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Code Generation for Higher Inductive Types
Higher inductive types are inductive types that include nontrivial
higher-dimensional structure, represented as identifications that are not
reflexivity. While work proceeds on type theories with a computational
interpretation of univalence and higher inductive types, it is convenient to
encode these structures in more traditional type theories with mature
implementations. However, these encodings involve a great deal of error-prone
additional syntax. We present a library that uses Agda's metaprogramming
facilities to automate this process, allowing higher inductive types to be
specified with minimal additional syntax.Comment: 16 pages, Accepted for presentation in WFLP 201