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#### 2.1.2.3 Explanation of `expr`

The `exp`

grouping has several rules, one for each kind of expression.
The first rule handles the simplest expressions: those that are just numbers.
The second handles an addition-expression, which looks like two expressions
followed by a plus-sign. The third handles subtraction, and so on.

exp: NUM | exp exp '+' { $$ = $1 + $2; } | exp exp '-' { $$ = $1 - $2; } … ;

We have used ‘`|`’ to join all the rules for `exp`

, but we could
equally well have written them separately:

exp: NUM ; exp: exp exp '+' { $$ = $1 + $2; }; exp: exp exp '-' { $$ = $1 - $2; }; …

Most of the rules have actions that compute the value of the expression in
terms of the value of its parts. For example, in the rule for addition,
`$1`

refers to the first component `exp`

and `$2`

refers to
the second one. The third component, `'+'`

, has no meaningful
associated semantic value, but if it had one you could refer to it as
`$3`

. When `yyparse`

recognizes a sum expression using this
rule, the sum of the two subexpressions’ values is produced as the value of
the entire expression. See section Actions.

You don’t have to give an action for every rule. When a rule has no
action, Bison by default copies the value of `$1`

into `$$`

.
This is what happens in the first rule (the one that uses `NUM`

).

The formatting shown here is the recommended convention, but Bison does not require it. You can add or change white space as much as you wish. For example, this:

exp: NUM | exp exp '+' {$$ = $1 + $2; } | … ;

means the same thing as this:

exp: NUM | exp exp '+' { $$ = $1 + $2; } | … ;

The latter, however, is much more readable.

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