Looking for the Wrong Fixed Point

you then violently shake the tree, probably killing it and also annoying anybody using the birds. The only thing that’s left still attached is what is actually needed. This isn’t how trees work: holding the trunk doesn’t give you information as to which branches are somehow necessary for the tree’s mission. It also primes your mind to look for the wrong fixed point, removing unneeded code instead of keeping only the necessary code. But, tree-shaking is an evocative name, and so despite its horticultural and algorithmic inaccuracies, we will stick to it. The thing is that maximal tree-shaking for languages with a thicker run-time has not been a huge priority. Consider Go: according to the golang wiki, the most trivial program compiled to WebAssembly from Go is 2 megabytes, and adding imports can make this go to 10 megabytes or more. Or look at Pyodide, the Python WebAssembly port: the REPL example downloads about 20 megabytes of data. These are fine sizes for technology demos or, in the limit, very rich applications, but they aren’t winners for web development. shake a different tree To be fair, both the built-in Wasm support for Go and the Pyodide port of Python both derive from the upstream toolchains, where Fixed Points and Strike Mandates Feb 19th, 2012 | 4 Comments Many tasks in compilation and program analysis (in symbolic computation in general, I suppose) amount to finding solutions to systems of the form x = f(x). However, when asked to define algorithms to find such fixed points, we rarely stop and ask “which fixed point are we looking for?” In practice, we tend to be interested in fixed points of monotone functions: given a partial order (<), we have a < b ⇒ f(a) < f(b). Now, in addition to being a fairly reasonable hypothesis, this condition usually lets us exploit Tarski’s fixed point theorem. If the domain of f (with <) forms a complete lattice, so does the set of fixpoints of f ! As a corollary, there then exists exactly one least and one greatest fixed point under <. This is extremely useful, because we can usually define useful meet and join operations, and enjoy a complete lattice. For example, for a domain that’s the power set of a given set, we can use ⊆ as the order relation, ∪ as join, and ∩ as meet.

На экране прокручивается статья о fixed points и tree-shaking в компиляторах и WebAssembly. В углу молодой мужчина у микрофона реагирует на чтение, а курсор выделяет фразу «the wrong fixed point», связывая математический термин с ошибочным выбором точки и удалением не того кода. Это реакционный программистский мем о чрезмерно буквальном или неправильном понимании технической формулировки. EN: A webpage article about fixed points, tree-shaking, compilers, and WebAssembly scrolls on screen. In the corner, a young man at a microphone reacts while the cursor highlights “the wrong fixed point,” connecting the mathematical term to choosing the wrong point and removing the wrong code. It is a programmer reaction meme about taking a technical phrase too literally or misunderstanding it.

• @gentoomemes / 10752 2024-04-20