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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.

A business object s AddBusinessRules() method would associate a property to this rule like this: protected override void AddBusinessRules() { ValidationRules.AddRule( new RuleHandler(CommonRules.StringMaxLength), new CommonRules.MaxLengthRuleArgs("Name", 50)); } Remember that in 3 the ValidationRules.AddRule() method included an overload that accepted a rule method delegate along with a RuleArgs object. In this case, the RuleArgs object is an instance of MaxLengthRuleArgs, initialized with the property name and the maximum length allowed for the property. The CommonRules class includes other similar rule method implementations that you may choose to use as is, or as the basis for creating your own library of reusable rules for an application.

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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))))

To allow for styling, also add a placeholder class to the input when the placeholder value is displayed.

Almost all applications employ some data access. Obviously, the CSLA .NET framework puts heavy emphasis on enabling data access through the data portal, as described in 4. Beyond the basic requirement to create, read, update, and delete data, however, there are other needs. During the process of reading data from a database, many application developers find themselves writing repetitive code to eliminate null database values. SafeDataReader is a wrapper around any ADO.NET data reader object that automatically eliminates any null values that might come from the database. When creating many web applications using either Web Forms or Web Services, data must be copied into and out of business objects. In the case of Web Forms data binding, data comes from the page in a dictionary of name/value pairs, which must be copied into the business object s properties. With Web Services, the data sent or received over the network often travels through simple data transfer objects (DTOs). The properties of those DTOs must be copied into or out of a business object within the web service. The DataMapper class contains methods to simplify these tasks.

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