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Refutation-based synthesis in SMT
Related concepts (39)
Generating function
In mathematics, a generating function is a way of encoding an infinite sequence of numbers (an) by treating them as the coefficients of a formal power series. This series is called the generating function of the sequence. Unlike an ordinary series, the formal power series is not required to converge: in fact, the generating function is not actually regarded as a function, and the "variable" remains an indeterminate. Generating functions were first introduced by Abraham de Moivre in 1730, in order to solve the general linear recurrence problem.
Satisfiability modulo theories
In computer science and mathematical logic, satisfiability modulo theories (SMT) is the problem of determining whether a mathematical formula is satisfiable. It generalizes the Boolean satisfiability problem (SAT) to more complex formulas involving real numbers, integers, and/or various data structures such as lists, arrays, bit vectors, and strings. The name is derived from the fact that these expressions are interpreted within ("modulo") a certain formal theory in first-order logic with equality (often disallowing quantifiers).
Self-modifying code
In computer science, self-modifying code (SMC or SMoC) is code that alters its own instructions while it is executing – usually to reduce the instruction path length and improve performance or simply to reduce otherwise repetitively similar code, thus simplifying maintenance. The term is usually only applied to code where the self-modification is intentional, not in situations where code accidentally modifies itself due to an error such as a buffer overflow.
Axiom of reducibility
The axiom of reducibility was introduced by Bertrand Russell in the early 20th century as part of his ramified theory of types. Russell devised and introduced the axiom in an attempt to manage the contradictions he had discovered in his analysis of set theory. With Russell's discovery (1901, 1902) of a paradox in Gottlob Frege's 1879 Begriffsschrift and Frege's acknowledgment of the same (1902), Russell tentatively introduced his solution as "Appendix B: Doctrine of Types" in his 1903 The Principles of Mathematics.
Algorithmic art
Algorithmic art or algorithm art is art, mostly visual art, in which the design is generated by an algorithm. Algorithmic artists are sometimes called algorists. Algorithmic art, also known as computer-generated art, is a subset of generative art (generated by an autonomous system) and is related to systems art (influenced by systems theory). Fractal art is an example of algorithmic art. For an image of reasonable size, even the simplest algorithms require too much calculation for manual execution to be practical, and they are thus executed on either a single computer or on a cluster of computers.
Chemical synthesis
In chemistry, chemical synthesis (chemical combination) is the artificial execution of chemical reactions to obtain one or several products. This occurs by physical and chemical manipulations usually involving one or more reactions. In modern laboratory uses, the process is reproducible and reliable. A chemical synthesis involves one or more compounds (known as reagents or reactants) that will experience a transformation when subjected to certain conditions. Various reaction types can be applied to formulate a desired product.
Finding Dory
Finding Dory is a 2016 American computer-animated comedy-drama adventure film produced by Pixar Animation Studios and released by Walt Disney Pictures. Directed by Andrew Stanton, produced by Lindsey Collins and written by Stanton and Victoria Strouse, the film is the sequel to Finding Nemo (2003). Ellen DeGeneres and Albert Brooks reprise their roles from the first film, with Hayden Rolence (replacing Alexander Gould), Ed O'Neill, Kaitlin Olson, Ty Burrell, Diane Keaton and Eugene Levy joining the cast.
Partial application
In computer science, partial application (or partial function application) refers to the process of fixing a number of arguments to a function, producing another function of smaller arity. Given a function , we might fix (or 'bind') the first argument, producing a function of type . Evaluation of this function might be represented as . Note that the result of partial function application in this case is a function that takes two arguments. Partial application is sometimes incorrectly called currying, which is a related, but distinct concept.
Principia Mathematica
right right The Principia Mathematica (often abbreviated PM) is a three-volume work on the foundations of mathematics written by mathematician–philosophers Alfred North Whitehead and Bertrand Russell and published in 1910, 1912, and 1913. In 1925–1927, it appeared in a second edition with an important Introduction to the Second Edition, an Appendix A that replaced ✸9 and all-new Appendix B and Appendix C. PM is not to be confused with Russell's 1903 The Principles of Mathematics.
Parametric polymorphism
In programming languages and type theory, parametric polymorphism allows a single piece of code to be given a "generic" type, using variables in place of actual types, and then instantiated with particular types as needed. Parametrically polymorphic functions and data types are sometimes called generic functions and generic datatypes, respectively, and they form the basis of generic programming. Parametric polymorphism may be contrasted with ad hoc polymorphism.