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Summary: Higher-Order Subtyping for Dependent Types
Andreas Abel
Department of Computer Science
Ludwig-Maximilians-University Munich
Theory Seminar
Institute of Cybernetics, Tallinn, Estonia
24 November 2011
Andreas Abel (LMU) Subtyping Dependent IOC 2011 1 / 32
Introduction
Subtyping
Definition (Subtype)
A is a subtype of B, written A B, if a value of type A can be supplied
wherever a value of type B is demanded.
Examples:
Pos Nat. A function that can handle natural numbers n Nat,
meaning n 0, is not embarrased by a positive number n Pos,
meaning n > 0.
List Pos List Nat. If I can process a list of natural numbers, I can
process a list of positive numbers.
Nat Pos Pos Nat. I want a function that turns positive
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