PLDI '88 Proceedings of the ACM SIGPLAN 1988 conference on Programming Language design and Implementation
Proofs and types
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)
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
Communicating and mobile systems: the &pgr;-calculus
Communicating and mobile systems: the &pgr;-calculus
Reasoning with higher-order abstract syntax in a logical framework
ACM Transactions on Computational Logic (TOCL)
Communication and Concurrency
Cut Elimination for Logics with Definitional Reflection
Proceedings of the International Workshop on Nonclassical Logics and Information Processing
Abstract Syntax for Variable Binders: An Overview
CL '00 Proceedings of the First International Conference on Computational Logic
Automated Theorem Proving in a Simple Meta-Logic for LF
CADE-15 Proceedings of the 15th 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
Encoding transition systems in sequent calculus
Theoretical Computer Science - Linear logic
A Proof Theory for Generic Judgments: An extended abstract
LICS '03 Proceedings of the 18th Annual IEEE Symposium on Logic in Computer Science
Reasoning in a logic with definitions and induction
Reasoning in a logic with definitions and induction
Nominal logic, a first order theory of names and binding
Information and Computation - TACS 2001
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)
Alpha-structural recursion and induction
Journal of the ACM (JACM)
A Logic for Reasoning about Generic Judgments
Electronic Notes in Theoretical Computer Science (ENTCS)
Nominal Reasoning Techniques in Coq
Electronic Notes in Theoretical Computer Science (ENTCS)
Nominal Techniques in Isabelle/HOL
Journal of Automated Reasoning
Combining Generic Judgments with Recursive Definitions
LICS '08 Proceedings of the 2008 23rd Annual IEEE Symposium on Logic in Computer Science
ACM Transactions on Programming Languages and Systems (TOPLAS)
The Bedwyr System for Model Checking over Syntactic Expressions
CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
The Abella Interactive Theorem Prover (System Description)
IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
Reasoning in Abella about Structural Operational Semantics Specifications
Electronic Notes in Theoretical Computer Science (ENTCS)
On the Expressivity of Minimal Generic Quantification
Electronic Notes in Theoretical Computer Science (ENTCS)
Proof search specifications of bisimulation and modal logics for the π-calculus
ACM Transactions on Computational Logic (TOCL)
A Proof Search Specification of the π-Calculus
Electronic Notes in Theoretical Computer Science (ENTCS)
A framework for specifying, prototyping, and reasoning about computational systems
A framework for specifying, prototyping, and reasoning about computational systems
Relating nominal and higher-order abstract syntax specifications
Proceedings of the 12th international ACM SIGPLAN symposium on Principles and practice of declarative programming
Journal of Automated Reasoning
A simpler proof theory for nominal logic
FOSSACS'05 Proceedings of the 8th international conference on Foundations of Software Science and Computation Structures
A Two-Level Logic Approach to Reasoning About Computations
Journal of Automated Reasoning
Combining Deduction Modulo and Logics of Fixed-Point Definitions
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
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
Proof pearl: abella formalization of λ-calculus cube property
CPP'12 Proceedings of the Second international conference on Certified Programs and Proofs
Reasoning about higher-order relational specifications
Proceedings of the 15th Symposium on Principles and Practice of Declarative Programming
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Recursive relational specifications are commonly used to describe the computational structure of formal systems. Recent research in proof theory has identified two features that facilitate direct, logic-based reasoning about such descriptions: the interpretation of atomic judgments through recursive definitions and an encoding of binding constructs via generic judgments. However, logics encompassing these two features do not currently allow for the definition of relations that embody dynamic aspects related to binding, a capability needed in many reasoning tasks. We propose a new relation between terms called nominal abstraction as a means for overcoming this deficiency. We incorporate nominal abstraction into a rich logic also including definitions, generic quantification, induction, and co-induction that we then prove to be consistent. We present examples to show that this logic can provide elegant treatments of binding contexts that appear in many proofs, such as those establishing properties of typing calculi and of arbitrarily cascading substitutions that play a role in reducibility arguments.