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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
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
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
category-theoretic equivalent First-class function Function space, set-theoretic equivalent Pierce, Benjamin C. (2002). Types and Programming Languages
Function_type
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
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
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
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
Subfield of computer science and mathematics
journals. In programming language theory, semantics is the field concerned with the rigorous mathematical study of the meaning of programming languages.
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
nature: it focuses on a broad programming language of choice, and seeks to determine by syntactic means whether given programs in that language are feasible
Static_program_analysis
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
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
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
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
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
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
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
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
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)
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
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
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
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
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
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
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
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
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
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
Area of mathematical logic
Barwise, J. (2016), "Model-Theoretic Logics: Background and Aims", in Barwise, J; Feferman, S (eds.), Model-Theoretic Logics, Cambridge: Cambridge University
Model_theory
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
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
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
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
Basic framework of mathematics
theory. Type theoretic foundations have become more common than set-theoretic ones for use in proof assistants, which are computer programs that assist
Foundations_of_mathematics
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
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
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
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
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 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
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
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
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
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
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)
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
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
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
Programming paradigm
In computing, aspect-oriented programming (AOP) is a programming paradigm that aims to increase modularity by allowing the separation of cross-cutting
Aspect-oriented_programming
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
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
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
American computer scientist
He is an author of Extreme Programming Installed, the second book published about XP. He has also written Extreme Programming Adventures in C#. He is one
Ron_Jeffries
Mathematical study of the meaning of programming languages
In programming language theory, semantics is the rigorous mathematical logic study of the meaning of programming languages. Semantics assigns computational
Semantics (programming languages)
Semantics_(programming_languages)
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
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
Subfield of convex optimization
Semidefinite programming (SDP) is a subfield of mathematical programming concerned with the optimization of a linear objective function (a user-specified
Semidefinite_programming
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 produces a value, plus some extra information
Monad (functional programming)
Monad_(functional_programming)
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
Functional programming language
language, and proofs are written in a functional programming style. The language has ordinary programming constructs such as data types, pattern matching
Agda_(programming_language)
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
Mathematical-logic system
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
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
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
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
Soviet ternary computer
Dijkstra's ideas of structured programming were implemented in the hardware of this computer. The short instructions set was developed and implemented
Setun
Study of the semantics, or interpretations, of formal and natural languages
several influential approaches, including model-theoretic semantics (pioneered by Alfred Tarski), proof-theoretic semantics (associated with Gerhard Gentzen
Semantics_(logic)
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
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
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)
Functional programming language
typed, purely functional programming language with type inference and lazy evaluation. Haskell pioneered several programming language features including
Haskell
Concept in the philosophy of mathematics
number theoretic functions like exponentiation over natural numbers. Like other finitists, ultrafinitists deny the existence of the infinite set N {\displaystyle
Ultrafinitism
Transforming a function in such a way that it only takes a single argument
International Summer School in Computer Programming at Copenhagen in August, 1967.]. "Fundamental Concepts in Programming Languages". Higher-Order and Symbolic
Currying
General theory of mathematical structures
non-syntactic description of a lambda calculus. At the very least, category theoretic language clarifies what exactly these related areas have in common (in
Category_theory
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
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
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
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)
Programming paradigm
enables developers to write programs and develop code that falls under the generic programming paradigm. Having the programming language itself as a first-class
Metaprogramming
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
logic programming A type of programming paradigm which is largely based on formal logic. Any program written in a logic programming language is a set of
Glossary_of_computer_science
Interchange format for rule systems
Core Answer Set Programming Dialect (CASPD) is based on answer set programming, that is, declarative logic programming based on the answer set semantics
Rule_Interchange_Format
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
British mathematician (born 1945)
Wolsey, Laurence A. (1971). "Extensions of the Group Theoretic Approach in Integer Programming". Management Science. 18: 1 74–183. doi:10.1287/mnsc.18
Laurence_Wolsey
American mathematician (1914–2005)
algorithm, an algorithm for solving linear programming problems, and for his other work with linear programming. In statistics, Dantzig solved two open problems
George_Dantzig
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
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)
Computer programming for quantum computers
cases, quantum programming serves as the bridge between theoretical algorithms and physical implementation. Quantum instruction sets are used to turn
Quantum_programming
Iterative method for minimizing convex functions
Thapa. 1997. Linear programming 1: Introduction. Springer-Verlag. George B. Dantzig and Mukund N. Thapa. 2003. Linear Programming 2: Theory and Extensions
Ellipsoid_method
Set of methods that extend the functionality of a class
In computer programming, a trait is a language concept that represents a set of methods that can be used to extend the functionality of a class. In object-oriented
Trait_(computer_programming)
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)
Problem in computer science
computation includes all programs in Turing-equivalent programming languages. Given a program and an input, the question is whether the program will eventually
Halting_problem
Branch of linguistics which inquires into the nature of language
Theoretical linguistics, or general linguistics, is the branch of linguistics which inquires into the nature of language itself and seeks to answer fundamental
Theoretical_linguistics
Set of rules defining correctly structured programs
The syntax of the Python programming language is the set of rules that defines how a Python program will be written and interpreted (by both the runtime
Python_syntax_and_semantics
American mathematician and computer scientist
scientist. Blind since childhood, she is chiefly known for her work in set-theoretic topology and Braille technology. Navy was born in Brooklyn, New York
Caryn_Navy
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