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The two functions, weightedCases and countedCases, build distributions from the weighted selection of a finite number of cases. The types are as follows: val weightedCases : ('a * float) list -> Distribution<'a> val countedCases : ('a * int) list -> Distribution<'a> For example, here is the distribution of outcomes on a fair European roulette wheel: type Outcome = Even | Odd | Zero let roulette = countedCases [ Even,18; Odd,18; Zero,1] We can now use sampling to draw from this distribution: > roulette.Sample;; val it: Outcome = Even > roulette.Sample;; val it: Outcome = Odd And we can compute the expected payout of a $5 bet on Even, where we would get a $10 return: > roulette.Expectation (function Even -> 10.0 | Odd -> 0.0 | Zero -> 0.0);; val it: float = 4.864864865 Now let s model another scenario. Let s say you have a traffic light with the following probability distribution for showing red/yellow/green: type Light = | Red | Green | Yellow let trafficLightD = weightedCases [ Red,0.50; Yellow,0.10; Green, 0.40 ] A driver is defined by his/her behavior with respect to a traffic light. For example, a cautious driver is highly likely to brake on a yellow light and always stops on a red: type Action = Stop | Drive let cautiousDriver light = dist { match light with | Red -> return Stop | Yellow -> return! weightedCases [ Stop, 0.9; Drive, 0.1 ] | Green -> return Drive } An aggressive driver is unlikely to brake on yellow and may even go through a red light:

null values should be allowed in database columns for only two reasons The first is when the business rules dictate that the application cares about the difference between a value that was never entered and a value that is zero (or an empty string) In other words, the end user actually cares about the difference between "" and null, or between 0 and null There are applications where this matters where the business rules revolve around whether a field ever had a value (even an empty one) or never had a value at all The second reason for using a null value is when a data type doesn t intrinsically support the concept of an empty field The most common example is the SQL DateTime data type, which has no way to represent an empty date value; it always contains a valid date.

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workerMenu.MenuItems.Add(new MenuItem("Cancel",onClick=(fun _ args -> text.Text <- "Cancelling"; worker.CancelAsync()))) form.Closed.Add(fun _ -> worker.CancelAsync()) When run in F# Interactive, a window appears as in Figure 13-1.

In such a case, null values in the database column are used specifically to indicate an empty date Of course, these two reasons are mutually exclusive When using null values to differentiate between an empty field and one that never had a value, you need to come up with some other scheme to indicate an empty DateTime field The solution to this problem is outside the scope of this book but thankfully, the problem itself is quite rare The reality is that very few applications ever care about the difference between an empty value and one that was never entered, so the first scenario seldom applies If it does apply to your application, then dealing with null values at the database level isn t an issue, because you ll use nullable types from the database all the way through to the UI.

Here s the function: function resetFields(whichform) { if (Modernizr.input.placeholder) return; for (var i=0; i<whichform.elements.length; i++) { var element = whichform.elements[i]; if (element.type == "submit") continue; var check = element.placeholder || element.getAttribute('placeholder'); if (!check) continue; element.onfocus = function() { var text = this.placeholder || this.getAttribute('placeholder'); if (this.value == text) { this.className = ''; this.value = ""; } } element.onblur = function() { if (this.value == "") { this.className = 'placeholder'; this.value = this.placeholder || this.getAttribute('placeholder'); } } element.onblur(); } } The function is using two event handlers. The onfocus event is triggered when the user tabs to or clicks an element. The onblur event is triggered when the user moves out of the form element. For good measure, onblur is called immediately after it is created to apply the placeholder value if necessary.

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