This is step 6 of the calculator project in Exploration 68 of Exploring C++: The Programmer's Introduction to C++.

This version of the calculator adds data types by implementing the number class, as a pimpl wrapper around number_impl and derived classes. The number::coerce() function ensures that both operands of an arithmetic expression have the same type, promoting integers to floating point numbers.

This version also adds rational numbers as one of the data types. Dividing two integers yields a rational result. Integers, rational numbers, and floating-point numbers can be freely mixed in expressions. Integers promote to rational; rational promotes to floating point. A rational result with a demoninator of one is automatically downgraded back to integer.

This calculator has a simple syntax:

start ::= statement-list
statement-list ::= empty | statement-list statement
statement ::= definition | quit | expression | "load" string | "save" string
definition ::= "def" identifier optional-parameters "=" expression
optional-parameters ::= empty | "(" optional-identifier-list ")"
optional-identifier-list ::= empty | identifier-list
identifier-list ::= identifier | identifier-list "," identifier
expression ::= multiplicative-expression "+" multiplicative-expression |
               multiplicative-expression "-" multiplicative-expression
multiplicative-expression ::= unary-expression "*" unary-expression |
                              unary-expression "/" unary-expression
unary-expression ::= "-" primary | "+" primary | primary
primary ::= number | function-call | "(" expression ")"
function-call ::= identifier optional_arguments
optional_arguments ::= empty | "(" optional-expression-list ")"
optional-expression-list ::= empty | expression-list
expression-list ::= expression | expression-list "," expression

Function arguments are evaluated lazily. There are no variables, only functions, but function definitions can look just like variable assignments:

def pi = 3.141592653589792

so there really isn't any difference between a variable and a function.

The calculator reads expressions from the standard input, evaluates them, and prints the results to the standard output. It's that simple.

The calculator parses expression into a parse tree. The parser uses node objects. The node class uses the pimpl idiom with a tree of node_impl-derived classes.