1 Department of Computer Science, Faculty of Science, Aarhus University, Aarhus University2 unknown3 Department of Computer Science, Science and Technology, Aarhus University4 Department of Computer Science, Science and Technology, Aarhus University
We use a code generator—type-directed partial evaluation— to verify conversions between isomorphic types, or more precisely to verify that a composite function is the identity function at some complicated type. A typed functional language such as ML provides a natural support to express the functions and type-directed partial evaluation provides a convenient setting to obtain the normal form of their composition. However, off-the-shelf type-directed partial evaluation turns out to yield gigantic normal forms. We identify that this gigantism is due to redundancies, and that these redundancies originate in the handling of sums, which uses delimited continuations. We successfully eliminate these redundancies by extending type-directed partial evaluation with memoization capabilities. The result only works for pure functional programs, but it provides an unexpected use of code generation and it yields orders-of-magnitude improvements both in time and in space for type isomorphisms. Basic Research in Computer Science (www. brics. dk), funded by the Danish National Research Foundation.