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Type theory - Wikipedia

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In mathematics and theoretical computer science, a type theory is the formal presentation of a specific type system.[a] 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 have been proposed as foundations are: Most computerized proof-writing systems use a type theory for their foundation. A common one is Thierry Coquand's Calculus of Inductive Constructions. Type theory was created to avoid a paradox in a mathematical equation based on naive set theory and formal logic. Russell's paradox (first described in Gottlob Frege's The Foundations of Arithmetic) is that, without proper axioms, it is possible to define the set of all sets that are not members of themselves; this set both contains itself and does not contain itself. Between 1902 and 1908, Bertrand Russell proposed various solutions to this problem. By 1908, Russell arrived at a ramified theory of types togethe

Type theory - Wikipedia Jump to content From Wikipedia, the free encyclopedia Mathematical theory of data types "Theory of types" redirects here. For an architectural term, see Form (architecture) § Theories . In mathematical logic , and theoretical computer science , type theory is the study of formal systems that classify expressions or mathematical objects by their types . Roughly speaking, a type plays a similar role to that played by a data 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

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