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The goal is certainly to have a language suitable for "real-time applications" (read games/audio), that's not my area of expertise however so your definition of real-time might not be different than mine.
As it compiles to C, any microcontroller with a compiler that supports something that looks like C can work. I've run Carp code on a GBA (as mentionned somewhere else in the comments), esp32, esp8266, as well as Arduboy & Pygamer via Arduino.
There is some more information about running Carp on embedded platforms in the docs[0].
One last thing I wanted to mention is that Carp is still very much in flux so it might not be the best choice for longterm projects, but if you're interested in playing with the language there is usually always someone to answer questions on the Gitter[1].
[0] https://github.com/carp-lang/Carp/blob/master/docs/Embedded....