2009-02-22

function = lambda

Japanese version

The first my problem about lambda calculus is that there is only one function, lambda. Actually, lambda means function, therefore, it is natural to call function as ``function'' -- lambda. This sounded strange for me. But lambda calculus's function is a bit different from the conventional function at that time, I assume they needed a name to distinguish them.

Anyway, function is lambda. I don't know that why the symbol ``lambda'' is selected as representing function. There are several hypotheses, but we don't exploit it here. (One hypothesis is the lambda calculus is first started in logic. Greek `L' is lambda. But actually I don't know, so it is nice way to write that ``We don't exploit it here.'')

My second trouble was why ``calculus?'' lambda calculus seems more like Algebra. In symbolic logic, these are called calculus. However, I am a amateur mathematician, I do not know about this also.

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