The Only Piece of Writing Advice That Matters | No Film School
Forget all the rules and just focus on this one thing.| No Film School
$$ $$ Category theory often sheds light on old problems by redescribing them in a conceptually cleaner way, but it less frequently gets used to develop concrete algorithms for practical problems. In this post, the problem we address involves a query we care about: we want to maintain the answer set to some query (e.g. “how many paths of length two are there in this graph?”) when the thing being queried is changing frequently. If the changes are frequent enough, we don’t want to have to...| Topos Institute
How we can think about pushouts as applying rules via substitution, featuring examples in categorical databases and Datalog.| Topos Institute
Forget all the rules and just focus on this one thing.| No Film School
This is the second part in a series about diagrammatic reasoning, inspired by e-graphs. Last time, we reviewed the concept of initial functor and showed by example how to calculate with diagrams and initial functors. This time, we make that calculus more systematic and we reconceive e-graphs in terms of initial functors. 1 Weak equivalence of diagrams We’ve been deriving equations by chaining together initial functors between diagrams, going in either direction. Let’s give a name to this ...| Topos Institute
An e-graph, short for “equality graph,” is a data structure that maintains a congruence relation on expression trees: an equivalence relation stable under forming new expressions. First devised by Nelson and Oppen in 1980 (Nelson 1980; Nelson and Oppen 1980), e-graphs received a surge of new attention when Willsey et al demonstrated, via their software package egg, that e-graphs combined with equality saturation can be a fast, powerful, and adaptable tool for equational reasoning (Willsey...| Topos Institute
Rewrite rules are organized via a graphical syntax into discrete-time simulations which can be understood as agent-based models. This representation is transparent, compositional, and serializable.| blog.algebraicjulia.org
It’s breakfast time! You wake up and walk to your kitchen and notice a loaf of bread, a knife, a raw egg (in its shell), a skillet, and a stove burner sitting on the counter. You’re hungry and your preferred state of existence is to, instead, have an egg sandwich sitting on your counter. You are saddened by the situation, but feel empowered to change it! You compare what you have and what you want, recall what cooking skills you have, and devise the following steps:| blog.algebraicjulia.org
Paraphrasing, quoting and summarizing - these three are significant components that can make your content credible and better if you use them smartly.| Rewriting Tools Blog
