b) One. That a grammar is ambiguous means that for some input, more than one parse tree can be constructed. Not for all input!
c) The parse tree:
d) The parse tree decorated with the values of the result attribute:
e)
| Production | Semantic Rule |
|---|---|
| expression -> set-literal | expression.result = set-literal.result |
| expression1 -> expression2 union expression3 | expression1.result = union(expression2.result, expression3.result) |
| set-literal -> { number-list } | set-literal.result = number-list.result |
| number-list1 -> number number-list2 | number-list1.result = prepend(number.value, number-list2.result) |
| number-list -> empty | number-list = { } |
b) ...
c)
| Production | Semantic Rule |
|---|---|
| expression -> set-literal | expression.type = set |
| expression1 -> expression2 union expression3 |
if (expression2.type == set && expression3.type == set)
expression1.type = set else expression1.type = error |
| set-literal -> { number-list } | set-literal.type = set |
| number-list1 -> number number-list2 | number-list1.type = set |
| number-list -> empty | number-list.type = set |
| expression -> number | expression.type = int |
| expression1 -> expression2 in expression3 |
if (expression2.type == int && expression3.type == set)
expression1.type = bool else expression1.type = error |
Some of the semantic rules contain error checking, but some don't need it, because the grammar doesn't allow for an expression with the wrong type. For example, in the first production, it is impossible to write a syntactically correct set-literal with a data type that is not set.
d) ...
e) Yes.
f) No.