Cayenne—a language with dependent types
ICFP '98 Proceedings of the third ACM SIGPLAN international conference on Functional programming
A Natural Language Explanation for Formal Proofs
LACL '96 Selected papers from the First International Conference on Logical Aspects of Computational Linguistics
TLCA '95 Proceedings of the Second International Conference on Typed Lambda Calculi and Applications
Context-Relative Syntactic Categories and the Formalization of Mathematical Text
TYPES '95 Selected papers from the International Workshop on Types for Proofs and Programs
A multilingual natural-language interface to regular expressions
FSMNLP '09 Proceedings of the International Workshop on Finite State Methods in Natural Language Processing
An Authoring Tool for Informal and Formal Requirements Specifications
FASE '02 Proceedings of the 5th International Conference on Fundamental Approaches to Software Engineering
Amphion/NAV: Deductive Synthesis of State Estimation Software
Proceedings of the 16th IEEE international conference on Automated software engineering
Multilingual syntax editing in GF
CICLing'03 Proceedings of the 4th international conference on Computational linguistics and intelligent text processing
Tools for multilingual grammar-based translation on the web
ACLDemos '10 Proceedings of the ACL 2010 System Demonstrations
Implementing controlled languages in GF
CNL'09 Proceedings of the 2009 conference on Controlled natural language
Translating between language and logic: what is easy and what is difficult
CADE'11 Proceedings of the 23rd international conference on Automated deduction
Translating formal software specifications to natural language
LACL'05 Proceedings of the 5th international conference on Logical Aspects of Computational Linguistics
A User-friendly Interface for a Lightweight Verification System
Electronic Notes in Theoretical Computer Science (ENTCS)
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The paper presents an extension of the proof editor Alfa with natural-language input and output. The basis of the new functionality is an automatic translation to syntactic structures that are closer to natural language than the type-theoretical syntax of Alfa. These syntactic structures are mapped into texts in languages such as English, French, and Swedish. In this way, every theory, definition, proposition, and proof in Alfa can be translated into a text in any of these languages. The translation is defined for incomplete proof objects as well, so that a text with "holes" (i.e. metavariables) in it can be viewed simultaneously with a formal proof constructed. The mappings into natural language also work in the parsing direction, so that input can be given to the proof editor in a natural language. The natural-language interface is implemented using the Grammatical Framework GF, so that it is possible to change and extend the interface without recompiling the proof editor. Such extensions can be made on two dimensions: by adding new target languages, and by adding theory-specific grammatical annotations to make texts more idiomatic.