Zend certified PHP/Magento developer

Are ARM instruction sets retro-compatible?

I need a Pi to make some program run. However, it is noted somewhere on the program’s FAQ that it is “supporting the most popular platforms arm7 and arm64”.

My Pi Zero only has the ARMv6 instruction set; when I run that program, segmentation faults are all over the place.

I want to be sure to buy the right Pi for the usage I want. The Raspberry Pi 4, uses an ARMv8 ruleset AFAIK.
Can I use that v8 device to run the v7 program? Thanks!