Truncation is a search technique used in databases that replaces the ending of a word with a symbol. This allows different forms of a word to be searched simultaneously, increasing the number of results found. Depending on the database, certain symbols can be used to search for different spellings or plurals. It is important to consult the help screens of the database to determine which symbols are appropriate.
Truncation is similar but distinct from statistical censorship. A truncated sample is equivalent to an underlying sample with all values outside the limits completely omitted, without even a count of the omitted ones being maintained. Statistical censorship, on the other hand, records which limit (upper or lower) was exceeded and the value of that limit. When trying to demonstrate something about each point of a truncated upper inductive type, a dependent eliminator is needed.
This general concept is referred to as “higher inductive n-type” for an arbitrary n (also known as “truncated superior inductive type”). The objective of this publication is to explain how to define n-truncations for each n using higher inductive types and how to use truncations in 0 to construct free algebras for algebraic theories (free groups, for example). In practice, it is not necessary to use the elimination rule given by the top and rays constructors, but rather the rule of removing the truncated upper inductive types. Therefore, we define the n-truncation of A as the upper inductive type containing A and such that each sphere (n+) is full.
Using truncation can help you complete your search faster, as you won't have to manually type and search every variation of the word. Another type of truncation, edging, cuts edges and vertices, removing the original edges and replacing them with rectangles, and removing the original vertices and replacing them with double faces of the original regular polyhedra or mosaic tiles.
