Computable decision making on the reals and other spaces via partiality and nondeterminism
Author(s)Sherman, Benjamin; Sciarappa, Luke; Chlipala, Adam; Carbin, Michael James
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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.
DepartmentMassachusetts 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
LICS 2018: Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science
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
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