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Constraint solving in non-permutative nominal abstract syntax
Nominal abstract syntax is a popular first-order technique for encoding, and
reasoning about, abstract syntax involving binders. Many of its applications
involve constraint solving. The most commonly used constraint solving algorithm
over nominal abstract syntax is the Urban-Pitts-Gabbay nominal unification
algorithm, which is well-behaved, has a well-developed theory and is applicable
in many cases. However, certain problems require a constraint solver which
respects the equivariance property of nominal logic, such as Cheney's
equivariant unification algorithm. This is more powerful but is more
complicated and computationally hard. In this paper we present a novel
algorithm for solving constraints over a simple variant of nominal abstract
syntax which we call non-permutative. This constraint problem has similar
complexity to equivariant unification but without many of the additional
complications of the equivariant unification term language. We prove our
algorithm correct, paying particular attention to issues of termination, and
present an explicit translation of name-name equivariant unification problems
into non-permutative constraints