Higher-Order Pushdown Trees Are Easy
FoSSaCS '02 Proceedings of the 5th International Conference on Foundations of Software Science and Computation Structures
On Model-Checking Trees Generated by Higher-Order Recursion Schemes
LICS '06 Proceedings of the 21st Annual IEEE Symposium on Logic in Computer Science
A call-by-name lambda-calculus machine
Higher-Order and Symbolic Computation
Collapsible Pushdown Automata and Recursion Schemes
LICS '08 Proceedings of the 2008 23rd Annual IEEE Symposium on Logic in Computer Science
Positional Strategies for Higher-Order Pushdown Parity Games
MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
A Type System Equivalent to the Modal Mu-Calculus Model Checking of Higher-Order Recursion Schemes
LICS '09 Proceedings of the 2009 24th Annual IEEE Symposium on Logic In Computer Science
Deciding monadic theories of hyperalgebraic trees
TLCA'01 Proceedings of the 5th international conference on Typed lambda calculi and applications
Selection and uniformization problems in the monadic theory of ordinals: a survey
Pillars of computer science
Recursion Schemes and Logical Reflection
LICS '10 Proceedings of the 2010 25th Annual IEEE Symposium on Logic in Computer Science
Krivine machines and higher-order schemes
ICALP'11 Proceedings of the 38th international conference on Automata, languages and programming - Volume Part II
Unsafe grammars and panic automata
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
On the Significance of the Collapse Operation
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
Recursive schemes, krivine machines, and collapsible pushdown automata
RP'12 Proceedings of the 6th international conference on Reachability Problems
Program certification by higher-order model checking
CPP'12 Proceedings of the Second international conference on Certified Programs and Proofs
C-SHORe: a collapsible approach to higher-order verification
Proceedings of the 18th ACM SIGPLAN international conference on Functional programming
LICS '13 Proceedings of the 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science
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Higher-order recursion schemes are rewriting systems for simply typed terms and they are known to be equi-expressive with collapsible pushdown automata (CPDA) for generating trees. We argue that CPDA are an essential model when working with recursion schemes. First, we give a new proof of the translation of schemes into CPDA that does not appeal to game semantics. Second, we show that this translation permits to revisit the safety constraint and allows CPDA to be seen as Krivine machines. Finally, we show that CPDA permit one to prove the effective MSO selection property for schemes, subsuming all known decidability results for MSO on schemes.