Proofs and types
Theoretical Computer Science - Special issue: Fourth workshop on mathematical foundations of programming semantics, Boulder, CO, May 1988
FPCA '89 Proceedings of the fourth international conference on Functional programming languages and computer architecture
A framework for defining logics
Journal of the ACM (JACM)
May I borrow your logic? (Transporting logical structures along maps)
Theoretical Computer Science - Special issue: algebraic development techniques
Types and programming languages
Types and programming languages
A Generalization of Short-Cut Fusion and its Correctness Proof
Higher-Order and Symbolic Computation
A Logic for Parametric Polymorphism
TLCA '93 Proceedings of the International Conference on Typed Lambda Calculi and Applications
On the Relation between Direct and Continuation Semantics
Proceedings of the 2nd Colloquium on Automata, Languages and Programming
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
System Description: Twelf - A Meta-Logical Framework for Deductive Systems
CADE-16 Proceedings of the 16th International Conference on Automated Deduction: Automated Deduction
Outline of a Proof Theory of Parametricity
Proceedings of the 5th ACM Conference on Functional Programming Languages and Computer Architecture
Handbook of automated reasoning
On equivalence and canonical forms in the LF type theory
ACM Transactions on Computational Logic (TOCL)
Translating Higher-Order Clauses to First-Order Clauses
Journal of Automated Reasoning
LICS '08 Proceedings of the 2008 23rd Annual IEEE Symposium on Logic in Computer Science
The Abella Interactive Theorem Prover (System Description)
IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
A practical module system for LF
Proceedings of the Fourth International Workshop on Logical Frameworks and Meta-Languages: Theory and Practice
Parametricity, type equality, and higher-order polymorphism
Journal of Functional Programming
Parametricity and dependent types
Proceedings of the 15th ACM SIGPLAN international conference on Functional programming
Representing model theory in a type-theoretical logical framework
Theoretical Computer Science
Project abstract: logic atlas and integrator (LATIN)
MKM'11 Proceedings of the 18th Calculemus and 10th international conference on Intelligent computer mathematics
Journal of Functional Programming - Dedicated to ICFP 2009
Proofs for free: Parametricity for dependent types
Journal of Functional Programming
The Impact of seq on Free Theorems-Based Program Transformations
Fundamenta Informaticae - Program Transformation: Theoretical Foundations and Basic Techniques. Part 2
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Logical relations are a central concept used to study various higher-order type theories and occur frequently in the proofs of a wide variety of meta-theorems. Besides extending the logical relation principle to more general languages, an important research question has been how to represent and thus verify logical relation arguments in logical frameworks. We formulate a theory of logical relations for Dependent Type Theory (DTT) with β η-equality which guarantees that any valid logical relation satisfies the Basic Lemma. Our definition is syntactic and reflective in the sense that a relation at a type is represented as a DTT type family but also permits expressing certain semantic definitions. We use the Edinburgh Logical Framework (LF) incarnation of DTT and implement our notion of logical relations in the type-checker Twelf. This enables us to formalize and mechanically decide the validity of logical relation arguments. Furthermore, our implementation includes a module system so that logical relations can be built modularly. We validate our approach by formalizing and verifying several syntactic and semantic meta-theorems in Twelf. Moreover, we show how object languages encoded in DTT can inherit a notion of logical relation from the logical framework.