Writing a bf interpreter

I have recently written a brainfuck interpreter, which is mostly for education purposes and a little bit of fun but that is beside the point. My question is, is there a reliable source for a specification for the language?

Like, for example, if the stack pointer is pointing at the first element, what behaviour would occur if a "<" is encountered? If a "," is encountered, should the input be processed in canonical mode (input is only passed through when enter is pressed), or in immediate mode?

Essentially, is there some sort of implicit behaviour that everyone expects, or is there leeway for interpreter-specific implementation?