Equality in lazy computation systems
Proceedings of the Fourth Annual Symposium on Logic in computer science
Proving congruence of bisimulation in functional programming languages
Information and Computation
&pgr;-calculus in (Co)inductive-type theory
Theoretical Computer Science - Special issues on models and paradigms for concurrency
Reasoning with higher-order abstract syntax in a logical framework
ACM Transactions on Computational Logic (TOCL)
Mechanized Operational Semantics via (Co)Induction
TPHOLs '99 Proceedings of the 12th International Conference on Theorem Proving in Higher Order Logics
Combining Higher Order Abstract Syntax with Tactical Theorem Proving and (Co)Induction
TPHOLs '02 Proceedings of the 15th International Conference on Theorem Proving in Higher Order Logics
Formal Foundations of Operational Semantics
Higher-Order and Symbolic Computation
Reasoning in Abella about Structural Operational Semantics Specifications
Electronic Notes in Theoretical Computer Science (ENTCS)
Coinductive big-step operational semantics
Information and Computation
Trace-Based Coinductive Operational Semantics for While
TPHOLs '09 Proceedings of the 22nd International Conference on Theorem Proving in Higher Order Logics
Proof search specifications of bisimulation and modal logics for the π-calculus
ACM Transactions on Computational Logic (TOCL)
A framework for specifying, prototyping, and reasoning about computational systems
A framework for specifying, prototyping, and reasoning about computational systems
Information and Computation
Journal of Automated Reasoning
The marriage of bisimulations and Kripke logical relations
POPL '12 Proceedings of the 39th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Sequent calculi for induction and infinite descent
Journal of Logic and Computation
Mechanized metatheory for the masses: the PoplMark challenge
TPHOLs'05 Proceedings of the 18th international conference on Theorem Proving in Higher Order Logics
Reasoning with higher-order abstract syntax and contexts: a comparison
ITP'10 Proceedings of the First international conference on Interactive Theorem Proving
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We formally verify in Abella that similarity in the call-by-name lambda calculus is a pre-congruence, using Howe's method. This turns out to be a very challenging task for HOAS-based systems, as it entails a demanding combination of inductive and coinductive reasoning on open terms, for which no other existing HOAS-based system is equipped for. We also offer a proof using a version of Abella supplemented with predicate quantification; this results in a more structured presentation that is largely independent of the operational semantics as well of the chosen notion of (bi)similarity. While the end result is significantly more succinct and elegant than previous attempts, the exercise highlights some limitations of the two-level approach in general and of Abella in particular.