measurable is a simple shallowly-embedded DSL for dealing with measures.
It uses a Measure synonym for a standard continuation type with a restricted
output type and no callCC implementation. You can construct measures from
samples, mass/density functions, or even sampling functions.
Construct image measures by fmap-ing measurable functions over them, or
create new measures from existing ones by measure convolution and friends
provided by a simple Num instance enabled by an Applicative instance.
Create measures from graphs of other measures using the Monad instance and
do-notation.
Query measures by integrating measurable functions against them. Extract moments, cumulative density functions, or probabilities.
You can check out a few blog posts I wrote about the theoretical foundations and implementation of the library here:
- Foundations of the Giry Monad
- Implementing the Giry Monad
- The Applicative Structure of the Giry Monad
A more polished and extended version of the above appears in chapter three of my dissertation.
Caveat: while fun to play with, and rewarding to see how measures fit together, measure operations as nested integrals are exponentially complex. Don't expect them to scale very far!