In late 2013, I created a functional implementation of CMSIS-DAP called "Dapper Miser" that runs in a low-cost USB microcontroller such as the PIC16F1454. My interest was seeing it deployed as a CMSIS-DAP debugger integrated into a low-cost hobbyist/educational ARM development board.
From 2013 to 2017, ARM only made the CMSIS-DAP specification available under a EULA (defunct link); this precluded anyone from releasing an open-source implementation that honored the EULA. However, sometime in 2017, ARM changed their tune and published (devoid of a EULA) a CMSIS-DAP specification here.
What distinguishes Dapper Miser from ARM's reference implementation (and its assorted clones) is that Dapper Miser's architecture was optimized to have a lightweight program footprint. This made it possible to implement CMSIS-DAP on an 8-bit microcontroller with far less resources than what ARM says is necessary. Please read the app note for more information on the implementation, and the associated README.md with each processor target.