A calculus for probabilistic languages

Sungwoo Park
2003 Proceedings of the 2003 ACM SIGPLAN international workshop on Types in languages design and implementation - TLDI '03  
As probabilistic computation plays an increasing role in diverse fields in computer science, researchers have designed new languages to facilitate the development of probabilistic programs. In this paper, we develop a probabilistic calculus by extending the traditional lambda calculus. In our calculus, every expression denotes a probability distribution yet evaluates to a regular value. The most notable feature of our calculus is that it is founded upon sampling functions, which map the unit
more » ... erval to probability domains. As a consequence, we achieve a unified representation scheme for all types of probability distributions. In order to support an efficient implementation of the calculus, we also develop a refinement type system which is capable of distinguishing expressions denoting regular values from expressions denoting probability distributions. We use a novel formulation of the intuitionistic modal logic S4 with an intersection connective in the refinement type system. We present preliminary evidence that a probabilistic language based upon our calculus is viable in applications involving massive probabilistic computation.
doi:10.1145/604174.604180 dblp:conf/tldi/Park03 fatcat:g37ka5mfp5ajbltq6gpws22fwe