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let text = new Label(Text="Paused", Anchor=AnchorStyles.Left, Height=20, TextAlign= ContentAlignment.MiddleLeft) panel.Controls.Add(progress) panel.Controls.Add(text) form.Controls.Add(panel) let fibOneStep (fibPrevPrev:bigint,fibPrev) = (fibPrev, fibPrevPrev+fibPrev) // Run the iterative algorithm 500 times before reporting intermediate results // Burn some additional cycles to make sure it runs slowly enough let rec RepeatN n f s = if n <= 0 then s else RepeatN (n-1) f (f s) let rec BurnN n f s = if n <= 0 then f s else ignore (f s); BurnN (n-1) f s let step = (RepeatN 500 (BurnN 1000 fibOneStep)) // Create the iterative worker. let worker = new IterativeBackgroundWorker<_>(step,(1I,1I),100) worker.ProgressChanged.Add(fun (progressPercentage,state)-> progress.Value <- progressPercentage) worker.WorkerCompleted.Add(fun (_,result) -> progress.Visible <- false; text.Text <- "Paused"; MessageBox.Show(sprintf "Result = %A" result) |> ignore) worker.WorkerCancelled.Add(fun () -> progress.Visible <- false; text.Text <- "Paused"; MessageBox.Show(sprintf "Cancelled OK!") |> ignore) worker.WorkerError.Add(fun exn -> text.Text <- "Paused"; MessageBox.Show(sprintf "Error: %A" exn) |> ignore) form.Menu <- new MainMenu() let workerMenu = form.Menu.MenuItems.Add("&Worker") workerMenu.MenuItems.Add(new MenuItem("Run",onClick=(fun _ args -> text.Text <- "Running"; progress.Visible <- true; worker.RunWorkerAsync())))

"Humpty Dumpty" "c:\\Program Files" @"c:\Program Files" "xyZy3d2"B 'c'

Query OK, 0 rows affected (0.00 sec)

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Listing 9-7. Implementing Probabilistic Modeling Using Computation Expressions type Distribution<'a> = abstract Sample : 'a abstract Support : Set<'a> abstract Expectation: ('a -> float) -> float let always x = { new Distribution<'a> with member d.Sample = x member d.Support = Set.singleton x member d.Expectation(H) = H(x) } let rnd = System.Random() let coinFlip (p:float) (d1:Distribution<'a>) (d2:Distribution<'a>) = if p < 0.0 || p > 1.0 then failwith "invalid probability in coinFlip" { new Distribution<'a> with member d.Sample = if rnd.NextDouble() < p then d1.Sample else d2.Sample member d.Support = Set.Union(d1.Support,d2.Support) member d.Expectation(H) = p * d1.Expectation(H) + (1.0-p) * d2.Expectation(H) } The types of these primitives are as follows: type Distribution<'a> = abstract Expectation: ('a -> float) -> float abstract Sample : 'a abstract Support : Set<'a> val always: 'a -> Distribution<'a> val coinFlip : float -> Distribution<'a> -> Distribution<'a> -> Distribution<'a> The simplest distribution is always x; this is a distribution that always samples to the same value. Its expectation and support are easy to calculate. The expectation of a function H is just H applied to the value, and the support is just a set containing the single value x. The next distribution defined is coinFlip, which is a distribution that models the ability to choose between two outcomes. Listing 9-8 shows how you can define a workflow builder for distribution objects.

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Listing 9-8. Defining a Builder for Probabilistic Modeling Using Computation Expressions let bind (dist:Distribution<'a>) (k: 'a -> Distribution<'b>) = { new Distribution<'b> with member d.Sample = (k(dist.Sample)).Sample member d.Support = Set.Union(dist.Support.Map(fun d -> (k d).Support)) member d.Expectation(H) = dist.Expectation(fun x -> (k x).Expectation(H)) } type DistributionBuilder() = member x.Delay(f) = bind (always ()) f member x.Let(v,f) = bind (always v) f member x.Bind(d,f) = bind d f member x.Return(x) = always x let dist = new DistributionBuilder() The types of these primitives are as follows: val bind: Distribution<'a> -> ('a -> Distribution<'b>) -> Distribution<'b> val dist: DistributionBuilder Listing 9-8 shows the all-important bind primitive; this combines two distributions, using the sample from the first to guide the sample from the second. The support and expectation are calculated by taking the support from the first and splaying it over the support of the second. The expectation is computed by using the first distribution to compute the expectation of a function derived from the second. These are standard results in probability theory and are the basic machinery you need to get going with some interesting modeling. Before we begin using workflow syntax, we define two derived functions to compute distributions. Listing 9-9 shows the additional derived operations for distribution objects that we will use later in this example. Listing 9-9. Defining the Derived Operations for Probabilistic Modeling Using Computation Expressions let weightedCases (inp: ('a * float) list) = let rec coinFlips w l = match l with | [] -> failwith "no coinFlips" | [(d,_)] -> always d | (d,p)::rest -> coinFlip (p/(1.0-w)) (always d) (coinFlips (w+p) rest) coinFlips 0.0 inp let countedCases inp = let total = List.sumByInt (fun (_,v) -> v) inp weightedCases (inp.Map (fun (x,v) -> (x,(float v/float total))))

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Query OK, 0 rows affected (0.00 sec)

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