[tannhaeuser]

Straightforward searching through combinatoric spaces for planning and optimization, including robotic and eg. discrete investment planning for models where solutions can't be described by a finite number of variables (see [1] for in-browser container logistics planning).

Composition of programs with complex rule-based semantics and large specs (the Prince CSS renderer is written in Mercury).

Diagnostics, capturing legal, medical, and other taxonomic knowledge in executable form, possibly as implementation, extension, or replacement for semantic web stuff and description logic.

All of the above with easy and powerful DSL capabilities ranging from built-in customizable operator precedence parsing, over natural recursive descent parsing with backtracking, to attribute grammars and arbitrary logic (Prolog started out as a 70's natural language understanding approach employing logic grammars).

[1]: https://quantumprolog.sgml.io/