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Precomputation is one important way to amortize the costs of computation in F#. Another is called memoization. A memoizing function is one that avoids recomputing its results by keeping an internal table, often called a lookaside table. For example, consider the well-known Fibonacci function, whose naive, unmemoized version is as follows: let rec fib n = if n <= 2 then 1 else fib (n-1) + fib (n-2) Not surprisingly, a version keeping a lookaside table is much faster: #nowarn "40" // do not warn on recursive computed objects and functions let fibFast = let t = new System.Collections.Generic.Dictionary<int,int>() let rec fibCached n = if t.ContainsKey(n) then t.[n] else if n <= 2 then 1 else let res = fibCached(n-1) + fibCached(n-2) t.Add(n,res) res fun n -> fibCached n On one of our laptops, with n = 30, the first runs in 3.65 seconds, and the second runs in 0.015 seconds. Listing 8-4 shows how to write a generic function that encapsulates the memoization technique. Listing 8-4. A Generic Memoization Function open System.Collections.Generic let memoize (f: 'T -> 'U) = let t = new Dictionary<'T,'U>(HashIdentity.Structural) fun n -> if t.ContainsKey(n) then t.[n] else let res = f n t.Add(n,res) res let rec fibFast = memoize (fun n -> if n <= 2 then 1 else fibFast (n-1) + fibFast (n-2)) Here, the functions have the following types: val memoize : ('T -> 'U) -> ('T -> 'U) when 'T : equality val fibFast : (int -> int) In the definition of fibFast, you use let rec because fibFast is self-referential that is, used as part of its own definition. You can think of fibFast as a computed, recursive function. Such a function

NOTE: Due to the fact that the option to reclaim disk space unnecessarily used by FileVault is only presented when a user logs out, if the user never logs out, the system will never reclaim the lost space.

Google Goggles (Figure 13 3) is an experimental app that attempts to search by phone picture. You take a picture of an item while using Goggles, and it will attempt to identify the item. If that fails, it will search for similar images. It works well for bar codes and terrible for plant or bug identification. Theoretically, you can also use it for identifying landmarks, books, DVDs, logos, and other items. You can also use it to translate text, which makes it handy for ordering from a foreign menu.

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generates an informational warning when used in F# code, because it s important to understand when this feature of F# is being used; you then suppress the warning with #nowarn "40" As with the examples of computed functions from the previous section, it s important not to include the extra argument in the application of memoize, because it would lead to a fresh memoization table being allocated each time the function fibNotFast was called: let rec fibNotFast n = memoize (fun n -> if n <= 2 then 1 else fibNotFast (n-1) + fibNotFast (n-2)) n Due to this subtlety, it s often a good idea to define your memoization strategies to generate objects other than functions (note that you can think of functions as very simple kinds of objects).

In some cases, the technologies we ve mentioned will not meet the burden of criteria of a corporation s security policies While FileVault on a technology level provides very strong encryption, it is not without its own limitations At its heart, FileVault is a userspecific technology, and in fact it only seeks to protect an individual user s data The main issue is that it leaves to chance the idea that a user will actually utilize their own home directory for document storage In fact, users have a number of places where they can tuck away data, and certainly not all of these fall under the purview of their own home directory Consider for instance the directory found at /Users/Shared, which is globally writeable, and to which there are no provisions preventing a user from saving data.

For example, Listing 8-5 shows how to define a new variation on memoize that returns a Table object that supports both a lookup and a Discard method Listing 8-5 A Generic Memoization Service open SystemCollectionsGeneric type Table<'T,'U> = abstract Item : 'T -> 'U with get abstract Discard : unit -> unit let memoizeAndPermitDiscard f = let lookasideTable = new Dictionary<_,_>(HashIdentityStructural) { new Table<'T,'U> with member tItem with get(n) = if lookasideTableContainsKey(n) then lookasideTable[n] else let res = f n lookasideTableAdd(n,res) res member tDiscard() = lookasideTableClear() } #nowarn "40" // do not warn on recursive computed objects and functions let rec fibFast = memoizeAndPermitDiscard (fun n -> printfn "computing fibFast %d" n if n <= 2 then 1 else fibFast[n-1] + fibFast[n-2]) In Listing 8-5, lookup uses the a.

While at first glance the obvious thought might be to prevent a user from utilizing this directory by restricting write access, and this certainly may prove to be an approachable angle in your environment The inherent problem with this strategy is that it goes against standard system conventions where-in the expected behavior is for users to have the ability to modify this directory Third party software therefore that relies on this expectation may then find itself non-functional or impaired with such a restriction in place Secondly, if the user is an administrator user (which you would generally want to avoid if possible), they have the potential ability to save data on local disks wherever they please This then, leaves the security provided by FileVault (or any encrypted disk images for that matter) up to the discretion of the end user, and invariably, this introduces a margin-for-error.

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