Specialization of Real Life CLP Languages

interpretation [CC77] is a technique for static program analysis in which execution of the program is simulated on a description (or abstract) domain (Dα) which is simpler than the actual (or concrete) domain (D). Values in the description domain and sets of values in the actual domain are related via a pair of monotonic mappings 〈α, γ〉: abstraction α : 2D → Dα and concretization γ : Dα→ 2D which form a Galois connection, i.e. ∀x ∈ 2D : γ(α(x)) ⊇ x and ∀λ ∈ Dα : α(γ(λ)) = λ. The set of all possible descriptions represents a description domain Dα which is usually a complete lattice or cpo for which all ascending chains are finite. Note that in generalv is induced by ⊆ and α (in such a way that ∀λ, λ′ ∈ Dα : λ v λ′ ⇔ γ(λ) ⊆ γ(λ′)). Similarly, the operations of least upper bound (t) and greatest lower bound (u) mimic those of 2D in some precise sense. A description λ ∈ Dα approximates a set of concrete values x ∈ 2D if α(x) v λ. Correctness of abstract interpretation guarantees that the descriptions computed approximate all of the actual values which occur during execution of the program. Different description domains may be used which capture different properties with different accuracy and cost. Also, for a given description domain, program, and set of initial call patterns there may be many different analysis graphs. However, for a given set of initial call patterns, a