Abstract:Starting with the concept of Ideal, the paper presents their properties when Ideals are taken as the semantic model for types. Under the ideal model of types, the paper discusses the semantics for polymorphic types in a mechanism for abstraction and encapsulation of languages named Garment, including parametric polymorphic types and constrained polymorphic types. Finally, the semantic soundness of typing rules in Garment is proved within the Ideal model.