How to clear history in zsh

To get an empty history, temporarily set HISTSIZE to zero.

function erase_history { local HISTSIZE=0; }
erase_history

If you want to erase the new history from this shell instance but keep the old history that was loaded initially, empty the history as above then reload the saved history fc -R afterwards.

If you don't want the erase_history call to be recorded in the history, you can filter it out in the zshaddhistory hook.

function zshaddhistory_erase_history {
  [[ $1 != [[:space:]]#erase_history[[:space:]]# ]]
}
zshaddhistory_functions+=(zshaddhistory_erase_history)

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Deleting one specific history element (history -d NUM in bash) is another matter. I don't think there's a way other than:

1. Save the history: fc -AI to append to the history file, or fc -WI to overwrite the history file, depending on your history sharing preferences.
2. Edit the history file ($HISTFILE).
3. Reload the history file: fc -R.