Programming in Martin-Lo¨f's type theory: an introduction
Programming in Martin-Lo¨f's type theory: an introduction
Inductive data types: well-ordering types revisited
Papers presented at the second annual Workshop on Logical environments
Representing inductively defined sets by wellorderings in Martin-Löf's type theory
Theoretical Computer Science
Handbook of logic in computer science
Extensional Constructs in Intensional Type Theory
Extensional Constructs in Intensional Type Theory
Inductive Definitions in the system Coq - Rules and Properties
TLCA '93 Proceedings of the International Conference on Typed Lambda Calculi and Applications
A Set Constructor for Inductive Sets in Martin-Löf's Type Theory
Category Theory and Computer Science
COLOG '88 Proceedings of the International Conference on Computer Logic
Journal of Functional Programming
Interactive Theorem Proving and Program Development
Interactive Theorem Proving and Program Development
Journal of Logic and Computation
Containers: constructing strictly positive types
Theoretical Computer Science - Applied semantics: Selected topics
PLPV '07 Proceedings of the 2007 workshop on Programming languages meets program verification
Weak ω-Categories from Intensional Type Theory
TLCA '09 Proceedings of the 9th International Conference on Typed Lambda Calculi and Applications
Topological and Simplicial Models of Identity Types
ACM Transactions on Computational Logic (TOCL)
Higher categories from type theories
Higher categories from type theories
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Homotopy type theory is an interpretation of Martin-L脙露f's constructive type theory into abstract homotopy theory. There results a link between constructive mathematics and algebraic topology, providing topological semantics for intensional systems of type theory as well as a computational approach to algebraic topology via type theory-based proof assistants such as Coq. The present work investigates inductive types in this setting. Modified rules for inductive types, including types of well-founded trees, or W-types, are presented, and the basic homotopical semantics of such types are determined. Proofs of all results have been formally verified by the Coq proof assistant, and the proof scripts for this verification form an essential component of this research.