SDE 3 Proceedings of the third ACM SIGSOFT/SIGPLAN software engineering symposium on Practical software development environments
A framework for defining logics
Journal of the ACM (JACM)
A finitary version of the calculus of partial inductive definitions
ELP'91 Conference Proceedings on Extensions of logic programming
Proceedings of the 24th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
A semantic model of types and machine instructions for proof-carrying code
Proceedings of the 27th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Lightweight Lemmas in &lgr;Prolog
Proceedings of the 1999 international conference on Logic programming
&pgr;-calculus in (Co)inductive-type theory
Theoretical Computer Science - Special issues on models and paradigms for concurrency
On the formalization of the modal &mgr;-calculus in the calculus of inductive constructions
Information and Computation
Reasoning with higher-order abstract syntax in a logical framework
ACM Transactions on Computational Logic (TOCL)
Higher-Order Abstract Syntax with Induction in Coq
LPAR '94 Proceedings of the 5th International Conference on Logic Programming and Automated Reasoning
Higher-Order Abstract Syntax in Coq
TLCA '95 Proceedings of the Second International Conference on Typed Lambda Calculi and Applications
Primitive Recursion for Higher-Order Abstract Syntax
TLCA '97 Proceedings of the Third International Conference on Typed Lambda Calculi and Applications
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
Implementing the Meta-Theory of Deductive Systems
CADE-11 Proceedings of the 11th International Conference on Automated Deduction: Automated Deduction
System Description: Twelf - A Meta-Logical Framework for Deductive Systems
CADE-16 Proceedings of the 16th International Conference on Automated Deduction: Automated Deduction
Semantical Analysis of Higher-Order Abstract Syntax
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
Reasoning in a logic with definitions and induction
Reasoning in a logic with definitions and induction
Automating the meta theory of deductive systems
Automating the meta theory of deductive systems
A definitional approach to primitivexs recursion over higher order abstract syntax
MERLIN '03 Proceedings of the 2003 ACM SIGPLAN workshop on Mechanized reasoning about languages with variable binding
A formalization of an Ordered Logical Framework in Hybrid with applications to continuation machines
MERLIN '03 Proceedings of the 2003 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
Two-Level Hybrid: A System for Reasoning Using Higher-Order Abstract Syntax
Electronic Notes in Theoretical Computer Science (ENTCS)
Reasoning with hypothetical judgments and open terms in hybrid
PPDP '09 Proceedings of the 11th ACM SIGPLAN conference on Principles and practice of declarative programming
Multi-level meta-reasoning with higher-order abstract syntax
FOSSACS'03/ETAPS'03 Proceedings of the 6th International conference on Foundations of Software Science and Computation Structures and joint European conference on Theory and practice of software
Combining de Bruijn indices and higher-order abstract syntax in Coq
TYPES'06 Proceedings of the 2006 international conference on Types for proofs and programs
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
Journal of Automated Reasoning
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The use of higher-order abstract syntax is central to the direct, concise, and modular specification of languages and deductive systems in a logical framework. Developing a framework in which it is also possible to reason about such deductive systems is particularly challenging. One difficulty is that the use of higher-order abstract syntax complicates reasoning by induction because it leads to definitions for which there are no monotone inductive operators. In this paper, we present a methodology which allows Coq to be used as a framework for such meta-reasoning. This methodology is directly inspired by the two-level approach to reasoning used in the FO驴驴N (pronounced fold-n) logic. In our setting, the Calculus of Inductive Constructions (CIC) implemented by Coq represents the highest level, or meta-logic, and a separate specification logic is encoded as an inductive definition in Coq. Then, in our method as in FO驴驴N, the deductive systems that we want to reason about are the object logics which are encoded in the specification logic. We first give an approach to reasoning in Coq which very closely mimics reasoning in FO驴驴N illustrating a close correspondence between the two frameworks. We then generalize the approach to take advantage of other constructs in Coq such as the use of direct structural induction provided by inductive types.