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Impredicative polymorphism (also called first-class polymorphism) is the most powerful form of parametric polymorphism. [1]: 340 In formal logic, a definition is said to be impredicative if it is self-referential; in type theory, it refers to the ability for a type to be in the domain of a quantifier it contains. This allows the instantiation ...
Polymorphism can be distinguished by when the implementation is selected: statically (at compile time) or dynamically (at run time, typically via a virtual function). This is known respectively as static dispatch and dynamic dispatch, and the corresponding forms of polymorphism are accordingly called static polymorphism and dynamic polymorphism.
For example, some definitions focus on mental activities, and some on program structuring. One of the simpler definitions is that OOP is the act of using "map" data structures or arrays that can contain functions and pointers to other maps, all with some syntactic and scoping sugar on top. Inheritance can be performed by cloning the maps ...
While System F corresponds to the first axis of Barendregt's lambda cube, System F ω or the higher-order polymorphic lambda calculus combines the first axis (polymorphism) with the second axis (type operators); it is a different, more complex system.
The same function name is used for more than one function definition in a particular module, class or namespace; The functions must have different type signatures, i.e. differ in the number or the types of their formal parameters (as in C++) or additionally in their return type (as in Ada).
Contrary to the type systems used for example in Pascal (1970) or C (1972), which only support monomorphic types, HM is designed with emphasis on parametric polymorphism. The successors of the languages mentioned, like C++ (1985), focused on different types of polymorphism, namely subtyping in connection with object-oriented programming and ...
For example, in the GHC standard library, the class IArray expresses a general immutable array interface. In this class, the type class constraint IArray a e means that a is an array type that contains elements of type e. (This restriction on polymorphism is used to implement unboxed array types, for example.)
Python allows operator overloading through the implementation of methods with special names. [48] For example, the addition (+) operator can be overloaded by implementing the method obj.__add__(self, other). Ruby allows operator overloading as syntactic sugar for simple method calls.