 
Summary: A Finite Semantics of SimplyTyped Lambda Terms
for Infinite Runs of Automata
Klaus Aehlig
Mathematisches Institut
LudwigMaximiliansUniversit˜at M˜unchen
Theresienstr. 39, 80333 M˜unchen, Germany
aehlig@math.lmu.de
Abstract. Model checking properties are often described by means of finite au
tomata. Any particular such automaton divides the set of infinite trees into finitely
many classes, according to which state has an infinite run. Building the full type
hierarchy upon this interpretation of the base type gives a finite semantics for
simplytyped lambdatrees.
A calculus based on this semantics is proven sound and complete. In particular,
for regular infinite lambdatrees it is decidable whether a given automaton has a
run or not. As regular lambdatrees are precisely recursion schemes, this decid
ability result holds for arbitrary recursion schemes of arbitrary level, without any
syntactical restriction. This partially solves an open problem of Knapik, Niwinski
and Urzyczyn.
1 Introduction and Related Work
The lambda calculus has long been used as a model of computation. Restricting it to
