PFP - Probabilistic Functional Programming in Haskell

A Probabilistic Functional Programming Library for Haskell
Version: June 2006

The PFP library is a collection of modules for Haskell that facilitates probabilistic functional programming, that is, programming with stochastic values. The probabilistic functional programming approach is based on a data type for representing distributions. A distribution represent the outcome of a probabilistic event as a collection of all possible values, tagged with their likelihood.

Distributions can represent events, such as the roll of a die or the flip of a coin. For example, or example, the outcome of a die roll can be expressed as follows.

die :: Dist Int
die = uniform [1..6]

The evaluation of die yields a distribution:

> die
1  16.7%
2  16.7%
3  16.7%
4  16.7%
5  16.7%
6  16.7%

The function uniform takes a list of elements and produces a distribution where each element is equally likely. We can also use functions like uniform to construct probabilistic functions, called transitions. Here is a transition which, given a number, either adds one or doesn't with equal probability.

succOrId x = uniform [x, x+1]

We could also represent this function using the choose operator which constructs a distribution of two elements.

succOrId x = choose 0.5 x (x+1)

Imagine we want to roll a dice, then either add one or not. We can use monadic operators to combine probabilistic operations. This can be represented concisely, or in a more verbose way.

droll = die >>= succOrId

Or:

droll = do d <- die
           succOrId d

The PFP library provides a set of function definitions that allow the declarative description and evaluation of probabilistic situations. These function can be employed in many different ways - be it solving of statistics problem from textbooks or the application to scientific problems. The approach is constructive by defining and applying probabilistic functions.

To use the library:

Download pfp-jun06.tar.gz
Gunzip and untar the archive. This will create a directory pfp-jun06. Change to that directory.
Load an example file:
```
ghci Dice.hs
```

Formulate queries. For example, what is the distribution of points when rolling two dice?

*Dice> mapD (uncurry (+)) (prod die die)
 7  16.7%
 6  13.9%
 8  13.9%
 5  11.1%
 9  11.1%
 4   8.3%
10   8.3%
 3   5.6%
11   5.6%
 2   2.8%
12   2.8%

Or, what is the probability of the two dice differing by one point?

*Dice> (==1) ?? mapD (abs . uncurry (-)) (prod die die)
 27.8%

More examples are included in the papers listed below.

Further Information

Probabilistic Functional Programming in Haskell, Martin Erwig and Steve Kollmansberger
Journal of Functional Programming, Vol. 16, No. 1, 21-34, 2006

Modeling Genome Evolution with a DSEL for Probabilistic Programming, Martin Erwig and Steve Kollmansberger
8th Int. Symp. on Practical Aspects of Declarative Languages, LNCS 3819, 134-149, 2006

Modeling Biological Systems wit FuSE, Martin Erwig and Steve Kollmansberger
A short tutorial, November 2005, under construction

A Domain-Specific Embedded Language for Probabilistic Programming, Steve Kollmansberger
Master's Thesis, Dec 2005

Contact

For more information, please contact: Martin Erwig

last change: May 29, 2006

Martin Erwig erwig@eecs.oregonstate.edu