Based on the "super effective" and "not very effective" messages, it's obvious type [dis]advantages are implemented in Pokémon Go. However, I noticed immunities do not seem to be implemented (I hit a Pidgeot with the ground-type move Dig). Since originally posting this question, I've learned that the multipliers are different (1.25/0.8 vs the old 2/0.5), but still don't know about compounding [dis]advantages.
Do type [dis]advantages compound like in other Pokémon games, or is all [dis]advantage equal? E.g., will the damage Golbat (poison/flying) receives from a bug type attack be 0.8x, or will it be 0.64x? And will a Dragonite (dragon/flying) take 1.25x or 1.5625x damage from an ice type attack?
This answer claims that compounding [dis]advantages are not implemented, but my personal experience having a Golbat battle a much higher CP Pinsir made it feel as if they were (but that's hardly a confirmation).
Is there any information to indicate how thoroughly type [dis]advantages are implemented, since type immunities indicate this may differ from the games?