... in mathematics a circle is a kind
of an ellipse, but in most programs a circle should not be derived from an ellipse or an ellipse
derived from a circle. The oftenheard
arguments ‘‘because that’s the way it is in mathematics’’
and ‘‘because the representation of a circle is a subset of that of an ellipse’’ are not conclusive and
most often wrong. This is because for most programs, the key property of a circle is that it has a
center and a fixed distance to its perimeter. All behavior of a circle (all operations) must maintain
this property (invariant; §24.3.7.1).

Square specializes Rectangle
{
  invariant { base.a == base.b; }
  ...
}

Rectangle rect (2, 3);
Rectangle rect2 = SomeOperations (rect);
if (rect2 is Square) // проверка всего-лишь инварианта rect2.a == rect2.b
{
  ...
}

VE>Square specializes Rectangle
VE>{
VE>  invariant { base.a == base.b; }
VE>  ...
VE>}

VE>Rectangle rect (2, 3);
VE>Rectangle rect2 = SomeOperations (rect);
VE>if (rect2 is Square) // проверка всего-лишь инварианта rect2.a == rect2.b
VE>{
VE>  ...
VE>}
VE>

Button b = new ButtonWithText("bla-bla");

Let q(x) be a property provable about objects x of type T. Then q(y) should be true for objects y of type S where S is a subtype of T.

T>Let q(x) be a property provable about objects x of type T. Then q(y) should be true for objects y of type S where S is a subtype of T.