flag=false
while !$flag
do
   read x
   if [ "$x" -eq "true" ]
   then
     flag=true
   fi
   echo "${x} : ${flag}"
done

flag=false
while [ "$flag" != "true" ]
do
   read x
   if [ "$x" = "true" ]
   then
     flag=true
   fi
   echo "${x} : ${flag}"
done

while true; do
  read -r x
  if [ "$x" = "true" ]; then break; fi
  echo "$x: false"
done

flag= # False
flag=0 # False
flag=1 # True (actually any integer number != 0 will do, but see remark below about toggling)
flag="some string" # Maybe False (make sure that the string isn't interpreted as a number)

if ((flag)) # Test for True
then
  : # do something
fi

if ! ((flag)) # Test for False
then
  : # do something
fi

flag=$((1-flag)) # Toggle flag (only works when flag is either empty or unset, 0, 1, or a string which doesn't represent a number)

$ foo=0
$ echo $foo
0
$ ((foo ^= 1))
$ echo $foo
1
$ ((foo ^= 1))
$echo $foo
0

flag=false
while [[ "$flag" == "false" ]]
do
   read x
   if [[ "$x" == "true" ]]
   then
     flag=true
   fi
   echo "${x} : ${flag}"
done

while ! $flag

$flag; if [ "$?" -eq 0 ]; then ... fi

if "$flag"; then ... fi

if ! "$flag"; then ... fi

flag=false
while ! "$flag"
do
   read x
   if [ "$x" == "true" ]
   then
     flag=true
   fi
   echo "${x} : ${flag}"
done

flag=0; if [ "$((flag))" -eq 0 ]; then ... fi      # test for a number
flag=0; if [ "$((flag))"  == 0 ]; then ... fi      # test for the string "0"

flag=0
while ((!flag))
do
   read x
   [ "$x" == "true" ] && flag=1
   echo "${x} : ${flag}"
done

[ ${FOO:-0} == 0 ] && FOO=1 || FOO=0

[ ${FOO:-false} == false ] && FOO=true || FOO=false