A pattern, i.e., a term possibly with variables, denotes the set
(language) of all its ground instances. In an untyped setting,
symbolic operations on finite sets of patterns can represent Boolean
operations on languages. But for the more expressive patterns needed
in declarative languages supporting rich type disciplines such as
subtype polymorphism untyped pattern operations and algorithms break
down. We show how they can be properly defined by means of a
signature transformation that enriches the types of the original
signature. We also show that this transformation allows a systematic
reduction of the first-order logic properties of an initial
order-sorted algebra supporting subtype-polymorphic functions to
equivalent properties of an initial many-sorted (i.e., simply typed)
algebra. This yields a new, simple proof of the known decidability of
the first-order theory of an initial order-sorted algebra.Partially supported by NSF Grant CNS 13-19109.Ope