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// 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 let trueNode = Node("",trueIdx,trueIdx) let falseNode = Node("",falseIdx,falseIdx) // Map indexes to nodes. Negative indexes go to their negation. The special // indexes -1 and 1 go to special true/false nodes. let idxToNode(idx) = if idx = trueIdx then trueNode elif idx = falseIdx then falseNode elif idx > 0 then nodeTab.[idx] else let (Node(v,l,r)) = nodeTab.[-idx] Node(v,-l,-r) // Map nodes to indexes. Add an entry to the table if needed. let nodeToUniqueIdx(node) = if uniqueTab.ContainsKey(node) then uniqueTab.[node] else let idx = nextIdx uniqueTab.[node] <- idx nodeTab.[idx] <- node nextIdx <- nextIdx + 1 idx // Get the canonical index for a node. Preserve the invariant that the // left-hand node of a conditional is always a positive node let mkNode(v:Var,l:BddIndex,r:BddIndex) = if l = r then l elif l >= 0 then nodeToUniqueIdx(Node(v,l,r) ) else -nodeToUniqueIdx(Node(v,-l,-r))

Object-oriented database systems (OODBSs) are storage and retrieval mechanisms that support the object-oriented programming (OOP) paradigm through direct manipulation of the data as objects They contain true object-oriented (OO) type systems that permit objects to persist between applications and usage However, most lack a standard query language1 (access to the data is typically via a programming interface) and therefore are not true database management systems OODBSs are an attractive alternative to RDBSs, especially in application areas where the modeling power or performance of RDBSs to store data as objects in tables is insufficient These applications maintain large amounts of data that is never deleted, thereby managing the history of individual objects The most unique feature of OODBSs is to provide support for complex objects by specifying both the structure and the operations that can be applied to these objects via an OOP interface.

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Sometimes you may need to write a few primitives to map .NET asynchronous operations into the F# asynchronous framework. We give some examples later in this section and in 14.

// Construct the BDD for a conjunction "m1 AND m2" let rec mkAnd(m1,m2) = if m1 = falseIdx || m2 = falseIdx then falseIdx elif m1 = trueIdx then m2 elif m2 = trueIdx then m1 else let (Node(x,l1,r1)) = idxToNode(m1) let (Node(y,l2,r2)) = idxToNode(m2) let v,(la,lb),(ra,rb) = match order x y with | c when c = 0 -> x,(l1,l2),(r1,r2) | c when c < 0 -> x,(l1,m2),(r1,m2) | c -> y,(m1,l2),(m1,r2) mkNode(v,mkAnd(la,lb), mkAnd(ra,rb)) // Memoize this function let mkAnd = memoize mkAnd // Publish the construction functions that make BDDs from existing BDDs member gFalse = Bdd falseIdx member gAnd(Bdd m1,Bdd m2) = Bdd(mkAnd(m1,m2)) member gNot(Bdd m) = Bdd(-m) member gVar(nm) = Bdd(mkNode(nm,trueIdx,falseIdx)) member g.

OODBSs are particularly suitable for modeling the real world as closely as possible without forcing unnatural relationships between and within entities The philosophy of object orientation offers a holistic as well as a modeling-oriented view of the real world These views are necessary for dealing with an elusive subject like modeling temporal change, particularly in adding OO features to structured data Despite the general availability of numerous open source OODBSs, most are based in part on relational systems that support query language interfaces and therefore are not truly OODBSs; rather, they operate more like relational databases with OO interfaces A true OODBS requires access via a programming interface Application areas of OO database systems include geographical information systems (GISs), scientific and statistical databases, multimedia systems, picture archiving and communications systems, and XML warehouses.

Let s take a moment to look at how to implement one of the primitive Async<'a> actions we ve been using earlier in the chapter. Listing 13-8 shows the essence of the implementation of Stream.ReadAsync, which is a primitive asynchronous action that wraps a pair of Stream.BeginRead and Stream.EndRead calls using Async.Primitive. We implement this as an extension to the System.IO.Stream type to ensure it is easy to find the asynchronous version of this functionality alongside existing functions (extension members were described in 6). Listing 13-8. An Implementation of an Async.Primitive open System let trylet f x = (try Choice2_1 (f x) with exn -> Choice2_2(exn)) let protect cont econt f x = match trylet f x with | Choice2_1 v -> cont v | Choice2_2 exn -> econt exn type System.IO.Stream with member stream.ReadAsync (buffer,offset,count) = Async.Primitive (fun (cont,econt) -> stream.BeginRead (buffer=buffer, offset=offset, count=count, state=null, callback=AsyncCallback(protect cont econt stream.EndRead)) |> ignore) The type of Async.Primitive is as follows:

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