Will it get a so called foldback current mechanism in software.
I mean if I short the power supply for longer as lets say three seconds
Will it switch the Current down to zero mA and the Voltage also to zero Volts?
So that I have to reset it before the Voltage comes up again ?
I am sure you could implement that, but foldback current limiting is not normally wanted in a lab supply and what is normally meant by it is not actually what you have described.
The normal purpose of foldback current limiting is to protect a fixed voltage linear power supply in case of a short circuit. The problem is that when a load exceeds the current limit, the voltage will start to drop, but this increases the power dissipation in the pass transistor. In the ultimate limit, when you have short circuited the output, the pass transistor(s) are dissipating more than 100% of the supply rating. Bipolar transistors also have second breakdown which further limits their safe operating area. Foldback current limiting uses a separate analog feedback loop to reduce the current limit and keep within the transistor SOA when the output voltage is below the setpoint. Generally once the short is removed the supply will recover naturally -- it doesn't require a hard reset. Of course, if the short circuit is caused by a crowbar circuit, it won't reset until the power is removed.
A software defined limit with a 3 second delay is not nearly fast enough to provide protection for the majority of circuits that need foldback current limiting. That might help if your thermal limit is an undersized heatsink, but more often you have to deal with the package juction->case rating or second breakdown. These time constants are quite fast, 3 seconds is much too long.
In any case, by design a bench supply must not be susceptible to such overloads. The supply has to be able to survive being programmed to the lowest possible voltage and the highest possible current. The transistor doesn't care whether the set point is 10 volts and drops to 1 volt due to the current limit, or whether the setpoint is 1 volt.
In any case, the LT3080 has built in thermal protection. If you do manage to overload it, it will shut off to protect itself. However, this would be a sign of a design error, or use of the supply outside its design parameters (i.e., too high ambient temperature).
If you want to protect the device under test rather than the supply, that would normally be considered overcurrent protection, and then you would generally design it to shut off the supply until reset. There are not that many situations where you need overvoltage / overcurrent protection, and again, usually 3 seconds is way to long -- if you are powering a very delicate transducer or something, normally you would want to shut off the supply within microseconds.