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Set theoretic programming is a programming paradigm based on mathematical set theory. One example of a programming language based on this paradigm is SETL
Set_theoretic_programming
Branch of mathematics that studies sets
precisely with equivalence relations, partitions of sets, and homomorphisms. Thus, many of the usual set-theoretic procedures of twentieth-century mathematics
Set_theory
Programming language
SETL (SET Language) is a very high-level programming language based on the mathematical theory of sets. It was originally developed at the New York University
SETL
Formal semantics of logic programming languages
widely-used approaches to the semantics of Datalog programs: model-theoretic, fixed-point, and proof-theoretic. These three approaches can be proven to be equivalent
Syntax and semantics of logic programming
Syntax_and_semantics_of_logic_programming
Declarative logic programming language
of the program. There are three widely-used approaches to the semantics of Datalog programs: model-theoretic, fixed-point, and proof-theoretic. These
Datalog
Programming paradigm based on objects
Object-oriented programming (OOP) is a programming paradigm based on objects – software entities that encapsulate data and function(s).[clarification needed]
Object-oriented_programming
Subfield of computer science and mathematics
algorithmic number theory, is the study of algorithms for performing number theoretic computations. The best known problem in the field is integer factorization
Theoretical_computer_science
Method to solve optimization problems
Linear programming is a special case of mathematical programming (also known as mathematical optimization). More formally, linear programming is a technique
Linear_programming
Language for controlling a computer
not considered a programming language.[citation needed] Some regard a programming language as a theoretical construct for programming an abstract machine
Programming_language
Analysis of computer programs without executing them
computer programs. There is tool support for some programming languages (e.g., the SPARK programming language (a subset of Ada) and the Java Modeling Language—JML—using
Static_program_analysis
Approach to the semantics of logic that locates meaning in inferential role
Deduction: A Proof-Theoretical Study. Dover Publications. Proof-Theoretic Semantics, at the Stanford Encyclopedia of Philosophy Proof-Theoretic Semantics Network
Proof-theoretic_semantics
Programming paradigm based on formal logic
Logic programming is a programming, database, and knowledge representation paradigm based on formal logic. A logic program is a set of sentences in logical
Logic_programming
Formal logic whose entailment relation is not monotonic
model-theoretic means include first-order circumscription, closed-world assumption, and autoepistemic logic. Philosophy portal Logic programming Negation
Non-monotonic_logic
Number in {..., –2, –1, 0, 1, 2, ...}
numbers are not themselves a subset of this set-theoretic representation of the integers. Rather, the set of all integers contains a subset consisting
Integer
Mathematical models of strategic interactions
naturalists such as Charles Darwin made game-theoretic kinds of statements, the use of game-theoretic analysis in biology began with Ronald Fisher's
Game_theory
Computer software
MICRO Relational Database Management System was the first large-scale set-theoretic database management system to be used in production. Though MICRO was
MICRO Relational Database Management System
MICRO_Relational_Database_Management_System
category-theoretic equivalent First-class function Function space, set-theoretic equivalent Pierce, Benjamin C. (2002). Types and Programming Languages
Function_type
Type of algorithm in computer science
Logic, Maths, and Programming. King's College Publications. ISBN 978-0-9543006-9-2. David Turner (2004-07-28). "Total Functional Programming". Journal of Universal
Corecursion
Study of mathematical algorithms for optimization problems
optimisation) or mathematical programming is the selection of a best element, with regard to some criteria, from some set of available alternatives. It
Mathematical_optimization
Overview of and topical guide to computer science
Database Imperative programming/Procedural programming Functional programming Logic programming Declarative Programming Event-Driven Programming Object oriented
Outline_of_computer_science
Branch of mathematics
General topology is the branch of topology dealing with the basic set-theoretic definitions and constructions used in topology. It is the foundation
Topology
Dialect of Lisp
support for functional programming and associated techniques such as recursive algorithms. It was also one of the first programming languages to support
Scheme_(programming_language)
Attribute of data
computer programming, a data type (or simply type) is a collection or grouping of data values, usually specified by a set of possible values, a set of allowed
Data_type
Mathematical-logic system based on functions
substitution at the nLab de Queiroz, Ruy J. G. B. (1988). "A Proof-Theoretic Account of Programming and the Role of Reduction Rules". Dialectica. 42 (4): 265–282
Lambda_calculus
Study of programming languages via mathematical objects
and unboundedness in domain-theoretic models of non-determinism. Many researchers have argued that the domain-theoretic models given above do not suffice
Denotational_semantics
Standard system of axiomatic set theory
of thought leans on expanding the "iterative" concept of a set to produce a set-theoretic universe with an interesting and complex but reasonably tractable
Zermelo–Fraenkel_set_theory
Classical problem in combinatorics
the linear programming relaxation. Let x S ∗ {\displaystyle {x_{S}^{*}}} be an optimal fractional solution to the LP relaxation. Each set S ∈ S {\displaystyle
Set_cover_problem
Abstract data type for storing distinct values
ordered sets. Further, in languages that support maps but not sets, sets can be implemented in terms of maps. For example, a common programming idiom in
Set_(abstract_data_type)
Formal system of logic
logics with their standard semantics are more expressive, but their model-theoretic properties are less well-behaved than those of first-order logic. The
Higher-order_logic
Argument in philosophy of mathematics
problem is a philosophical argument developed by Paul Benacerraf against set-theoretic Platonism and published in 1965 in an article entitled "What Numbers
Benacerraf's identification problem
Benacerraf's_identification_problem
Paradox in set theory
a set-theoretic paradox published by the British philosopher and mathematician, Bertrand Russell, in 1901. Russell's paradox shows that every set theory
Russell's_paradox
Sequence of words formed by specific rules
the set of syntactically correct programs in a given programming language (the syntax of which is usually defined by a context-free grammar); the set of
Formal_language
Concept in integral mathematics
(integer programming) into a related problem that is solvable in polynomial time (linear programming); the solution to the relaxed linear program can be
Linear_programming_relaxation
Computer science concept
sometimes call the use of certain forms of polymorphism generic programming. The type-theoretic foundations of polymorphism are closely related to those of
Type_system
Type of logical formula
(1976) investigated the model-theoretic properties of Horn clauses in the context of logic programming, showing that every set of definite clauses D has a
Horn_clause
Set of data types that represent numbers in a given programming language
impermissible. Principally, the numerical tower is designed to codify the set theoretic properties of numbers in an easy-to-implement language facility: every
Numerical_tower
Analysis of software performed when running a program
Miroslav; Mahmoud, Anas (2018-01-01). "Just enough semantics: An information theoretic approach for IR-based software bug localization". Information and Software
Dynamic_program_analysis
Mathematical construction of a set with an equivalence relation
type-theoretic foundations of mathematics. Often in mathematics, when one defines an equivalence relation on a set, one immediately forms the quotient set
Setoid
Topics referred to by the same term
often, a mathematics term sometimes written "i.o."; see an example in set-theoretic limit io (company), an artificial intelligence hardware company Bureau
Io
Ordinals in mathematics and set theory
the proof-theoretic strength of Peano's axioms. But we can do this for systems far beyond Peano's axioms. For example, the proof-theoretic strength of
Large_countable_ordinal
Programming paradigm based on block-based control flow
Structured programming is a programming paradigm characterized by source code that uses block-based source code structure to encode control flow such as
Structured_programming
Ordinal-indexed family of rapidly increasing functions
Cichon & Wainer 1983. Wainer 1989. Beklemishev, L.D. (2003). "Proof-theoretic analysis by iterated reflection". Archive for Mathematical Logic. 42 (6):
Fast-growing_hierarchy
Mathematical algorithm for eliminating variables from a system of linear inequalities
for Information Theoretic Inequalities". arXiv:1610.03990 [cs.IT]. Schrijver, Alexander (1998). Theory of Linear and Integer Programming. John Wiley & sons
Fourier–Motzkin_elimination
Solution process for some optimization problems
In mathematics, nonlinear programming (NLP), also known as nonlinear optimization, is the process of solving an optimization problem where some of the
Nonlinear_programming
Programming language that uses first order logic
Unlike many other programming languages, Prolog is intended primarily as a declarative programming language: the program is a set of facts and rules
Prolog
Subfield of mathematics
first-order provability and set-theoretic forcing. Intuitionistic logic was developed by Heyting to study Brouwer's program of intuitionism, in which Brouwer
Mathematical_logic
Instructions a computer can execute
A computer program is a sequence or set of instructions in a programming language for a computer to execute. It is one component of software, which also
Computer_program
Task to construct a program meeting a formal specification
research communities considered the problem of program synthesis. Notable works include the 1969 automata-theoretic approach by Büchi and Landweber, and the
Program_synthesis
Generalization of "n-th" to infinite cases
commutativity at the expense of continuity. Interpreted as nimbers, a game-theoretic variant of numbers, ordinals can also be combined via nimber arithmetic
Ordinal_number
Class of logic puzzles
These problems may be analyzed using graph-theoretic methods, by dynamic programming, or by integer programming. Let G = ( V , E ) {\displaystyle G=(V,E)}
River_crossing_puzzle
Process of repeating items in a self-similar way
also appears in The UNIX Programming Environment by Kernighan and Pike. It did not appear in the first edition of The C Programming Language. The joke is
Recursion
Mathematical expression with disputed status
b-element set; there is exactly one 0-tuple. The set-theoretic interpretation of b0 is the number of functions from the empty set to a b-element set; there
Zero_to_the_power_of_zero
Department of the Oxford University Computing Laboratory
mathematical and theoretical work is sterile because it has no point of contact with real computing. One of the central aims of the Programming Research Group
Programming_Research_Group
In mathematics and theoretical computer science, a set constraint is an equation or an inequation between sets of terms. Similar to systems of (in)equations
Set_constraint
Pseudoscientific approach to psychotherapy
Neuro-linguistic programming at Wiktionary Media related to Neuro-linguistic programming at Wikimedia Commons Quotations related to Neuro-linguistic programming at
Neuro-linguistic_programming
Area of mathematical logic
(2016), Barwise, J; Feferman, S (eds.), "Model-Theoretic Logics: Background and Aims", Model-Theoretic Logics, Cambridge: Cambridge University Press,
Model_theory
Topics referred to by the same term
a partially ordered set. Filter on a set, a special family of subsets that forms an (order theoretic) filter with respect to set inclusion Filters in
Filter
Approach to formal semantics
formal semantics that grounds the concepts of truth or validity on game-theoretic concepts, such as the existence of a winning strategy for a player. In
Game_semantics
Mathematical optimization concept
between linear programming problems, eigenequations, and von Neumann's general equilibrium model. The solution to a linear programming problem can be
Dual_linear_program
Probabilistic logic programming language
(2012). Constraints for probabilistic logic programming. Proceedings of the NIPS Probabilistic Programming Workshop. pp. 1–4. De Raedt, Luc; Kimmig, Angelika
ProbLog
Formal study of linguistic meaning
These entailment relations are also referred to as deductive-theoretic and model-theoretic consequence. Portner & Partee 2002, pp. 1–2 Partee 2016, pp
Formal semantics (natural language)
Formal_semantics_(natural_language)
Low-level programming language family
decades of computing, it was commonplace for both systems programming and application programming to take place entirely in assembly language. While still
Assembly_language
Organized collection of data in computing
development of the MICRO Information Management System based on D.L. Childs' Set-Theoretic Data model. The university in 1974 hosted a debate between Codd and
Database
Mathematical theory of data types
type in programming: it specifies what kind of thing an expression is and how it may be used. Type theories are used in the study of programming languages
Type_theory
Branch of computer science
characterization, and classification of formal languages known as programming languages. Programming language theory is closely related to other fields including
Programming_language_theory
Ability of a computing system to simulate Turing machines
data-manipulation rules (such as a model of computation, a computer's instruction set, a programming language, or a cellular automaton) is said to be Turing-complete or
Turing_completeness
Approximation of a mathematical set
systems Decision-theoretic rough sets Version space Dominance-based rough set approach Pawlak, Zdzisław (1991). Rough Sets: Theoretical Aspects of Reasoning
Rough_set
Processor executing one instruction in minimal clock cycles
In electronics and computer science, a reduced instruction set computer (RISC, pronounced "risk") is a computer architecture designed to simplify the
Reduced instruction set computer
Reduced_instruction_set_computer
Study of discrete mathematical structures
ISBN 978-0-201-72634-3. Knuth, Donald E. (2011). The Art of Computer Programming. Vol. 1–4a Boxed Set. Addison-Wesley. ISBN 978-0-321-75104-1. Matoušek, Jiří; Nešetřil
Discrete_mathematics
American mathematician
Eric; Sawin, William F.; Umans, Christopher (2017). "On cap sets and the group-theoretic approach to matrix multiplication". Discrete Analysis. arXiv:1605
Henry_Cohn
Topics referred to by the same term
used to connect two or more formulas Set operation (Boolean), a set-theoretic operation in the algebra of sets (union, intersection, and complementation)
Boolean_operation
Model selection principle
generates a shorter description of the same data set. The theoretic minimum description length of a data set, called its Kolmogorov complexity, cannot, however
Minimum_description_length
Algorithm for finding shortest paths
From a dynamic programming point of view, Dijkstra's algorithm is a successive approximation scheme that solves the dynamic programming functional equation
Dijkstra's_algorithm
Branch of mathematics relating to posets
articles for each concept. A list of general order-theoretic definitions, which include domain theoretic notions as well can be found in the order theory
Domain_theory
General purpose functional programming language
paper A theory of type polymorphism in programming in 1978, which laid out the ideas of what it meant for a program to be well-typed in the context of a
ML_(programming_language)
IEEE standard for wireless networks
High Throughput (EHT), is a wireless networking standard in the IEEE 802.11 set of protocols which is designated Wi-Fi 7 by the Wi-Fi Alliance. It is built
Wi-Fi_7
System of mathematical set theory
the step-by-step construction of the formula with classes. Since all set-theoretic formulas are constructed from two kinds of atomic formulas (membership
Von Neumann–Bernays–Gödel set theory
Von_Neumann–Bernays–Gödel_set_theory
Design pattern in functional programming to build generic types
In functional programming, monads are a way to structure computations as a sequence of steps, where each step not only produces a value but also some
Monad (functional programming)
Monad_(functional_programming)
Topics referred to by the same term
a set Flow (psychology), a mental state of being fully immersed and focused Flow, a spacecraft of NASA's GRAIL program Flow network, graph-theoretic version
Flow
American computer scientist
Mathematics, Case Western Reserve University (1961). Dissertation: "A Set-Theoretic Model For Logical Systems", Advisor: Raymond John Nelson M.S. Physics
Melvin_Conway
Sequence of characters, data type
In computer programming, a string is traditionally a sequence of characters, either as a literal constant or as some kind of variable. The latter may
String_(computer_science)
Modal temporal logic with modalities referring to time
games against an LTL winning condition is 2EXPTIME-complete. Automata-theoretic linear temporal logic model checking LTL formulas are commonly used to
Linear_temporal_logic
Mathematical optimization problem restricted to integers
linear programming (ILP), in which the objective function and the constraints (other than the integer constraints) are linear. Integer programming is NP-complete
Integer_programming
Association of one output to each input
formal definition of a function could be provided, in terms of set theory. This set-theoretic definition is based on the fact that a function establishes
Function_(mathematics)
Logical connective AND
of expressions such as English "and"; In programming languages, the short-circuit and control structure; In set theory, intersection. In lattice theory
Logical_conjunction
Study of computation
computer to perform. Imperative programming focuses on describing how a program operates. Object-oriented programming, a programming paradigm based on the concept
Computer_science
Object-oriented programming principle
proof-theoretic definitions of some behavioral subtyping notions, but their definitions did not take into account aliasing that may occur in programming languages
Liskov_substitution_principle
Mathematical concept
programming Decision-making software Goal programming Interactive Decision Maps Multiple-criteria decision-making Multi-objective linear programming Multi-disciplinary
Multi-objective_optimization
Result from multiplying no factors
sometimes employed when discussing set-theoretic intersections, categorical products, and products in computer programming. Let a1, a2, a3, ... be a sequence
Empty_product
Indian-American economist (born 1971)
dissertation titled "Three essays on international capital flows: a search theoretic approach", under the supervision of Ben Bernanke, Kenneth Rogoff, and
Gita_Gopinath
Form of type polymorphism
object-oriented programming. Typically, functional programming languages also provide some, usually restricted, form of parametric polymorphism. In a theoretical setting
Subtyping
Unrelated vertices in graphs
independent set, stable set, coclique or anticlique is a set of vertices in a graph, no two of which are adjacent. That is, it is a set S {\displaystyle
Independent set (graph theory)
Independent_set_(graph_theory)
Informal set theories
believe that Georg Cantor's set theory was not actually implicated in the set-theoretic paradoxes (see Frápolli 1991). One difficulty in determining this with
Naive_set_theory
Historical research project in mathematics
limit; and the naïve set-theoretic definition of function. An important spinoff of the arithmetization of analysis is set theory. Naive set theory was created
Arithmetization_of_analysis
Axiomatic set theories based on the principles of mathematical constructivism
reduce the proof-theoretical strength. Even without Exponentiation, the present theory with set induction has the same proof theoretic strength as C Z
Constructive_set_theory
Diagram that represents a workflow or process
interactive computer terminals and third-generation programming languages became common tools for computer programming, since algorithms can be expressed more concisely
Flowchart
Scientific study of digital information
in a letter to Vannevar Bush. Prior to this paper, limited information-theoretic ideas had been developed at Bell Labs, all implicitly assuming events
Information_theory
Functional programming language
typed, purely functional programming language with type inference and lazy evaluation. Haskell pioneered several programming language features including
Haskell
Set whose pairs have minima and maxima
connections between related partially ordered sets—an approach of special interest for the category theoretic approach to lattices, and for formal concept
Lattice_(order)
Type of sorting algorithm that works by comparing pairs of elements
via information theory is phrased as 'information-theoretic lower bound'. The information-theoretic lower bound is correct, but may be far from the strongest
Comparison_sort
SET THEORETIC-PROGRAMMING
SET THEORETIC-PROGRAMMING
Surname or Lastname
English and German
English and German : topographic name for someone who lived by the sea-shore or beside a lake, from Middle English see ‘sea’, ‘lake’ (Old English sǣ), Middle High German sē. Alternatively, the English name may denote someone who lived by a watercourse, from an Old English sēoh ‘watercourse’, ‘drain’.
Female
Egyptian
, the wife of Osirtesen.
Male
Egyptian
, the seven great spirits of the Ritual of the Dead.
Male
Hebrew
Variant spelling of Hebrew Sheth, SHET means "buttocks."
Surname or Lastname
English
English : variant spelling of See.
Male
Egyptian
, the seven great spirits of the Ritual of the Dead.
Female
Egyptian
, a sister of Sekherta.
Male
Hindi/Indian
(सेठ) Hindi name derived from the Sanskrit word setu, SETH means "bridge." Compare with other forms of Seth.
Female
Egyptian
, the wife of the usurper Sipthah.
Male
English
Anglicized form of Hebrew Sheth, SETH means "buttocks." In the bible, this is the name of the third son of Adam and Eve. Compare with other forms of Seth.
Female
Egyptian
, the mother of Fai-hor-ou-oer.
Female
Egyptian
, a sister of Sekherta.
Boy/Male
Egyptian Hebrew Swedish
Son of Seb and Nut.
Surname or Lastname
English
English : perhaps a variant of Sait, from the Old English personal name Sǣgēat (‘sea Geat’).
Female
Hungarian
Hungarian form of Greek Elisabet, ERZSÉBET means "God is my oath."
Female
English
Short form of English Elizabeth, BET means "God is my oath."Â
Female
Egyptian
, a wife and daughter of Antef.
Male
English
Short form of English Stephen, STE means "crown."
Female
Egyptian
, second wife of Antef.
Female
Egyptian
, an uncertain goddess.
SET THEORETIC-PROGRAMMING
SET THEORETIC-PROGRAMMING
Male
African
an obscure Ethiopian king.
Boy/Male
Indian
Heroic brother of the original one
Girl/Female
Bengali, Greek, Hindu, Indian, Malayalam, Marathi, Sindhi
Light
Biblical
trodden under foot; mangers
Girl/Female
Arabic, Muslim
Noble; Dear One; Clever
Girl/Female
Tamil
Harithra | ஹரீதà¯à®°à®¾Â
History
Boy/Male
Irish
Great lord.
Male
Basque
, son of the raven.
Girl/Female
Indian, Marathi
Normal
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
God of Mountains; Himalaya
SET THEORETIC-PROGRAMMING
SET THEORETIC-PROGRAMMING
SET THEORETIC-PROGRAMMING
SET THEORETIC-PROGRAMMING
SET THEORETIC-PROGRAMMING
n.
The speculative part of a science; speculation.
n.
That which is set, placed, or fixed.
a.
Regular; uniform; formal; as, a set discourse; a set battle.
v. t.
To establish as a rule; to furnish; to prescribe; to assign; as, to set an example; to set lessons to be learned.
a.
Established; prescribed; as, set forms of prayer.
n.
One of the theoretic transverse divisions of any segmented animal.
v. t.
To put in order in a particular manner; to prepare; as, to set (that is, to hone) a razor; to set a saw.
a.
Fixed in position; immovable; rigid; as, a set line; a set countenance.
a.
Pertaining to theory; depending on, or confined to, theory or speculation; speculative; terminating in theory or speculation: not practical; as, theoretical learning; theoretic sciences.
v. i.
To fit or suit one; to sit; as, the coat sets well.
n.
See Set, n., 2 (e) and 3.
adv.
In a theoretic manner.
v. t.
To determine; to appoint; to assign; to fix; as, to set a time for a meeting; to set a price on a horse.
v. t.
To cause to sit; to make to assume a specified position or attitude; to give site or place to; to place; to put; to fix; as, to set a house on a stone foundation; to set a book on a shelf; to set a dish on a table; to set a chest or trunk on its bottom or on end.
imp. & p. p.
of Set
a.
Theoretic.
a.
Firm; unchanging; obstinate; as, set opinions or prejudices.
a.
Alt. of Theoretical
v. t.
To compose; to arrange in words, lines, etc.; as, to set type; to set a page.
a.
Theorematic.