[Haskell-cafe] Monads with "The" contexts?

[Takayuki Muranushi]

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 <muranushi at 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,