program

a program can be thought of as an algorithm. in a more rigorous context, it can be considered a turing program or a program written in the $\langS$ programming language.

we say that a program diverges on an input if it broken link: blk:blk-S-program-exec-case-2 on that input.

we say that a program converges on an input if it broken link: blk:blk-S-program-exec-case-2 on that input.

we write $\text{[math]}$ , and $\text{[math]}$ .
notice that this is a special case of the language of a machine.