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Snippet from Wikipedia: Abstraction (computer science)

In software engineering and computer science, abstraction is the process of generalizing concrete details, such as attributes, away from the study of objects and systems to focus attention on details of greater importance. Abstraction is a fundamental concept in computer science and software engineering, especially within the object-oriented programming paradigm. Examples of this include:

• the usage of abstract data types to separate usage from working representations of data within programs;
• the concept of functions or subroutines which represent a specific way of implementing control flow;
• the process of reorganizing common behavior from groups of non-abstract classes into abstract classes using inheritance and sub-classes, as seen in object-oriented programming languages.

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Snippet from Wikipedia: Liskov substitution principle

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 1987 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) may be replaced by a sub-object (such as a class that extends the first class) without breaking the program. It is a semantic rather than merely syntactic relation, because it intends to guarantee semantic interoperability of types in a hierarchy, object types in particular. Barbara Liskov and Jeannette Wing described the principle succinctly in a 1994 paper as follows:

Subtype Requirement: Let ⁠${\displaystyle \phi (x)}$⁠ be a property provable about objects ⁠${\displaystyle x}$⁠ of type T. Then ⁠${\displaystyle \phi (y)}$⁠ should be true for objects ⁠${\displaystyle y}$⁠ of type S where S is a subtype of T.

Symbolically:

${\displaystyle S\leq T\to (\forall x{:}T.\phi (x)\to \forall y{:}S.\phi (y))}$

That is, if S subtypes T, what holds for T-objects holds for S-objects. In the same paper, Liskov and Wing detailed their notion of behavioral subtyping in an extension of Hoare logic, which bears a certain resemblance to Bertrand Meyer's design by contract in that it considers the interaction of subtyping with preconditions, postconditions and invariants.

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