| lambda-calculus (Normally written with a Greek letter lambda). A branch of mathematical logic developed by in the late 1930s and early 1940s, dealing with the application of to their arguments. The contains no constants - neither numbers nor mathematical functions such as plus - and is untyped. It consists only of s (functions), variables and applications of one function to another. All entities must therefore be represented as functions. For example, the natural number N can be represented as the function which applies its first argument to its second N times ( N). Church invented lambda-calculus in order to set up a foundational project restricting mathematics to quantities with "". Unfortunately, the resulting system admits {Russell's paradox} in a particularly nasty way; Church couldn't see any way to get rid of it, and gave the project up. Most languages are equivalent to lambda-calculus extended with constants and types. uses a variant of lambda notation for defining functions but only its subset is really equivalent to lambda-calculus. See . (1995-04-13) |
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