Foundational aspects of syntax
ACM Computing Surveys (CSUR)
FLOPS '01 Proceedings of the 5th International Symposium on Functional and Logic Programming
An Axiomatic Approach to Metareasoning on Nominal Algebras in HOAS
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
A Modal Lambda Calculus with Iteration and Case Constructs
TYPES '98 Selected papers from the International Workshop on Types for Proofs and Programs
Rewriting Logic as a Metalogical Framework
FST TCS 2000 Proceedings of the 20th Conference on Foundations of Software Technology and Theoretical Computer Science
FST TCS '02 Proceedings of the 22nd Conference Kanpur on Foundations of Software Technology and Theoretical Computer Science
A Higher-Order Specification of the pi-Calculus
TCS '00 Proceedings of the International Conference IFIP on Theoretical Computer Science, Exploring New Frontiers of Theoretical Informatics
Elimination of Negation in a Logical Framework
Proceedings of the 14th Annual Conference of the EACSL on Computer Science Logic
Recursion for Higher-Order Encodings
CSL '01 Proceedings of the 15th International Workshop on Computer Science Logic
Encoding transition systems in sequent calculus
Theoretical Computer Science - Linear logic
Handbook of automated reasoning
A framework for typed HOAS and semantics
Proceedings of the 5th ACM SIGPLAN international conference on Principles and practice of declaritive programming
Recursion over objects of functional type
Mathematical Structures in Computer Science
A specification logic for concurrent object-oriented programming
Mathematical Structures in Computer Science
Reflective metalogical frameworks
ACM Transactions on Computational Logic (TOCL)
Combining higher-order abstract syntax with first-order abstract syntax in ATS
Proceedings of the 3rd ACM SIGPLAN workshop on Mechanized reasoning about languages with variable binding
Reasoning about Object-based Calculi in (Co)Inductive Type Theory and the Theory of Contexts
Journal of Automated Reasoning
A Meta Linear Logical Framework
Electronic Notes in Theoretical Computer Science (ENTCS)
The Bedwyr System for Model Checking over Syntactic Expressions
CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
On the Expressivity of Minimal Generic Quantification
Electronic Notes in Theoretical Computer Science (ENTCS)
Hiord: a type-free higher-order logic programming language with predicate abstraction
ASIAN'04 Proceedings of the 9th Asian Computing Science conference on Advances in Computer Science: dedicated to Jean-Louis Lassez on the Occasion of His 5th Cycle Birthday
Representing and reasoning with operational semantics
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
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Logical frameworks based on intuitionistic or linear logics with higher-type quantification have been successfully used to give high-level, modular, and formal specifications of many important judgments in the area of programming languages and inference systems. Given such specifications, it is natural to consider proving properties about the specified systems in the framework: for example, given the specification of evaluation for a functional programming language, prove that the language is deterministic or that the subject-reduction theorem holds. One challenge in developing a framework for such reasoning is that higher-order abstract syntax (HOAS), an elegant and declarative treatment of object-level abstraction and substitution, is difficult to treat in proofs involving induction. In this paper, we present a meta-logic that can be used to reason about judgments coded using HOAS; this meta-logic is an extension of a simple intuitionistic logic that admits higher-order quantification over simply typed lambda-terms (key ingredients for HOAS) as well as induction and a notion of definition. The latter concept of a definition is a proof-theoretic device that allows certain theories to be treated as ``closed'' or as defining fixed points. The resulting meta-logic can specify various logical frameworks and a large range of judgments regarding programming languages and inference systems. We illustrate this point through examples, including the admissibility of cut for a simple logic and subject reduction, determinacy of evaluation, and the equivalence of SOS and natural semantics presentations of evaluation for a simple functional programming language.