How to know if you're in a typescript?

Maybe with:

if lsof -tac script "$(tty)" > /dev/null; then
  echo "I'm running under script"
else
  echo "I'm not"
fi

You could add something like:

lsof -tac script "$(tty)" > /dev/null && PS1="[script] $PS1"

To your ~/.zshrc or ~/.bashrc, so the information on whether you're in script or not would be visible on your shell prompt.

Alternatively, if you can't guarantee that lsof be installed you could do (assuming an unmodified IFS):

terminal=$(ps -o comm= -p $(ps -o ppid= -p $(ps -o sid= -p "$$")))
[ "$terminal" = script ] && PS1="[script] $PS1"

The heuristic is to get the command name of the parent of the session leader which generally would be the terminal emulator (xterm, script, screen...).

Interesting problem. I found a small bash script could do the job pretty reliably:

#!/bin/bash

PP=$(ps -o ppid= $$)

while [[ $PP != 1 ]]
do
    LINE=$(ps -o ppid= -o comm= $PP | sed 's/^  *//')
    COMM=${LINE#* }
    PP=${LINE%% *}
    if [[ $COMM == script ]]  # Might need a different comparison
    then
        echo "In script"
        exit 0
    fi
done
echo "Not in script"

I think this is slightly different than proposed by Stephane Chazelas, in that my script works its way up the parent:child relationship that Linux/Unix processes have until it finds PID 1, or it finds "script" as the process.