CMPS 260 Spring 2024
HW #6: LL(1) Parsing
Due: May 1
1.
Consider the following context-free grammar (which produces a
nonsense language). As you can infer from its description,
its start symbol is S, its terminal alphabet Σ is
{a,b,c,d,e}, and its nonterminal set V is {S, H, K, M}.
| S | ⟶ | HcK | e |
(1) (2) |
| H | ⟶ | MHc | K |
(3) (4) |
| K | ⟶ | dSe | λ |
(5) (6) |
| M | ⟶ | b | abc |
(7) (8) |
Nonterminal
Symbol |
FIRST( ) |
FOLLOW( ) |
|---|
| S |
|
|
| H |
|
|
| K |
|
|
| M |
|
|
(a)
For each nonterminal A, compute both FIRST(A) and FOLLOW(A).
Convey that information by filling in the table to the right.
Recall that
FIRST'(A) =
{ t ∈ Σ | A ⟹+ tα for some α }
FOLLOW(A) = { t ∈ Σ ∪ {$} |
S$ ⟹+ αAtβ
for some α, β }
Now, if A is nullable (i.e., A ⟹+ λ), then
FIRST(A) = FIRST'(A) ∪ {λ}. Otherwise,
FIRST(A) = FIRST'(A).
(b)
Using the information provided by FIRST( ) and FOLLOW( ), fill in the
table below to define a one-symbol-lookahead stack machine parser
for the grammar.
Each table entry should identify which production (if any) to apply
based upon the next input symbol
(i.e., the first symbol of the input string that has yet to be consumed)
and the nonterminal symbol on top of the stack.
(If a terminal symbol is on top of the stack, then of course it
gets popped when it is matched with the next input symbol.)
top of
stack |
next input symbol |
| |
a |
b |
c |
d |
e |
$ |
| S |
|
|
|
|
|
|
| H |
|
|
|
|
|
|
| K |
|
|
|
|
|
|
| M |
|
|
|
|
|
|
(c)
Implement a Recursive Descent parser for the grammar and submit it
to the designated Brightspace dropbox.
As a model, you can use the Java class
RecDescentParser,
which provides a recursive descent parser for the
LL(1) grammar
discussed in a course web page.