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CHAPTER 9 INTRODUCING LANGUAGE-ORIENTED PROGRAMMING
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> let t1 = Not(And(Not(Var("x")),Not(Var("y"))));; val t1 : Prop > fsi.AddPrinter(showProp);; > t1;; val it : Prop = not (not x && not y) > let t2 = Or(Not(Not(Var("x"))),Var("y"));; val t2 : Prop > t2;; val it : Prop = not (not x) || y > (t1 = t2);; val it : bool = false > NNF t1;; val it : Prop = x || y > NNF t2;; val it : Prop = x || y > NNF t1 = NNF t2;; val it : bool = true
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Embedded Computational Languages with Workflows
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3 introduced a useful notation for generating sequences of data, called sequence expressions. For example: > seq { for i in 0 .. 3 -> (i,i*i) };; val it : seq<int * int> = seq [ (0,0); (1,1); (2,4); (3,9) ] Sequence expressions are used extensively throughout this book. For example, 15 uses sequence expressions for queries that are executed on a database. It turns out that sequence expressions are just one instance of a more general construct called computation expressions. These are also called workflows, although they bear only a passing similarity to the workflows used to model business processes. The general form of a computation expression is builder { comp-expr }. Table 9-2 shows the primary constructs that can be used within the braces of a computation expression and how these constructs are de-sugared by the F# compiler given a computation expression builder builder. The three most important applications of computation expressions in F# programming are as follows: General-purpose programming with sequences, lists, and arrays Parallel, asynchronous, and concurrent programming using asynchronous workflows, discussed in detail in 13 Database queries, by quoting a workflow and translating it to SQL via the .NET LINQ libraries, a technique demonstrated in 15
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CHAPTER 9 INTRODUCING LANGUAGE-ORIENTED PROGRAMMING
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This section covers briefly how computation expressions work through some simple examples. Table 9-2. Main Constructs in Computation Expressions and Their De-sugaring
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Construct
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let! pat = expr in cexpr let pat = expr in cexpr use pat = expr in cexpr use! pat = expr in cexpr do! expr in cexpr do expr in cexpr for pat in expr do cexpr while expr do cexpr if expr then cexpr1 else cexpr2 if expr then cexpr cexpr1cexpr2 yield expr yield! expr return expr return! expr
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De-sugared Form
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b.Bind (expr, (fun pat -> cexpr )) b.Let (expr, (fun pat -> cexpr )) b.Using (expr, (fun pat -> cexpr )) b.Bind (expr, (fun x -> b.Using (x, fun pat -> cexpr ))) b.Bind (expr, (fun () -> cexpr )) b.Let (expr, (fun () -> cexpr )) b.For (expr, (fun pat -> cexpr )) b.While ((fun () -> expr), b.Delay (fun () -> cexpr )) if expr then cexpr1 else cexpr2 if expr then cexpr else b.Zero() v.Combine ( cexpr1 , b.Delay(fun () -> cexpr2 )) b.Yield expr b.YieldFrom expr b.Return expr b.ReturnFrom expr
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Note If you ve never seen F# workflows or Haskell monads before, then you may find that workflows take a bit
of getting used to. They give you a way to write computations that may behave and execute quite differently than normal programs.
CHAPTER 9 INTRODUCING LANGUAGE-ORIENTED PROGRAMMING
F# Workflows and Haskell Monads
Computation expressions are the F# equivalent of monadic syntax in the programming language Haskell. Monads are a powerful and expressive design pattern and are characterized by a generic type M<'T> combined with at least two operations:
bind : M<'T> -> ('T -> return : 'T -> M<'T> M<'U>) -> M<'U>
These correspond to the primitives let! and return in the F# computation expression syntax. Several other elements of the computation expression syntax can be implemented in terms of these primitives; but the F# de-sugaring process leaves this up to the implementer of the workflow, because sometimes derived operations can have more efficient implementations. Well-behaved monads should satisfy three important rules called the monad laws. F# uses the terms computation expression and workflow for four reasons: When the designers of F# talked with the designers of Haskell about this, they agreed that the word monad is obscure and sounds a little daunting and that using other names might be wise. There are some technical differences: for example, some F# workflows can be combined with imperative programming, utilizing the fact that workflows can have side effects that aren t tracked by the F# type system. In Haskell, all side-effecting operations must be lifted into the corresponding monad. The Haskell approach has some important advantages: you can know for sure what side effects a function can have by looking at its type. However, it also makes it more difficult to use external libraries from within a computation expression. F# workflows can be reified using F# quotations, providing a way to execute the workflow by alternative means for example, by translation to SQL. This gives them a different role in practice, because they can be used to model both concrete languages and computational languages. F# workflows can also be used to embed computations that generate multiple results (called monoids) such as sequence expressions (also known as comprehension syntax). These generally use yield and yield! instead of return and return! and often have no let!.
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