Recent works have shown the power of linear indexed type systems for
enforcing complex program properties. These systems combine linear types with a
language of type-level indices, allowing more fine-grained analyses. Such
systems have been fruitfully applied in diverse domains, including implicit
complexity and differential privacy. A natural way to enhance the
expressiveness of this approach is by allowing the indices to depend on runtime
information, in the spirit of dependent types. This approach is used in DFuzz,
a language for differential privacy. The DFuzz type system relies on an index
language supporting real and natural number arithmetic over constants and
variables. Moreover, DFuzz uses a subtyping mechanism to make types more
flexible. By themselves, linearity, dependency, and subtyping each require
delicate handling when performing type checking or type inference; their
combination increases this challenge substantially, as the features can
interact in non-trivial ways. In this paper, we study the type-checking problem
for DFuzz. We show how we can reduce type checking for (a simple extension of)
DFuzz to constraint solving over a first-order theory of naturals and real
numbers which, although undecidable, can often be handled in practice by
standard numeric solvers