Re: [stack] S-K Construction of Dip?

I think you are wrong about cons.

First consideration: The pure (data independent) stack shufflers swap, dup,
rollup,and also pure combinators like i and dip, cannot be used to define
data (numbers,strings,lists) dependent operations and combinators

Second: in my scheme of things b is a combinator which expects two
quotations. It executes both, first the quotation second from the top, and
then the other. It satisfies the law:  b = [i] dip i. I assume you mean the
same

Third, the combinator  satisfies the law:  i = [] b. The two laws are true,
and either could be used as a definition. But you could not use both as
definitions because of the circularity.

Hence: [...] [] b  = [...] [i] dip i = ... [] i = .... [] i = ....

In other words what you called cons is just the i combinator. Hope this
helps.

Another law: b = concat i. This assumes that  concat is already given.
But normally concat has to be defined in terms of cons. Alternatively,
given concat and unitlist, define cons = [unitlist] dip concat.

New year¹s greetings to all. I have been reading the recent contributions
but could not contribute for lack of understanding and my sparse time here
at uni. But I shall report separately on what I have been doing at home.

  - Manfred

On 22/2/07 4:59 AM, "Christopher Diggins" <[email protected]> wrote:

> 
> 
> 
> 
> From http://tunes.org/~iepos/joy.html
> 
> This sentence never quite sat well with me:
> 
> "however, there is no way to form "dip" or "sip" using just "s" and "k"
> because, roughly speaking, they provide no way to dequote items buried in
> the stack."
> 
> I may have found a counter-example:
> 
> We know that we can construct: c b and i from s
> 
> Then we can go on to define:
> 
> swap = [] c cons = [] b zap = [] k unit = [] [zap] s cat = swap [i] cons
> swap cons
> 
> And finally:
> 
> dip = swap unit cat i
> 
> Can anyone verify if this is this correct for me?



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