We introduce the simply-typed lambda-calculus as a first representation
language approximating the logical framework LF. We show how it can be
used to encode Mini-ML expressions in an elegant and concise way. The
technique we use, called higher-order abstract syntax,
represents variables of the object language by variables in the
meta-language, with far-reaching consequences. We also point out the
inadequacy of the simply-typed lambda-calculus when it comes to the
representation of deductions and begin to investigate how the
meta-language might be extended to account for judgments and their
derivations.