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We now modify tt(rpn) to handle infix operators instead of postfix. Infix
notation involves the concept of operator precedence and the need for
parentheses nested to arbitrary depth. Here is the b() grammar
specification for tt(calc), an infix desk-top calculator:
verbinclude(calc/parser/grammar)
The functions tt(lex()), tt(error()) and tt(main()) can be the same as
used with tt(rpn).
There are two important new features shown in this code.
In the second section (B() directives), tt(%left) declares token types
and says they are left-associative operators. The directives tt(%left) and
tt(%right) (right associativity) take the place of tt(%token) which is used to
declare a token type name without associativity. (These tokens are
single-character literals, which ordinarily don't need to be declared. We
declare them here to specify the associativity.)
Operator precedence is determined by the line ordering of the directives;
the higher the line number of the directive (lower on the page or screen),
the higher the precedence. Hence, exponentiation has the highest precedence,
unary minus (tt(NEG)) is next, followed by `tt(*)' and `tt(/)', and so on. See
section ref(PRECEDENCE).
The other important new feature is the tt(%prec) in the grammar section for
the unary minus operator. The tt(%prec) simply instructs b() that the
rule `tt(| '-' exp)' has the same precedence as tt(NEG) (in this case the
next-to-highest). 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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