On understanding types, data abstraction, and polymorphism
ACM Computing Surveys (CSUR) - The MIT Press scientific computation series
Proofs and types
Structural subtyping and the notion of power type
POPL '88 Proceedings of the 15th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Toward a typed foundation for method specialization and inheritance
POPL '90 Proceedings of the 17th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Bounded quantification is undecidable
POPL '92 Proceedings of the 19th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Theoretical Computer Science
Domains and lambda-calculi
Types and programming languages
Types and programming languages
A Theory of Objects
Decidability of Higher-Order Subtyping with Intersection Types
CSL '94 Selected Papers from the 8th International Workshop on Computer Science Logic
Typed operational semantics for higher-order subtyping
Information and Computation
Anti-symmetry of higher-order subtyping and equality by subtyping
Mathematical Structures in Computer Science
Towards a mechanized metatheory of standard ML
Proceedings of the 34th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Mechanizing metatheory in a logical framework
Journal of Functional Programming
Polarized subtyping for sized types
CSR'06 Proceedings of the First international computer science conference on Theory and Applications
Implementing a normalizer using sized heterogeneous types
MSFP'06 Proceedings of the 2006 international conference on Mathematically Structured Functional Programming
Hereditary substitutions for simple types, formalized
Proceedings of the third ACM SIGPLAN workshop on Mathematically structured functional programming
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We present a new proof of decidability of higher-order subtyping in the presence of bounded quantification. The algorithm is formulated as a judgement which operates on beta-eta-normal forms. Transitivity and closure under application are proven directly and syntactically, without the need for a model construction or reasoning on longest beta-reduction sequences. The main technical tool is hereditary substitution, i.e., substitution of one normal form into another, resolving all freshly generated redexes on the fly. Hereditary substitutions are used to keep types in normal-form during execution of the subtyping algorithm. Termination of hereditary substitutions can be proven in an elementary way, by a lexicographic induction on the kind of the substituted variable and the size of the expression substituted into--this is what enables a purely syntactic metatheory.