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async { let req = WebRequest.Create("http://moma.org/") let! resp = req.GetResponseAsync() let stream = resp.GetResponseStream() let reader = new StreamReader(stream) let! html = reader.ReadToEndAsync() html } is shorthand for the following code: async.Delay(fun () -> async.Let(WebRequest.Async("http://moma.org/"), (fun req -> async.Bind(req.GetResponseAsync(), (fun resp -> async.Let(resp.GetResponseStream(), (fun stream -> async.Let(new StreamReader(stream), (fun reader -> async.Bind(reader.ReadToEndAsync(), (fun html -> async.Return(html)))))))))) As you saw in 9, the key to understanding the F# workflow syntax is always to understand the meaning of let!. In the case of async workflows, let! executes one asynchronous computation and schedules the next computation for execution once the first asynchronous computation completes. This is syntactic sugar for the Bind operation on the async object.

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Before tackling the problem of representing hardware using propositional logic, let s look at some naive approaches for working with propositional logic formulae. Listing 12-14 shows routines that evaluate formulae given an assignment of variables and that generate the rows of a truth table for a Prop formula.

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Execute the asynchronous computation expr and bind its result to pat when it completes. If expr has type Async<'a>, then pat has type 'a. Equivalent to async.Bind(expr,(fun pat -> ...)). Execute an expression synchronously and bind its result to pat immediately. If expr has type 'a, then pat has type 'a. Equivalent to async.Let(expr,(fun pat -> ...)). Equivalent to let! () = expr. Equivalent to let () = expr. Evaluate the expression, and return its value as the result of the containing asynchronous workflow. Equivalent to async.Return(expr). Execute the expression as an asynchronous computation, and return its result as the overall result of the containing asynchronous workflow. Equivalent to expr. Execute the expression immediately, and bind its result immediately. Call the Dispose method on each variable bound in the pattern when the subsequent asynchronous workflow terminates, regardless of whether it terminates normally or by an exception. Equivalent to async.Using(expr,(fun pat -> ...)).

Listing 12-14. Evaluating Propositional Logic Formulae let rec eval (env : Map<Var,bool>) inp = match inp with | Exists(v,p) -> eval (env.Add(v,false)) p || eval (env.Add(v,true)) p | And(p1,p2) -> eval env p1 && eval env p2 | Var(v) -> if env.ContainsKey(v) then env.[v] else failwithf "env didn't contain a value for %A" v | Not(p) -> not (eval env p) | False -> false let rec support f match f with | And(x,y) | Exists(v,p) | Var(p) | Not(x) | False = -> -> -> -> -> Set.union (support x) (support y) (support p).Remove(v) Set.singleton p support x Set.empty

Query OK, 0 rows affected (0.00 sec)

We now show a slightly longer sample of asynchronous I/O processing. Our running sample is an application that must read a large number of image files and perform some processing on them. This kind of application may be compute bound (if the processing takes a long time and the file system is fast) or I/O bound (if the processing is quick and the file system is slow). Using asynchronous techniques tends to give good overall performance gains when an application is I/O bound and can also give performance improvements for compute-bound applications if asynchronous operations are executed in parallel on multicore machines. Listing 13-6 shows a synchronous implementation of our image transformation program. Listing 13-6. A Synchronous Image Processor open System.IO let numImages = 200 let size = 512 let numPixels = size * size let MakeImageFiles() = printfn "making %d %dx%d images... " numImages size size let pixels = Array.init numPixels (fun i -> byte i) for i = 1 to numImages do System.IO.File.WriteAllBytes(sprintf "Image%d.tmp" i, pixels) printfn "done." let processImageRepeats = 20 let TransformImage(pixels, imageNum) = printfn "TransformImage %d" imageNum; // Perform a CPU-intensive operation on the image. pixels |> Func.repeatN processImageRepeats (Array.map (fun b -> b + 1uy)) let ProcessImageSync(i) = use inStream = File.OpenRead(sprintf "Image%d.tmp" i) let pixels = Array.zero_create numPixels let nPixels = inStream.Read(pixels,0,numPixels); let pixels' = TransformImage(pixels,i) use outStream = File.OpenWrite(sprintf "Image%d.done" i) outStream.Write(pixels',0,numPixels) let ProcessImagesSync() = printfn "ProcessImagesSync..."; for i in 1 .. numImages do ProcessImageSync(i) We assume the image files are already created using the following code:

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