On 7/23/2015 8:37 AM, Orchid Win7 v1 wrote:
> On 23/07/2015 08:02 AM, Mr wrote:

>> I'm sure however that it could find unpredicted real applications one
>> day!
>
> Well, no, the SKI combinators are of theoretical interest, because they
> show you something about how small a Turing-complete programming
> language can be.
>
> It's like, Turning machines have to *practical* use (unless you enjoy
> writing excruciatingly complicated programs!), but they are
> theoretically important.
>

Wrong argument, I think. The outcome and next step is. Who would have 
thought that quantum mechanic theory in the 1920's would lead to 
transistors and your job. ;-)
Which is what Mr said.

> So, using only X, we can recover S, K and I, which we already know to be
> Turing-complete. Therefore, any possible computable function can be
> constructed just using X and brackets.
>
> OTOH, if you look at the size of "S" verses "X(X(X(XX)))", you can see
> that anything in the Iota calculus is going to be *really huge*!
>
> This seems to be the general thing; the simpler your programming
> language, the more complicated your programs get!

Isn't that the point of high level languages? To get rid of all those 
brackets.
Have you just proved: 1 = 1?


-- 

Regards
     Stephen

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