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Lambda CalculusTheoretical Pearl: Church numerals, twice!
Ralf Hinze. Theoretical Pearl: Church numerals, twice! Journal of Functional Programming, 2004. To appear.
This pearl explains Church numerals, twice. The first explanation links Church numerals to Peano numerals via the wellknown encoding of data types in the polymorphic LC. This view suggests that Church numerals are folds in disguise. The second explanation, which is more elaborate, but also more insightful, derives Church numerals from first principles, that is, from an algebraic specification of addition and multiplication. Additionally, we illustrate the use of the parametricity theorem by proving exponentiation as reverse application correct. A simple concept is used to demonstrate several interesting and useful techniques. By Ehud Lamm at 20040715 13:27  Lambda Calculus  login or register to post comments  other blogs  4436 reads
Reflections on reflection  Henk Barendregt(Link)Here's something to exercise both brain hemispheres. Henk Barendregt needs no introduction for many LtU readers  he literally wrote "the book" on the lambda calculus, and that only hints at the profound impact his work has had on lambda calculus and type theory.The page linked above lists two overlapping papers, both about reflection:
As the first paragraph quoted above implies, the scope of these two papers extends far beyond the lambda calculus, into fields such as biology and meditation. Between the two papers, there's something for everyone: "Reflection and its use, from science to meditation" is wideranging, covering reflection related to living cells, formal languages, mathematics, art, computers, and the human mind. "Reflection and its use, with an emphasis on languages and lambda calculus", focuses specifically on reflection in formal languages, including combinatory logic and lambda calculus.
By Anton van Straaten at 20040713 16:32  Fun  General  Lambda Calculus  login or register to post comments  other blogs  11360 reads

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