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CHAPTER 9 INTRODUCING LANGUAGE-ORIENTED PROGRAMMING
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let aggressiveDriver light = dist { match light with | Red -> return! weightedCases [ Stop, 0.9; Drive, 0.1 ] | Yellow -> return! weightedCases [ Stop, 0.1; Drive, 0.9 ] | Green -> return Drive } The following gives the value of the light showing in the other direction: let otherLight light = match light with | Red -> Green | Yellow -> Red | Green -> Red You can now model the probability of a crash between two drivers given a traffic light. Assume there is a 10 percent chance that two drivers going through the intersection will avoid a crash: type CrashResult = Crash | NoCrash let crash (driverOneD, driverTwoD, lightD) = dist { // Sample from the traffic light let! light = lightD // Sample the first driver's behavior given the traffic light let! driverOne = driverOneD light // Sample the second driver's behavior given the traffic light let! driverTwo = driverTwoD (otherLight light) // Work out the probability of a crash match driverOne, driverTwo with | Drive,Drive -> return! weightedCases [ Crash, 0.9; NoCrash, 0.1 ] | _ -> return NoCrash } You can now instantiate the model to a cautious/aggressive driver pair, sample the overall model, and compute the overall expectation of a crash as approximately 3.7 percent: > let model = crash (cautiousDriver, aggressiveDriver, trafficLightD);; val model : Distribution<CrashResult> > model.Sample;; val it : CrashResult = NoCrash ... > model.Sample;; val it : CrashResult = Crash > model.Expectation (function Crash -> 1.0 | NoCrash -> 0.0);; val it : float = 0.0369
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CHAPTER 9 INTRODUCING LANGUAGE-ORIENTED PROGRAMMING
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Note This section showed how to define a simplistic embedded computational probabilistic modeling language.
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There are many more efficient and sophisticated techniques to apply to the description, evaluation, and analysis of probabilistic models than those shown here, and you can make the implementation of the primitives shown here more efficient by being more careful about the underlying computational representations.
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In some situations, workflows can sensibly make use of transient resources such as files. The tricky thing is that you still want to be careful about closing and disposing of resources when the workflow is complete or when it s no longer being used. For this reason, the workflow type must be carefully designed to correctly dispose of resources halfway through a computation if necessary. Sequence expressions are a great example where this is useful. For example, the following sequence expression opens a file and reads lines on demand: let linesOfFile(fileName) = seq { use textReader = System.IO.File.OpenText(fileName) while not textReader.EndOfStream do yield textReader.ReadLine() } 8 discussed the construct use pat = expr. As shown in Table 9-2, you can also use this construct within workflows. In this case, the use pat = expr construct de-sugars into a call to seq.Using. In the case of sequence expressions, this function is carefully implemented to ensure that textReader is kept open for the duration of the process of reading from the file. Furthermore, the Dispose function on each generated IEnumerator object for a sequence calls the textReader.Dispose() method. This ensures that the file is closed even if you enumerate only half of the lines in the file. Workflows thus allow you to scope the lifetime of a resource over a delayed computation.
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Like functions, workflow expressions can be defined recursively. Many of the best examples are generative sequences. For example: let rnd = System.Random() let rec randomWalk k = seq { yield k yield! randomWalk (k + rnd.NextDouble() - 0.5) } > randomWalk 10.0;; val it: seq<float> = seq [10.0; 10.23817784; 9.956430122; 10.18110362; ...] > randomWalk 10.0;; val it : seq<float> = seq [10.0; 10.19761089; 10.26774703; 9.888072922; ...]
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