An algorithm for testing conversion in type theory
Logical frameworks
Handbook of logic in computer science (vol. 2)
Subtyping with Singleton Types
CSL '94 Selected Papers from the 8th International Workshop on Computer Science Logic
A syntactic approach to eta equality in type theory
Proceedings of the 32nd ACM SIGPLAN-SIGACT symposium on Principles of programming languages
On equivalence and canonical forms in the LF type theory
ACM Transactions on Computational Logic (TOCL)
A syntactic approach to eta equality in type theory
Proceedings of the 32nd ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Untyped Algorithmic Equality for Martin-Löf's Logical Framework with Surjective Pairs
Fundamenta Informaticae - Typed Lambda Calculi and Applications 2005, Selected Papers
Mechanizing the metatheory of LF
ACM Transactions on Computational Logic (TOCL)
A Partial Type Checking Algorithm for Type: Type
Electronic Notes in Theoretical Computer Science (ENTCS)
Higher-order dynamic pattern unification for dependent types and records
TLCA'11 Proceedings of the 10th international conference on Typed lambda calculi and applications
Polarized subtyping for sized types
CSR'06 Proceedings of the First international computer science conference on Theory and Applications
Untyped algorithmic equality for martin-löf's logical framework with surjective pairs
TLCA'05 Proceedings of the 7th international conference on Typed Lambda Calculi and Applications
Untyped Algorithmic Equality for Martin-Löf's Logical Framework with Surjective Pairs
Fundamenta Informaticae - Typed Lambda Calculi and Applications 2005, Selected Papers
| Hi-index | 0.00 |
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 Pfenning [8] 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.