Re: precedences vs. hierarchy

On 2016-06-06, Dmitry A. Kazakov <mailbox@dmitry-kazakov.de> wrote:
> On 06/06/2016 09:08, Andreas Schramm wrote:
>
>> for specifying the syntax of operator expressions
>> with multiple levels of precedences,
>> there are essentially two approaches:
>> (i) by precedence and associativity declarations, and
>> (ii) by a hierarchy of non-terminals.
>
> (iii) By only precedence, which I prefer. Associativity is not needed if
> operator precedence is split into the left and right ones. That allows
> to express any associativity, unary operators included.


What?


You need the concept of associativity to tell whether
A + B + C is (A + B) + C or A + (B + C).


The + here is the same operator and so it precedence is equal to itself.
Moreover, it may be on the same precedence level as other operators such
as the binary -.


In table shift-reduce parsers (Yacc, and such), associativity rules
resolve conflicts.


When the generated parser has seen the input A + B, and the lookahead
symbol is +, it needs to know whether to shift the + (right
associativity), or to reduce the A + B (left associativity).


Unary and postfix operators do not require associativity because
they are not ambiguous. op op op expr where op is a unary op,
this can only mean op ( op ( op expr )), by the grammar alone.


Ambiguity arises if there are both postfix and prefix operators
hanging on the same expression; that is resolved by precedence.
[If you can specify the left and right precedence for an operator
separately, that gives you the associativity. -John]

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