Question

Please help me with the coding for LL(1)!!

The given grammar was:

P → PL | L
L → N; | M; | C
N → print E
M → print "W"
W → TW | ε
C → if E {P} | if E {P} else {P}
E → (EOE) | V (note: this has a variable O)
O → + | - | * V → 0 | 1 | 2 | 3 (note: this has a terminal 0 (zero))
T → a | b | c | d

And the grammar transformed in LL(1) is:

1. T all clad V 0 1 2 3 E CEOE) C' else (P) E 8, N' print M 10, L N IC 12.

5.1 Parsing strings with an LL(1) table driven parser

Implement a program which parses strings using an LL(1) table driven parser using the table you determined for G′ in the previous exercise.

You may use Python, Java, C, C++, or Haskell. If you’d like to use a different language then please check with us first.

• Input: The first command line argument is the filename of a file containing the string of characters to test.

• Output: 1. Print a trace of the execution, showing the steps followed by the program as it performs the left-most derivation. This should look similar to parsing the string through a PDA. An example of this is given in the appendices.

2. After parsing the whole input file, print ACCEPTED or REJECTED, depending on whether or not the string could be derived by the grammar.

3. If there is a symbol in the input string which is not a terminal from the grammar, the program should output ERROR_INVALID_SYMBOL (This could be during or before trying to parse the input.) Note: all whitespace in the input file should be ignored (line breaks, spaces, etc.) The output will be easier to read if you remove the whitespace before starting the parse. Examples of the program output syntax are provided in the appendices.

5.2 Evaluating programs written in G′

If a second command line argument “eval” is given, then instead of printing the trace of the parse, your program should:

1. Build a parse tree as it performs the leftmost derivation

2. Evaluate that parse tree. The semantics (meaning) which we are applying to our rules are as follows:

• V variables derive integers • W variables derive strings • E expressions are evaluated like normal integer arithmetic

• print E statements output (to screen) the result of evaluating the expression E. (i.e. print (1+1) outputs 2)

• print "W" statements output the string derived from W (i.e. print "abba" outputs abba)

• if statements evaluate the contents of their if block if and only if the condition evaluated to a non-zero value, otherwise the else block is evaluated instead (if there is one). If the input could not be parsed then output REJECTED instead. Some examples of programs and their expected output are provided in the appendices.

Answer 1

Propositional logic, also known as sentential logic and statement logic, is the branch of logic that studies ways of joining and/or modifying entire propositions, statements or sentences to form more complicated propositions, statements or sentences, as well as the logical relationships and properties that are derived from these methods of combining or altering statements. In propositional logic, the simplest statements are considered as indivisible units, and hence, propositional logic does not study those logical properties and relations that depend upon parts of statements that are not themselves statements on their own, such as the subject and predicate of a statement. The most thoroughly researched branch of propositional logic is classical truth-functional propositional logic, which studies logical operators and connectives that are used to produce complex statements whose truth-value depends entirely on the truth-values of the simpler statements making them up, and in which it is assumed that every statement is either true or false and not both. However, there are other forms of propositional logic in which other truth-values are considered, or in which there is consideration of connectives that are used to produce statements whose truth-values depend not simply on the truth-values of the parts, but additional things such as their necessity, possibility or relatedness to one another.