This paper introduces a framework of parametric descriptive directional types for Constraint Logic Programming (CLP). It proposes a method for locating type errors in CLP programs, and presents a prototype debugging tool. The main technique used is checking correctness of programs w.r.t. type specifications. The approach is based on a generalization of known methods for proving the correctness of logic programs to the case of parametric specifications. Set constraint techniques are used for formulating and checking verification conditions for (parametric) polymorphic type specifications. The specifications are expressed in a parametric extension of the formalism of term grammars. The soundness of the method is proved, and the prototype debugging tool supporting the proposed approach is illustrated on examples. The paper is a substantial extension of the previous work by the same authors concerning monomorphic directional types.