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Selective Functors & Probabilistic Programming

In functional programming, selective applicative functors (SAF) are an abstraction between applicative functors and monads. This abstraction requires all effects to be statically declared, but provides a way to select which effects to execute dynamically. SAF have been shown to be a useful abstraction in several examples, including two industrial case studies. Selective functors have been used for their static analysis capabilities. The collection of information about all possible effects in a computation and the fact that they enable speculative execution make it possible to take advantage to describe probabilistic computations instead of using monads. In particular, selective functors appear to provide a way to obtain a more efficient implementation of probability distributions than monads.

This dissertation addresses a probabilistic interpretation for the arrow and selective abstractions in the light of the linear algebra of programming discipline, as well as exploring ways of offering SAF capabilities to probabilistic programming, by exposing sampling as a concurrency problem. As a result, provides a Haskell type-safe matrix library capable of expressing probability distributions and probabilistic computations as typed matrices, and a probabilistic programming eDSL that explores various techniques in order to offer a novel, performant solution to probabilistic functional programming.