I think you are hitting an issue because the library was written when only NXP cpus were supported by mbed. LPC_UART1 is implying an NXP LPC part, your board has an ST CPU and so LPC_UART1 is undefined.
Taking a quick look at it you should be able to replace the switch in GPS.cpp lines 37 to 42 with
_base = NULL;
Also "a Trimble GPS" doesn't narrow it down a lot, They have GPS systems varying in price from $10 to $10,000. I'm guessing you have one towards the lower end of that range but if you need more help getting it working then a little more detail would be useful. :-)
Whenever I try to compile MODGPS examples I get an error. That error, identifier "_uidx" is undefined, line 37 of GPS.cpp.
If I comment out the switch statements it compiles but I get only zero's as output.
I am not sure what the developer was trying to do so I would appreciate any help fixing the error.
Thank you.