  Over the past three decades, the logic programming paradigm has been
successfully expanded to support probabilistic modeling, inference and
learning. The resulting paradigm of probabilistic logic programming (PLP) and
its programming languages owes much of its success to a declarative semantics,
the so-called distribution semantics. However, the distribution semantics is
limited to discrete random variables only. While PLP has been extended in
various ways for supporting hybrid, that is, mixed discrete and continuous
random variables, we are still lacking a declarative semantics for hybrid PLP
that not only generalizes the distribution semantics and the modeling language
but also the standard inference algorithm that is based on knowledge
compilation. We contribute the hybrid distribution semantics together with the
hybrid PLP language DC-ProbLog and its inference engine infinitesimal algebraic
likelihood weighting (IALW). These have the original distribution semantics,
standard PLP languages such as ProbLog, and standard inference engines for PLP
based on knowledge compilation as special cases. Thus, we generalize the
state-of-the-art of PLP towards hybrid PLP in three different aspects:
semantics, language and inference. Furthermore, IALW is the first inference
algorithm for hybrid probabilistic programming based on knowledge compilation.
