The concept of a supercompiler
ACM Transactions on Programming Languages and Systems (TOPLAS) - The MIT Press scientific computation series
Local model checking for infinite state spaces
Selected papers of the Second Workshop on Concurrency and compositionality
Introduction to HOL: a theorem proving environment for higher order logic
Introduction to HOL: a theorem proving environment for higher order logic
Infinite objects in type theory
TYPES '93 Proceedings of the international workshop on Types for proofs and programs
Cut-elimination for a logic with definitions and induction
Theoretical Computer Science - Special issue on proof-search in type-theoretic languages
Computer-Aided Reasoning: An Approach
Computer-Aided Reasoning: An Approach
Verifying Temporal Properties Using Explicit Approximants: Completeness for Context-free Processes
FoSSaCS '02 Proceedings of the 5th International Conference on Foundations of Software Science and Computation Structures
Automating the meta theory of deductive systems
Automating the meta theory of deductive systems
Interactive Theorem Proving and Program Development
Interactive Theorem Proving and Program Development
On the structure of inductive reasoning: circular and tree-shaped proofs in the µ-calculus
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
Isabelle/HOL: a proof assistant for higher-order logic
Isabelle/HOL: a proof assistant for higher-order logic
Electronic Notes in Theoretical Computer Science (ENTCS)
Distilling Programs for Verification
Electronic Notes in Theoretical Computer Science (ENTCS)
Cyclic proofs of program termination in separation logic
Proceedings of the 35th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Initial Algebra Semantics for Cyclic Sharing Structures
TLCA '09 Proceedings of the 9th International Conference on Typed Lambda Calculi and Applications
On the Proof Theory of Regular Fixed Points
TABLEAUX '09 Proceedings of the 18th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
Decidability and undecidability results for propositional schemata
Journal of Artificial Intelligence Research
Least and Greatest Fixed Points in Linear Logic
ACM Transactions on Computational Logic (TOCL)
Complexity of the satisfiability problem for a class of propositional schemata
LATA'10 Proceedings of the 4th international conference on Language and Automata Theory and Applications
Incremental pattern-based coinduction for process algebra and its isabelle formalization
FOSSACS'10 Proceedings of the 13th international conference on Foundations of Software Science and Computational Structures
Formalised inductive reasoning in the logic of bunched implications
SAS'07 Proceedings of the 14th international conference on Static Analysis
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We consider a cyclic approach to inductive reasoning in the setting of first-order logic with inductive definitions. We present a proof system for this language in which proofs are represented as finite, locally sound derivation trees with a “repeat function” identifying cyclic proof sections. Soundness is guaranteed by a well-foundedness condition formulated globally in terms of traces over the proof tree, following an idea due to Sprenger and Dam. However, in contrast to their work, our proof system does not require an extension of logical syntax by ordinal variables. A fundamental question in our setting is the strength of the cyclic proof system compared to the more familiar use of a non-cyclic proof system using explicit induction rules. We show that the cyclic proof system subsumes the use of explicit induction rules. In addition, we provide machinery for manipulating and analysing the structure of cyclic proofs, based primarily on viewing them as generating regular infinite trees, and also formulate a finitary trace condition sufficient (but not necessary) for soundness, that is computationally and combinatorially simpler than the general trace condition.