Multi-stage programming (MSP) is a style of writing program
generators---programs which generate programs---supported by special
annotations that direct construction, combination, and execution of
object programs. Various researchers have shown MSP to be effective
in writing efficient programs without sacrificing genericity.
However, correctness proofs of such programs have so far received
limited attention, and approaches and challenges for that task have
been largely unexplored. In this thesis, I establish formal
equational properties of the multi-stage lambda calculus and related
proof techniques, as well as results that delineate the intricacies
of multi-stage languages that one must be aware of.
In particular, I settle three basic questions that naturally arise
when verifying multi-stage functional programs. Firstly, can adding
staging MSP to a language compromise the interchangeability of terms
that held in the original language? Unfortunately it can, and more
care is needed to reason about terms with free variables. Secondly,
staging annotations, as the term ``annotations'' suggests, are often
thought to be orthogonal to the behavior of a program, but when is
this formally guaranteed to be the case? I give termination
conditions that characterize when this guarantee holds. Finally, do
multi-stage languages satisfy extensional facts, for example that
functions agreeing on all arguments are equivalent? I develop a
sound and complete notion of applicative bisimulation, which can
establish not only extensionality but, in principle, any other valid
program equivalence as well. These results improve our general
understanding of staging and enable us to prove the correctness of
complicated multi-stage programs
