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We present a CLP(FD)-based constraint solver able to deal with unboundeddomains. It is based on constraint propagation, resorting to enumeration if allother methods fail. An important aspect is detecting when enumeration wascomplete and if this has an impact on the soundness of the result. We present atechnique which guarantees soundness in the following way: if the constraintsolver finds a solution it is guaranteed to be correct; if the constraintsolver fails to find a solution it can either return the result "definitelyfalse" in case it knows enumeration was exhaustive, or "unknown" in case it wasaborted. The technique can deal with nested universal and existentialquantifiers. It can easily be extended to set comprehensions and otheroperators introducing new quantified variables. We show applications in datavalidation and proof.

Constraint Logic Programming over Infinite Domains with an Application to Proof