Types and Recursion Schemes for Higher-Order Program Verification

Naoki Kobayashi

Abstract: Higher-order recursion schemes (recursion schemes, for short) are expressive grammars for describing infinite trees. The modal μ-calculus model checking problem for recursion schemes (“Given a recursion scheme G and a modal μ-calculus formula ϕ, does the tree generated by G satisfy ϕ?”) has been a hot research topic in the theoretical community for recent years [1,2,3,4,5,6,7]. In 2006, it has been shown to be decidable, and n-EXPTIME complete (where n is the order of a recursion scheme) by Ong [5].