Type theory
Concept in mathematical logic / From Wikipedia, the free encyclopedia
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"Theory of types" redirects here. For an architectural term, see Form (architecture) § Theories.
In mathematics and theoretical computer science, a type theory is the formal presentation of a specific type system.[lower-alpha 1] 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.