The expression parsing is done with a Lezer grammar. See calc.grammar for the grammar definition.
Once we have a tree from the parser, evaluating it to calculate the result is a case of matching on the type (BinaryExpression, Number, etc) and acting accordingly. See here for the actual "calculator" functionality.
We also maintain a context object to hold the values of assignments from previous results such as 4 + 5 = subtotal.