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Therefore, compilers will attempt to transform the first form into the second; this type of optimization is known as map fusion and is the functional analog of loop fusion. [2] Map functions can be and often are defined in terms of a fold such as foldr, which means one can do a map-fold fusion: foldr f z . map g is equivalent to foldr (f .
As sets can be interpreted as a kind of map (by the indicator function), sets are commonly implemented in the same way as (partial) maps (associative arrays) – in this case in which the value of each key-value pair has the unit type or a sentinel value (like 1) – namely, a self-balancing binary search tree for sorted sets [definition needed ...
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]
In C++, associative containers are a group of class templates in the standard library of the C++ programming language that implement ordered associative arrays. [1] Being templates, they can be used to store arbitrary elements, such as integers or custom classes.
This function maps each image to its unique preimage. The composition of two bijections is again a bijection, but if g ∘ f {\displaystyle g\circ f} is a bijection, then it can only be concluded that f {\displaystyle f} is injective and g {\displaystyle g} is surjective (see the figure at right and the remarks above regarding injections and ...
First-class functions have often only been supported in later revisions of the language, including C# 2.0 and Apple's Blocks extension to C, C++, and Objective-C. C++11 has added support for anonymous functions and closures to the language, but because of the non-garbage collected nature of the language, special care has to be taken for non ...
Self-concordant function; Semi-differentiability; Semilinear map; Set function; List of set identities and relations; Shear mapping; Shekel function; Signomial; Similarity invariance; Soboleva modified hyperbolic tangent; Softmax function; Softplus; Splitting lemma (functions) Squeeze theorem; Steiner's calculus problem; Strongly unimodal ...
Pointed maps are the homomorphisms of these algebraic structures. The class of all pointed sets together with the class of all based maps forms a category. Every pointed set can be converted to an ordinary set by forgetting the basepoint (the forgetful functor is faithful), but the reverse is not true.