Type Isomorphisms for Module Signatures

This work focuses on software reuse for languages equipped with a module system. To retrieve modules from a library, it is quite reasonable to use module signatures as a search key, up to a suitable notion of signature isomorphism. We study a formal notion of isomorphism for module signatures, which naturally extends the notion of isomorphism for types in functional languages. Isomorphisms between module types surprisingly have nontrivial interactions with the theory of isomorphisms of the base language to which the module system is added. We investigate the power of this notion in equating module signatures, and we study its decidability. This work does not impose any limitative assumption on the module system as we handle type declarations in signatures, type sharing and higher order modules.