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Paint Data Matrix in VB.NET MASTERING TYPES AND GENERICS

CHAPTER 5 MASTERING TYPES AND GENERICS
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For example: > hcf 18 12;; val it : int = 6 > hcf 33 24;; val it : int = 3 But this algorithm isn t generic, because as written it works only over integers. In particular, although the operator (-) is by default overloaded in F#, each use of the operator must be associated with at most one type decided at compile time. This restriction is discussed in more detail in the section Understanding Generic Overloaded Operators. In addition, the constant 0 is an integer and isn t overloaded. Despite this, this algorithm can be easily generalized to work over any type. To achieve this, you must provide an explicit zero, a subtraction function, and an ordering. Here s one way: let hcfGeneric (zero,sub,lessThan) = let rec hcf a b = if a=zero then b elif lessThan a b then hcf a (sub b a) else hcf (sub a b) b hcf The inferred, generic type of this function is as follows: val hcfGeneric : 'a * ('a -> 'a -> 'a) * ('a -> 'a -> bool) -> ('a -> 'a -> 'a) when 'a : equality The numeric type being manipulated has type 'a in the inferred type, and the result is a computed function. This approach uses techniques for computing functions similar to those discussed in 3. Here are some examples of using this generic function: let hcfInt = hcfGeneric (0, (-),(<)) let hcfInt64 = hcfGeneric (0L,(-),(<)) let hcfBigInt = hcfGeneric (0I,(-),(<)) Note that when you instantiate the generic function for these cases, you re drawing on particular instances of the default overloaded operator (-). You can check that the code is executing correctly as follows: > hcfInt 18 12;; val it : int = 6 > hcfBigInt 1810287116162232383039576I 1239028178293092830480239032I;; val it : bigint = 33224I
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CHAPTER 5 MASTERING TYPES AND GENERICS
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Generic Algorithms through Abstract Object Types
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The generic implementation from the previous section took three related parameters for zero, comparison, and subtraction. It s common practice to package related operations together. One way to do this is to use a concrete record type containing function values: type Numeric<'T> = { Zero: 'T; Subtract: ('T -> 'T -> 'T); LessThan: ('T -> 'T -> bool); } let intOps = { Zero=0 ; Subtract=(-); LessThan=(<) } let bigintOps = { Zero=0I; Subtract=(-); LessThan=(<) } let int64Ops = { Zero=0L; Subtract=(-); LessThan=(<) } let hcfGeneric (ops : Numeric<'T>) = let rec hcf a b = if a = ops.Zero then b elif ops.LessThan a b then hcf a (ops.Subtract b a) else hcf (ops.Subtract a b) b hcf let hcfInt = hcfGeneric intOps let hcfBigInt = hcfGeneric bigintOps The inferred types are as follows: val hcfGeneric : Numeric<'T> -> ('T -> 'T -> 'T) when 'T : equality val hcfInt : (int -> int -> int) val hcfBigInt : (bigint -> bigint -> bigint) Here are some examples of the functions in action: > hcfInt 18 12;; val it : int = 6 > hcfBigInt 1810287116162232383039576I 1239028178293092830480239032I;; val it : bigint = 33224I Record types such as Numeric<'T> are often called dictionaries of operations and are similar to vtables from object-oriented programming and the compiled form of type classes from Haskell. As you ve seen, dictionaries such as these can be represented in different ways according to your tastes, using tuples or records. For larger frameworks, a carefully constructed classification of object interface types is often used in place of records. Here is an interface type definition that plays the same role as the record in the previous example: type INumeric<'T> = abstract Zero : 'T abstract Subtract: 'T * 'T -> 'T abstract LessThan: 'T * 'T -> bool
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