Once Upon a Polymorphic

We present a sound type-basedùsage analysis' for a realistic lazy functional language. Accurate information on the usage of program subexpressions in a lazy functional language permits a compiler to perform a number of useful optimi-sations. However, existing analyses are either ad-hoc and approximate, or deened over restricted languages. Our work extends the Once Upon A Type system of Turner, Mossin, and Wadler (FPCA'95). Firstly, we add type poly-morphism, an essential feature of typed functional programming languages. Secondly, we include general Haskell-style user-deened algebraic data types. Thirdly, we explain and solve thèpoisoning problem', which causes the earlier analysis to yield poor results. Interesting design choices turn up in each of these areas. Our analysis is sound with respect to a Launchbury-style operational semantics, and it is straightforward to implement. Good results have been obtained from a prototype implementation , and we are currently integrating the system into the Glasgow Haskell Compiler.