Re: Pure recursive functions
- To: mathgroup at smc.vnet.net
- Subject: [mg38377] Re: [mg38341] Pure recursive functions
- From: Sseziwa Mukasa <mukasa at jeol.com>
- Date: Fri, 13 Dec 2002 04:09:36 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
On Thursday, December 12, 2002, at 01:36 AM, Niall Palfreyman wrote:
> Hello,
>
> I'm new to Mathematica, and I have a question to which I've found no
> answers in the archives. Can you help?
>
> The issue is: how do I create a pure recursive function? Normally when
> creating a recursive function I use the name of the function to perform
> the recursive call:
>
> fact[n_] :=
> If[n == 1, 1, n fact[n - 1]]
>
> However this has the disadvantage that the symbol "fact" is now global.
> The logical step to make the name of the function local is something
> like:
>
> Function[factl, factl[5]] @@ {Function[n, If[n == 0, 1, n factl[n -
> 1]]]}
>
> or maybe:
>
> With[{fact = Function[n, If[n == 0, 1, n fact[n - 1]]]}, fact[5]]
>
> However both of these solutions steadfastly return the value "5
> fact[4]". I assume the problem is that the variables initialised in
> Function[] and With[] must be symbols, and cannot be patterns. But a
> recursion requires a pattern (n_ in the first, global, solution above).
> What do I do to get factorial to work _without_ making the symbol
> "fact"
> global?
>
> I'd be grateful for any help.
>
#0 is the function itself when the & notation is used. Unfortunately
it appears you cannot write recursive lambda functions without using &
So
If[# == 1, 1, # #0[# - 1]] &
is a recursive factorial function.
Regards,
Sseziwa