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These days most program development on the ZX81 happens using tools on other operating systems and running the program on the ZX81. Basic tools like zxtext2p or the C compiler Z88DK, or a cross assembler like PASMO are examples.
It is still possible to do development only on the ZX81. With Basic, there is the old fashion ZX81 BASIC, but there is also Coral Basic Interpreter written by Carlo Delhez. It provides a number of new BASIC commands and a new way of typing in BASIC programs with a Full Entry Editor, allowing for non-keyword-based entry of commands.