Consider the following grammar:
%token IF EXP ELSE XX
%%
stmts : stmts stmt ';'
| stmt ';'
;
stmt : IF '(' EXP ')' stmt ELSE stmt
| IF '(' EXP ')' stmt
| XX
;
%%
In the above grammars in this file
tokens that are all uppercase are terminals that
match the same string in lower case. For instance
in the above grammar: if ( exp ) xx else xx ; is
a legal statement.
Unfortunately the grammar has a problem when compiled in bison:
+ bison -v -t -d check.y check.y contains 1 shift/reduce conflict.
Checking the .output file shows:
State 11 contains 1 shift/reduce conflict.
Grammar
rule 1 stmts -> stmts stmt ';'
rule 2 stmts -> stmt ';'
rule 3 stmt -> IF '(' EXP ')' stmt ELSE stmt
rule 4 stmt -> IF '(' EXP ')' stmt
rule 5 stmt -> XX
state 11
stmt -> IF '(' EXP ')' stmt . ELSE stmt (rule 3)
stmt -> IF '(' EXP ')' stmt . (rule 4)
ELSE shift, and go to state 12
ELSE [reduce using rule 4 (stmt)]
$default reduce using rule 4 (stmt)
It is clear that a shift would move the ELSE using rule 3 but
where did the problem with the reduce come from? The problem is that
rule 3 also shows that a stmt stmt can be followed by
ELSE because the then-part is a stmt and can be followed by
ELSE. But rule 4 is a stmt therefore rule 4 can be
followed by an ELSE! So if an ELSE token is seen then
it should reduce AND it should shift it. Hence an shift/reduce error.
The fix is this we need to make sure there is no ambiguity in our grammar that would suggest that both parses that shift and reduce are viable. The classic ambiguous case is:
if ( exp ) if ( exp ) xx else xx ;does that mean (case 1) as indicated by the brackets:
if ( exp ) [ if ( exp ) xx else xx ];or does that mean (case 2):
if ( exp ) [ if ( exp ) xx ] else xx ;? The fix is to be sure that the else is either always with the nearest if (case 1) or farthest if (case 2). Classically the fix is to do case 1.
We enforce this by using a grammar like this:
%token IF EXP ELSE XX
%%
stmts : stmts stmt ';'
| stmt ';'
;
stmt : matched
| unmatched
;
matched : IF '(' EXP ')' matched ELSE matched
| XX
;
unmatched : IF '(' EXP ')' matched
| IF '(' EXP ')' unmatched
| IF '(' EXP ')' matched ELSE unmatched
;
%%
Statements that match matched are like:
if ( exp )
xx
else
xx
if ( exp )
xx
else
if ( exp ) xx else xx
if ( exp )
if ( exp )
xx
else
if ( exp ) xx else xx
else
if ( exp ) xx else xx
Statements that match unmatched are like:
if ( exp ) xx if ( exp ) xx else if ( exp ) xx if ( exp ) if ( exp ) xx else xx else if ( exp ) xxMost importantly is what is left out of the grammar above! There are 4 posssible combinations of if-else:
IF '(' EXP ')' matched ELSE matched
IF '(' EXP ')' matched ELSE unmatched
IF '(' EXP ')' unmatched ELSE matched
IF '(' EXP ')' unmatched ELSE unmatched
However, the last two do not occur in the grammar and are not allowed.
It is this that prohibits the occurrence of an else that
is NOT matched to the nearest if! That is the grammar
simply does not allow an unmatched if to come between an else and
its if. This removes the ambiguity of two parses and leaves
only the one we want.
Now that we understand what is going on, how can we add a while statement? While statements are of the form:
WHILE '(' EXP ')' stmt
but stmt can be either matched or unmatched. Consider
the expression:
if ( exp ) while ( exp ) if ( exp ) xx else xxAs before we have two cases (parsings) indicated by the brackets:
if ( exp ) while ( exp ) [ if ( exp ) xx else xx ] if ( exp ) [ while ( exp ) if ( exp ) xx ] else xxWe need to write our grammar to preclude the second of these two parses. That is a while with an unmatched if must not occur between an if and its else. This removes the ambiguity and allows the grammar to parse only the first meaning (the one we want).
This suggests that there are two kinds of while. A while that has an unmatched after it and a while that has a matched after it. The while with the unmatched must not be allowed to come before an else in the same way that the if without the else must not.
I have all but told you the answer but most importantly the reasoning behind it. I must leave something for you to figure out so I will stop here except to point out that the grammar I gave above for solving the dangling if could be slightly shorter by replacing
unmatched : IF '(' EXP ')' matched
| IF '(' EXP ')' unmatched
with
unmatched : IF '(' EXP ')' stmt
Do not hesitate to send me email questions with the timestamp of you submit or to drop by and ask questions. Appointments (send email) work best since I have lots of meetings.
Good luck,
| Robert Heckendorn | Up One Level | Last updated: |