On 03/24/08 15:16, Eric Niebler wrote:
Larry Evans wrote:
sort of succinct formula. My last attempt was:
http://archives.free.net.ph/message/20080324.160640.f8aed314.en.html
I confess I don't understand your notation in that message.
The notation is supposed to be a language grammar similar to that shown in compiler texts, except it doesn't surround the grammar terminals with quotes. So, to make it closer to that, use: expr_type = 'terminal::type' //rule0 | (expr_type+)'::type' //rule1 ; and where the postfix + means 1 or more of the preceding. So, one possible instance of sentence satisfying this grammar is (tracing the derivations and subscripting different instances of grammar symbols with _i, where i is an positive integer, and showing the derivations steps with -(ruleX->, where ruleX is one of the comments labelling the grammar altenatives in the above equattion): expr_type -rule1-> (expr_type_1, expr_type_2, expr_type_3)'::type' -rule0-> ('terminal::type'_1 'terminal::type'_2 'terminal::type'_3)'::type' Now, the terminal symbol, 'terminal::type' is supposed to represent any proto::terminal<> grammar and the appending '::type' is supposed to represent the conversion of the proto::grammar to the corresponding expression. The (expr_type+) is supposed to represent any other proto "expression" grammar. The reason expr<Tag,expr_type+,Size> was not used was because that's just the concrete syntax version of expr_type+; hence, just detail. A concrete instance of this would be: shift_right<terminal<int>::type,terminal<char>::type>::type where the concrete symbols corresponding to the last step in the example abstract derivation above are: 'terminal::type'_1 == terminal<int>::type 'terminal:;type'_2 == terminal<char>::type 'terminal::type'_3 == //none because shift_right is binary ('terminal::type'_1 'terminal::type'_2)'::type' == shift_right<terminal<int>,terminal<char>::type>::type
I also don't understand what you're trying to get at with morphisms, a concept I don't grasp. Do you think you could try again to explain what you're trying to achieve?
Before I try that, I better make sure the above is clear enough. Could you let me know if it's not clear.