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Everything about Induction-recursion
Concept in mathematical logic
In intuitionistic type theory (ITT), a discipline within mathematical logic, induction-recursion is a feature for simultaneously declaring a type and function on that type. It allows the creation of larger types than inductive types, such as universes. The types created still remain predicative inside ITT. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Induction-recursionA 5-minute orientation
- Skim a recent paper: The God-given Naturals: Induction and RecursionInfluential work since 2022
- Pick up a classic book: Elementary induction on abstract structuresThe most-reprinted book on the subject
- Read the landmark paper: Alpha-structural recursion and inductionCited 72 times
- Go sideways: Induction-inductionA closely related topic
- Go sideways: Inductive typeA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Alpha-structural recursion and induction
Selection functions, bar recursion and backward induction
Induction–recursion and initial algebras
Set theory for verification. II: Induction and recursion
Indexed induction–recursion
Another recursion induction principle
Induction and recursion on the partial real line with applications to Real PCF
Recursion induction for real-time processes
🆕 Influential since 2022
📚 Books worth reading
Elementary induction on abstract structuresYiannis N. Moschovakis · 1974
Introduction to algorithmsUdi Manber · 1989- 📕L' induzione matematica o ragionamento ricorsivoItalo Aimonetto · 1980
Induction, recursion, and programmingMitchell Wand · 1980
Computable economicsKumaraswamy Velupillai · 2000- 📕Uniform learning of recursive functionsSandra Zilles · 2003
Logiske MetoderRoger Antonsen · 2014
Al-JabrHatem Al-Ani, Ali Al-Ani · 2026
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Induction-induction In intuitionistic type theory (ITT), a discipline within mathematical logic, induction-induction is for simultaneously declaring some inductive type and…
- Inductive type 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.…
- Intuitionistic type theory Intuitionistic type theory (also known as constructive type theory, or Martin-Löf type theory (MLTT)) is a type theory and an alternative foundation of…
- Constructive set theory Axiomatic constructive set theory is an approach to mathematical constructivism following the program of axiomatic set theory. The same first-order language…
- Recursive definition In mathematics and computer science, a recursive definition, or inductive definition, is used to define the elements in a set in terms of other elements…
- Bar recursion Bar recursion is a generalized form of recursion developed by C. Spector in his 1962 paper. It is related to bar induction in the same fashion that primitive…
- Recursion Recursion occurs when the definition of a concept or process depends on a simpler or previous version of itself. Recursion is used in a variety of disciplines…
- Ordinal analysis In proof theory, ordinal analysis assigns ordinals (often large countable ordinals) to mathematical theories as a measure of their strength. If theories…