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

[Takayuki Muranushi]

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,
-- 
Takayuki MURANUSHI
The Hakubi Center for Advanced Research, Kyoto University
http://www.hakubi.kyoto-u.ac.jp/02_mem/h22/muranushi.html
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