We present the design and implementation of a generative geometric kernel 1 . The kernel generator is generic, type-safe, parametrized by many design-level choices and extensible. The resulting code has minimal traces of the design abstractions. We achieve genericity through a layered design deriving concepts from affine geometry, linear algebra and abstract algebra. We achieve parametrization and type-safety by using OCaml's module system, including higher order modules. The cost of

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... is removed by using MetaO-Caml's support for code generation coupled with some annotations atop the code type.