4 research outputs found
A Theory of Termination via Indirection
Step-indexed models provide approximations to a class of domain
equations and can prove type safety, partial correctness, and program
equivalence; however, a common misconception is that they
are inapplicable to liveness problems. We disprove this by applying
step-indexing to develop the first Hoare logic of total correctness
for a language with function pointers and semantic assertions.
In fact, from a liveness perspective, our logic is stronger: we verify
explicit time resource bounds. We apply our logic to examples containing
nontrivial "higher-order" uses of function pointers and we
prove soundness with respect to a standard operational semantics.
Our core technique is very compact and may be applicable to other
liveness problems. Our results are machine checked in Coq
Step-Indexed Normalization for a Language with General Recursion
The Trellys project has produced several designs for practical dependently
typed languages. These languages are broken into two
fragments-a_logical_fragment where every term normalizes and which is
consistent when interpreted as a logic, and a_programmatic_fragment with
general recursion and other convenient but unsound features. In this paper, we
present a small example language in this style. Our design allows the
programmer to explicitly mention and pass information between the two
fragments. We show that this feature substantially complicates the metatheory
and present a new technique, combining the traditional Girard-Tait method with
step-indexed logical relations, which we use to show normalization for the
logical fragment.Comment: In Proceedings MSFP 2012, arXiv:1202.240