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Using models to modelcheck recursive schemes
, 2012
"... We propose a modelbased approach to the model checking problem for recursive schemes. Since simply typed lambda calculus with the fixpoint operator, λYcalculus, is equivalent to schemes, we propose to use a model of λY to discriminate the terms that satisfy a given property. If a model is finite i ..."
Abstract

Cited by 3 (2 self)
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We propose a modelbased approach to the model checking problem for recursive schemes. Since simply typed lambda calculus with the fixpoint operator, λYcalculus, is equivalent to schemes, we propose to use a model of λY to discriminate the terms that satisfy a given property. If a model is finite in every type, this gives a decision procedure. We provide a construction of such a model for every property expressed by automata with trivial acceptance conditions and divergence testing. We argue that having a model capable of recognizing terms satisfying a given property has other benefits than just providing decidability of the modelchecking problem. We show a very simple construction transforming a scheme to a scheme reflecting a given property. 1
The IO and OI hierarchies revisitedI
"... We study languages of λterms generated by IO and OI unsafe grammars. These languages can be used to model meaning representations in the formal semantics of natural languages following the tradition of Montague [25]. Using techniques pertaining to the denotational semantics of the simply typed λca ..."
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We study languages of λterms generated by IO and OI unsafe grammars. These languages can be used to model meaning representations in the formal semantics of natural languages following the tradition of Montague [25]. Using techniques pertaining to the denotational semantics of the simply typed λcalculus, we show that the emptiness and membership problems for both types of grammars are decidable. In the course of the proof of the decidability results for OI, we identify a decidable variant of the λdefinability problem, and prove a stronger form of Statman’s finite completeness Theorem [35].
Krivine machines and higherorder schemesI
"... We propose a new approach to analyzing higherorder recursive schemes. Many results in the literature use automata models generalizing pushdown automata, most notably higherorder pushdown automata with collapse (CPDA). Instead, we propose to use the Krivine machine model. Compared to CPDA, this mod ..."
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We propose a new approach to analyzing higherorder recursive schemes. Many results in the literature use automata models generalizing pushdown automata, most notably higherorder pushdown automata with collapse (CPDA). Instead, we propose to use the Krivine machine model. Compared to CPDA, this model is closer to lambdacalculus, and incorporates nicely many invariants of computations, as for example the typing information. The usefulness of the proposed approach is demonstrated with new proofs of two central results in the field: the decidability of the local and global model checking problems for higherorder schemes with respect to the mucalculus.