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The recursivity is a step which consists in thus referring to what is the subject of the step, it is the fact of describing a process dependant on data by calling upon this same process on other “simple” data more, to show an image containing of the similar images, to define a concept by calling upon the same concept.

The recursive algorithms constitute a typical example of recursive processes.

Recursivity in data processing and logic

In Data-processing and Logical, a function or more generally an algorithm which contains a call to itself is known as recursive. Two functions can be called one the other, one then speaks about Récursivité cross.

Recursivity in linguistics

The grammar of the Sanskrit of Pānini uses already the recursivity at fifth century BC while constructions of the languages are primarily recursive, like, for example, the construction of the nominal groups: the key of the lock of the main door of the house of the street of the end of the village .

Recursivity in arts

In art, the recursive process is called Mise in abyme. The artist Maurits Cornelis Escher is known for his works inspired of the recursivity. Publicity also made use of the recursivity. Most famous French publicities of this style are those of the cow which laughs (image above) and of the label of Dubonnet.

Recursivity in biology

The recursivity is particularly present in biology, in particular in the reasons for plants and the development processes. The Diatomée S have in particular beautiful recursive structures.

Recursivity, impredicativity and autoreference

The fact of defining a concept from itself was called by the logicians and the mathematicians, the Imprédicativité (see the English article) and that should not be confused with the recursivity, although that is connected there. One also speaks about Auto-référence. There exist imprédicatives logical theories (like the system F due to Jean-Yves Girard), but they must be defined with precautions if one wants to preserve their coherence, because the paradoxes are not far. Thus in set theory, the paradox of Russell shows that it cannot overall have constituted there of the units who aren't contained themselves (not popularized like the paradox of the barber , indeed “if the barber is that which shaves those which do not shave themselves, which shaves the barber? ”). Always in set theory, the Axiome of foundation proscribes the units which are contained themselves.

It is to exploit these principles that facetious data processing specialists defined recursive acronyms which do not define anything since they are imprédicatifs and incoherent. The same is imprédicatif, the following aphorism: " To include/understand the principle of recursivity, it is initially necessary to include/understand the principle of récursivité".

Internal bonds

recursion

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