Re: Oh Boy...More Brower Weirdness!!!

Prisoner at War wrote:
heck, I'm still wondering why
variables can also be functions!

Why not?

Javascript (and other ECMAScript implementations) is a "functional" programming language, which means that functions are first-class entities: they can be created and manipulated in various ways while the program runs. Other well-known functional languages are the LISP family (LISP, Scheme), the ML family (Standard ML, OCaml), and Haskell.

But even non-functional languages usually offer support for variables that refer to functions and can be used to evaluate functions. C has function pointer types. COBOL has procedure-pointers. Most modern CPUs have some variation on a von Neumann architecture, which treats code as data. If a variable can hold a reference to data, why can't that data be code? And it's not a far step from there to making code directly manipulable.

(There are stranger things than that in programming, such as languages that treat types as data and let you manipulate *those* dynamically. Ultimately, in a von Neumann computer, it's all just data anyway.)

Treating code as data goes back to Goedel, Turing, and Church, all of whom developed mathematics that could manipulate mathematical expressions (Goedel-numbering, Turing machines, and lambda calculus). They were inspired by Hilbert, who was curious about how far mathematics could be formalized - specifically, if mathematics could be extended to the point where you could algorithmically generate all true mathematical statements.

As it turns out, you can't; but as Gregory Chaitin has pointed out, this was one of the happiest failures ever in mathematics, since it led more or less directly to modern information technology.

So: if you want to see formally why you can assign a function to a variable, take a look at lambda calculus (various introductions to Scheme are often good at explaining it) or Goedel-coding (Hofstadter's _Goedel, Escher, Bach_ is a popular, if peripatetic, introduction) or Turing machines. But it's really not such a stretch; and once you get used to it, you'll find it can be quite a useful feature, since it lets you express some solutions very elegantly.

--
Michael Wojcik
.

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