In Probabilistic Programming, dedicated programming languages provide the means to describe the structure of a stochastic process and to then use machine learning to learn the parameters of that process from data. Usually, these languages use approximate methods to ensure tractability. We can however also use exact tractable models for this task.
To this end, the set of legal programs needs to be restricted, preferably at compile time. This restriction can be seen as a type inference problem, where types represent the permitted operations and algorithms of an expression.
The topic of this thesis is to find a way to express these restrictions as a type inference problem, for example as a Hindley-Milner type system.