Re: Why are ambiguous grammars usually a bad idea? Why are languages usually defined and implemented with ambiguous grammars?

You already have lots of relevant commentary on your answer.


However, I want to offer some counterpoint.


The 1973 paper by Aho, Johnson, and Ullman: Deterministic Parsing of
Ambiguous Grammars,
gives the background for how this is handled in yacc.


https://www.researchgate.net/publication/234791287_Deterministic_parsing_of_ambiguous_grammars


Thus, the use of the various directives is a long-known solution to
the issue. However, LR conflicts frighten people. Their resolution
hides the fact that the grammar is ambiguous and at least two parses
are possible. But, with practice, one can get good at using them
judiciously and knowing when they are simply expressing the desired
intent or hiding a potential source of confusion.


More recently, GLR parsing has deferred the resolution and builds a
parse forest when the grammar is truly ambiguous and not the result of
the limitations of the LR parsing methodology. When that happens, one
can use semantics to determine which parse was correct or declare a
relevant error.


By the way, an LR conflict doesn't guarantee that the grammar is
actually ambiguous, just that resolving whether it is or not is beyond
the capacity of the LR algorithm.


So, while it is good to know when your grammar is ambiguous (or even
just potentially ambiguous) is useful in knowing whether your grammar
describes the language you think it describes, it is not always the
worst thing.


Ambiguous grammars can have valuable properties. As you noted, writing
an unambiguous grammar can be quite complicated (and in some cases not
even possible), and the comparable ambiguous grammar can be quite
concise, simple, and easy to read. And, putting the disambiguation
outside the grammar can be a more maintainable solution.


This is particularly, true if you want a language with user defined
operators or ones where the user might want to adjust the precedence
or associativity of the existing operators. Using numbers to indicate
precedence is a well-known technique. It maps well onto things people
understand. And the ability to compare the precedence of two operators
based upon an associated number is easy to implement (while strictly
outside the capacity of most parser generators).


Kind regards,
Chris


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