Functions-as-constructors higher-order unification: extended pattern unification

Abstract Unification is a central operation in constructing range of computational logic systems based on first-order and higher-order logics. First-order unification has several properties that guide its incorporation such systems. In particular, decidable, unary, can be performed untyped term structures. None these three hold for full unification: undecidable, unifiers incomparable, term-level typing dominate the search unifiers. The so-called pattern subset was designed to small extension respects laws governing λ -binding (i.e., equalities α , β η -conversion) but which also satisfied those properties. While fragment been used numerous implemented various theoretical settings, it too weak many applications. This paper defines an should make more generally applicable, especially proof assistants allow functions. extension’s main idea arguments higher-order, free variable than just distinct bound variables. terms constructed from (sufficient numbers of) variables using constructors where no argument subterm any other argument. We show this satisfies mentioned above.