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In computer science, a set is an abstract data type that can store unique values, without any particular order. It is a computer implementation of the mathematical concept of a finite set. Unlike most other collection types, rather than retrieving a specific element from a set, one typically tests a value for membership in a set.
A computer program is a sequence or set [a] of instructions in a programming language for a computer to execute. It is one component of software, which also includes documentation and other intangible components. [1] A computer program in its human-readable form is called source code.
A set is countable if it can be enumerated, that is, if there exists an enumeration of it. Otherwise, it is uncountable. For example, the set of the real numbers is uncountable. A set is finite if it can be enumerated by means of a proper initial segment {1, ..., n} of the natural numbers, in which case, its cardinality is n.
‘If’ gives the program a conditional split of tasks, where a set of skeleton code is split into two main sections. A conditional statement is given to the program, therefore giving it a specified algorithm to follow. ‘For’ operates a task a number of times, both specified by the programmer, allowing for a more efficient set of code.
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.
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.
Consider the problem of Linearly Constrained Convex Quadratic Programming. Under reasonable assumptions (the problem is feasible, the system of constraints is regular at every point, and the quadratic objective is strongly convex), the active-set method terminates after finitely many steps, and yields a global solution to the problem.
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]