Done with some exercises on Gaussian distribution as a monad! http://en.pk.paraiso-lang.org/Haskell/Monad-Gaussian What do you think? Will this be a good approach or bad?
Also this is the first page in my attempt to create runnable, and even testable wiki pages. To run the tests, please use hackage.haskell.org/package/doctest . 2012/7/18 Takayuki Muranushi <muranu...@gmail.com>: > Thank you Oleg, for your detailed instructions! > > First, let me clarify my problem here (in sacrifice of physical accuracy.) > c.f. Wrong.hs . > >> earthMass, sunMass, marsMass :: [Double] >> earthMass = [1,10,100] >> sunMass = (*) <$> [9,10,11] <*> earthMass >> marsMass = (*) <$> [0.09,0.1,0.11] <*> earthMass >> >> sunPerMars = (/) <$> sunMass <*> marsMass >> sunPerMars_range = (minimum sunPerMars, maximum sunPerMars) >> >> sunPerMars_range > gives> (0.8181818181818182,12222.222222222223) > > These extreme answers close to 1 or 10000 are inconsistent in sense > that they used different Earth mass value for calculating Sun and Mars > mass. Factoring out Earth mass is perfect and efficient solution in > this case, but is not always viable when more complicated functions > are involved. > > We want to remove such inconsistency. > >> -- Exercise: why do we need the seemingly redundant EarthMass >> -- and deriving Typeable? >> -- Could we use TemplateHaskell instead? > > Aha! you use the Types as unique keys that resides in "The" context. > Smart! To understand this, I have made MassStr.hs, which > essentially does the same thing with more familiar type Strings. Of > course using Strings are naive and collision-prone approach. Printing > `stateAfter` shows pretty much what have happened. > > I'll remember that we can use Types as global identifiers. > >> -- The following is essentially Control.Monad.Sharing.Memoization >> -- with one important addition >> -- Can you spot the important addition? >> >> type NonDet a = StateT FirstClassStore [] a >> data Key = KeyDyn Int | KeySta TypeRep >> deriving (Show, Ord, Eq) >> > > Hmm, I don't see what Control.Monad.Sharing.Memoization is; googling > https://www.google.co.jp/search?q=Control.Monad.Sharing.Memoization > gives our conversation at the top. > > If it's Memo in chapter 4.2 of your JFP paper, the difference I see is > that you used Data.Set here instead of list of pairs for better > efficiency. > > >> Exercise: how does the approach in the code relate to the approaches >> to sharing explained in >> http://okmij.org/ftp/tagless-final/sharing/sharing.html >> > Chapter 3 introduces an implicit impure counter, and Chapter 4 uses a > database that is passed around. > let_ in Chapter 5 of sharing.pdf realizes the sharing with sort of > continuation-passing style.The unsafe counter works across the module > (c.f. counter.zip) but is generally unpredictable... > > > Now I'm on to the next task; how we represent continuous probability > distributions? The existing libraries: > > http://hackage.haskell.org/package/probability-0.2.4 > http://hackage.haskell.org/package/ProbabilityMonads-0.1.0 > > Seemingly have restricted themselves to discrete distributions, or at > least providing Random support for Monte-Carlo simulations. There's > some hope; I guess Gaussian distributions form a Monad provided that > 1. the standard deviations you are dealing with are small compared to > the scale you deal with, and 2. the monadic functions are > differentiable. > > Maybe I can use non-standard analysis and automatic differentiation; > maybe I can resort to numerical differentiation; maybe I just give up > and be satisfied with random sampling. I have to try first; then > finally we can abstract upon different approaches. > > Also, I can start writing my Knowledge libraries from the part our > knowledge is so accurate enough that the deviations are negligible > (such as Earth mass!) > > > P.S. extra spaces may have annoyed you. I'm sorry for that. My > keyboard is chattering badly now; I have to update him soon. > > > Best wishes, _______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
