Proofs and types
Cut-elimination for a logic with definitions and induction
Theoretical Computer Science - Special issue on proof-search in type-theoretic languages
Inductive Definitions in the system Coq - Rules and Properties
TLCA '93 Proceedings of the International Conference on Typed Lambda Calculi and Applications
Monotone Fixed-Point Types and Strong Normalization
Proceedings of the 12th International Workshop on Computer Science Logic
Journal of Automated Reasoning
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)
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
A framework for specifying, prototyping, and reasoning about computational systems
A framework for specifying, prototyping, and reasoning about computational systems
Algorithmic equality in Heyting arithmetic modulo
TYPES'07 Proceedings of the 2007 international conference on Types for proofs and programs
Information and Computation
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
Stratification in logics of definitions
IJCAR'12 Proceedings of the 6th international joint conference on Automated Reasoning
Unbounded proof-length speed-up in deduction modulo
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
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Inductive and coinductive specifications are widely used in formalizing computational systems. Such specifications have a natural rendition in logics that support fixed-point definitions. Another useful formalization device is that of recursive specifications. These specifications are not directly complemented by fixed-point reasoning techniques and, correspondingly, do not have to satisfy strong monotonicity restrictions. We show how to incorporate a rewriting capability into logics of fixed-point definitions towards additionally supporting recursive specifications. Specifically, we describe a natural deduction calculus that adds a form of ``closed-world'' equality---a key ingredient to supporting fixed-point definitions---to deduction modulo, a framework for extending a logic with a rewriting layer operating on formulas. We show that our calculus enjoys strong normalizability when the rewrite system satisfies general properties and we demonstrate its usefulness in specifying and reasoning about syntax-based descriptions. Our integration of closed-world equality into deduction modulo is based on an elimination principle for this form of equality that, for the first time, allows us to require finiteness of proofs without sacrificing stability under reduction.