A mediator between texteditors and proof assistance systems
, 2007
"... We present a generic mediator, called PlatΩ, between texteditors and proof assistants. PlatΩ aims at integrated support for the development, publication, formalization, and verification of mathematical documents in a natural way as possible: The user authors his mathematical documents with a scient ..."
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Cited by 6 (3 self)
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We present a generic mediator, called PlatΩ, between texteditors and proof assistants. PlatΩ aims at integrated support for the development, publication, formalization, and verification of mathematical documents in a natural way as possible: The user authors his mathematical documents with a scientific WYSIWYG texteditor in the informal language he is used to, that is a mixture of natural language and formulas. These documents are then semantically annotated preserving the textual structure by using the flexible, parameterized proof language which we present. From this informal semantic representation PlatΩ automatically generates the corresponding formal representation for a proof assistant, in our case Ωmega. The primary task of PlatΩ is the maintenance of consistent formal and informal representations during the interactive development of the document.
Generating Statistical Language Models from Interpretation Grammars in Dialogue Systems
 In ”Proceedings of 11th Conference of the European Association of Computational Linguistics
, 2006
"... In this paper, we explore statistical language modelling for a speechenabled MP3 player application by generating a corpus from the interpretation grammar written for the application with the Grammatical Framework (GF) (Ranta, 2004). ..."
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Cited by 6 (2 self)
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In this paper, we explore statistical language modelling for a speechenabled MP3 player application by generating a corpus from the interpretation grammar written for the application with the Grammatical Framework (GF) (Ranta, 2004).
Efficient Ambiguous Parsing of Mathematical Formulae
 IN: PROCEEDINGS OF MATHEMATICAL KNOWLEDGE MANAGEMENT 2004, VOL. 3119 OF LNCS
, 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 interp ..."
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Cited by 6 (3 self)
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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.