Nominal Unification and Matching of Higher Order Expressions with Recursive Let

Abstract

A sound and complete algorithm for nominal unification of higher-order expressions with a recursive let is described, and shown to run in nondeterministic polynomial time. We also explore specializations like nominal letrec-matching for expressions, for DAGs, and for garbage-free expressions and determine their complexity. We also provide a nominal unification algorithm for higher-order expressions with recursive let and atom-variables, where we show that it also runs in nondeterministic polynomial time. In addition we prove that there is a guessing strategy for nominal unification with letrec and atom-variable that is a trade-off between exponential growth and non-determinism. Nominal matching with variables representing partial letrec-environments is also shown to be in NP.

Higher-order pattern generalization modulo equational theories

“…Simple linear loops can be described as a type of first-order cyclic term graph [19,6]. To the best of our knowledge, the only work investigating unification of syntactic objects related to cyclic term graphs is the nominal-unification algorithm presented in [24]. This is likely due to the plethora of problems with undecidable unification in this area.…”