On the syntax of Martin-Lo¨f's type theories
Theoretical Computer Science
Programming in Martin-Lo¨f's type theory: an introduction
Programming in Martin-Lo¨f's type theory: an introduction
Inductive Definitions in the system Coq - Rules and Properties
TLCA '93 Proceedings of the International Conference on Typed Lambda Calculi and Applications
COLOG '88 Proceedings of the International Conference on Computer Logic
A non-type-theoretic semantics for type-theoretic language
A non-type-theoretic semantics for type-theoretic language
TPHOLs '99 Proceedings of the 12th International Conference on Theorem Proving in Higher Order Logics
On Relating Type Theories and Set Theories
TYPES '98 Selected papers from the International Workshop on Types for Proofs and Programs
PTCS '01 Proceedings of the International Seminar on Proof Theory in Computer Science
Central European Functional Programming School
Outrageous but meaningful coincidences: dependent type-safe syntax and evaluation
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Proceedings of the 15th ACM SIGPLAN international conference on Functional programming
Inductive-inductive definitions
CSL'10/EACSL'10 Proceedings of the 24th international conference/19th annual conference on Computer science logic
IDRIS ---: systems programming meets full dependent types
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A categorical semantics for inductive-inductive definitions
CALCO'11 Proceedings of the 4th international conference on Algebra and coalgebra in computer science
Partial recursive functions in martin-löf type theory
CiE'06 Proceedings of the Second conference on Computability in Europe: logical Approaches to Computational Barriers
MSFP'06 Proceedings of the 2006 international conference on Mathematically Structured Functional Programming
GMETA: a generic formal metatheory framework for first-order representations
ESOP'12 Proceedings of the 21st European conference on Programming Languages and Systems
Typed syntactic meta-programming
Proceedings of the 18th ACM SIGPLAN international conference on Functional programming
New equations for neutral terms: a sound and complete decision procedure, formalized
Proceedings of the 2013 ACM SIGPLAN workshop on Dependently-typed programming
Leveling up dependent types: generic programming over a predicative hierarchy of universes
Proceedings of the 2013 ACM SIGPLAN workshop on Dependently-typed programming
LICS '13 Proceedings of the 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science
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Induction-recursion is a schema which formalizes the principles for introducing new sets in Martin-Löf's type theory. It states that we may inductively define a set while simultaneously defining a function from this set into an arbitrary type by structural recursion. This extends the notion of an inductively defined set substantially and allows us to introduce universes and higher order universes (but not a Mahlo universe). In this article we give a finite axiomatization of inductive-recursive definitions. We prove consistency by constructing a set-theoretic model which makes use of one Mahlo cardinal.