38 research outputs found
A Finite Semantics of Simply-Typed Lambda Terms for Infinite Runs of<br> Automata
Model checking properties are often described by means of finite automata.
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 simply-typed lambda-trees.
A calculus based on this semantics is proven sound and complete. In
particular, for regular infinite 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.Comment: 23 page
An Elementary Fragment of Second-Order Lambda Calculus
A fragment of second-order lambda calculus (System F) is defined that
characterizes the elementary recursive functions. Type quantification is
restricted to be non-interleaved and stratified, i.e., the types are assigned
levels, and a quantified variable can only be instantiated by a type of smaller
level, with a slightly liberalized treatment of the level zero.Comment: 16 pages; correction
IO vs OI in Higher-Order Recursion Schemes
We propose a study of the modes of derivation of higher-order recursion
schemes, proving that value trees obtained from schemes using
innermost-outermost derivations (IO) are the same as those obtained using
unrestricted derivations. Given that higher-order recursion schemes can be used
as a model of functional programs, innermost-outermost derivations policy
represents a theoretical view point of call by value evaluation strategy.Comment: In Proceedings FICS 2012, arXiv:1202.317
A Finite Semantics of Simply-Typed Lambda Terms for Infinite Runs of Automata
Model checking properties are often described by means of finite automata.
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 simply-typed lambda-trees.
A calculus based on this semantics is proven sound and complete. In
particular, for regular infinite 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
A finite semantics for simply-typed lambda terms for infinite runs of automata. preprint
Abstract. Model checking properties are often described by means of finite automata. 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 simply-typed lambda-trees. A calculus based on this semantics is proven sound and complete. In particular, for regular infinite 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. 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 simple types allows for a particularly simple set-theoretic semantics. The drawback, however, is that only few functions can be defined in the simply-typed lambda calculus