Interval Arithmetic on 32-Bit Words

Brandon Bohrer

27 November 2019

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.
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