tl;dr: Is there any way to pass the Supercombinator level names (the names in haskell source codes with zero indent) as context to a Monad so that it will read from "The" context? Hello, everyone. I'm thinking of representing our knowledge about our life, the universe and everything as Haskell values. I'd also like to address the uncertainties in our knowledge. The uncertainties are usually continuous (probabilistic distributions) but that's another story. Please forget about it for a while. We learned that List is for nondeterministic context.

earthMass, sunMass, marsMass :: [Double]

Let's pretend that there are large uncertainty in our knowledge of the Earth mass.

earthMass = [5.96e24, 5.97e24, 5.98e24]

Let's also pretend that we can measure the other bodys' masses only by their ratio to the earth mass, and the measurements have large uncertainties.

sunMass = (*) <$> [2.5e5, 3e5, 4e5] <*> earthMass marsMass = (*) <$> [0.01, 0.1, 1.0] <*> earthMass

Then, how many Mars mass object can we create by taking the sun apart?

sunPerMars :: [Double] sunPerMars = (/) <$> sunMass <*> marsMass

Sadly, this gives too many answers, and some of them are wrong because they assume different Earth mass in calculating Sun and Mars masses, which led to inconsistent calculation. *Main> length $ sunPerMars 81 We had to do this way;

sunMass' e = map (e*) [2.5e5, 3e5, 4e5] marsMass' e = map (e*) [0.01, 0.1, 1.0]

sunPerMars' :: [Double] sunPerMars' = do e <- earthMass (/) <$> sunMass' e <*> marsMass' e

to have correct candidates (with duplicates.) *Main> length $ sunPerMars' 27 The use of (e <- earthMass) seems inevitable for representing that the two Earth masses are taken from the same source of nondeterminism. However, as the chain of the reasoning grows, we can easily imagine the function arguments will grow impractically large. To get the Higgs mass, we will need to feed them all the history of research that led to the measurement of it. There is "the" source of nondeterminism for Earth mass we will always use. Is there a way to represent this? For example, can we define earthMass'' , sunMass'' , marsMass'' all in separate modules, and yet have (length $ sunPerMars'' == 27) ? By the way, *Main> length $ nub $ sort sunPerMars' 16 is not 9. That's another story, I said! Thanks in advance. -- Takayuki MURANUSHI The Hakubi Center for Advanced Research, Kyoto University http://www.hakubi.kyoto-u.ac.jp/02_mem/h22/muranushi.html