Concept
System U
Related concepts (4)
Pure type system
NOTOC In the branches of mathematical logic known as proof theory and type theory, a pure type system (PTS), previously known as a generalized type system (GTS), is a form of typed lambda calculus that allows an arbitrary number of sorts and dependencies between any of these. The framework can be seen as a generalisation of Barendregt's lambda cube, in the sense that all corners of the cube can be represented as instances of a PTS with just two sorts. In fact, Barendregt (1991) framed his cube in this setting.
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.
Intuitionistic type theory
Intuitionistic type theory (also known as constructive type theory, or Martin-Löf type theory) is a type theory and an alternative foundation of mathematics. Intuitionistic type theory was created by Per Martin-Löf, a Swedish mathematician and philosopher, who first published it in 1972. There are multiple versions of the type theory: Martin-Löf proposed both intensional and extensional variants of the theory and early impredicative versions, shown to be inconsistent by Girard's paradox, gave way to predicative versions.
Type theory
In 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.