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We now modify tt(rpn) to handle infix operators instead of postfix. Infix
notation requires us to define operator precedence and to extend the grammar
with nested expressions. Here is b()'s grammar specification for tt(calc), an
infix calculator:
verbinclude(calc/parser/grammar)
The functions tt(lex), tt(error) and tt(main) are identical to the ones
used with tt(rpn).
This example illustrates several important new features:
itemization(
it() In the first section (b() directives), tt(%left) declares token types
stating that the mentioned operators are left-associative. The directives
tt(%left) and tt(%right) (right associativity) are used instead of tt(%token),
which is merely used to declare a token identifier. The tokens mentioned with
tt(%left) and tt(%right) are single-character tokens, which ordinarily don't
need to be declared. We declare them here to specify their priority and
associativity.
it() Operator precedence is determined by the ordering of the directives;
the earlier tt(%left) and tt(%right) are specified, the lower the priority of
the operators that are following these keywords. So addition/subtraction have
the lowest precedence, multiplication and division are next, then unary minus
(tt(NEG)), and exponentiation has the highest precedence. See section
ref(PRECEDENCE).
it() Another important new feature is the tt(%prec) directive encountered
in the grammar section at the definition of the unary minus operator
production rule. The tt(%prec) directive indicates that the minus operator in
the production rule `tt('-' exp)' has tt(NEG's), rather than the minus
(tt('-')) operator's precedence. See section ref(CONDEP).
)
Here is a sample run of tt(calc):
verb(
% calc
4 + 4.5 - (34/(8*3+-3))
6.88095
-56 + 2
-54
3 ^ 2
9
)
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