A framework for defining logics
Journal of the ACM (JACM)
Using typed lambda calculus to implement formal systems on a machine
Journal of Automated Reasoning
Autarkic Computations in Formal Proofs
Journal of Automated Reasoning
POPL '03 Proceedings of the 30th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
FoSSaCS '01 Proceedings of the 4th International Conference on Foundations of Software Science and Computation Structures
Natural Deduction for Intuitionistic Non-communicative Linear Logic
TLCA '99 Proceedings of the 4th International Conference on Typed Lambda Calculi and Applications
Intensionality, Extensionality, and Proof Irrelevance in Modal Type Theory
LICS '01 Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science
Journal of Automated Reasoning
A Framework for Defining Logical Frameworks
Electronic Notes in Theoretical Computer Science (ENTCS)
Mechanizing metatheory in a logical framework
Journal of Functional Programming
ACM Transactions on Computational Logic (TOCL)
Programming with proofs and explicit contexts
Proceedings of the 10th international ACM SIGPLAN conference on Principles and practice of declarative programming
A Conditional Logical Framework
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
System Description: Delphin -- A Functional Programming Language for Deductive Systems
Electronic Notes in Theoretical Computer Science (ENTCS)
A universe of binding and computation
Proceedings of the 14th ACM SIGPLAN international conference on Functional programming
Higher-order representation of substructural logics
Proceedings of the 15th ACM SIGPLAN international conference on Functional programming
Beluga: a framework for programming and reasoning with deductive systems (system description)
IJCAR'10 Proceedings of the 5th international conference on Automated Reasoning
25 years of formal proof cultures: some problems, some philosophy, bright future
Proceedings of the Eighth ACM SIGPLAN international workshop on Logical frameworks & meta-languages: theory & practice
Foundational proof certificates in first-order logic
CADE'13 Proceedings of the 24th international conference on Automated Deduction
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The LFP Framework is an extension of the Harper-Honsell-Plotkin's Edinburgh Logical Framework LF with external predicates. This is accomplished by defining lock type constructors, which are a sort of diamond-modality constructors, releasing their argument under the condition that a possibly external predicate is satisfied on an appropriate typed judgement. Lock types are defined using the standard pattern of constructive type theory, i.e. via introduction, elimination, and equality rules. Using LFP, one can factor out the complexity of encoding specific features of logical systems which would otherwise be awkwardly encoded in LF, e.g. side-conditions in the application of rules in Modal Logics, and substructural rules, as in non-commutative Linear Logic. The idea of LFP is that these conditions need only to be specified, while their verification can be delegated to an external proof engine, in the style of the Poincaré Principle. We investigate and characterize the metatheoretical properties of the calculus underpinning LFP: strong normalization, confluence, and subject reduction. This latter property holds under the assumption that the predicates are well-behaved, i.e. closed under weakening, permutation, substitution, and reduction in the arguments.