As the OP, I also wish to see some form of conversation_id and parent_id parameters, which correspond to the state of the last prompt and the state of the conversation at any point. In the web UI we can recall a conversation session, only adding new prompts to already existing context and even branch of from a previous prompt into a new timeline. This is already achieved with gpt-3.5-turbo in the context of ChatGPT. If we could get that feature through the API for gpt-3.5-turbo, we could avoid resending the previous messages with every prompt.
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