Various static analyses of functional programming languages that permit infinite data structures make use of set constants like Top, Inf, and Bot, denoting all terms, all lists not eventually ending in Nil, and all non-terminating programs, respectively. We use a set language that permits union, constructors and recursive definition of set constants with a greatest fixpoint semantics in the set of all, also infinite, computable trees, where all term constructors are non-strict. This paper proves decidability, in particular DEXPTIME-completeness, of inclusion of co-inductively defined sets by using algorithms and results from tree automata and set constraints. The test for set inclusion is required by certain strictness analysis algorithms in lazy functional programming languages and could also be the basis for further set-based analyses.

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.