This is step 4 of the calculator project in Exploration 68 of Exploring C++: The Programmer's Introduction to C++.

This version of the calculator adds functions. In doing so, it changes the var keyword to def to encompass the definition of variables and functions.

This version of the calculator has a more complicated syntax, but still simple enough for a recursive descent parser:

start ::= statement-list
statement-list ::= empty | statement-list statement
statement ::= definition | quit | expression
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.