Programming in Martin-Lo¨f's type theory: an introduction
Programming in Martin-Lo¨f's type theory: an introduction
Some Lambda Calculus and Type Theory Formalized
Journal of Automated Reasoning
Guarded recursive datatype constructors
POPL '03 Proceedings of the 30th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Higher-Order and Symbolic Computation
TYPES '95 Selected papers from the International Workshop on Types for Proofs and Programs
Intuitionistic model constructions and normalization proofs
Mathematical Structures in Computer Science
Journal of Functional Programming
A predicative analysis of structural recursion
Journal of Functional Programming
Formalized metatheory with terms represented by an indexed family of types
TYPES'04 Proceedings of the 2004 international conference on Types for Proofs and Programs
MSFP'06 Proceedings of the 2006 international conference on Mathematically Structured Functional Programming
Normalization by Evaluation for Martin-Löf Type Theory with One Universe
Electronic Notes in Theoretical Computer Science (ENTCS)
Towards Formalizing Categorical Models of Type Theory in Type Theory
Electronic Notes in Theoretical Computer Science (ENTCS)
Electronic Notes in Theoretical Computer Science (ENTCS)
Outrageous but meaningful coincidences: dependent type-safe syntax and evaluation
Proceedings of the 6th ACM SIGPLAN workshop on Generic programming
Inductive-inductive definitions
CSL'10/EACSL'10 Proceedings of the 24th international conference/19th annual conference on Computer science logic
A categorical semantics for inductive-inductive definitions
CALCO'11 Proceedings of the 4th international conference on Algebra and coalgebra in computer science
Towards normalization by evaluation for the βη-calculus of constructions
FLOPS'10 Proceedings of the 10th international conference on Functional and Logic Programming
Strongly Typed Term Representations in Coq
Journal of Automated Reasoning
Proceedings of the 8th ACM SIGPLAN workshop on Generic programming
Typed syntactic meta-programming
Proceedings of the 18th ACM SIGPLAN international conference on Functional programming
New equations for neutral terms: a sound and complete decision procedure, formalized
Proceedings of the 2013 ACM SIGPLAN workshop on Dependently-typed programming
LICS '13 Proceedings of the 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science
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It is demonstrated how a dependently typed lambda calculus (a logical framework) can be formalised inside a language with inductiverecursive families. The formalisation does not use raw terms; the welltyped terms are defined directly. It is hence impossible to create ill-typed terms. As an example of programming with strong invariants, and to show that the formalisation is usable, normalisation is proved. Moreover, this proof seems to be the first formal account of normalisation by evaluation for a dependently typed language.