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Leveling Up Dependent Types

Agda source code accompanying the paper (DTP 2013):

Leveling Up Dependent Types - Generic programming over a predicative hierarchy of universes. (Draft)

Code from the paper

The underlying type system

Extra examples of generic functions over indexed types

  • Extras.FixedHierarchy
    • A fixed dependently typed universe with some indexed types in it.
    • Contains examples of applying a generic double over indexed types. Applying generic functions to dependent types changes the result type, prefixing them by Π's that act as "preconditions" that are used to preserve type correctness.
    • Generically double the dependent function `fun and get results out by satisfying its generated preconditions.
    • Generically double the dependent pair `pair and get results out by satisfying its generated preconditions.
  • Extras.FixedHierarchyEverywhere WARNING: CONTAINS OMGBBQ AWESOME!
    • Mostly the same as Extras.FixedHierarchy.
    • Defines the fully-generic mapping combinator every.
    • Apply every to a simple double function, and the double function will be applied to nested values on your behalf!
    • The same fun and pair examples are given, but using the new every combinator.

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Source code accompanying the paper "Leveling Up Dependent Types"

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