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Sound laws such as the Canaanite shift, which is the proposed law that Proto-NW-Semitic *ā -> Proto-Canaanite ō, and the celebrated Grimm's Law.

Is there a database that lists all transformations of ā -> ō in various languages? Conversely, is there a database that can list ā -> [phoneme] sorted by which phoneme it morphed into?

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Yes, there is Index Diachronica that is available as a searchable online database (in the link given above) or as a pdf file with all the sound laws nicely typeset.

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  • it's worth noting that index diachronica is far from complete even for the languages it does describe, many of its subgroupings are controversial, there is little to no distinction between universally-accepted and relatively tentatively suggested changes, and notation is not always completely consistent (but such is the way with random projects done for free online)
    – Tristan
    Jul 1 at 9:11

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