ACM Transactions on Programming Languages and Systems (TOPLAS)
POPL '93 Proceedings of the 20th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Algebra of programming
Coinductive Axiomatization of Recursive Type Equality and Subtyping
TLCA '97 Proceedings of the Third International Conference on Typed Lambda Calculi and Applications
Certifying the Fast Fourier Transform with Coq
TPHOLs '01 Proceedings of the 14th International Conference on Theorem Proving in Higher Order Logics
Monadic Presentations of Lambda Terms Using Generalized Inductive Types
CSL '99 Proceedings of the 13th International Workshop and 8th Annual Conference of the EACSL on Computer Science Logic
Journal of Functional Programming
Iteration and coiteration schemes for higher-order and nested datatypes
Theoretical Computer Science - Foundations of software science and computation structures
Let's see how things unfold: reconciling the infinite with the intensional
CALCO'09 Proceedings of the 3rd international conference on Algebra and coalgebra in computer science
Subtyping, declaratively: an exercise in mixed induction and coinduction
MPC'10 Proceedings of the 10th international conference on Mathematics of program construction
Contractive signatures with recursive types, type parameters, and abstract types
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part II
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In this paper we show that a prototypical subtype relation that can neither be defined as a least fixed point nor as a greatest fixed point can nevertheless be defined in a dependently typed language with inductive and coinductive types. The definition proceeds alike a fold in functional programming, although a rather unusual one: that is not applied to any starting object. There has been a related construction of bisimilarity in Coq by Nakata and Uustalu recently, however, our case is not concerned with bisimilarity but a weaker notion of similarity that corresponds to recursive subtyping and has it's own interesting problems.