Fine-Grained Semantics for Probabilistic Programs

Abstract

Probabilistic programming is an emerging technique for modeling processes involving uncertainty. Thus, it is important to ensure these programs are assigned precise formal semantics that also cleanly handle typical exceptions such as non-termination or division by zero. However, existing semantics of probabilistic programs do not fully accommodate different exceptions and their interaction, often ignoring some or conflating multiple ones into a single exception state, making it impossible to distinguish exceptions or to study their interaction.In this paper, we provide an expressive probabilistic programming language together with a fine-grained measure-theoretic denotational semantics that handles and distinguishes non-termination, observation failures and error states. We then investigate the properties of this semantics, focusing on the interaction of different kinds of exceptions. Our work helps to better understand the intricacies of probabilistic programs and ensures their behavior matches the intended semantics.

Densities of Almost Surely Terminating Probabilistic Programs are Differentiable Almost Everywhere

“…the literature, we make no distinction between non-terminating runs and aborted runs of a (closed) term M : both could result in the value semantics M being a sub-probabilty measure (cf. [4]).…”

Universal Equivalence and Majority of Probabilistic Programs over Finite Fields

“…While the above introduced syntax is convenient for writing programs, we introduce a more pure, core language that is actually equally expressive and will ease the technical developments in the remaining of the paper. To define this core language, we add an explicit failure instruction ⊥, similarly to [7]…”

Universal equivalence and majority of probabilistic programs over finite fields

“…While the above introduced syntax is convenient for writing programs, we introduce a more pure, core language that is actually equally expressive and will ease the technical developments in the remaining of the paper. To define this core language, we add an explicit failure instruction ⊥, similarly to [7]. It allows us to get rid of conditioning in random samples and observe instructions.…”