Sequential pattern mining under various constraints is a challenging data mining task. The paper provides a generic framework based on constraint programming to discover sequence patterns defined by constraints on local patterns (e.g., Gap, regular expressions) or constraints on patterns involving combination of local patterns such as relevant subgroups and top-k patterns. This framework enables the user to mine in a declarative way both kinds of patterns. The solving step is done by exploiting the machinery of Constraint Programming. For complex patterns involving combination of local patterns, we improve the mining step by using dynamic CSP. Finally, we present two case studies in biomedical information extraction and stylistic analysis in linguistics.