A Gradual Probabilistic Lambda Calculus

Probabilistic programming languages have recently gained a lot of attention, in particular due to their applications domains such as machine learning and differential privacy. To establish invariants interest, many include some form static checking the type systems. However, adopting discipline can be cumbersome or overly conservative. Gradual typing addresses this problem by supporting smooth transition between dynamic checking, has been successfully applied for with different constructs abstractions. Nevertheless, its benefits never explored context probabilistic languages. In work, we present formalize GPLC, gradual source lambda calculus. GPLC includes binary choice operator allows programmers gradually introduce/remove type–and probability–annotations. The semantics heavily relies on notion couplings, required defining several relations, consistency, precision, consistent transitivity. is given via elaboration target language TPLC, which features distribution-based interpreting programs probability distributions over final values. Regarding metatheory, that TPLC–and therefore also GPLC–is safe satisfies two so-called refined criteria languages, namely, it conservative extension fully variant guarantee, behaving smoothly respect precision.