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- W2091718659 abstract "This paper treats semantics of numerical programs generally, but is principally concerned with limits as error tends to zero. We define three kinds of semantics for a simple programming language whose only data type is a real number type: a family of finite accuracy semantics, which explicitly represent numerical error, and two types of limiting program semantics. One limiting semantics models the limit as machine roundoff error becomes small; the other models the limit over programs as the mathematical error inherent in the algorithm used tends to zero. These three kinds of program semantics are based on domains that are similar to those commonly used in denotational semantics, but are continuous rather than algebraic, a slightly weaker property. Using these continuous bounded-complete domains, we are able to show that the two kinds of limiting semantics are in fact limits of the finite accuracy semantics." @default.
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- W2091718659 date "1997-04-01" @default.
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- W2091718659 title "Limiting semantics of numerical programs" @default.
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- W2091718659 doi "https://doi.org/10.1016/s0304-3975(96)00050-3" @default.
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