Talk:Higher-order function

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[edit] Power

"Macros can also be used to achieve some of the effects of higher order functions. These do not have the efficiency problems of run-time evaluation, but are more limited in what they can achieve. These also tend to not be strongly typed."

I thought macros (as in, Lisp macros, not simple textual search-and-replace) could do everything first-order functions could do? Am I missing something? --Maru (talk) Contribs 20:51, 29 November 2005 (UTC)

It depends exactly what you mean by "macro". In general, macros don't do capture-avoiding substitution, and macros can almost never be recursive -- higher-order functions do both. --bmills 16:37, 30 November 2005 (UTC)

Well, what about hygienic macros? I had understood they allowed arbitary transformations, which to my mind implies allowing recursion. --Maru (talk) Contribs 00:22, 1 December 2005 (UTC)

Proper hygienic macros do fix the problem of variable capture. The exact power of macros depends on the macro system, but if they can do "arbitrary transformations" that seems to imply turing-completeness, which in turn means that macro-expansion may not terminate -- that is, programs may be infinite. Usually we want to restrict ourselves to only finite programs, which puts some serious limits on what we can actually do with macros. Moreover, if the number of times a function recurses isn't known until run-time, there's no way we could write a macro that captures it. (The problem is mostly one of phase distinction or phase separation.) --bmills 23:28, 4 December 2005 (UTC)

This needs to be updated. As an example, Higher-ordered functions can be implemented in C# 2.0 as anonymous delegates (and they are statically typed). Java, Ruby, and a host of other languages also support these. Google for "closures."

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