Dependently Typed Grammars

Parser combinators are a popular tool for designing parsers in functional programming languages. If such combinators generate an abstract representation of the grammar as an intermediate step, it becomes easier to perform analyses and transformations that can improve the behaviour of the resulting parser. Grammar transformations must satisfy a number of invariants. In particular, they have to preserve the semantics associated with the grammar. Using conventional type systems, these constraints cannot be expressed satisfactorily, but as we show in this article, dependent types are a natural fit. We present a framework for grammars and grammar transformations using Agda. We implement the left-corner transformation for left-recursion removal and prove a language-inclusion property as use cases. Key words: context-free grammars, grammar transformation, dependently typed programming

• Type: Conference
• Year: 2010
• Where: MPC
• Authors: Kasper Brink, Stefan Holdermans, Andres Löh
• Keywords: Functional Programming Languages, Grammar Transformation, Mathematics, MPC 2010, Parser Combinators