Suppose that people have forward looking expectations, that is, they
take into account all available information about the economy.  What
would be the shape of the Phillips curve in the short run in this
case?

Given their forward looking expectations are rational and they are
reasonably well informed, the Phillips curve would be vertical in the
long run.

The Phillips curve in the short run (within 2 years for US/UK) may be
diagonal upwards because of lags in the economy caused by
inefficiencies on the supply side.

However how people act on information taken in is an interesting
point.  If they were fully rational there would be no point stdying
economics as we would understand already... then there is herding
behaviour - the curve could work out backwards!