https://en.wikipedia.org/wiki/IOS#Kernel
iOS uses the XNU Mach 2.5 derivative that underlies Darwin, the Open Source BSD Unix variant.
Mac OS X is the base off of which iOS is designed.
Obviously, the kernel was ported to ARM type processors. This is not difficult given that Mach was designed for heterogeneous environments (processor agnostic/independent).
Your iPhone and iPad run an optimized Mac OS X, using Cocoa (CocoaTouch) and Darwin BSD.
Both Mac OS Sierra and iOS 10 are running Darwin 16.0.
For all intents and purposes, it already is.
However, you mean the actual Mac OS with its full libraries and APIs.
Let's benchmark the slowest machine Apple lists on its updateable list as the lowest possible requirements.
High Sierra will be used as the benchmark.
This, of course will be the Macbook Air 11 Inch in Late 2010.
1.4GHz Intel Core 2 Duo processor with 3MB on-chip shared L2 cache; or optional 1.6GHz Intel Core 2 Duo processor with 3MB shared L2 cache
800MHz frontside bus
2GB of 1066MHz DDR3 SDRAM onboard (4GB maximum)
Now, let's look at the iPhone 7 (not the Plus)
Quad-core (2× Hurricane + 2× Zephyr) 2.34 GHz max clock on Hurricane. Zephyr assumed anything below that.
L1 cache Per core: 64 KB instruction + 64 KB data
L2 cache 3 MB shared
L3 cache 4 MB shared
Although ARM chips used to be severely underpowered versus their mobile and desktop variants, you can still compare based on pure computational scores.
Daring Gruber gives us this info.
https://www.macrumors.com/2016/09/15/iphone-7-faster-than-macbook-air/
The iPhone 7 (not the Plus) outperformed the Macbook Air 2015 in single core score but was in a technical tie on multicore scores (the MacBook Air 2015 barely beat it).
Therefore, the iPhone 7 is capable of running the full Mac OS X, Darwin/Mach/Cocoa and all of their full desktop APIs, calls, and plug-ins.
I hope this answers your questions.
