Abstract

Polymorphic higher-order unification is a method for unifying terms in the polymorphically typed -calculus, that is, given a set of pairs of terms S 0 = fs 1 ? = t 2 ; : : : ; s n ? = t n g, called a unification problem, finding a substitution oe such that oe(s i ) and oe(t i ) are equivalent under the conversion rules of the calculus for all i, 1 i n. I present the method as a transformation system, i.e. as a set of schematic rules U =) U 0 such that any unification problem ffi (U ) can be transformed into ffi (U 0 ) where ffi is an instantiation of the meta-level variables in U and U 0 . By successive use of transformation rules one possibly obtains a solved unification problem with obvious unifier. I show that the transformation system is correct and complete, i.e. if ffi (U ) =) ffi (U 0 ) is an instance of a transformation rule, then the set of all unifiers of ffi (U 0 ) is a subset of the set of all unifiers of ffi (U ) and if U is the set of all unification ...

Citations