The paper describes a novel methodology to compute stable models in Answer Set Programming. The proposed approach relies on a bottom-up computation that does not require a preliminary grounding phase. The implementation of the framework can be completely realized within the framework of Constraint Logic Programming over finite domains. The use of a high level language for the implementation and the clean structure of the computation offer an ideal framework for the implementation of extensions of Answer Set Programming. In this work, we demonstrate how non-ground arithmetic constraints can be easily introduced in the computation model. The paper provides preliminary experimental results which confirm the potential for this approach.