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

[Benjamin Redelings]

Hi Olaf,

I think you need to look at two things:

1. The Giry monad, and how it deals with continuous spaces.

2. The paper "Practical Probabilistic Programming with Monads" - 
https://doi.org/10.1145/2804302.2804317

Also, observing 2.0 from a continuous distribution is not nonsensical.

-BenRI

On 7/21/21 11:15 PM, Olaf Klinke wrote:
>> 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.