A.I think the inside of the exterior wall is the best place to install foam insulation board. If it is to be used as a vapor retarder, it must be an extruded foam or a foil-covered foam board. The joints and any holes in the surface must be sealed with tape, just as you would with a polyethylene vapor retarder. The joint between the floor and the foam can be sealed with caulk or the gasketing used for airtight drywall installations. The simplest approach is to apply foam board over the inside face of the studs after the wall cavity is filled with insulation, and then screw the drywall to the studs through the foam, using longer drywall screws.
I know of several houses built this way more than 10 years ago, and they have performed exceptionally well.
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