Closure under alpha-conversion
TYPES '93 Proceedings of the international workshop on Types for proofs and programs
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
Type-Directed Partial Evaluation
Partial Evaluation - Practice and Theory, DIKU 1998 International Summer School
TYPES '95 Selected papers from the International Workshop on Types for Proofs and Programs
From Semantics to Rules: A Machine Assisted Analysis
CSL '93 Selected Papers from the 7th Workshop on Computer Science Logic
System Description: Twelf - A Meta-Logical Framework for Deductive Systems
CADE-16 Proceedings of the 16th International Conference on Automated Deduction: Automated Deduction
On equivalence and canonical forms in the LF type theory
ACM Transactions on Computational Logic (TOCL)
Formal certification of a compiler back-end or: programming a compiler with a proof assistant
Conference record of the 33rd ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Alpha-structural recursion and induction
Journal of the ACM (JACM)
A Logical Framework with Dependently Typed Records
Fundamenta Informaticae - Typed Lambda Calculi and Applications 2003, Selected Papers
Normalization by Evaluation for Martin-Löf Type Theory with One Universe
Electronic Notes in Theoretical Computer Science (ENTCS)
Normalization by Evaluation for Martin-Lof Type Theory with Typed Equality Judgements
LICS '07 Proceedings of the 22nd Annual IEEE Symposium on Logic in Computer Science
Untyped Algorithmic Equality for Martin-Löf's Logical Framework with Surjective Pairs
Fundamenta Informaticae - Typed Lambda Calculi and Applications 2005, Selected Papers
LICS '08 Proceedings of the 2008 23rd Annual IEEE Symposium on Logic in Computer Science
Weak βη -Normalization and Normalization by Evaluation for System F
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
A Modular Type-Checking Algorithm for Type Theory with Singleton Types and Proof Irrelevance
TLCA '09 Proceedings of the 9th International Conference on Typed Lambda Calculi and Applications
Greedy bidirectional polymorphism
Proceedings of the 2009 ACM SIGPLAN workshop on ML
A Partial Type Checking Algorithm for Type: Type
Electronic Notes in Theoretical Computer Science (ENTCS)
Irrelevance in type theory with a heterogeneous equality judgement
FOSSACS'11/ETAPS'11 Proceedings of the 14th international conference on Foundations of software science and computational structures: part of the joint European conferences on theory and practice of software
Towards normalization by evaluation for the βη-calculus of constructions
FLOPS'10 Proceedings of the 10th international conference on Functional and Logic Programming
Complete and easy bidirectional typechecking for higher-rank polymorphism
Proceedings of the 18th ACM SIGPLAN international conference on Functional programming
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Type-checking algorithms for dependent type theories often relyon the interpretation of terms in some semantic domain ofvalueswhen checking equalities. Here we analyze a versionof Coquand's algorithm for checking theβη-equality of such semantic values in a theorywith a predicative universe hierarchy and large elimination rules.Although this algorithm does not rely on normalization byevaluation explicitly, we show that similar ideas can be employedfor its verification. In particular, our proof uses the new notionsof contextualreification and strong semanticequality.The algorithm is part of a bi-directional type checkingalgorithm which checks whether a normal term has a certain semantictype, a technique used in the proof assistants Agda and Epigram. Wework with an abstract notion of semantic domain in order toaccommodate a variety of possible implementation techniques, suchas normal forms, weak head normal forms, closures, and compiledcode. Our aim is to get closer than previous work to verifying thetype-checking algorithms which are actually used in practice.