Indexed linear logic and higher-order model checking

TL;DR

This paper establishes a theoretical connection between higher-order model checking, automata acceptance, and indexed linear logic, providing a new logical framework for understanding complex recursion schemes.

Contribution

It links higher-order model checking with indexed linear logic through an infinitary intersection type system, revealing a promising new perspective.

Findings

Recast Kobayashi's automata acceptance as a type system

Showed the type system is a fragment of indexed linear logic

Revealed a theoretical connection between model checking and linear logic

Abstract

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.