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Lambda Calculus with Types by Richard Statman, Wil Dekkers, Henk Barendregt

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2

Properties

2.1 Normalization

For several applications, for example for the problem of finding all possible inhabitants of a given type, we will need the weak normalization theorem, which states that all typable terms do have a βη-nf (normal form). The result is valid for all versions of image and a fortiori for the subsystem image. The proof is due to Turing and was published posthumously in Gandy (1980). In fact all typable terms in these systems are βη strongly normalizing, which means that all βη-reductions are terminating. This fact requires more work ...

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