Indexed linear logic and higher-order model checking

Charles Grellois
(Laboratoires PPS and LIAFA, Université Paris Diderot)
Paul-André Melliès
(Laboratoire PPS, CNRS and Université Paris Diderot)

In recent work, Kobayashi observed that the acceptance by an alternating tree automaton A of an infinite tree T generated by a higher-order recursion scheme G may be formulated as the typability of the recursion scheme G in an appropriate intersection type system associated to the automaton A. The purpose of this article is to establish a clean connection between this line of work and Bucciarelli and Ehrhard's indexed linear logic. This is achieved in two steps. First, we recast Kobayashi's result in an equivalent infinitary intersection type system where intersection is not idempotent anymore. Then, we show that the resulting type system is a fragment of an infinitary version of Bucciarelli and Ehrhard's indexed linear logic. While this work is very preliminary and does not integrate key ingredients of higher-order model-checking like priorities, it reveals an interesting and promising connection between higher-order model-checking and linear logic.

In Jakob Rehof: Proceedings Seventh Workshop on Intersection Types and Related Systems (ITRS 2014), Vienna, Austria, 18 July 2014, Electronic Proceedings in Theoretical Computer Science 177, pp. 43–52.
Published: 17th March 2015.

ArXived at: http://dx.doi.org/10.4204/EPTCS.177.4 bibtex PDF
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