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

Hmm... most of the constructions I used (except dip and cons) were lifted
directly from Brent's article.
It sounds like perhaps the your definition of b differs from Brent's?

I'll have to look into this in more depth.

I look forward to hearing more about your work!

Cheers,
Christopher


On 2/21/07, Manfred Von Thun <[email protected]> wrote:
>
>   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]<cdiggins%40gmail.com>>
> 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?
>
> [Non-text portions of this message have been removed]
>
> 
>



-- 
http://www.cdiggins.com


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