Justifying Algorithms for βη-Conversion [chapter]

Healfdene Goguen
2005 Lecture Notes in Computer Science  
Deciding the typing judgement of type theories with dependent types such as the Logical Framework relies on deciding the equality judgement for the same theory. Implementing the conversion algorithm for βη equality and justifying this algorithm is therefore an important problem for applications such as proof assistants and modules systems. This article gives a proof of decidability, correctness and completeness of the conversion algorithms for βη equality defined by Coquand [3] and Harper and
more » ... enning [9] for the Logical Framework, relying on established metatheoretic results for the type theory. Proofs are also given of the same properties for a typed algorithm for conversion for System F, a new result. Having validated the approach for its two most important axes, dependent types and polymorphism, it seems likely that the techniques here can be extended to the Calculus of Constructions with βη equality.
doi:10.1007/978-3-540-31982-5_26 fatcat:rfpv4yncgfe27h4zwsscxk5c3e