The attached part has one "input" expression, p1, a locked expression "my_locked_exp" that uses the input expression p1 as part of the formula. And it has expression p2 which uses "my_locked_exp as part of its formula.
my_locked_exp is a ug_expression KF child rule with lockRule set to TRUE.
In the Tools ->Expression dialog and in the Part Navigator the "my_locked_exp" is not editable.
The example expression is quite simple but it should meet the requirement for being able to define the expression to be used for a curve by equation where that expression is not directly editable but still can react to other expression edits.