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let exprs' = [ for e in exprs do if e.IsNegative then let e' = exp opt precAdd2 e.Negate yield! [sym opt "+"; e'] else let e' = exp opt precAdd2 e yield! [sym opt "-"; e'] ] mkSequence opt prec precAdd1 (e1'::exprs') | Prod (e1, e2) -> let e1' = exp opt precProd1 e1 let e2' = exp opt precProd2 e2 let exprs' = if Expr.StarNeeded e1 e2 then [e1'; sym opt "*"; e2'] else [e1'; e2'] mkSequence opt prec precProd1 exprs' | Pow (e1, e2) -> let e1' = exp opt precPow e1 let e2' = exp { opt with IsSuper=true } precPow (Num e2) Power (e1', e2', e1'.Size.AddPower e2') | Sin e -> expFunc opt "sin" e | Cos e -> expFunc opt "cos" e | Exp expo -> let e' = sym opt "e" let expo' = exp { opt with IsSuper=true } precPow expo Power (e', expo', e'.Size.AddPower expo') | Frac (e1, e2) -> let e1' = exp opt precStart e1 let e2' = exp opt precStart e2 Fraction (e1', e2', e1'.Size.Frac e2'.Size opt) let exp = exp opt precStart e { Expression=exp; RenderOptions=opt; } The conversion implemented in Listing 12-10 is relatively straightforward. It uses various local helper functions to break each expression into smaller visual elements, carefully keeping track of the bounding-box calculation. There are a number of things to consider: precedence is enforced, and expressions are parenthesized as necessary. For example, consider how you convert a product: | Prod (e1, e2) -> let e1' = exp opt precProd1 e1 let e2' = exp opt precProd2 e2 let exprs' = if Expr.StarNeeded e1 e2 then [e1'; sym opt "*"; e2'] else [e1'; e2'] mkSequence opt prec precProd1 exprs'

Summary

This code converts the two interior expressions and decides on a list of display symbols by first checking whether a multiplication symbol is required. The function mkSequence then calculates the size of this new list of expressions, applies precedence rules to determine whether parentheses are required, and produces a final visual element as a result. Other cases are handled similarly; for sums, you iterate through the elements exprs in the sum using sequence expression notation. If you find a negative term, you omit the plus sign (so 1+(-2) is rendered as 1-2). Differences are treated similarly, but here you change negative terms to positive, so 3-2-(-1) becomes 3-2+1. When converting products, you omit the multiplication operator if you can.

RunWorkerAsync: unit -> unit CancelAsync: unit -> unit CancellationPending: bool WorkerReportsProgress: bool WorkerSupportsCancellation: bool

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In this chapter, I ve taken you on a tour of the pluggable storage engine source code and showed you how to create your own storage engine Through the Spartan storage engine, you learned how to construct a storage engine that can read and write data and that supports concurrent access and indexing Although I explain all of the stages of building this storage engine, I leave adding transactional support for you to experiment with I have also not implemented all of the possible functions of a storage handler Rather, I implemented just the basics Now that you ve seen the basics in action and had a chance to experiment, I recommend studying the online documentation and the source code while you design your own storage engine If you found this chapter a challenge, it s OK Creating a database physical storage mechanism is not a trivial task.

Listing 12-11 shows the code for rendering visual expressions You may have noticed in the definition of the VisualElement type that the only directly drawable visual element is Symbol The other constructors carry one or more visual elements that must be drawn recursively and according to a well-defined logic The key observation in the rendering function in Listing 12-11 is that, when drawing each element, you pass in the x and y coordinates of the bounding box in which it s to be drawn You also pass in the size of the parent box in which the element is to be aligned (as guided by the midline property) Listing 12-11 VisualExprfs (continued): Rendering Visual Expressions type VisualExpr = .. member self.

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