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type 'a option = | None | Some of 'a Discriminated unions can include recursive references (the same is true of records and other type definitions). This is frequently used when representing structured languages via discriminated unions, a topic covered in depth in 9: type Proposition = | True | And of Proposition * Proposition | Or of Proposition * Proposition | Not of Proposition Recursive functions can be used to traverse such a type. For example: let rec eval (p: Proposition) = match p with | True -> true | And(p1,p2) -> eval p1 && eval p2 | Or (p1,p2) -> eval p1 || eval p2 | Not(p1) -> not (eval p1) Indeed, the F# type of immutable lists is defined in this way: type 'a list = | ([]) | (::) of 'a * 'a list A broad range of tree-like data structures are conveniently represented as discriminated unions. For example: type Tree<'a> = | Tree of 'a * Tree<'a> * Tree<'a> | Tip of 'a You can use recursive functions to compute properties of trees: let rec size tree = match tree with | Tree(_,l,r) -> 1 + size l + size r | Tip _ -> 1 Here is the inferred type of size:
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val size : Tree<'a> -> int
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Here is an example of a constructed tree term and the use of the size function:
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C HAPTE R 3 INTRODU CING FUNCTION AL PROGRAM MIN G
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> let small = Tree("1",Tree("2",Tip("a"),Tip("b")),Tip("c"));; val small : Tree<string> > small;; val it : Tree<string> = Tree ("1",Tree ("2",Tip("a"),Tip("b")),Tip("c")) > size small;; val it : int = 5 We discuss symbolic manipulation based on trees in detail in s 8, 9, and 12.
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Note Discriminated unions are a powerful and important construct and are useful when modeling a finite,
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sealed set of choices. This makes them a perfect fit for many constructs that arise in applications and symbolic analysis libraries. They are, by design, nonextensible: subsequent modules cannot add new cases to a discriminated union. This is deliberate: you get strong and useful guarantees by placing a limit on the range of possible values for a type. Extensible types can be defined through the use of records of functions and object interface types, discussed in 5 and 6.
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Using Discriminated Unions As Records
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Discriminated union types with only one data tag are an effective way to implement recordlike types: type Point3D let origin = let unitX = let unitY = let unitZ = = Vector3D of float * float * float Vector3D(0.,0.,0.) Vector3D(1.,0.,0.) Vector3D(0.,1.,0.) Vector3D(0.,0.,1.)
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These are particularly effective because they can be decomposed using succinct patterns in the same way as tuple arguments: let length (Vector3D(dx,dy,dz)) = sqrt(dx*dx+dy*dy+dz*dz) This technique is most useful for record-like values where there is some natural order on the constituent elements of the value (as shown earlier) or where the elements have different types.
Defining Multiple Types Simultaneously
Multiple types can be declared together to give a mutually recursive collection of types, including record types, discriminated unions, and abbreviations. The type definitions must be separated by the keyword and:
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type node = { Name : string; Links : link list } and link = | Dangling | Link of node
Summary
F# is a multiparadigm language, and in this chapter you looked at the core language constructs used for functional programming. In the next chapter, you ll look at how to use F# for imperative programming, that is, how to use mutable state, raise and handle exceptions, and perform I/O.
Introducing Imperative Programming
n 3 you saw some of the simple but powerful data types and language constructs that make up F# functional programming. The functional programming paradigm is strongly associated with programming without side effects, called pure functional programming. In this paradigm, programs compute the result of a mathematical expression and do not cause any side effects, except perhaps reporting the result of the computation. The formulae used in spreadsheets are often pure, as is the core of functional programming languages such as Haskell. F# is not, however, a pure functional language; for example, you can write programs that mutate data, perform I/O communications, start threads, and raise exceptions. Furthermore, the F# type system doesn t enforce a strict distinction between expressions that perform these actions and expressions that don t. Programming with side effects is called imperative programming. In this chapter, we look more closely at a number of constructs related to imperative programming. We describe how to use loops, mutable data, arrays, and some common input/output techniques. If your primary programming experience has been with an imperative language such as C, C#, or Java, you will initially find yourself using imperative constructs fairly frequently in F#. However, over time F# programmers generally learn how to perform many routine programming tasks within the side-effect-free subset of the language. F# programmers tend to use side effects in the following situations: When scripting and prototyping using F# Interactive When working with .NET library components that use side effects heavily, such as GUI libraries and I/O libraries When initializing complex data structures When using inherently imperative, efficient data structures such as hash tables and hash sets When locally optimizing routines in a way that improves on the performance of the functional version of the routine When working with very large data structures or in scenarios where the allocation of data structures must be minimized for performance reasons
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