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Capture conversion is designed to make wildcards more useful To understand the motivation, let s begin by looking at the method javautilCollectionsreverse():
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public static void reverse(List< > list);
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The method reverses the list provided as a parameter It works for any type of list, and so the use of the wildcard type List< > as the type of the formal parameter is entirely appropriate Now consider how one would implement reverse()
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public static void reverse(List< > list) { rev(list);} private static <T> void rev(List<T> list) { List<T> tmp = new ArrayList<T>(list); for (int i = 0; i < listsize(); i++) { listset(i, tmpget(listsize() - i - 1)); } }
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The implementation needs to copy the list, extract elements from the copy , and insert them into the original To do this in a type safe manner, we need to give a name, T, to the element type of the incoming list We do this in the private service method rev()
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This requires us to pass the incoming argument list, of type List< >, as an argument to rev() Note that in general, List< > is a list of unknown type It is not a subtype of List<T>, for any type T Allowing such a subtype relation would be unsound Given the method:
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public static <T> void fill(List<T> l, T obj)
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List<String> ls = new ArrayList<String>(); List< > l = ls; Collectionsfill(l, new Object()); // not really legal - but assume // it was String s = lsget(0); // ClassCastException - ls contains Objects, //not Strings
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would undermine the type system So, without some special dispensation, we can see that the call from reverse() to rev() would be disallowed If this were the case, the author of reverse() would be forced to write its signature as:
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public static <T> void reverse(List<T> list)
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Mathematically sophisticated readers will want to relate capture conversion to established type theory Readers unfamiliar with type theory can skip this discussion - or else study a suitable text, such as Types and Programming Languages by Benjamin Pierce, and then revisit this section Here then is a brief summary of the relationship of capture conversion to established type theoretical notions Wildcard types are a restricted form of existential types Capture conversion corresponds loosely to an opening of a value of existential type A capture conversion of an expression e, can be thought of as an open of e in a scope that comprises the top-level expression that encloses e
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This is undesirable, as it exposes implementation information to the caller Worse, the designer of an API might reason that the signature using a wildcard is what the callers of the API require, and only later realize that a type safe implementation was precluded The call from reverse() to rev() is in fact harmless, but it cannot be justi ed on the basis of a general subtyping relation between List< > and List<T> The call is harmless, because the incoming argument is doubtless a list of some type (albeit an unknown one) If we can capture this unknown type in a type variable X, we can infer T to be X That is the essence of capture conversion The speci cation of course must cope with complications, like non-trivial (and possibly recursively de ned) upper or lower bounds, the presence of multiple arguments etc
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5111 String Conversions
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There is a string conversion to type String from every other type, including the null type See ( 54) for details of the string conversion context 5112 Forbidden Conversions
Any conversion that is not explicitly allowed is forbidden 5113 Value Set Conversion
Value set conversion is the process of mapping a oating-point value from one value set to another without changing its type Within an expression that is not FP-strict ( 154), value set conversion provides choices to an implementation of the Java programming language:
If the value is an element of the oat-extended-exponent value set, then the implementation may, at its option, map the value to the nearest element of the oat value set This conversion may result in over ow (in which case the value is replaced by an in nity of the same sign) or under ow (in which case the value may lose precision because it is replaced by a denormalized number or zero of the same sign) If the value is an element of the double-extended-exponent value set, then the implementation may, at its option, map the value to the nearest element of the double value set This conversion may result in over ow (in which case the value is replaced by an in nity of the same sign) or under ow (in which case the value may lose precision because it is replaced by a denormalized number or zero of the same sign)
The classical open operation on existentials requires that the captured type variable must not escape the opened expression The open that corresponds to capture conversion is always on a scope suf ciently large that the captured type variable can never be visible outside that scope The advantage of this scheme is that there is no need for a close operation, as de ned in the paper On Variance-Based Subtyping for Parametric Types by Atsushi Igarashi and Mirko Viroli, in the proceedings of the 16th European Conference on Object Oriented Programming (ECOOP 2002) For a formal account of wildcards, see Wild FJ by Mads Torgersen, Erik Ernst and Christian Plesner Hansen, in the 12th workshop on Foundations of Object Oriented Programming (FOOL 2005)