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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 ...
Set theoretic programming is a programming paradigm based on mathematical set theory. One example of a programming language based on this paradigm is SETL . The goal of set theoretic programming is to improve programmer speed and productivity significantly, and also enhance program clarity and readability.
SETL (SET Language) is a very high-level programming language [1] based on the mathematical theory of sets. [2] [3] It was originally developed at the New York University (NYU) Courant Institute of Mathematical Sciences in the late 1960s, by a group containing (Jack) Jacob T. Schwartz, [1] [3] R.B.K. Dewar, and E. Schonberg. [1]
Set-builder notation can be used to describe a set that is defined by a predicate, that is, a logical formula that evaluates to true for an element of the set, and false otherwise. [2] In this form, set-builder notation has three parts: a variable, a colon or vertical bar separator, and a predicate.
In set theory, the notation is used to denote the set of functions from the set to the set . Currying is the natural bijection between the set A B × C {\displaystyle A^{B\times C}} of functions from B × C {\displaystyle B\times C} to A {\displaystyle A} , and the set ( A C ) B {\displaystyle (A^{C})^{B}} of functions from B {\displaystyle B ...
A list comprehension is a syntactic construct available in some programming languages for creating a list based on existing lists. It follows the form of the mathematical set-builder notation (set comprehension) as distinct from the use of map and filter functions.
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This article lists mathematical properties and laws of sets, involving the set-theoretic operations of union, intersection, and complementation and the relations of set equality and set inclusion. It also provides systematic procedures for evaluating expressions, and performing calculations, involving these operations and relations.