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scroll.Controls.Add label cform.Show() exception SyntaxError let Parse s = let lex = Lexing.LexBuffer<char>.FromString s try ExprParser.expr ExprLexer.main lex with _ -> raise SyntaxError let NewStringExpression form s = try let e1 = Parse s let e2 = Utils.Simplify e1 let e3 = Utils.Differentiate "x" e2 let e4 = Utils.Simplify e3 NewExpression form s ["Original:", e1; "Simplified:", e2; "Derivative:", e3; "Simplified:", e4] with | SyntaxError -> let msg = Printf.sprintf "Syntax error in:\n%s" s NewExpressionError form msg | Failure msg -> NewExpressionError form msg let ConstructMainForm () = let form = new Form(Text="Symbolic Differentiation Example", IsMdiContainer=true, Visible=true, Height=600, Width=700) let label = new Label(Text="Enter function=", Width=100, Height=20) let tb = new TextBox(Width=150, Left=100) let panel = new Panel(Dock=DockStyle.Top, Height=tb.Height+50) let preview = new Panel(Dock=DockStyle.Bottom, BackColor=Color.White, Height=50, BorderStyle=BorderStyle.FixedSingle) panel.Controls.AddRange([|label; preview; tb |]) form.Controls.Add(panel) tb.KeyUp.Add (fun arg -> if arg.KeyCode = Keys.Enter then NewStringExpression form tb.Text tb.Text <- "" tb.Focus() |> ignore else try let e = Parse tb.Text UpdatePreview preview e with | _ -> ()) form let form = ConstructMainForm () NewStringExpression form "cos(sin(1/(x^2+1)))" Application.Run(form)

The CREATE FUNCTION command registers the function with the server, placing a row in the func table for the selected database. The syntax is as follows:

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For this reason, it can often be useful to build abstractions that are similar to BackgroundWorker but that capture richer or different control patterns, preferably in a way that does not rely on the use of mutable state and that interferes less with the structure of the overall computation Much of the rest of this chapter will look at various techniques to build these control structures We start with a case study where we build a type IterativeBackgroundWorker that represents a variation on the BackgroundWorker design pattern Listing 13-2 shows the code Listing 13-2 A Variation on the BackgroundWorker Design Pattern for Iterative Computations open SystemComponentModel open SystemWindowsForms /// An IterativeBackgroudWorker follows the BackgroundWorker design pattern /// but instead of running an arbitrary computation it iterates a function /// a fixed number of times and reports intermediate and final results.

To recap, in this example you ve seen the following: Two abstract syntax representations for different classes of algebraic expressions: one simple, and one much more realistic How to implement simplification and symbolic differentiation routines on these representations of algebraic expressions How to implement parsing and lexing for concrete representations of algebraic expressions How to perform size estimation and visual layout for abstract syntax representations of algebraic expressions, here using Windows Forms How to put this together into a final application

CREATE FUNCTION function_name RETURNS [STRING | INTEGER | REAL] SONAME "mylib.so"; function_name represents the name of the function you are creating. The return type can be one of STRING, INTEGER, or REAL and the SONAME refers to the name of the library (.so or .dll) that contains the function. These libraries contain the source code for the functions. They are normally written as C functions and then compiled as an object file. The CREATE FUNCTION command tells the MySQL server to create a mapping of the function name in the command (function_name) to the object file. When the function is invoked, the server calls the function in the library for execution.

/// The worker is paramaterized by its internal state type /// /// Percentage progress is based on the iteration number Cancellation checks /// are made at each iteration Implemented via an internal BackgroundWorker type IterativeBackgroundWorker<'a>(oneStep:('a -> 'a), initialState:'a, numIterations:int) = let worker = new BackgroundWorker(WorkerReportsProgress=true, WorkerSupportsCancellation=true).

The next example turns to a traditional application area for functional programming: describing digital hardware circuits and symbolically verifying their properties. We assume a passing familiarity with hardware design, but if you haven t looked inside a microprocessor chip for some time, a brief recap is included in the About Hardware Design sidebar. In this example, you model circuits by propositional logic, a simple and familiar symbolic language made up of constructs such as AND, OR, NOT, and TRUE/FALSE values. You then implement an analysis that converts propositional logic formulae into a canonical form called binary decision diagrams (BDDs). Converting to a canonical form allows you to check conditions and properties associated with the digital circuits.

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