An algorithm for testing conversion in type theory
Logical frameworks
A framework for defining logics
Journal of the ACM (JACM)
Proceedings of the 24th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Communications of the ACM
Some Lambda Calculus and Type Theory Formalized
Journal of Automated Reasoning
TLCA '95 Proceedings of the Second International Conference on Typed Lambda Calculi and Applications
TYPES '00 Selected papers from the International Workshop on Types for Proofs and Programs
System Description: Twelf - A Meta-Logical Framework for Deductive Systems
CADE-16 Proceedings of the 16th International Conference on Automated Deduction: Automated Deduction
Handbook of automated reasoning
FreshML: programming with binders made simple
ICFP '03 Proceedings of the eighth ACM SIGPLAN international conference on Functional programming
Nominal logic, a first order theory of names and binding
Information and Computation - TACS 2001
Some logical and syntactical observations concerning the first-order dependent type system λP
Mathematical Structures in Computer Science
Journal of Automated Reasoning
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)
Alpha-structural recursion and induction
Journal of the ACM (JACM)
Mechanizing metatheory in a logical framework
Journal of Functional Programming
Proceedings of the 35th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Formalising in Nominal Isabelle Crary's Completeness Proof for Equivalence Checking
Electronic Notes in Theoretical Computer Science (ENTCS)
Nominal Techniques in Isabelle/HOL
Journal of Automated Reasoning
Combining Generic Judgments with Recursive Definitions
LICS '08 Proceedings of the 2008 23rd Annual IEEE Symposium on Logic in Computer Science
Mechanizing the Metatheory of LF
LICS '08 Proceedings of the 2008 23rd Annual IEEE Symposium on Logic in Computer Science
LICS '08 Proceedings of the 2008 23rd Annual IEEE Symposium on Logic in Computer Science
Parametric higher-order abstract syntax for mechanized semantics
Proceedings of the 13th ACM SIGPLAN international conference on Functional programming
Barendregt's Variable Convention in Rule Inductions
CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
Revisiting Cut-Elimination: One Difficult Proof Is Really a Proof
RTA '08 Proceedings of the 19th international conference on Rewriting Techniques and Applications
TPHOLs '08 Proceedings of the 21st International Conference on Theorem Proving in Higher Order Logics
Electronic Notes in Theoretical Computer Science (ENTCS)
The calculus of nominal inductive constructions: an intensional approach to encoding name-bindings
Proceedings of the Fourth International Workshop on Logical Frameworks and Meta-Languages: Theory and Practice
Isabelle/HOL: a proof assistant for higher-order logic
Isabelle/HOL: a proof assistant for higher-order logic
Proof pearl: de Bruijn terms really do work
TPHOLs'07 Proceedings of the 20th international conference on Theorem proving in higher order logics
Proof pearl: the power of higher-order encodings in the logical framework LF
TPHOLs'07 Proceedings of the 20th international conference on Theorem proving in higher order logics
Mechanized metatheory for the masses: the PoplMark challenge
TPHOLs'05 Proceedings of the 18th international conference on Theorem Proving in Higher Order Logics
Nominal techniques in Isabelle/HOL
CADE' 20 Proceedings of the 20th international conference on Automated Deduction
Justifying algorithms for βη-conversion
FOSSACS'05 Proceedings of the 8th international conference on Foundations of Software Science and Computation Structures
Mechanised computability theory
ITP'11 Proceedings of the Second international conference on Interactive theorem proving
Mechanizing the metatheory of mini-XQuery
CPP'11 Proceedings of the First international conference on Certified Programs and Proofs
Formalizing Adequacy: A Case Study for Higher-order Abstract Syntax
Journal of Automated Reasoning
LF in LF: mechanizing the metatheories of LF in twelf
Proceedings of the seventh international workshop on Logical frameworks and meta-languages, theory and practice
Hi-index | 0.00 |
LF is a dependent type theory in which many other formal systems can be conveniently embedded. However, correct use of LF relies on nontrivial metatheoretic developments such as proofs of correctness of decision procedures for LF's judgments. Although detailed informal proofs of these properties have been published, they have not been formally verified in a theorem prover. We have formalized these properties within Isabelle/HOL using the Nominal Datatype Package, closely following a recent article by Harper and Pfenning. In the process, we identified and resolved a gap in one of the proofs and a small number of minor lacunae in others. We also formally derive a version of the type checking algorithm from which Isabelle/HOL can generate executable code. Besides its intrinsic interest, our formalization provides a foundation for studying the adequacy of LF encodings, the correctness of Twelf-style metatheoretic reasoning, and the metatheory of extensions to LF.