this paper (Compagnoni, Intersection Types and Bounded Polymorphism 3 1994; Compagnoni, 1995) has been used in a type-theoretic model of object-oriented multiple inheritance (Compagnoni & Pierce, 1996). Related calculi combining restricted forms of intersection types with higher-order polymorphism and dependent types have been studied by Pfenning (Pfenning, 1993). Following a more detailed discussion of the pure systems of intersections and bounded quantification (Section 2), we describe, in Section 3, a typed -calculus called F ("Fmeet ") integrating the features of both. Section 4 gives some examples illustrating this system's expressive power. Section 5 presents the main results of the paper: a prooftheoretic analysis of F 's subtyping and typechecking relations leading to algorithms for checking subtyping and for synthesizing minimal types for terms. Section 6 discusses semantic aspects of the calculus, obtaining a simple soundness proof for the typing rules by interpreting types as partial equivalence relations; however, another proof-theoretic result, the nonexistence of least upper bounds for arbitrary pairs of types, implies that typed models may be more difficult to construct. Section 7 offers concluding remarks. 2. Background

We define the typed lambda calculus F ω ∧ , a natural generalization of Girard’s system F ω with intersection types and bounded polymorphism. A novel aspect of our presentation is the use of term rewriting techniques to present intersection types, which clearly splits the computational semantics (reduction rules) from the syntax (inference rules) of the system. We establish properties such as Church-Rosser for the reduction relation on types and terms, and Strong Normalization for the reduction on types. We prove that types are preserved by computation (Subject Reduction property), and that the system satisfies the Minimal Types property. On the way to establishing these results, we define algorithms for type inference and subtype checking. 1

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