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CHAPTER 5 MASTERING TYPES AND GENERICS
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applied when a let or member definition doesn t fully constrain the types of inputs or outputs. You can tell automatic generalization has been applied by the presence of type variables in an inferred type and ultimately by the fact that you can reuse a construct with multiple types. Automatic generalization is particularly useful when taking functions as inputs. For example, the following takes two functions as input and applies them to each side of a tuple: let mapPair f g (x,y) = (f x, g y) The generalized, inferred type is as follows: val mapPair : ('a -> 'b) -> ('c -> 'd) -> ('a * 'c) -> ('b * 'd)
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Understanding Some Important Generic Functions
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The F# and .NET libraries include definitions for some important generic functions. You saw a number of these in action in earlier chapters. It s important to have a working knowledge of these building blocks, because often your code will automatically become generic when you use these primitives.
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Generic Comparison
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The first primitives are all related to generic comparison, also often called structural comparison. Every time you use operators such as <, >, <=, >=, =, <>, compare, min, and max in F# code, you re using generic comparison. All of these operators are located in the Microsoft.FSharp.Core.Operators module, which is opened by default in all F# code. Some important data structures also use generic comparison internally; for example, you may also be using generic comparison when you use F# collection types such as Microsoft.FSharp.Collections.Set and Microsoft.FSharp.Collections.Map. This is discussed in the documentation for these types. The type signatures of the basic generic comparison operators are shown here: val val val val val val val val compare : 'T -> 'T -> int when 'T : comparison (=) : 'T -> 'T -> bool when 'T : equality (<) : 'T -> 'T -> bool when 'T : comparison (<=) : 'T -> 'T -> bool when 'T : comparison (>) : 'T -> 'T -> bool when 'T : comparison (>=) : 'T -> 'T -> bool when 'T : comparison (min) : 'T -> 'T -> 'T when 'T : comparison (max) : 'T -> 'T -> 'T when 'T : comparison
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All of these routines are constrained, which means they may only be used on a subset of types that are known to support either equality (for =) or ordered comparison (for the others). It may help to think of those that implement ordered comparison as being implemented in terms of compare, which returns 0 if the arguments are equal and returns 1 and 1 for less than and greater than, respectively. On ordinary simple types such as integers, generic comparison works by invoking the default .NET behavior for these types, giving the natural ordering for these types. For strings, culture-neutral ordinal comparison is used, which means the local culture settings on your machine don t affect string comparison (see System.Globalization for more information about local settings). Most other .NET base types implement the System.IComparable interface, such as System.DateTime values, and generic comparison uses these implementations where necessary.
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CHAPTER 5 MASTERING TYPES AND GENERICS
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You can also use the comparison operators on most structured types. For example, you can use them on F# tuple values, where a lexicographic left-to-right comparison is used: > ("abc","def") < ("abc","xyz");; val it : bool = true > compare (10,30) (10,20);; val it : int = 1 Likewise, you can use generic comparison with list and array values: > compare [10;30] [10;20];; val it : int = 1 > compare [| 10;30 |] [| 10;20 |];; val it : int = 1 > compare [| 10;20 |] [| 10;30 |];; val it : int = -1
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