[Haskell-cafe] Help on syntactic sugar for combining lazy & strict monads?

[Olaf Klinke]

> However, a lazy interpreter causes problems when trying to introduce
> *observation* statements (aka conditioning statements) into the monad
> [3].  For example,
>
> run_lazy $ do
>    x <- normal 0 1
>    y <- normal x 1
>    z <- normal y 1
>    2.0 `observe_from` normal z 1
>    return y
>
> In the above code fragment, y will be forced because it is returned, and
> y will force x.  However, the "observe_from" statement will never be
> forced, because it does not produce a result that is demanded.

I'm very confused. If the observe_from statement is never demanded, then 
what semantics should it have? What is the type of observe_from? It seems 
it is
a -> m a -> m ()
for whatever monad m you are using. But conditioning usually is a function
Observation a -> Dist a -> Dist a
so you must use the result of the conditioning somehow. And isn't the 
principle of Monte Carlo to approximate the posterior by sampling from it? 
I tend to agree with your suggestion that observations and sampling can not 
be mixed (in the same do-notation) but the latter have to be collected in 
a prior, then conditioned by an observation.

What is the semantic connection between your sample and obsersvation 
monad? What is the connection between both and the semantic probability 
distributions? I claim that once you have typed everything, it becomes 
clear where the problem is.

Olaf

P.S. It has always bugged me that probabilists use elements and 
events interchangingly, while this can only be done on discrete 
spaces. So above I would rather like to write
(2.0==) `observe_from` (normal 0 1)
which still is a non-sensical statement if (normal 0 1) is a continuous 
distribution where each point set has probability zero.