PLDI '88 Proceedings of the ACM SIGPLAN 1988 conference on Programming Language design and Implementation
Reasoning with higher-order abstract syntax in a logical framework
ACM Transactions on Computational Logic (TOCL)
A Logic for Reasoning with Higher-Order Abstract Syntax
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
A Proof Theory for Generic Judgments: An extended abstract
LICS '03 Proceedings of the 18th Annual IEEE Symposium on Logic in Computer Science
A logical framework for reasoning about logical specifications
A logical framework for reasoning about logical specifications
A proof theory for generic judgments
ACM Transactions on Computational Logic (TOCL)
Model checking for π-calculus using proof search
CONCUR 2005 - Concurrency Theory
Proceedings of the 35th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Least and greatest fixed points in linear logic
LPAR'07 Proceedings of the 14th international conference on Logic for programming, artificial intelligence and reasoning
Information and Computation
Reasoning about computations using two-levels of logic
APLAS'10 Proceedings of the 8th Asian conference on Programming languages and systems
Least and Greatest Fixed Points in Linear Logic
ACM Transactions on Computational Logic (TOCL)
Focused inductive theorem proving
IJCAR'10 Proceedings of the 5th international conference on Automated Reasoning
Proof pearl: abella formalization of λ-calculus cube property
CPP'12 Proceedings of the Second international conference on Certified Programs and Proofs
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We come back to the initial design of the @? quantifier by Miller and Tiu, which we call minimal generic quantification. In the absence of fixed points, it is equivalent to seemingly stronger designs. However, several expected theorems about (co)inductive specifications can not be derived in that setting. We present a refinement of minimal generic quantification that brings the expected expressivity while keeping the minimal semantic, which we claim is useful to get natural adequate specifications. We build on the idea that generic quantification is not a logical connective but one that is defined, like negation in classical logics. This allows us to use the standard (co)induction rule, but obtain much more expressivity than before. We show classes of theorems that can now be derived in the logic, and present a few practical examples.