On Thursday, September 13, 2018 at 9:18:15 AM UTC-5, Bruno Marchal wrote: > > > On 13 Sep 2018, at 14:21, Philip Thrift <[email protected] <javascript:>> > 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 > <https://poesophicalbits.blogspot.com/2013/06/skip-probabilistic-ski-combinator.html>* > Add to the *S*, *K*, and *I* combinators of the SKI combinator calculus > <http://en.wikipedia.org/wiki/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 > <http://poesophicalbits.blogspot.com/2013/05/evolutionary-code-and-probabilistic.html> > > and a SKI fixed-point combinator > <http://en.wikipedia.org/wiki/Fixed-point_combinator#Other_fixed-point_combinators> > > > > - pt > > > -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
