Intersection and union types in the λμ̃μ-calculus

The originalλμ̃μ of Curien and Herbelin has a system of simple types, based on sequent calculus, embodying a Curry-Howard correspondence with classical logic. We introduce and discuss three type assignment systems that are extensions of λμ̃μ with intersection and union types. The intrinsic symmetry in the λμ̃μ calculus leads to an essential use of both intersection and union types.

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