Computation & Deduction
Spring 1997
Frank Pfenning

Lecture 24: The Polymorphic Lambda-Calculus

We discuss the polymorphic lambda-calculus, using formulations in the style of Curry (where types are assigned to untyped terms) and Church (where every terms has a unique type). We talk about the practical issues of type inference and type reconstruction (both of which are known to be undecidable) and give representations of these languages in Elf. Interestingly, despite the expressiveness of the polymorphic lambda-calculus, it is possible to give and intrinsic encoding, where only well-typed expression are representable. We also show how the natural numbers, iteration, and primitive recursion can be encoded in the polymorphic lambda calculus via polymorphic Church numerals.
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