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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:

As shown in Table 3-6, a literal form is also available for arrays of bytes: the characters are interpreted as ASCII characters, and non-ASCII characters can be embedded using escape codes. This can be useful when you re working with binary protocols: > "MAGIC"B;; val it : byte [] = [|77uy; 65uy; 71uy; 73uy; 67uy|] Verbatim string literals are particularly useful for file and path names that contain the backslash character (\): > let dir = @"c:\Program Files";; val dir : string You can also use multiline string literals: > let s = "All the kings horses - and all the kings men";; val s : string The operator .[] is used to access the elements of a string, and the property Length retrieves its length:

mysql> CREATE FUNCTION myfunc_int RETURNS INTEGER SONAME "expert_udf.dll";

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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.

> let s = "Couldn't put Humpty";; val s : string > s.Length;; val it : int = 19 > s.[13];; val it : char = 'H' The operator .[index..index] can be used to take substrings: > let s = "Couldn't put Humpty";; val s : string > s.[13..16];; val it : string = "Hump" Strings are immutable; that is, a string value can t be modified after it s built. For example, the Substring method on the string type doesn t modify the original string but returns a new string representing the result. As mentioned in 2, immutability is a key concept for many F# values, and you encounter it many places in this book. If you attempt to mutate a string, you get an error like the one shown here: > let s = "Couldn't put Humpty";; val s : string = "Couldn't put Humpty" > s.[13] <- 'h';; s.[13] <- 'h';; ^^ stdin(75,0): error: FS0001: Type error in the use of the overloaded operator 'set_Item'. The type 'string' does not support any operators named 'set_Item'

Query OK, 0 rows affected (0.00 sec)

Note Forcibly aborting computations uncooperatively is not recommended in .NET programming. You can attempt to do this using System.Threading.Thread.Abort(), but the use of this method may have many unintended consequences, discussed later in this chapter.

Digital hardware circuits such as microprocessors almost universally manipulate bits that is, signals that are either low or high, represented by 0/1 or false/true values, respectively. The building blocks of interesting hardware circuits are primitives such as gates and registers. Gates are logical components that relate their inputs to their outputs; for example, an AND gate takes two input signals, and if both are high, it gives a high signal on its output. Registers are stateful components associated with a clock. This chapter doesn t consider registers and stateful circuits, although they can be tackled using techniques similar to those described here. Hardware design is largely about building interesting behavior out of these primitives. For example, you can build arithmetic circuits that compute the sum or product of integers by using logical gates alone. These combinatorial circuits can be massive, and a key concern is to both verify their correctness and minimize the overall electrical delay through the circuit.

Note The examples in this section are inspired by the tutorials for the HOL88 system, a symbolic theorem

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