In type theory, a system has inductive types if it has facilities for creating a new type from constants and functions that create terms of that type. The feature serves a role similar to data structures in a programming language and allows a type theory to add concepts like numbers, relations, and trees. As the name suggests, inductive types can be self-referential, but usually only in a way that permits structural recursion. The standard example is encoding the natural numbers using Peano's encoding. Inductive nat : Type := | 0 : nat | S : nat -> nat. Here, a natural number is created either from the constant "0" or by applying the function "S" to another natural number. "S" is the successor function which represents adding 1 to a number. Thus, "0" is zero, "S 0" is one, "S (S 0)" is two, "S (S (S 0))" is three, and so on. Since their introduction, inductive types have been extended to encode more and more structures, while still being predicative and supporting structural recursion. (Wikipedia).
Higher Inductive Types - Peter Lumsdaine
Peter Lumsdaine Dalhousie University; Member, School of Mathematics October 1, 2012 For more videos, visit http://video.ias.edu
From playlist Mathematics
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Inductive Construction of a Subsequence In this video, I present the idea of an inductive construction of a subsequence. I illustrate this by showing that for every real number, there is a sequence of rational numbers that converges to that real number. Enjoy! Another Inductive Construct
From playlist Sequences
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From playlist GEOMETRY CH 2 PROOFS & REASONING
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From playlist cs273a
Semantics of Higher Inductive Types - Michael Shulman
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From playlist Mathematics
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From playlist Functions
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Michael Shulman University of California, San Diego; Member, School of Mathematics November 14, 2012 For more videos, visit http://video.ias.edu
From playlist Mathematics
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Petra Hozzova - Automation of Induction in Saturation - IPAM at UCLA
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From playlist 2023 Machine Assisted Proofs Workshop
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