One simple grammar for describing expressions was discussed in class:
Goal = Expression .
Expression = Term | Expression "-" Term .
Term = Factor | Term "*" Factor .
Factor = "a" | "b" | "c" | "d" .
Show the parse tree corresponding to the string "a - b - c"
Another grammar is
Goal = Expression .
Expression = Term | Term "-" Expression .
Term = Factor | Factor "*" Term .
Factor = "a" | "b" | "c" | "d" .
Show the parse tree corresponding to the string "a - b - c" and discuss the differences between this grammar and the last.
Yet another grammar for describing expressions might be:
Goal = Expression .
Expression = Term | Expression "*" Term .
Term = Factor | Term "-" Factor .
Factor = "a" | "b" | "c" | "d" .
Show the parse tree corresponding to the string "a - b * c"
How does one find a grammar that will allow all four operators (+ - * and /) with the familiar precedence and associativity conventions, and will also allow for parentheses within expressions - so that one can derive strings like (a - b) * (c + d)?
What grammar would we need if we wished to allow for leading (unary) operators, as in expressions like "- a + ( -b + ( + c / d ))"