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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 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) 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 be a property provable about objects of type . Then should be true for objects of type where is a subtype of . Symbolically: :S <: T \to (\forall xT) \phi(x) \to (\forall yS) \phi(y) T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Barbara Liskov MIT Computer Scientist 2010
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Subtyping Of Functions
In programming language theory, subtyping (also subtype polymorphism or inclusion polymorphism) is a form of type polymorphism in which a subtype is a datatype that is related to another datatype (the supertype) by some notion of substitutability, meaning that program elements, typically subroutines or functions, written to operate on elements of the supertype can also operate on elements of the subtype. If S is a subtype of T, the subtyping relation (written as , , or ) means that any term of type S can ''safely be used'' in ''any context'' where a term of type T is expected. The precise semantics of subtyping here crucially depends on the particulars of how ''"safely be used"'' and ''"any context"'' are defined by a given type formalism or programming language. The type system of a programming language essentially defines its own subtyping relation, which may well be trivial, should the language support no (or very little) conversion mechanisms. Due to the sub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proof-theoretic
Proof theory is a major branchAccording to Wang (1981), pp. 3–4, proof theory is one of four domains mathematical logic, together with model theory, axiomatic set theory, and recursion theory. Barwise (1978) consists of four corresponding parts, with part D being about "Proof Theory and Constructive Mathematics". of mathematical logic that represents proofs as formal mathematical objects, facilitating their analysis by mathematical techniques. Proofs are typically presented as inductively-defined data structures such as lists, boxed lists, or trees, which are constructed according to the axioms and rules of inference of the logical system. Consequently, proof theory is syntactic in nature, in contrast to model theory, which is semantic in nature. Some of the major areas of proof theory include structural proof theory, ordinal analysis, provability logic, reverse mathematics, proof mining, automated theorem proving, and proof complexity. Much research also focuses on applicatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Object-Oriented Software Construction
''Object-Oriented Software Construction'' is a book by Bertrand Meyer, widely considered a foundational text of object-oriented programming. The first edition was published in 1988; the second, extensively revised and expanded edition (more than 1300 pages), in 1997. Numerous translations are available including Dutch (first edition only), French (1+2), German (1), Italian (1), Japanese (1+2), Persian (1), Polish (2), Romanian (1), Russian (2), Serbian (2), and Spanish (2). The book has been cited thousands of timesThe ACM's ''Guide to Computing Literature'' count2,233 citations as of December, 15, 2011for the second edition alone in computer science journals and technical books; Google Scholar (December 15, 2011) lists 7,305 citations; the book appears as number 35 in th(books, articles etc.) in computer science, with 1260 citations (September 2006). in computer science literature. The book won a Jolt award in 1994. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Encapsulation (computer Science)
In software systems, encapsulation refers to the bundling of data with the mechanisms or methods that operate on the data, or the limiting of direct access to some data, such as an object's components. Encapsulation allows developers to present a consistent and usable interface which is independent of how a system is implemented internally. As one example, encapsulation can be used to hide the values or state of a structured data object inside a class, preventing direct access to them by clients in a way that could expose hidden implementation details or violate state invariance maintained by the methods. All object-oriented programming (OOP) systems support encapsulation, but encapsulation is not unique to OOP. Implementations of abstract data types, modules, and libraries, among other systems, also offer encapsulation. The similarity has been explained by programming language theorists in terms of existential types. Meaning In object-oriented programming languages, and other ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Postcondition
In computer programming, a postcondition is a condition or predicate that must always be true just after the execution of some section of code or after an operation in a formal specification. Postconditions are sometimes tested using assertions within the code itself. Often, postconditions are simply included in the documentation of the affected section of code. For example: The result of a factorial is always an integer and greater than or equal to 1. So a program that calculates the factorial of an input number would have postconditions that the result after the calculation be an integer and that it be greater than or equal to 1. Another example: a program that calculates the square root of an input number might have the postconditions that the result be a number and that its square be equal to the input. Postconditions in object-oriented programming In some software design approaches, postconditions, along with preconditions and class invariants, are components of the software ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Precondition
In computer programming, a precondition is a condition or predicate that must always be true just prior to the execution of some section of code or before an operation in a formal specification. If a precondition is violated, the effect of the section of code becomes undefined and thus may or may not carry out its intended work. Security problems can arise due to incorrect preconditions. Often, preconditions are simply included in the documentation of the affected section of code. Preconditions are sometimes tested using guards or assertions within the code itself, and some languages have specific syntactic constructions for doing so. For example: the factorial is only defined for integers greater than or equal to zero. So a program that calculates the factorial of an input number would have preconditions that the number be an integer and that it be greater than or equal to zero. In object-oriented programming Preconditions in object-oriented software development are an ess ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inheritance (computer Science)
In object-oriented programming, inheritance is the mechanism of basing an object or class upon another object ( prototype-based inheritance) or class ( class-based inheritance), retaining similar implementation. Also defined as deriving new classes ( sub classes) from existing ones such as super class or base class and then forming them into a hierarchy of classes. In most class-based object-oriented languages, an object created through inheritance, a "child object", acquires all the properties and behaviors of the "parent object" , with the exception of: constructors, destructor, overloaded operators and friend functions of the base class. Inheritance allows programmers to create classes that are built upon existing classes, to specify a new implementation while maintaining the same behaviors ( realizing an interface), to reuse code and to independently extend original software via public classes and interfaces. The relationships of objects or classes through inheritance give ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Covariance And Contravariance (computer Science)
Many programming language type systems support subtyping. For instance, if the type is a subtype of , then an expression of type should be substitutable wherever an expression of type is used. Variance refers to how subtyping between more complex types relates to subtyping between their components. For example, how should a list of s relate to a list of s? Or how should a function that returns relate to a function that returns ? Depending on the variance of the type constructor, the subtyping relation of the simple types may be either preserved, reversed, or ignored for the respective complex types. In the OCaml programming language, for example, "list of Cat" is a subtype of "list of Animal" because the list type constructor is covariant. This means that the subtyping relation of the simple types are preserved for the complex types. On the other hand, "function from Animal to String" is a subtype of "function from Cat to String" because the function type constructor is cont ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Subtyping
In programming language theory, subtyping (also subtype polymorphism or inclusion polymorphism) is a form of type polymorphism in which a subtype is a datatype that is related to another datatype (the supertype) by some notion of substitutability, meaning that program elements, typically subroutines or functions, written to operate on elements of the supertype can also operate on elements of the subtype. If S is a subtype of T, the subtyping relation (written as , , or ) means that any term of type S can ''safely be used'' in ''any context'' where a term of type T is expected. The precise semantics of subtyping here crucially depends on the particulars of how ''"safely be used"'' and ''"any context"'' are defined by a given type formalism or programming language. The type system of a programming language essentially defines its own subtyping relation, which may well be trivial, should the language support no (or very little) conversion mechanisms. Due to the sub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
