Computable decision making on the reals and other spaces via partiality and nondeterminism
Name
p859-Sherman.pdf
Description
Published version
Size
766.76 KB
Format
Adobe PDF
Checksum (MD5)
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Author(s)
Sherman, Benjamin
Sciarappa, Luke
Chlipala, Adam
Carbin, Michael James
Date Issued
July 2018
Journal
LICS 2018: Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science
Publisher
ACM Press
Citation
Sherman, Benjamin et al. "Computable decision making on the reals and other spaces: via partiality and nondeterminism." LICS 2018: Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science 2018, July 2018, Oxford, United Kingdom, Association for Computing Machinery, July 2018 © 2018 ACM
Version
Final published version
Abstract
Though many safety-critical software systems use floating point to represent real-world input and output, the mathematical specifications of these systems' behaviors use real numbers. Significant deviations from those specifications can cause errors and jeopardize safety. To ensure system safety, some programming systems offer exact real arithmetic, which often enables a program's computation to match its mathematical specification exactly. However, exact real arithmetic complicates decision-making: in these systems, it is impossible to compute (total and deterministic) discrete decisions based on connected spaces such as R. We present programming-language semantics based on constructive topology with variants allowing nondeterminism and/or partiality. Either nondeterminism or partiality suffices to allow computable decision making on connected spaces such as R. We then introduce pattern matching on spaces, a language construct for creating programs on spaces, generalizing pattern matching in functional programming, where patterns need not represent decidable predicates and also may overlap or be inexhaustive, giving rise to nondeterminism or partiality, respectively. Nondeterminism and/or partiality also yield formal logics for constructing approximate decision procedures. We extended the Marshall language for exact real arithmetic with these constructs and implemented some programs with it.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Laboratory for Computer Science
Terms of Use
Creative Commons Attribution 4.0 International license
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1145/3209108.3209193
