really happy to see something of a revival of interest for logic programming lately. it's an extremely powerful tool if you know when to reach for it.
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Basically anything that excels when declarative specification of relationships is more natural than imperative algorithms.
Type systems would absolutely choke on trying to solve things like: Knowlege representation and querying - imagine medical diagnosis systems with thousands symptoms and conditions; Dynamic constraint solving - where constraints emerge at runtime; Exploratory search problems requiring bfs/dfs of large solution spaces - e.g., route finding with changing conditions; NLP tasks - grammar parsing and understanding; etc.