Summary: Logical Methods in Computer Science
Vol. 3 (3:?) 2007, pp. 1--22
Submitted Now. 24, 2006
Published Jul. , 2007
A FINITE SEMANTICS OF SIMPLY-TYPED LAMBDA TERMS
FOR INFINITE RUNS OF AUTOMATA
Department of Computer Science, University of Wales Swansea, Swansea SA2 8PP, United King-
e-mail address: email@example.com
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 simply-typed lambda-trees.
A calculus based on this semantics is proven sound and complete. In particular, for
regular innite lambda-trees it is decidable whether a given automaton has a run or not.
As regular lambda-trees are precisely recursion schemes, this decidability result holds for
arbitrary recursion schemes of arbitrary level, without any syntactical restriction.
1. Introduction and Related Work