Concepts inHigher-order functors with transparent signatures
Functor
In category theory, a branch of mathematics, a functor is a special type of mapping between categories. Functors can be thought of as homomorphisms between categories, or morphisms when in the category of small categories. Functors were first considered in algebraic topology, where algebraic objects are associated to topological spaces, and algebraic homomorphisms are associated to continuous maps. Nowadays, functors are used throughout modern mathematics to relate various categories.
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Standard ML
Standard ML (SML) is a general-purpose, modular, functional programming language with compile-time type checking and type inference. It is popular among compiler writers and programming language researchers, as well as in the development of theorem provers. SML is a modern descendant of the ML programming language used in the Logic for Computable Functions (LCF) theorem-proving project.
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Standard ML of New Jersey
Standard ML of New Jersey (SML/NJ) is a compiler and programming environment for Standard ML. Aside from its runtime system, which is written in C, SML/NJ is written in Standard ML. It was developed jointly by Bell Laboratories and Princeton University. Its name is a reference both to Princeton's home state and to Standard Oil of New Jersey, the famous oil monopoly of the early 20th century.
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Transparency and translucency
In the field of optics, transparency (also called pellucidity or diaphaneity) is the physical property of allowing light to pass through the material without being scattered. On a macroscopic scale (one where the dimensions investigated are much, much larger than the wavelength of the photons in question), the photons can be said to follow Snell's Law.
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First-order logic
First-order logic is a formal system used in mathematics, philosophy, linguistics, and computer science. It is also known as first-order predicate calculus, the lower predicate calculus, quantification theory, and predicate logic (a less precise term). First-order logic is distinguished from propositional logic by its use of quantified variables.
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Structure (mathematical logic)
In universal algebra and in model theory, a structure consists of a set along with a collection of finitary operations and relations which are defined on it. Universal algebra studies structures that generalize the algebraic structures such as groups, rings, fields and vector spaces. The term universal algebra is used for structures with no relation symbols.
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Module (mathematics)
In abstract algebra, the concept of a module over a ring is a generalization of the notion of vector space, wherein the corresponding scalars are allowed to lie in an arbitrary ring. Modules also generalize the notion of abelian groups, which are modules over the ring of integers.
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Modular programming
Modular programming (also known as top down design and stepwise refinement) is a software design technique that increases the extent to which software is composed of separate, interchangeable components called modules by breaking down program functions into modules, each of which accomplishes one function and contains everything necessary to accomplish this.
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