A framework for defining logics
Journal of the ACM (JACM)
Reasoning with higher-order abstract syntax in a logical framework
ACM Transactions on Computational Logic (TOCL)
System Description: Twelf - A Meta-Logical Framework for Deductive Systems
CADE-16 Proceedings of the 16th International Conference on Automated Deduction: Automated Deduction
Automating the meta theory of deductive systems
Automating the meta theory of deductive systems
Interactive Theorem Proving and Program Development
Interactive Theorem Proving and Program Development
Verifying Termination and Reduction Properties about Higher-Order Logic Programs
Journal of Automated Reasoning
Mechanizing metatheory in a logical framework
Journal of Functional Programming
Proceedings of the 35th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Two-Level Hybrid: A System for Reasoning Using Higher-Order Abstract Syntax
Electronic Notes in Theoretical Computer Science (ENTCS)
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
Case Analysis of Higher-Order Data
Electronic Notes in Theoretical Computer Science (ENTCS)
Practical programming with higher-order encodings and dependent types
ESOP'08/ETAPS'08 Proceedings of the Theory and practice of software, 17th European conference on Programming languages and systems
Journal of Automated Reasoning
Mechanized metatheory for the masses: the PoplMark challenge
TPHOLs'05 Proceedings of the 18th international conference on Theorem Proving in Higher Order Logics
Beluga: a framework for programming and reasoning with deductive systems (system description)
IJCAR'10 Proceedings of the 5th international conference on Automated Reasoning
Focused inductive theorem proving
IJCAR'10 Proceedings of the 5th international conference on Automated Reasoning
Programming inductive proofs: a new approach based on contextual types
Verification, induction termination analysis
Programming inductive proofs: a new approach based on contextual types
Verification, induction termination analysis
Journal of Automated Reasoning
A supposedly fun thing i may have to do again: a HOAS encoding of Howe's method
Proceedings of the seventh international workshop on Logical frameworks and meta-languages, theory and practice
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A variety of logical frameworks support the use of higher-order abstract syntax (HOAS) in representing formal systems given via axioms and inference rules and reasoning about them. In such frameworks, object-level binding is encoded directly using meta-level binding. Although these systems seem superficially the same, they differ in a variety of ways; for example, in how they handle a context of assumptions and in what theorems about a given formal system can be expressed and proven. In this paper, we present several case studies which highlight a variety of different aspects of reasoning using HOAS, with the intention of providing a basis for qualitative comparison of different systems. We then carry out such a comparison among three systems: Twelf, Beluga, and Hybrid. We also develop a general set of criteria for comparing such systems. We hope that others will implement these challenge problems, apply these criteria, and further our understanding of the trade-offs involved in choosing one system over another for this kind of reasoning.