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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 ...
Here, the list [0..] represents , x^2>3 represents the predicate, and 2*x represents the output expression.. List comprehensions give results in a defined order (unlike the members of sets); and list comprehensions may generate the members of a list in order, rather than produce the entirety of the list thus allowing, for example, the previous Haskell definition of the members of an infinite list.
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]
In set theory and its applications to logic, mathematics, and computer science, set-builder notation is a mathematical notation for describing a set by stating the properties that its members must satisfy. [1] Defining sets by properties is also known as set comprehension, set abstraction or as defining a set's intension.
Lisp is the second oldest family of programming languages in use today and as such has many dialects and implementations with a wide range of difficulties. Lisp was originally created as a practical mathematical notation for computer programs, based on lambda calculus, which makes it particularly well suited for teaching theories of computing.
Java is a high-level, class-based, object-oriented programming language that is designed to have as few implementation dependencies as possible. It is a general-purpose programming language intended to let programmers write once, run anywhere (), [16] meaning that compiled Java code can run on all platforms that support Java without the need to recompile. [17]
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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.