Signed and sealed

Language constructs for defining abstract types commonly come in two varieties: those that add and remove seals dynamically as values cross the abstraction boundary, and those that define the boundary statically using a type signature. Abstract types in dynamically-typed languages are generally defined using seals whereas statically-typed languages more typically use a signature; two prominent exceptions are Haskell, which uses seals, and Standard ML, which provides for both styles. We show that the two styles are interconvertible, and give a proof based on Pitts’ formulation of relational parametricity. In the light of this equivalence we revisit the decision to use seals for abstract types in Haskell and describe a library which extends Haskell with a construct for defining abstract types using signatures by a translation which inserts seals as necessary.