Formalising type-logical grammars in Agda

Wen Kokke

Research output: Contribution to conferencePaperpeer-review


In recent years, the interest in using proof assistants to formalise and reason about mathematics and programming languages has grown. Type-logical grammars, being closely related to type theories and systems used in functional programming, are a perfect candidate to next apply this curiosity to. The advantages of using proof assistants is that they allow one to write formally verified proofs about one’s type-logical systems, and that any theory, once implemented, can immediately be computed with. The downside is that in many cases the formal proofs are written as an afterthought, are incomplete, or use obtuse syntax. This makes it that the verified proofs are often much more difficult to read than the pen-andpaper proofs, and almost never directly published. In this paper, we will try to remedy that by example. Concretely, we use Agda to model the LambekGrishin calculus, a grammar logic with a rich vocabulary of type-forming operations. We then present a verified procedure for cut elimination in this system. Then we briefly outline a CPS translation from proofs in the Lambek-Grishin calculus to programs in Agda. And finally, we will put our system to use in the analysis of a simple example sentence.
Original languageEnglish
Number of pages7
Publication statusE-pub ahead of print - 14 Aug 2015
Event27th European Summer School in Logic, Language and Information - Poblenou Campus of Universitat Pompeu Fabra, Barcelona , Spain
Duration: 3 Aug 201514 Aug 2015
Conference number: 27


Conference27th European Summer School in Logic, Language and Information
Abbreviated titleESSLLI 2015
Internet address


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