There is growing interst in the use of richly-typed intermediate languages in sophisticated compilers for higher-order, typed source languages. these intermediate languages are typically stratified, involving terms, types, and kinds. As the sophistication of the type system increases, these three levels begin to look more and more similar, so an attractive approach is to use a single syntax, and a single data type in the compiler, to represent all three. The theory of so-called pure type systems makes precisely such an identification. This paper describes Henk, a new typed intermediate language based closely on a particular pure type system, the lambda cube. On the way we giv a tutorial introduction to the lambda cube.