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%ما هو (من)٪ 1 - تعريف
Liskov substitution principle
![Liskov substitution was introduced by [[Barbara Liskov]], photo taken in 2010](https://commons.wikimedia.org/wiki/Special:FilePath/Barbara Liskov MIT computer scientist 2010.jpg?width=200 "Liskov substitution was introduced by [[Barbara Liskov]], photo taken in 2010")
OBJECT-ORIENTED PROGRAMMING PRINCIPLE STATING THAT, IN A COMPUTER PROGRAM, IF S IS A SUBTYPE OF T, THEN OBJECTS OF TYPE T MAY BE REPLACED WITH OBJECTS OF TYPE S WITHOUT ALTERING ANY OF THE DESIRABLE PROPERTIES OF THE PROGRAM (CORRECTNESS, ETC.)
Liskov Substitution Principle; Substitutability; Liskov substitution
The Liskov substitution principle (LSP) is a particular definition of a subtyping relation, called strong behavioral subtyping, that was initially introduced by Barbara Liskov in a 1988 conference keynote address titled Data abstraction and hierarchy. It is based on the concept of "substitutability" a principle in object-oriented programming stating that an object (such as a class) and a sub-object (such as a class that extends the first class) must be interchangeable without breaking the program.
Liskov substitution principle
OBJECT-ORIENTED PROGRAMMING PRINCIPLE STATING THAT, IN A COMPUTER PROGRAM, IF S IS A SUBTYPE OF T, THEN OBJECTS OF TYPE T MAY BE REPLACED WITH OBJECTS OF TYPE S WITHOUT ALTERING ANY OF THE DESIRABLE PROPERTIES OF THE PROGRAM (CORRECTNESS, ETC.)
Liskov Substitution Principle; Substitutability; Liskov substitution
<programming, theory> (LSP) The principle that
object-oriented functions that use pointers or
references to a base class must be able to use objects of
a derived class without knowing it.
Barbara Liskov first wrote it as follows: If for each object
o1 of type S there is an object o2 of type T such that for all
programs P defined in terms of T, the behaviour of P is
unchanged when o1 is substituted for o2 then S is a subtype
of T.
A function that violates the LSP uses a reference to a base
class and must know about all the derivatives of that base
class. Such a function violates the open/closed principle
because it must be modified whenever a new derivative of the
base class is created.
[Liskov, B. Data Abstraction and Hierarchy, SIGPLAN
Notices. 23(5), May 1988 ].
(2001-09-14)
Weierstrass substitution
![(2/2) The tangent half-angle substitution illustrated as [[stereographic projection]] of the circle.](https://commons.wikimedia.org/wiki/Special:FilePath/WeierstrassSubstitution.svg?width=200 "(2/2) The tangent half-angle substitution illustrated as [[stereographic projection]] of the circle.")
TECHNIQUE TO INTEGRATE RATIONAL FUNCTIONS INVOLVING TRIGONOMETRIC FUNCTIONS.
Weierstraß substitution; Weierstrass substitution method; Weierstrass substitution formula; Weierstrass substitution formulas; Weierstrass' substitution; The Weierstrass Substitution; Weierstrass Substitution; The Weierstrass substitution; The tangent half-angle substitution; Tangent half angle substitution; Weierstrass substitution; Universal trigonometric substitution
In integral calculus, the Weierstrass substitution or tangent half-angle substitution is a method for evaluating integrals, which converts a rational function of trigonometric functions of x into an ordinary rational function of t by setting t = \tan (x /2).Weisstein, Eric W.
