interventions via Markov magmoids

Do-notation associates to the right but, in the normalization magmoid, we mostly want to associate to the left in order to do observations. What we can do is to control associativity explicitly: it becomes the difference between updating and intervening.

conditionalSmoking :: Maybe (Distribution HasCancer)
conditionalSmoking = do
    (gene, isSmoker) <- do 
        gene <- prevalence
        isSmoker <- smokes gene
        return (gene, isSmoker)
    intervene (isSmoker == Smoker)
    hasTar <- tar isSmoker
    cancer <- health gene hasTar
    return cancer
 
causalSmoking :: Maybe (Distribution HasCancer)
causalSmoking = do
    gene <- prevalence
    isSmoker <- smokes gene
    intervene (isSmoker == Smoker)
    hasTar <- tar isSmoker
    cancer <- health gene hasTar
    return cancer

In this fashion, we can do normalized probabilistic programming without a normalization operator: normalization is implicit in the order of composition.

Tags: normalization magmoid, do-notation.