A syntactic approach to eta equality in type theory

Healfdene Goguen
2005 Proceedings of the 32nd ACM SIGPLAN-SIGACT sysposium on Principles of programming languages - POPL '05  
This paper outlines a new approach to showing the decidability of type checking for type theories with βηequality, relevant to foundations for modules systems and type theory-based proof systems. The key to the approach is a syntactic translation mapping terms in the βη presentation into their full η-expansions in the β presentation. Decidability of type checking is lifted from the target β presentation to the βη presentation. The approach extends to other inductive types with a single
more » ... or, and is demonstrated for singleton types and Σ-types.
doi:10.1145/1040305.1040312 dblp:conf/popl/Goguen05 fatcat:ioyyd4nulzbjjc642hx74z6gta