51 lines
2.5 KiB
Markdown
51 lines
2.5 KiB
Markdown
|
# Left-recursive rules
|
||
|
|
|
||
|
|
The most natural expression of a some common language constructs is left recursive. For example C declarators and arithmetic expressions. Unfortunately, left recursive specifications of arithmetic expressions are typically ambiguous but much easier to write out than the multiple levels required in a typical top-down grammar. Here is a sample ANTLR 4 grammar with a left recursive expression rule:
|
||
|
|
|
||
|
|
```
|
||
|
|
stat: expr '=' expr ';' // e.g., x=y; or x=f(x);
|
||
|
|
| expr ';' // e.g., f(x); or f(g(x));
|
||
|
|
;
|
||
|
|
expr: expr '*' expr
|
||
|
|
| expr '+' expr
|
||
|
|
| expr '(' expr ')' // f(x)
|
||
|
|
| id
|
||
|
|
;
|
||
|
|
```
|
||
|
|
|
||
|
|
In straight context free grammars, such a rule is ambiguous because `1+2*3` it can interpret either operator as occurring first, but ANTLR rewrites that to be non-left recursive and unambiguous using semantic predicates:
|
||
|
|
|
||
|
|
```
|
||
|
|
expr[int pr] : id
|
||
|
|
( {4 >= $pr}? '*' expr[5]
|
||
|
|
| {3 >= $pr}? '+' expr[4]
|
||
|
|
| {2 >= $pr}? '(' expr[0] ')'
|
||
|
|
)*
|
||
|
|
;
|
||
|
|
```
|
||
|
|
|
||
|
|
The predicates resolve ambiguities by comparing the precedence of the current operator against the precedence of the previous operator. An expansion of expr[pr] can match only those subexpressions whose precedence meets or exceeds pr.
|
||
|
|
|
||
|
|
## Formal rules
|
||
|
|
|
||
|
|
The formal 4.0, 4.1 ANTLR left-recursion elimination rules were changed (simplified) for 4.2 and are laid out in the [ALL(*) tech report](http://www.antlr.org/papers/allstar-techreport.pdf):
|
||
|
|
|
||
|
|
* Binary expressions are expressions which contain a recursive invocation of the rule as the first and last element of the alternative.
|
||
|
|
* Suffix expressions contain a recursive invocation of the rule as the first element of the alternative, but not as the last element.
|
||
|
|
* Prefix expressions contain a recursive invocation of the rule as the last element of the alternative, but not as the first element.
|
||
|
|
|
||
|
|
There is no such thing as a "ternary" expression--they are just binary expressions in disguise.
|
||
|
|
|
||
|
|
The right associativity specifiers used to be on the individual tokens but it's done on alternative basis anyway so the option is now on the individual alternative; e.g.,
|
||
|
|
|
||
|
|
```
|
||
|
|
e : e '*' e
|
||
|
|
| e '+' e
|
||
|
|
|<assoc=right> e '?' e ':' e
|
||
|
|
|<assoc=right> e '=' e
|
||
|
|
| INT
|
||
|
|
;
|
||
|
|
```
|
||
|
|
|
||
|
|
If your 4.0 or 4.1 grammar uses a right-associative ternary operator, you will need to update your grammar to include `<assoc=right>` on the alternative operator. To smooth the transition, `<assoc=right>` is still allowed on token references but it is ignored.
|