A Domain-Theoretic Approach to Statistical Programming Languages
Jean Goubault-Larrecq, Xiaodong Jia, Clément Théron- Artificial Intelligence
- Hardware and Architecture
- Information Systems
- Control and Systems Engineering
- Software
We give a domain-theoretic semantics to a statistical programming language, using the plain old category of dcpos, in contrast to some more sophisticated recent proposals. Remarkably, our monad of minimal valuations is commutative, which allows for program transformations that permute the order of independent random draws, as one would expect. A similar property is not known for Jones and Plotkin’ s monad of continuous valuations. Instead of working with true real numbers, we work with exact real arithmetic, providing a bridge towards possible implementations. (Implementations by themselves are not addressed here.) Rather remarkably, we show that restricting ourselves to minimal valuations does not restrict us much:
all
measures on the real line can be modeled by minimal valuations on the domain