Principia Mathematica - The Foundations of Arithmetic in C++ - Lisa Lippincott - CppCon 2022

Discover Principles of Mathematics-inspired C++ programming foundations for clarity and reliability.

Key takeaways

The Principia Mathematica is a foundational work in mathematics that builds up arithmetic from first principles.
The talk is about applying similar principles to C++ to create a formal foundation for arithmetic.
The reference add axiom is a fundamental concept that allows for the addition of two numbers with different types.
The talk introduces the concept of widening types, which are types that are wider than the original types.
The widening types are used to perform arithmetic operations on numbers with different types.
The talk discusses the importance of stability, substitutability, and repeatability in programming.
Stability refers to the idea that the program will always produce the same output given the same input.
Substitutability refers to the idea that different implementations of the same function can be used interchangeably.
Repeatability refers to the idea that the program will always produce the same output given the same input, even if the implementation changes.
The talk also discusses the concept of category theory and how it can be used to understand the relationships between different types.
The talk concludes by discussing the importance of formal foundations in programming and how they can be used to create more reliable and maintainable code.

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