 
Summary: Logical Methods in Computer Science
Vol. 3 (3:?) 2007, pp. 122
www.lmcsonline.org
Submitted Now. 24, 2006
Published Jul. , 2007
A FINITE SEMANTICS OF SIMPLYTYPED LAMBDA TERMS
FOR INFINITE RUNS OF AUTOMATA
KLAUS AEHLIG
Department of Computer Science, University of Wales Swansea, Swansea SA2 8PP, United King
dom
email address: k.t.aehlig@swan.ac.uk
Abstract. Model checking properties are often described by means of nite automata.
Any particular such automaton divides the set of innite trees into nitely many classes,
according to which state has an innite run. Building the full type hierarchy upon this
interpretation of the base type gives a nite semantics for simplytyped lambdatrees.
A calculus based on this semantics is proven sound and complete. In particular, for
regular innite lambdatrees it is decidable whether a given automaton has a run or not.
As regular lambdatrees are precisely recursion schemes, this decidability result holds for
arbitrary recursion schemes of arbitrary level, without any syntactical restriction.
1. Introduction and Related Work
