In this paper we develop the language theory underpinning the logical framework PLF. This language features lambda abstraction with patterns and application via pattern-matching. Reductions are allowed in patterns. The framework is particularly suited as a metalanguage for encoding rewriting logics and logical systems where proof terms have a special syntactic constraints, as in term rewriting systems, and rule-based languages. PLF is a conservative extension of the well-known Edinburgh Logical Framework LF. Because of sophisticated pattern matching facilities PLF is suitable for verification and manipulation of HXML documents.