Handbook of logic in computer science (vol. 2)
From fast exponentiation to square matrices: an adventure in types
Proceedings of the fourth ACM SIGPLAN international conference on Functional programming
Generic Programming within Dependently Typed Programming
Proceedings of the IFIP TC2/WG2.1 Working Conference on Generic Programming
MPC '98 Proceedings of the Mathematics of Program Construction
A Typed Lambda Calculus with Categorical Type Constructors
Category Theory and Computer Science
A Note on Categorical Datatypes
Category Theory and Computer Science
de Bruijn notation as a nested datatype
Journal of Functional Programming
Journal of Functional Programming
Representations of first order function types as terminal coalgebras
TLCA'01 Proceedings of the 5th international conference on Typed lambda calculi and applications
Iteration and coiteration schemes for higher-order and nested datatypes
Theoretical Computer Science - Foundations of software science and computation structures
Recursion on Nested Datatypes in Dependent Type Theory
CiE '08 Proceedings of the 4th conference on Computability in Europe: Logic and Theory of Algorithms
Generalized iteration and coiteration for higher-order nested datatypes
FOSSACS'03/ETAPS'03 Proceedings of the 6th International conference on Foundations of Software Science and Computation Structures and joint European conference on Theory and practice of software
Map fusion for nested datatypes in intensional type theory
Science of Computer Programming
A datastructure for iterated powers
MPC'06 Proceedings of the 8th international conference on Mathematics of Program Construction
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The problem of defining iteration for higher-order nested datatypes of arbitrary (finite)rank is solved within the framework of System Fω of higher-order parametric polymorphism. The proposed solution heavily relies on a general notion of monotonicity as opposed to a syntactic criterion on the shape of the type constructors such as positivity or even being polynomial. Its use is demonstrated for some rank-2 heterogeneous/nested datatypes such as powerlists and de Bruijn terms with explicit substitutions. An important feature is the availability of an iterative definition of the mapping operation (the functoriality)for those rank-1 type transformers (i. e., functions from types to types)arising as least fixed-points of monotone rank-2 type transformers. Strong normalization is shown by an embedding into Fω. The results dualize to greatest fixed-points, hence to coinductive constructors with coiteration.