Programming in Martin-Lo¨f's type theory: an introduction
Programming in Martin-Lo¨f's type theory: an introduction
A framework for defining logics
Journal of the ACM (JACM)
Handbook of logic in computer science (vol. 3)
An algorithm for type-checking dependent types
Science of Computer Programming - Special issue on mathematics of program construction
A compiled implementation of strong reduction
Proceedings of the seventh ACM SIGPLAN international conference on Functional programming
Principles and Pragmatics of Subtyping in PVS
WADT '99 Selected papers from the 14th International Workshop on Recent Trends in Algebraic Development Techniques
Subtyping with Singleton Types
CSL '94 Selected Papers from the 8th International Workshop on Computer Science Logic
Operational aspects of untyped Normalisation by Evaluation
Mathematical Structures in Computer Science
Journal of Logic and Computation
Extensional equivalence and singleton types
ACM Transactions on Computational Logic (TOCL)
Towards a mechanized metatheory of standard ML
Proceedings of the 34th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
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
Verifying a Semantic βη-Conversion Test for Martin-Löf Type Theory
MPC '08 Proceedings of the 9th international conference on Mathematics of Program Construction
On the algebraic foundation of proof assistants for intuitionistic type theory
FLOPS'08 Proceedings of the 9th international conference on Functional and logic programming
TYPES'06 Proceedings of the 2006 international conference on Types for proofs and programs
Epigram: practical programming with dependent types
AFP'04 Proceedings of the 5th international conference on Advanced Functional Programming
Proceedings of the 15th ACM SIGPLAN international conference on Functional programming
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
Inductive consequences in the calculus of constructions
ITP'10 Proceedings of the First international conference on Interactive Theorem Proving
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We define a logical framework with singleton types and one universe of small types. We give the semantics using a PER model; it is used for constructing a normalisation-by-evaluation algorithm. We prove completeness and soundness of the algorithm; and get as a corollary the injectivity of type constructors. Then we give the definition of a correct and complete type-checking algorithm for terms in normal form. We extend the results to proof-irrelevant propositions.