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#### 2.1.2 Grammar Rules for `rpcalc`

Here are the grammar rules for the reverse polish notation calculator.

```input:
%empty
| input line
;
```
```
```
```line:
'\n'
| exp '\n'      { printf ("%.10g\n", \$1); }
;
```
```
```
```exp:
NUM           { \$\$ = \$1;           }
| exp exp '+'   { \$\$ = \$1 + \$2;      }
| exp exp '-'   { \$\$ = \$1 - \$2;      }
| exp exp '*'   { \$\$ = \$1 * \$2;      }
| exp exp '/'   { \$\$ = \$1 / \$2;      }
| exp exp '^'   { \$\$ = pow (\$1, \$2); }  /* Exponentiation */
| exp 'n'       { \$\$ = -\$1;          }  /* Unary minus    */
;
```
```%%
```

The groupings of the rpcalc “language” defined here are the expression (given the name `exp`), the line of input (`line`), and the complete input transcript (`input`). Each of these nonterminal symbols has several alternate rules, joined by the vertical bar ‘|’ which is read as “or”. The following sections explain what these rules mean.

The semantics of the language is determined by the actions taken when a grouping is recognized. The actions are the C code that appears inside braces. See Actions.

You must specify these actions in C, but Bison provides the means for passing semantic values between the rules. In each action, the pseudo-variable `\$\$` stands for the semantic value for the grouping that the rule is going to construct. Assigning a value to `\$\$` is the main job of most actions. The semantic values of the components of the rule are referred to as `\$1`, `\$2`, and so on.

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