I've been successfully using Vivado and the SDK to develop VHDL and C for the Zynq XC7Z010 on a Digilent Zybo board. I've also been using the GNAT GPS IDE to learn Ada targeted to an STM32F4 processor (using one of the supported development boards).
GPS also ships with a set of zynq7000 run-times targeted to the XC7Z020 (as far as I can tell). Having looked through the BSPs for these target I believe that the code generated should also run on the XC7Z010 as the ARM cores appear to be the same. It may turn out that there are differences, in which case I will have a go at building a specific run-time based on the existing zynq7000 BSP (Adacore have documented this process and give an example for generating a new STM32F4 BSP).
My main problem is I'm not sure how to load and run the generated Ada elf file on my Zybo. I have tried to generate a BOOT.ini file containing a FSBL (built with the SDK and using my exported hardware from Vivado), a bit-stream and the Ada elf file (The the Zybo has an MicroSD interface that can be configured as a boot device, this works perfectly with a bit-stream and C elf produced via Vivado / SDK).
Anyway, this didn't work... I'm guessing that it might be a linking issue, or a boot loader issue, or similar. With my current level of knowledge I'm just not sure at this stage.
Any advice or pointers would be greatly appreciated!