First version of the syntax definition:

lexical items:

  number = any sequence of one or more decimal digits
  name = any sequence of letters, digits, or underline, first must be a letter, not case sensitive
  string = any sequence of characters except " or newline inside a pair of "s
  spaces, newlines, etc allowed between any two lexemes
  reserved words not case sensitive
  operator = + - * / % < <= <> > >= == and or

grammar:

  <value>       ::= number | name | string | "read" | "(" <expression> ")"
  <simple>      ::= <value> 
                  | { "-" | "not" } <simple>
  <expression>  ::= <simple> ( operator <simple> ) *
  <expr-list>   ::= <expression> { "," <expr-list> }
  <print-stmt>  ::= "print" <expr-list>
  <assign-stmt> ::= name ":=" <expression>
  <while-stmt>  ::= "while" <expression> "do" <statement>
  <if-stmt>     ::= "if" <expression> "then" <statement> { "else" <statement> }
  <stmt-list>   ::= <statement> ( ";" <statement> ) *
  <compound>    ::= "{" <stmt-list> "}"
  <statement>   ::= <print-stmt> | <while-stmt> | <if-stmt> | <assign-stmt> | <compound>
  <program>     ::= <statement>

const int nt_error = 0, nt_number = 1, nt_name = 2, nt_string = 3, nt_read = 4, 
          nt_parenth = 5, nt_simple = 6, nt_expression = 7, nt_expr_list = 8,
          nt_print_stmt = 9, nt_assign_stmt = 10, nt_while_stmt = 11, nt_if_stmt = 12,
          nt_stmt_list = 13, nt_compound = 14;
string node_names[] = { "error", "number", "name", "string", "read",
                        "parenth", "simple", "expression", "expr-list",
                        "print-stmt", "assign-stmt", "while-stmt", "if-stmt",
                        "stmt-list", "compound" }
const int num_node_names = sizeof(node_names) / sizeof(node_names[0]);

struct node
{ int type;
  int int_val;
  string string_val;
  vector <node *> parts;

  node(int t, int v)
  { type = t; int_val = v; string_val = ""; }

  node(int t, string s)
  { type = t; int_val = 0; string_val = s; }

  node(int t, int v, string s)
  { type = t; int_val = v; string_val = s; }

  node(int t, string s, int v)
  { type = t; int_val = v; string_val = s; }

  ~node()
  { for (int i = 0; i < parts.size(); i += 1)
      delete parts[i]; }

  void add(node * n)
  { parts.push_back(n); }

  void print(int indent = 0)
  { cout << setw(4 * indent) << "";
    if (type >= 0 && type < num_node_names)
      cout << node_names[type];
    else
      cout << "bad(" << type << ")";
    cout << " " << int_val << " \"" << string_val << "\"\n";
    for (int i = 0; i < parts.size(); i += 1)
      parts[i].print(indent + 1); } };