A Simple Take on Typed Abstract Syntax in Haskell-like Languages

We present a simple way to program typed abstract syntax in a language following a Hindley-Milner typing discipline, such as Haskell and ML, and we apply it to automate two proofs about normalization functions as embodied in type-directed partial evaluation for the simply typed lambda calculus: normalization functions (1) preserve types and (2) yield long beta-eta normal forms.Keywords: Type-directed partial evaluation, normalization functions, simply-typed lambda-calculus, higher-order abstract syntax, Haskell