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Furthermore, negative indexes are used to represent the negation of a particular BDD node without creating a separate entry for the negated node Listing 12-15 shows our implementation of BDDs Fully polished BDD packages are often implemented in C It is easy to access those packages from F# using the techniques described in 19 Here we are content with a clear and simple implementation entirely in F# code Listing 12-15 Implementing Binary Decision Diagrams open SystemCollectionsGeneric let memoize f = let tab = new Dictionary<_,_>() fun x -> if tabContainsKey(x) then tab[x] else let res = f x in tab.

What Barton and Ramsay needed most was a system with a well-developed disk subsystem, supported multitasking, and the ability to optimize hardware (CPU, memory) usage. Linux therefore was the logical choice of operating systems for the TCD. Production goals and budget constraints limited the choice of CPU. The IBM PowerPC 403GCX processor was chosen for the TCD. Unfortunately, there were no ports of Linux that ran on the chosen processor. This meant Barton and Ramsay would have to port Linux to the processor platform. While the port was successful, Barton and Ramsay discovered they needed some specialized customizations of the Linux kernel to meet the needs and limits of the hardware. For example, they bypassed the file system buffer cache in order to permit faster movement, or processing, of the video signals to and from user space. They also added extensive performance enhancements, logging, and recovery features to ensure that the TCD could recover quickly from power loss or user error. The application that runs the TCD was built on Linux-based personal computers and ported to the modified Linux operating system with little drama a testament to the stability and interoperability of the Linux operating system. When Barton and Ramsay completed their porting and application work, they conducted extensive testing and delivered the world s first DVR in March 1999. The TCD is one of the most widely used consumer product running a customized embedded Linux operating system. Clearly, the TCD story is a shining example of what you can accomplish by modifying open source software. The story doesn t end here, though. Barton and Ramsay published their Linux kernel port complete with the source code. Their enhancements have found their way into the latest versions of the Linux kernel.

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Figure 12-2. The SymbolicDifferentiation project in Visual Studio 2010 Armed with the ability to encode and parse algebraic expressions, you place the derivation and simplification logic in its own module and file (ExprUtil.fs). The last piece is rendering (in VisualExpr.fs). Finally, a simple UI client in Main.fs completes the application.

[x] <- res; res type type type type BddIndex = int Bdd = Bdd of BddIndex BddNode = Node of Var * BddIndex * BddIndex BddBuilder(order : Var -> Var -> int) = // The core data structures that preserve uniqueness let uniqueTab = new Dictionary<BddNode,BddIndex>() let nodeTab = new Dictionary<BddIndex,BddNode>() // Keep track of the next index let mutable nextIdx = 2 let trueIdx = 1 let falseIdx = -1.

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