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Object–relational mapping (ORM, O/RM, and O/R mapping tool) in computer science is a programming technique for converting data between a relational database and the memory (usually the heap) of an object-oriented programming language.
The converse of this implication leads to functions that are order-reflecting, i.e. functions f as above for which f(a) ≤ f(b) implies a ≤ b. On the other hand, a function may also be order-reversing or antitone, if a ≤ b implies f(a) ≥ f(b). An order-embedding is a function f between orders that is both order-preserving and order ...
Relations among tables are mapped in the same way: by convention. For instance, to create a one-to-many relationship between two tables one assigns an array to the property bearing the name of the target table. This automatically creates the table as well as the required columns. Code example, demonstrating a simple CRUD operation and a relation:
Order-dual. The order dual of a partially ordered set is the same set with the partial order relation replaced by its converse. Order-embedding. A function f between posets P and Q is an order-embedding if, for all elements x, y of P, x ≤ y (in P) is equivalent to f(x) ≤ f(y) (in Q). Order isomorphism.
Given a set and a partial order relation, typically the non-strict partial order , we may uniquely extend our notation to define four partial order relations , <,, and >, where is a non-strict partial order relation on , < is the associated strict partial order relation on (the irreflexive kernel of ), is the dual of , and > is the dual of <.
Laravel 1 included built-in support for authentication, localisation, models, views, sessions, routing and other mechanisms, but lacked support for controllers that prevented it from being a true MVC framework. [1] Laravel 2 was released in September 2011, bringing various improvements from the author and community.
The nested set model is a technique for representing nested set collections (also known as trees or hierarchies) in relational databases.. It is based on Nested Intervals, that "are immune to hierarchy reorganization problem, and allow answering ancestor path hierarchical queries algorithmically — without accessing the stored hierarchy relation".
The incomparability relation is always symmetric and it will be reflexive if and only if < is an irreflexive relation (which is assumed by the above definition). Consequently, a strict partial order < is a strict weak order if and only if its induced incomparability relation is an equivalence relation.