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We present the design and implementation of a generative geometric kernel. 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 abstraction is removed by using MetaOCaml's support for code generation coupled with some annotations atop the code type.