CS 405/505 ASSIGNMENT #5
Due Thursday, February 24, 2005
1. Write a LISP function (derive P S L), where Pis a list of context-free grammar production
rules of the form (A X1 X2 ... Xn) corresponding to A →X1X2...Xn,Sis the start symbol
of the grammar, and Lis a list of integers, which returns the parse tree resulting from applying
the productions in Pin the order indicated by L. The first production rule to be applied must
be a production of the start symbol or a null tree is returned. The process terminates if the
integer indicated does not match any production rule which can be applied, e.g. is either
not a production rule or there is no corresponding nonterminal. If there are more than one
nonterminal to apply a production rule to, the leftmost one is always selected. The parse
tree will be of the form (A X1 X2 ... Xn) for A →X1X2...Xn, with each Xi replaced by
its corresponding parse tree. Test your function on the following:
(derive ’((E E + T) (E T) (T T * F) (T F) (F \(E\)) (F id)) ’E
’(1 2 4 6 3 4 6 6))
⇒(E (E (T (F id))) + (T (T (F id)) * (F id)))
(derive ’((E E + T) (E T) (T T * F) (T F) (F \(E\)) (F id)) ’E
’(1 3 6 4 6 2 4 6))
⇒(E (E (T (F id))) + (T (T (F id)) * (F id)))
(derive ’((E E + E) (E E * E) (E \(E\)) (E id)) ’E ’(1 4 2 4 4))
⇒(E (E id) + (E (E id) * (E id)))
2. Write a LISP function (parsetrees P S n), where Pand Sare as in the derive function
and nis an integer, which returns a list of all parse trees reached after nor less production
rules have been applied. If n≤0, a null list is returned. One way to design this function is to
produce a set of lists (0 0 ... 0) (n 0’s) ... (mm... m)(nm’s) in order and call derive
for each one, making a list of the non-null parse trees returned. Note that this approach has
complexity mn, which is exponential and will not be practical for large values of n, although
it should not cause problems for the test cases below. You are welcome to develop a more
efficient algorithm which does not need to try all of the mncombinations. Test your function
on the following:
(parsetrees ’((E E + T) (E T) (T T * F) (T F) (F \( E \)) (F id)) ’E 8)
(parsetrees ’((E E + E) (E E * E) (E \( E \)) (E id)) ’E 8)
3. Consider the Core program below:
input x; input y;
u := 1; v := 0;
while (v < y) loop
u := u * x;
v := v + 1;
end loop;
output u;
Assuming that the input file contains the integers 10 and 2 (i.e., the list <10, 2>), use the
denotational semantics of Core to trace the interpretation of the program.
