What to submit and when:
Work in pairs
The goal of the lab is to get practice with context-free grammars, push-down automata, and the pumping lemma for context-free languages.
Please refer to the corresponding sections of the JFLAP tutorial, namely Entering grammars (just pressing "enter" on the right hand side enters an empty string), Brute Force Parser for constructing parse trees, and Constructing a push-down automaton. If Brute Force Parser doesn't work on your grammar, contsruct your parse tree manually using User Control Parser.
Your tasks are as follows:
<,
>, ==
, a ternary conditional operator ?:
, and parentheses.
The order of precedence is as follows: parentheses, the comparison operations,
the conditional operator and then 0, 1, true and false (all at the same level).
The conditional operator is defined as following:
e1? e2 : e3
evalautes e1, and if it is true then it evaluates and returns e2,
otherwise it evaluates and returns e3. For example:
0 < 1? 0 : 1
would be interpreted as
(0 < 1) ? 0 : 1
which becomes
true ? 0 : 1
after the condition is evaluated, which would in turn result in 0.
The comparison operators <, >, ==
are left-associative, i.e.
0 == 1 == false
should be interpreted as
(0 == 1) == false
which evaluates to
false == false
which is true.
The conditional is right-associative:
0 > 1 ? 0 : 0 == 0 ? 1 : 0
is interpreted as
(0 > 1) ? 0 : ((0 == 0) ? 1 : 0)
then evaluated as
false ? 0 : ((0 == 0) ? 1 : 0)
then as
false ? 0 : (true ? 1 : 0)
then as
false ? 0 : 1
which will return 1.
Test your grammar on all of the test cases above and two more cases that check for precedence, associativity, and parentheses. Submit jpg files for the parse trees.
Note that language designers don't always get the associativity right.
Important: your grammar must enforce correct precedence and associativity for all operations. Your write-up for this problem should briefly explain how this is done.
Use the tutorial for the pumping lemma. Play the "pumping lemma game" for the following examples. For each example state whether the language is context-free; justify it based on which side has a winning strategy in the pumping lemma game. Clearly describe the strategy.
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