Introduction to higher order categorical logic
Introduction to higher order categorical logic
An algorithm for testing conversion in type theory
Logical frameworks
A framework for defining logics
Journal of the ACM (JACM)
An algorithm for type-checking dependent types
Science of Computer Programming - Special issue on mathematics of program construction
POPL '98 Proceedings of the 25th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Perpetual reductions in &lgr;-calculus
Information and Computation
Intersection types and computational effects
ICFP '00 Proceedings of the fifth ACM SIGPLAN international conference on Functional programming
Handbook of logic in computer science
Soundness of the Logical Framework for Its Typed Operational Semantics
TLCA '99 Proceedings of the 4th International Conference on Typed Lambda Calculi and Applications
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)
Pure type systems with judgemental equality
Journal of Functional Programming
Justifying algorithms for βη-conversion
FOSSACS'05 Proceedings of the 8th international conference on Foundations of Software Science and Computation Structures
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
A Logical Framework with Dependently Typed Records
Fundamenta Informaticae - Typed Lambda Calculi and Applications 2003, Selected Papers
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Martin-Löf's Logical Framework is extended by strong Σ-types and presented via judgmental equality with rules for extensionality and surjective pairing. Soundness of the framework rules is proven via a generic PER model on untyped terms. An algorithmic version of the framework is given through an untyped βη-equality test and a bidirectional type checking algorithm. Completeness is proven by instantiating the PER model with η-equality on β-normal forms, which is shown equivalent to the algorithmic equality.