PLDI '88 Proceedings of the ACM SIGPLAN 1988 conference on Programming Language design and Implementation
Unification under a mixed prefix
Journal of Symbolic Computation
Cut-elimination for a logic with definitions and induction
Theoretical Computer Science - Special issue on proof-search in type-theoretic languages
Foundational aspects of syntax
ACM Computing Surveys (CSUR)
Reasoning with higher-order abstract syntax in a logical framework
ACM Transactions on Computational Logic (TOCL)
Higher-Order Abstract Syntax in Coq
TLCA '95 Proceedings of the Second International Conference on Typed Lambda Calculi and Applications
Cut Elimination for Logics with Definitional Reflection
Proceedings of the International Workshop on Nonclassical Logics and Information Processing
Semantical Analysis of Higher-Order Abstract Syntax
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
Nominal logic, a first order theory of names and binding
Information and Computation - TACS 2001
A Sequent Calculus for Nominal Logic
LICS '04 Proceedings of the 19th 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 formal treatment of the barendregt variable convention in rule inductions
Proceedings of the 3rd ACM SIGPLAN workshop on Mechanized reasoning about languages with variable binding
A proof theory for generic judgments
ACM Transactions on Computational Logic (TOCL)
Mechanized metatheory for the masses: the PoplMark challenge
TPHOLs'05 Proceedings of the 18th international conference on Theorem Proving in Higher Order Logics
Nominal techniques in Isabelle/HOL
CADE' 20 Proceedings of the 20th international conference on Automated Deduction
A unifying model of variables and names
FOSSACS'05 Proceedings of the 8th international conference on Foundations of Software Science and Computation Structures
A simpler proof theory for nominal logic
FOSSACS'05 Proceedings of the 8th international conference on Foundations of Software Science and Computation Structures
ACM Transactions on Programming Languages and Systems (TOPLAS)
On the Role of Names in Reasoning about λ-tree Syntax Specifications
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
Proceedings of the 12th international ACM SIGPLAN symposium on Principles and practice of declarative programming
Information and Computation
Stone duality for nominal Boolean algebras with И
CALCO'11 Proceedings of the 4th international conference on Algebra and coalgebra in computer science
Journal of Automated Reasoning
Permissive-nominal logic: First-order logic over nominal terms and sets
ACM Transactions on Computational Logic (TOCL)
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This paper presents an extension of a proof system for encoding generic judgments, the logic FO@l^@D^@? of Miller and Tiu, with an induction principle. The logic FO@l^@D^@? is itself an extension of intuitionistic logic with fixed points and a ''generic quantifier'', @?, which is used to reason about the dynamics of bindings in object systems encoded in the logic. A previous attempt to extend FO@l^@D^@? with an induction principle has been unsuccessful in modeling some behaviours of bindings in inductive specifications. It turns out that this problem can be solved by relaxing some restrictions on @?, in particular by adding the axiom B=@?x.B, where x is not free in B. We show that by adopting the equivariance principle, the presentation of the extended logic can be much simplified. Cut-elimination for the extended logic is stated, and some applications in reasoning about an object logic and a simply typed @l-calculus are illustrated.