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A map, sometimes referred to as a dictionary, consists of a key/value pair. The key is used to order the sequence, and the value is somehow associated with that key. For example, a map might contain keys representing every unique word in a text and values representing the number of times that word appears in the text.
The function (,):= (+) is a pairing function. In 1990, Regan proposed the first known pairing function that is computable in linear time and with constant space (as the previously known examples can only be computed in linear time if multiplication can be too, which is doubtful). In fact, both this pairing function and its inverse can be ...
A dependent pair may have a second value, the type of which depends on the first value. Sticking with the array example, a dependent pair may be used to pair an array with its length in a type-safe way. Dependent types add complexity to a type system. Deciding the equality of dependent types in a program may require computations.
The C++ Standard Library is based upon conventions introduced by the Standard Template Library (STL), and has been influenced by research in generic programming and developers of the STL such as Alexander Stepanov and Meng Lee. [4] [5] Although the C++ Standard Library and the STL share many features, neither is a strict superset of the other.
For example, a portable library can not define an allocator type that will pull memory from different pools using different allocator objects of that type. (Meyers, p. 50) (addressed in C++11). The set of algorithms is not complete: for example, the copy_if algorithm was left out, [13] though it has been added in C++11. [14]
Due to their usefulness, they were later included in several other implementations of the C++ Standard Library (e.g., the GNU Compiler Collection's (GCC) libstdc++ [2] and the Visual C++ (MSVC) standard library). The hash_* class templates were proposed into C++ Technical Report 1 (C++ TR1) and were accepted under names unordered_*. [3]
Hom(A, –) maps each object X in C to the set of morphisms, Hom(A, X) Hom(A, –) maps each morphism f : X → Y to the function Hom(A, f) : Hom(A, X) → Hom(A, Y) given by for each g in Hom(A, X). This is a contravariant functor given by: Hom(–, B) maps each object X in C to the set of morphisms, Hom(X, B)
[2] [3] [4] Functionally, the mutator pop can be interpreted as the pair of selectors (pick, rest), where rest returns the set consisting of all elements except for the arbitrary element. [5] Can be interpreted in terms of iterate. [a] map(F,S): returns the set of distinct values resulting from applying function F to each element of S.