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diff --git a/content/posts/correctness-is-all-you-need.md b/content/posts/correctness-is-all-you-need.md new file mode 100644 index 0000000..20ded9a --- /dev/null +++ b/content/posts/correctness-is-all-you-need.md @@ -0,0 +1,32 @@ ++++ +title = "correctness is all you need" +author = ["santi"] +lastmod = 2024-05-09T23:35:32-03:00 +tags = ["coq", "rust"] +draft = false ++++ + +```python +>>> 0.1 + 0.2 +0.30000000000000004 +``` + +which of course is an annoying encounter for the unitiated in floats, but there's a much bigger problem, that usually isn't noticed at all until much later, that float addition itself isn't even associative: + +```python +>>> (0.1 + 0.2) + 0.3 +0.6000000000000001 +>>> 0.1 + (0.2 + 0.3) +0.6 +>>> 0.1 + (0.2 + 0.3) == (0.1 + 0.2) + 0.3 +False +>>> +``` + +and this is a problem, because associativity is a big underlying assumption that we commonly have for numbers, when, for example, summing a list in reverse. other common pitfalls include: + +- not all numbers have an additive inverse, ie. for some number `n`, `n + (-n) != n`. +- not all numbers different than 0 have a multiplicative inverse, ie. for some number `n`, `n / n != 1`. +- addition is not commutative, ie. for numbers `a` `b`, `a + b != b + a`. + +and the list goes you on, you get the idea. this usually isn't thought of the main problems in |