Re: What does & mean?

• To: mathgroup at smc.vnet.net
• Subject: [mg107229] Re: What does & mean?
• From: Richard Fateman <fateman at cs.berkeley.edu>
• Date: Sat, 6 Feb 2010 03:23:32 -0500 (EST)
• References: <201002041126.GAA29847@smc.vnet.net> <hkgks4\$6p9\$1@smc.vnet.net>

```Unfortunately, Leonid's explanation is wrong, and while some of
the discussion is correct and may clarify the meaning of "&",
some of it is slightly and more-than-slightly wrong.

Leonid's confusion relates to the pseudo-definition of a "function" by
pattern matching using

fn[arg_]:= .......

and the definition of a true function by

fn= Function[{arg}], ......]   or the brief but obscure ...#..& notation...
fn = ....#.... &

There is a widely held but technically bogus equivalence in the minds
of Mathematica users, so Leonid's not alone..

In particular, there is no pattern matching going on in the fn= ...
case, and the SetAttribute[fn, HoldAll] has no effect whatsoever.

(aside: Programming with "pure functions" in Mathematica follows from
its heritage in Lisp, where Function[{x,y},x+y]    or #1+#2& more
briefly, would be written as (lambda(x y)(+ x y)).  Further use of pure
functions can be viewed in the literature on Lisp. )

To see that the two forms are different most simply, try

f[x_]:=Hello[x]
g=Hello[#]&

f[1] is the same as g[1], namely Hello[1]   but

f[1,2,3]  returns Hello[1]
g[1,2,3]  returns g[1,2,3]

```

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