利用解析原理写一个简单的计算器

计算器在计算机诞生之前便已经产生，计算在人类远古时期就已经开始。

利用的是语法解析的思想，参考programming_principles_and_practice_using_c++_2nd_ed

grammer:

expression:

term;

expression + term;

expression - term;

term:

primary;

term * primary;

term / primary;

primary:

number;

'(' expression ')'

命名一个Token类，表示最小单位，比如*, 3.14, (，以及一个Token_stream类，stream中获取一个Token，或者把Token放入到stream中。

此类程序非常容易拓展，比如需要加上%运算符，可以在term上加上语法， term % primary.

#include "std_lib_facilities.h"

struct Token {
char kind;
double value;
string name;
Token(char ch) :kind(ch), value(0) { }
Token(char ch, double val) :kind(ch), value(val) { }
};

class Token_stream {
bool full;
Token buffer;
public:
Token_stream() :full(0), buffer(0) { }

Token get();
void unget(Token t) { buffer=t; full=true; }

void ignore(char);
};

const char let = 'L';
const char quit = 'Q';
const char print = ';';
const char number = '8';
const char name = 'a';

Token Token_stream::get()
{
if (full) { full=false; return buffer; }
char ch;
cin >> ch;
switch (ch) {
case '(':
case ')':
case '+':
case '-':
case '*':
case '/':
case '%':
case ';':
case '=':
return Token(ch);
case '.':
case '0':
case '1':
case '2':
case '3':
case '4':
case '5':
case '6':
case '7':
case '8':
case '9':
{	cin.unget();
double val;
cin >> val;
return Token(number,val);
}
default:
if (isalpha(ch)) {
string s;
s += ch;
while(cin.get(ch) && (isalpha(ch) || isdigit(ch))) s += ch;
cin.unget();
if (s == "let") return Token(let);
if (s == "quit") return Token(quit);
return Token(name);
}
error("Bad token");
}
}

void Token_stream::ignore(char c)
{
if (full && c==buffer.kind) {
full = false;
return;
}
full = false;

char ch;
while (cin>>ch)
if (ch==c) return;
}

struct Variable {
string name;
double value;
Variable(string n, double v) :name(n), value(v) { }
};

vector<Variable> names;

double get_value(string s)
{
for (int i = 0; i<names.size(); ++i)
if (names[i].name == s) return names[i].value;
error("get: undefined name ",s);
}

void set_value(string s, double d)
{
for (int i = 0; i<=names.size(); ++i)
if (names[i].name == s) {
names[i].value = d;
return;
}
error("set: undefined name ",s);
}

bool is_declared(string s)
{
for (int i = 0; i<names.size(); ++i)
if (names[i].name == s) return true;
return false;
}

Token_stream ts;

double expression();

double primary()
{
Token t = ts.get();
switch (t.kind) {
case '(':
{	double d = expression();
t = ts.get();
if (t.kind != ')') error("'(' expected");
}
case '-':
return - primary();
case number:
return t.value;
case name:
return get_value(t.name);
default:
error("primary expected");
}
}

double term()
{
double left = primary();
while(true) {
Token t = ts.get();
switch(t.kind) {
case '*':
left *= primary();
break;
case '/':
{	double d = primary();
if (d == 0) error("divide by zero");
left /= d;
break;
}
default:
ts.unget(t);
return left;
}
}
}

double expression()
{
double left = term();
while(true) {
Token t = ts.get();
switch(t.kind) {
case '+':
left += term();
break;
case '-':
left -= term();
break;
default:
ts.unget(t);
return left;
}
}
}

double declaration()
{
Token t = ts.get();
if (t.kind != 'a') error ("name expected in declaration");
string name = t.name;
if (is_declared(name)) error(name, " declared twice");
Token t2 = ts.get();
if (t2.kind != '=') error("= missing in declaration of " ,name);
double d = expression();
names.push_back(Variable(name,d));
return d;
}

double statement()
{
Token t = ts.get();
switch(t.kind) {
case let:
return declaration();
default:
ts.unget(t);
return expression();
}
}

void clean_up_mess()
{
ts.ignore(print);
}

const string prompt = "> ";
const string result = "= ";

vo
4000
id calculate()
{
while(true) try {
cout << prompt;
Token t = ts.get();
while (t.kind == print) t=ts.get();
if (t.kind == quit) return;
ts.unget(t);
cout << result << statement() << endl;
}
catch(runtime_error& e) {
cerr << e.what() << endl;
clean_up_mess();
}
}

int main()

try {
calculate();
return 0;
}
catch (exception& e) {
cerr << "exception: " << e.what() << endl;
char c;
while (cin >>c&& c!=';') ;
return 1;
}
catch (...) {
cerr << "exception\n";
char c;
while (cin>>c && c!=';');
return 2;
}