Re: SKIP: Probabilistic SKI combinator calculus

[Philip Thrift]

On Thursday, September 13, 2018 at 9:18:15 AM UTC-5, Bruno Marchal wrote:
>
>
> On 13 Sep 2018, at 14:21, Philip Thrift > 
> wrote:
>
>
>
> Something I wrote some years ago (SKI related). In practice one would use 
> a computer with a quantum-random number generator chip.
>
> https://spectrum.ieee.org/tech-talk/computing/hardware/a-chip-scale-source-for-quantum-random-number-generators
>
>
>
> https://poesophicalbits.blogspot.com/2013/06/skip-probabilistic-ski-combinator.html
>  
> :
>
>
> *SKIP: Probabilistic SKI combinator calculus 
> *
> Add to the *S*, *K*, and *I* combinators of the SKI combinator calculus 
>  the *P*
>  combinator: 
>
> *S**xyz* = *xz*(*yz*)
> *K**xy* = *x*
> *I**x* = *x*
> *P* = *K* or *KI* with equal probability (0.5)
>
> It follows that *P**xy* evaluates to *K**xy* or *KI**xy*, then to *x* or 
> *I**y* = *y *with equal probability. 
>
>
>
> Interesting. It is, I guess, equivalent with the Turing machine + a random 
> oracle. Have you studied the quantum related idea, with P = 1/sqrt(2)(K + 
> KI) ?
>
> Bruno
>
>
>
>
I haven't looked at that. I just noticed a simple way to throw a "coin 
tossing" combinator into the mix. SKI is apparently "Turing complete" [  
https://esolangs.org/wiki/S_and_K_Turing-completeness_proof ] so SKIP is in 
principle enough to write Monte Carlo programs.

- pt

>
> see also Evolutionary code and the probabilistic lambda calculus 
> 
>  
> and a SKI fixed-point combinator 
> 
>  
>
>
> - pt
>
>
>

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Re: SKIP: Probabilistic SKI combinator calculus

[Bruno Marchal]

> On 13 Sep 2018, at 14:21, Philip Thrift  wrote:
> 
> 
> 
> Something I wrote some years ago (SKI related). In practice one would use a 
> computer with a quantum-random number generator chip.
> https://spectrum.ieee.org/tech-talk/computing/hardware/a-chip-scale-source-for-quantum-random-number-generators
> 
> 
> https://poesophicalbits.blogspot.com/2013/06/skip-probabilistic-ski-combinator.html
>  :
> 
> 
> SKIP: Probabilistic SKI combinator calculus 
> 
> 
> Add to the S, K, and I combinators of the SKI combinator calculus 
>  the P combinator: 
> 
> Sxyz = xz(yz)
> Kxy = x
> Ix = x
> P = K or KI with equal probability (0.5)
> 
> It follows that Pxy evaluates to Kxy or KIxy, then to x or Iy = y with equal 
> probability. 


Interesting. It is, I guess, equivalent with the Turing machine + a random 
oracle. Have you studied the quantum related idea, with P = 1/sqrt(2)(K + KI) ?

Bruno



> 
> 
> see also Evolutionary code and the probabilistic lambda calculus 
> 
>  
> and a SKI fixed-point combinator 
> 
>  
> 
> 
> - pt
> 
> 
> 
> 
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SKIP: Probabilistic SKI combinator calculus

[Philip Thrift]

Something I wrote some years ago (SKI related). In practice one would use a 
computer with a quantum-random number generator chip.
https://spectrum.ieee.org/tech-talk/computing/hardware/a-chip-scale-source-for-quantum-random-number-generators


https://poesophicalbits.blogspot.com/2013/06/skip-probabilistic-ski-combinator.html
 
:


*SKIP: Probabilistic SKI combinator calculus 
*
Add to the *S*, *K*, and *I* combinators of the SKI combinator calculus 
 the *P* combinator: 

*S**xyz* = *xz*(*yz*)
*K**xy* = *x*
*I**x* = *x*
*P* = *K* or *KI* with equal probability (0.5)

It follows that *P**xy* evaluates to *K**xy* or *KI**xy*, then to *x* or *I*
*y* = *y *with equal probability. 


see also Evolutionary code and the probabilistic lambda calculus 

 
and a SKI fixed-point combinator 

 


- pt



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