The probability density function of a probability distribution is a fundamental concept in probability theory and a key ingredient in various widely used machine learning methods. However, the necessary framework for compiling probabilistic functional programs to density functions has only recently been developed. In this work, we present a density compiler for a probabilistic language with failure and both discrete and continuous distributions, and provide a proof of its soundness. The compiler greatly reduces the development effort of domain experts, which we demonstrate by solving inference problems from various scientific applications, such as modelling the global carbon cycle, using a standard Markov chain Monte Carlo framework.

There has been great interest in creating probabilistic programming languages to simplify the coding of statistical tasks; however, there still does not exist a formal language that simultaneously provides (1) continuous probability distributions, (2) the ability to naturally express custom probabilistic models, and (3) probability density functions (PDFs). This collection of features is necessary for mechanizing fundamental statistical techniques. We formalize the first probabilistic language that exhibits these features, and it serves as a foundational framework for extending the ideas to more general languages. Particularly novel are our type system for absolutely continuous (AC) distributions (those which permit PDFs) and our PDF calculation procedure, which calculates PDF s for a large class of AC distributions. Our formalization paves the way toward the rigorous encoding of powerful statistical reformulations.

Current programming languages and software engineering paradigms are proving insufficient for building intelligent multi-agent systems--such as interactive games and narratives--where developers are called upon to write increasingly complex behavior for agents in dynamic environments. A promising solution is to build adaptive systems; that is, to develop software written specifically to adapt to its environment by changing its behavior in response to what it observes in the world. In this paper we describe a new programming language, An Adaptive Behavior Language (A2BL), that implements adaptive programming primitives to support partial programming, a paradigm in which a programmer need only specify the details of behavior known at code-writing time, leaving the run-time system to learn the rest. Partial programming enables programmers to more easily encode software agents that are difficult to write in existing languages that do not offer language-level support for adaptivity. We motivate the use of partial programming with an example agent coded in a cutting-edge, but non-adaptive agent programming language (ABL), and show how A2BL can encode the same agent much more naturally.