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Monday, 15. August 2011

Some special monads in F# – Part 3 of n – DistributionMonad

Filed under: F#,Informatik — Steffen Forkmann at 18:41 Uhr

In part I of this blog series I showed a simple InfinityMonad, which allows to treat special calculations as infinity and in the second part I showed the UndoMonad, which defines an environment which allows to undo and redo state changes.

This and the following posts are based on a famous paper by Martin Erwig and Steve Kollmansberger called "Functional Pearls: Probabilistic functional programming in Haskell".

Let’s start by looking at a small scenario:

This simple query calculates the probability of the event, that an dice roll gives a value greater than 3 and an independent coin flip gives “Heads”. In order to do this the DistributionMonad enumerates all possibilities and calculates the joint probability using the following formula:


If we want the nice syntactic sugar we can easily define a computation expression builder:

In order to allow easier access to our monad, we define some helper functions and basic distributions for fair coins and dices:

In the next part of this blog series I will show how we can utilize the DistributionMonad in order to solve the famous Monty Hall problem.

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