Type systemIn computer programming, a type system is a logical system comprising a set of rules that assigns a property called a type (for example, integer, floating point, string) to every "term" (a word, phrase, or other set of symbols). Usually the terms are various constructs of a computer program, such as variables, expressions, functions, or modules. A type system dictates the operations that can be performed on a term. For variables, the type system determines the allowed values of that term.
Dynamical systemIn mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space, such as in a parametric curve. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, the random motion of particles in the air, and the number of fish each springtime in a lake. The most general definition unifies several concepts in mathematics such as ordinary differential equations and ergodic theory by allowing different choices of the space and how time is measured.
Type theoryIn mathematics, logic, and computer science, a type theory is the formal presentation of a specific type system, and in general, type theory is the academic study of type systems. Some type theories serve as alternatives to set theory as a foundation of mathematics. Two influential type theories that were proposed as foundations are Alonzo Church's typed λ-calculus and Per Martin-Löf's intuitionistic type theory. Most computerized proof-writing systems use a type theory for their foundation, a common one is Thierry Coquand's Calculus of Inductive Constructions.
Algebraic data typeIn computer programming, especially functional programming and type theory, an algebraic data type (ADT) is a kind of composite type, i.e., a type formed by combining other types. Two common classes of algebraic types are product types (i.e., tuples and records) and sum types (i.e., tagged or disjoint unions, coproduct types or variant types). The values of a product type typically contain several values, called fields. All values of that type have the same combination of field types.
Dependent typeIn computer science and logic, a dependent type is a type whose definition depends on a value. It is an overlapping feature of type theory and type systems. In intuitionistic type theory, dependent types are used to encode logic's quantifiers like "for all" and "there exists". In functional programming languages like Agda, ATS, Coq, F*, Epigram, and Idris, dependent types help reduce bugs by enabling the programmer to assign types that further restrain the set of possible implementations.
Despina (moon)Despina dɛˈspaɪnə, also known as Neptune V, is the third-closest inner moon of Neptune. It is named after Greek mythological character Despoina, a nymph who was a daughter of Poseidon and Demeter. Despina was discovered in late July 1989 from the images taken by the Voyager 2 probe. It was given the temporary designation S/1989 N 3. The discovery was announced (IAUC 4824) on 2 August 1989, and mentions "10 frames taken over 5 days", implying a discovery date of sometime before July 28. The name was given on 16 September 1991.
Thalassa (moon)Thalassa θəˈlæsə, also known as Neptune IV, is the second-innermost satellite of Neptune. Thalassa was named after sea goddess Thalassa, a daughter of Aether and Hemera from Greek mythology. "Thalassa" is also the Greek word for "sea". Thalassa was discovered sometime before mid-September 1989 from the images taken by the Voyager 2 probe. It was given the temporary designation S/1989 N 5. The discovery was announced (IAUC 4867) on 29 September 1989, and mentions "25 frames taken over 11 days", implying a discovery date of sometime before 18 September.
Galatea (moon)Galatea ɡæləˈtiːə, also known as Neptune VI, is the fourth-closest inner moon of Neptune. It is named after Galatea, one of the fifty Nereids of Greek legend, with whom Cyclops Polyphemus was vainly in love. Galatea was discovered in late July 1989 from the images taken by the Voyager 2 probe. It was given the temporary designation S/1989 N 4. The discovery was announced (IAUC 4824) on 2 August 1989, and mentions "10 frames taken over 5 days", implying a discovery date of sometime before July 28.
Weierstrass functionIn mathematics, the Weierstrass function is an example of a real-valued function that is continuous everywhere but differentiable nowhere. It is an example of a fractal curve. It is named after its discoverer Karl Weierstrass. The Weierstrass function has historically served the role of a pathological function, being the first published example (1872) specifically concocted to challenge the notion that every continuous function is differentiable except on a set of isolated points.
Mathematical economicsMathematical economics is the application of mathematical methods to represent theories and analyze problems in economics. Often, these applied methods are beyond simple geometry, and may include differential and integral calculus, difference and differential equations, matrix algebra, mathematical programming, or other computational methods. Proponents of this approach claim that it allows the formulation of theoretical relationships with rigor, generality, and simplicity.
