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Explore the foundations of arithmetic in C++ through this comprehensive conference talk from CppCon 2022. Delve into the challenges of formal interface design for C++ integral arithmetic operations, examining their preconditions, postconditions, and interconnected mathematical theorems. Learn how to address these challenges using lightly extended C++ for interfaces, theorems, and proofs. Drawing inspiration from Bertrand Russell's and Alfred North Whitehead's "Principia Mathematica," discover how arithmetic can be developed from procedural first principles, including stability of objects, substitutability of values, and repeatability of operations. Gain insights into formal interface design, C++ integral arithmetic, foundations of arithmetic, and writing mathematical proofs procedurally. Presented by Lisa Lippincott, chair of the numerics study group of the C++ standardization committee and designer of software architectures for Tanium and BigFix.
