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Memoizing Construction of Syntax Tree Nodes
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In some cases, abstract syntax tree nodes can end up consuming significant portions of the application s memory budget. In this situation, it can be worth memoizing some or all of the nodes constructed in the tree. You can even go as far as memoizing all equivalent nodes, ensuring that equivalence between nodes can be implemented by pointer equality, a technique often called hash-consing. Listing 9-3 shows an abstract representation of propositional logic terms that ensures that any two nodes that are syntactically identical are shared via a memoizing table. Propositional logic terms are terms constructed using P AND Q, P OR Q, NOT P, and variables a, b, and so on. A non-cached version of the expressions would be as follows:
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CHAPTER 9 IN TRODUCING LA NGUA GE-ORIEN TED PROGRAM MIN G
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type Prop = | And of | Or of | Not of | Var of | True
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Prop * Prop Prop * Prop Prop string
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Listing 9-3. Memoizing the Construction of Abstract Syntax Tree Nodes type Prop = | Prop of int and internal PropRepr = | AndRepr of Prop * Prop | OrRepr of Prop * Prop | NotRepr of Prop | VarRepr of string | TrueRepr open System.Collections.Generic module PropOps = let internal uniqStamp = ref 0 type internal PropTable() = let fwdTable = new Dictionary<PropRepr,Prop>(HashIdentity.Structural) let bwdTable = new Dictionary<int,PropRepr>(HashIdentity.Structural) member t.ToUnique(repr) = if fwdTable.ContainsKey(repr) then fwdTable.[repr] else let stamp = incr uniqStamp; !uniqStamp let prop = Prop(stamp) fwdTable.Add(repr,prop) bwdTable.Add(stamp,repr) prop member t.FromUnique(Prop(stamp)) = bwdTable.[stamp] let internal table = PropTable() // public construction functions let And(p1,p2) = table.ToUnique(AndRepr(p1,p2)) let Not(p) = table.ToUnique(NotRepr(p)) let Or(p1,p2) = table.ToUnique(OrRepr(p1,p2)) let Var(p) = table.ToUnique(VarRepr(p)) let True = table.ToUnique(TrueRepr) let False = Not(True) // deconstruction function let getRepr(p) = table.FromUnique(p)
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CHAPTER 9 INTRODUCING LA NGUA GE-ORIEN TED PROGRAM MIN G
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You can construct terms using the operations in PropOps much as you would construct terms using the nonmemoized representation: > open PropOps;; > True;; val it : Prop = Prop 1 > And(Var("x"),Var("y"));; val it : Prop = Prop 5 > getRepr(it);; val it : PropRepr = AndRepr(Prop 3, Prop 4) > And(Var("x"),Var("y"));; val it : Prop = Prop 5 In this example, when you create two syntax trees using the same specification, And(Var("x"),Var("y")), you get the same Prop object back with the same stamp 5. You can also use memoization techniques to implement interesting algorithms; in 12 you will see an important representation of propositional logic called a binary decision diagram (BDD) based on a memoization table similar to the previous example. The use of unique integer stamps and a lookaside table in the previous representation also has some drawbacks; it is harder to pattern match on abstract syntax representations, and you may need to reclaim and recycle stamps and remove entries from the lookaside table if a large number of terms is created or if the overall set of stamps must remain compact. You can solve the first problem by using active patterns, covered next in this chapter. If necessary, you can solve the second problem by scoping stamps in an object that encloses the uniqStamp state, the lookaside table, and the construction functions. Alternatively you can explicitly reclaim the stamps by using the IDisposable idiom described in 8, though this can be quite intrusive to your application.
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Introducing Active Patterns
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Pattern matching is one of the key techniques provided in F# for decomposing abstract syntax trees and other abstract representations of languages. So far in this book all the examples of pattern matching have been directly over the core representations of data structures, for example, directly matching on the structure of lists, options, records, and discriminated unions. However, pattern matching in F# is also extensible; that is, you can define new ways of matching over existing types. You do this through a mechanism called active patterns. We ll cover only the basics of active patterns in this book. However, they can be indispensable, since they can let you continue to use pattern matching with your types even after you hide their representations. Active patterns also let you use pattern matching with .NET object types. In the following section, we cover active patterns and how they work.
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