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MathGroup Archive 2006

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Something in the spirit of letrec

  • To: mathgroup at smc.vnet.net
  • Subject: [mg68421] Something in the spirit of letrec
  • From: "Mariano Suárez-Alvarez" <mariano.suarezalvarez at gmail.com>
  • Date: Fri, 4 Aug 2006 03:59:46 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Hi all,

I'm trying to somehow come up with a function WithSelf such that
evaluating

  WithSelf[{a,self[1]+b,self[2]+2}]

will result in {a,a+b,a+b+c}. The idea is that the each
item in the argument may depend on the previous ones;
so for example "self[1]+b" means "what's in the first position
in this list, plus b". There will be no "forward references"
in the argument.

I've tried with

  SetAttributes[WithSelf, HoldFirst];
  WithSelf[l_, self_] := Module[{ll, r = {}},
      ll = Function[self, #] & /@ l;
      Scan[AppendTo[r, #[r]] &, ll];
      r
      ]

This gives the correct correct results, but emits warnings:
for example,

  WithSelf[{1, self[[1]] + 2, self[[2]] + 3, self[[1]]}, self]

results in {1, 3, 6, 1}, which is OK, but emits a few of

  Part::partd: Part specification self[[1]] is longer than depth of
object.

I guess there is some evaluation going on which I am
not seeing...

I'm quite sure what I am trying to do is possible... but how?

Ideas?

-- m


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