.NET/Java PDF, Tiff, Barcode SDK Library

As I see it, the primary aim of the Liskov/Wing paper is not to propose an abstract model, as such, of subtyping and inheritance. Rather, it is to provide certain definitional constructs that allow assertions of the form S is a subtype of T to be formally verified, in the sense that: a. Methods associated with type S can be shown to behave the same as the corresponding methods associated with type T. b. Constraints associated with type S can be shown to imply those associated with type T. Note: The paper makes these two statements much more precise. I can t do the same here, because I haven t explained enough of the background and I don t want to explain more of the background just yet, because there are significant parts of it I don t agree with, as I ll make clear soon. The paper s main contribution is thus that it provides a way of checking whether an assertion on the part of the type definer to the effect that S is a subtype of T is valid, or at least plausible. By way of motivation for their work, the authors offer the following remarks among others: [Objects] of the subtype ought to behave the same as those of the supertype as far as anyone or any program using supertype objects can tell. Interestingly, this sentence (which as we saw earlier was repeated in the Tockey article) seems to be as close as the paper comes to actually providing a statement of the Liskov Substitution Principle. Certainly there is no formal statement of LSP, as such, anywhere in the paper.

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[Test(expected="flexunit.framework.AssertionFailedError")] public function testAssertNullNotEqualsNull():void { Assert.assertEquals( null, null ); }

Figure 6-7. The Lasso Select tool is more reliable, on some laptops at least, than right-click object selections.

Subtype Requirement: Let (x) be a property provable about objects x of type T Then (y) should be true for objects y of type S where S is a subtype of T This statement is highlighted in the paper (in the introduction, in fact), and it constitutes clear evidence in support of what I said at the beginning of this section: namely, that the aim of the paper is to provide a mechanism that supports formal verification of claims to the effect that some given type S is a subtype of some other type T14 Note: I think the word true in the second sentence would better be replaced by the word provable, but perhaps it s not important [We] were motivated primarily by pragmatics Our intention [was] to capture the intuition programmers apply when designing type hierarchies in object-oriented languages.

The test runner is similar to FlexUnit1 test runner. See the complete code in the following example.

However, intuition in the absence of precision can often go astray or lead to confusion This is why [in the past] it has been unclear how to organize certain type hierarchies such as integers [Sic! Presumably the authors mean type hierarchies such as ones involving different kinds of integers ] I find these remarks regarding pragmatics and intuition very revealing I could be quite wrong, but it seems to me that what Liskov and Wing are trying to do in their paper is retroactively to formalize, and impose some discipline on, a bunch of disparate preexisting notions that are all somehow related to some vague notions of subtyping and type inheritance The trouble is, there has never been there still isn t! any consensus as to what what these latter terms mean Instead, what there definitely has been is much confusion ...

< xml version="1.0" encoding="utf-8" > <s:Application xmlns:fx="http://ns.adobe.com/mxml/2009" xmlns:s="library://ns.adobe.com/flex/spark" xmlns:mx="library://ns.adobe.com/flex/halo" xmlns:flexUnitUIRunner="http://www.adobe.com/2009/flexUnitUIRunner" minWidth="1024" minHeight="768" creationComplete="creationCompleteHandler(event)"> <fx:Script> <![CDATA[ import import import import flexUnitTests.FlexUnit4TheorySuite; flexUnitTests.FlexUnit4HamcrestSuite; mx.events.FlexEvent; flexUnitTests.FlexUnit4Suite;

With only the cube selected, click the red, green, or blue arrowhead of the 3D Transform Manipulator to drag the object in that direction and back again (see Figure 6-8). It s as if the object slides on a rail, and Blender provides thin red and green guidelines on the plane to help you remember which axis is which. Notice how the cube looks larger as it gets closer to the camera on the plane and smaller as it gets further away; that s 3D perspective. If this isn t working for you, then again it may be due to incomplete 3D driver support for your graphics hardware.