### Abstract

Interval_Arithmetic implements conservative interval arithmetic
computations, then uses this interval arithmetic to implement a simple
programming language where all terms have 32-bit signed word values,
with explicit infinities for terms outside the representable bounds.
Our target use case is interpreters for languages that must have a
well-understood low-level behavior. We include a formalization of
bounded-length strings which are used for the identifiers of our
language. Bounded-length identifiers are useful in some applications,
for example the Differential_Dynamic_Logic article,
where a Euclidean space indexed by identifiers demands that identifiers
are finitely many.