Based on recursive functions defined on context-free language, LFC (language for context free recursive function) is a formal specification language and fits for dealing with phrase structure. LFC is yet another functional language with many general characteristics. It has been implemented in SAQ (specification acquisition system).The original type system for LFC is not polymorphic. With type variables, the original type system can be augmented and become a polymorphic type system. The type checking algorithm and some problems about implementation are also discussed. Polymorphic type system makes LFC more agile and predicts good future in the applications of LFC.