I am interested in writing my own app for my TI-84 Plus Silver Edition Calculator (not a program using the calculator's built in language). Does anyone know of a compiler for .8xk files, which are the file extension the TI-84 Apps use? Also, could someone provide me some sample code from an app just to show how hard it is to make one? I have no idea what language is used, and I really want to know.
The easiest way to write a flash application is to use TI-BASIC + Basic Builder
Alternatively, you can take the dive into z80 Assembly, though the learning curve is very steep. Here is some example assembly from Learning z80 Assembly in 28 Days.
LD HL, (stack_ptr) ; Load stack pointer
LD (HL), E ; Push the low-order byte
INC HL ; Move stack pointer to next byte of available space
LD (HL), D ; Push the high-order byte
INC HL
LD (stack_ptr), HL ; Save new stack pointer
If you would like the speed of assembly with the ease of BASIC, there are several ASM libraries (xLib for example) available, but I'm not too sure how well they would work as Flash apps.
You might also look into Axe, which is a programming language with near-assembly speeds.