Programming in Martin-Lo¨f's type theory: an introduction
Programming in Martin-Lo¨f's type theory: an introduction
Initial Algebra Semantics and Continuous Algebras
Journal of the ACM (JACM)
A Finite Axiomatization of Inductive-Recursive Definitions
TLCA '99 Proceedings of the 4th International Conference on Typed Lambda Calculi and Applications
TYPES '95 Selected papers from the International Workshop on Types for Proofs and Programs
A categorical programming language
A categorical programming language
Containers: constructing strictly positive types
Theoretical Computer Science - Applied semantics: Selected topics
Electronic Notes in Theoretical Computer Science (ENTCS)
LICS '09 Proceedings of the 2009 24th Annual IEEE Symposium on Logic In Computer Science
A formalisation of a dependently typed language as an inductive-recursive family
TYPES'06 Proceedings of the 2006 international conference on Types for proofs and programs
Fibrational induction rules for initial algebras
CSL'10/EACSL'10 Proceedings of the 24th international conference/19th annual conference on Computer science logic
Inductive-inductive definitions
CSL'10/EACSL'10 Proceedings of the 24th international conference/19th annual conference on Computer science logic
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Induction-induction is a principle for defining data types in Martin-Löf Type Theory. An inductive-inductive definition consists of a set A, together with an A-indexed family B : A → Set, where both A and B are inductively defined in such a way that the constructors for A can refer to B and vice versa. In addition, the constructors for B can refer to the constructors for A. We extend the usual initial algebra semantics for ordinary inductive data types to the inductive-inductive setting by considering dialgebras instead of ordinary algebras. This gives a new and compact formalisation of inductive-inductive definitions, which we prove is equivalent to the usual formulation with elimination rules.