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Even higher-order functions for parsing or Why would anyone ever want to use a sixth-order function?
Journal of Functional Programming
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On-the-fly techniques for game-based software model checking
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Third-order idealized algol with iteration is decidable
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Data-abstraction refinement: a game semantic approach
SAS'05 Proceedings of the 12th international conference on Static Analysis
A fragment of ML decidable by visibly pushdown automata
ICALP'11 Proceedings of the 38th international conference on Automata, languages and programming - Volume Part II
HECTOR: an equivalence checker for a higher-order fragment of ML
CAV'12 Proceedings of the 24th international conference on Computer Aided Verification
C-SHORe: a collapsible approach to higher-order verification
Proceedings of the 18th ACM SIGPLAN international conference on Functional programming
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We present Homer , an observational-equivalence model checker for the 3rd-order fragment of Idealized Algol (IA) augmented with iteration. It works by first translating terms of the fragment into a precise representation of their game semantics as visibly pushdown automata (VPA). The VPA-translates are then passed to a VPA toolkit (which we have implemented) to test for equivalence. Thanks to the fully abstract game semantics, observational equivalence of these IA-terms reduces to the VPA Equivalence Problem. Our checker is thus sound and complete; because it model checks open terms, our approach is also compositional. Further, if the terms are inequivalent, Homer will produce both a game-semantic and an operational-semantic counter-example, in the form of a play and a separating context respectively. We showcase these features on a number of examples and (where appropriate) compare its performance with similar tools. To the best of our knowledge, Homer is the first implementation of a model checker of 3rd-order programs.