Slide 8.7: Reduction rules for integer arithmetic expressions (cont.)

Slide 8.6: Reduction rules for integer arithmetic expressions (cont.)
Slide 8.8: Reduction rules for integer arithmetic expressions (cont.)
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Reduction Rules for Integer Expressions (Cont.)

         E ⇒ E₁         
 V '*' E ⇒ V '*' E₁

             E ⇒ E₁             
 '(' E ')' ⇒ '(' E₁ ')'

```
   E ⇒ E₁, E₁ ⇒ E₂   
 E ⇒ E₂
```

The following comments are about the above reduction rules:

Rules 1 through 6 are all axioms.

Rules 1 and 2 express the reduction of digits and numbers to values: '0' ⇒ 0 states that the character '0' (a syntactic entity) reduces to the value 0 (a semantic entity).

Rules 3, 4, and 5 say that whenever an expression consists of two values and an operator symbol, the expression can be reduced to a value by applying the operation whose symbol appears in the expression.

Rule 6 says that if an expression consists of a pair of parentheses surrounding a value, then the parentheses can be dropped.

Rules 7, 8, and 9 express the fact that, in an expression that consists of an operation applied to other expressions, the left subexpression may be reduced by itself and that reduction substituted into the larger expression.

Rules 10 through 12 express the fact that, once a value is obtained for the left subexpression, the right subexpression may be reduced.

Rule 13 says that we can first reduce the inside of an expression consisting of parentheses surrounding another expression.

Finally, rule 14 expresses the general fact that reductions can be performed stepwise.