Much recent work on the compilation of statically typed languages such as ML
relies on the propagation of type information from source to object code in
order to increase the reliability and maintainabilty of the compiler itself
and to improve the efficiency and verifiability of generated code.  To achieve
this the program transformations performed by a compiler must be cast as
type-preserving translations between typed intermediate languages.  In earlier
work with Minamide we studied one important compiler transformation, closure
conversion, for the case of pure simply-typed and polymorphic
$\lambda$-calculus.  Here we extend the treatment of simply-typed closure
conversion to account for recursively-defined functions such as are found in
ML.  We consider three main approaches, one based on a recursive code
construct, one based on a self-referential data structure, and one based on
recursive types.  We discuss their relative advantages and disadvantages, and
sketch correctness proofs for these transformations based on the method of
logical relations.