CLP*(D) is a class of constraint logic programming languages which incorporates the notion of abstraction. Predicates in CLP*(D) are (potentially) infinite rational trees which represent abstractions of constraint expressions. This view of predicates as constraint abstractions was motivated by the language Scheme, where closures are viewed as abstractions of functional expressions. A semantics and an efficient implementation of the language are provided, along with several examples of the novel programming techniques provided by this class of languages.