Typing and Computational Properties of Lambda Expressions

Abstract We use a perception of second-order typing in the λ-Calculus, as conveying semantic properties of expressions in models over λ-expressions, to exhibit natural and uniform proofs of theorems of Girard (1971/1972) and of Coppo, Dezani and Veneri (1981) about the relations between typing properties and computational properties of λ-expressions (solvability, normalizability, strong normalizability), and of some generalizations of these theorems.

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