Give a formal description of the grammar PY. You may assume that the given rules are in a set called RULES. Give parse trees for the following strings in the language of PY: a. if x == 9: print ((a,b,c)) else: print (0) b. a = 1 \n f = lambda (x) : x + a \n f (5)

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Here's a CFG, called PY, representing a small Python-like language:
(STMTS)→(STMT) (STMTS) | (STMT)
(STMT)→(ID) = (EXPR) | if (EXPR): (STMT) else: (STMT)
| print ((EXPR))| (EXPR)
(EXPRS)→(EXPR),(EXPRS)|(EXPR) | ɛ
(EXPR)→(ID)| (NUM)|(EXPR) == (EXPR) | (EXPR) + (EXPR)
| (TUP) | lambda ((IDS)) : (EXPR)| (ID) ((EXPRS) )
(TUP)→| ((EXPRS) )
(NUM)→0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9
(IDS)→(ID), (IDS)| (ID) | ɛ
(ID)→a | b | c | ….. | x | y | z
(Yes, real-world languages are much more complicated than textbook examples.)
The variables of the CFG are all the names enclosed in angle brackets, e.g., (EXPR) is a
variable name. All other symbols used in the rules are terminals.
Note, however, that unlike Python, this grammar ignores whitespace (so your answers to
this problem do not need to explicitly deal with whitespace).
Transcribed Image Text:Here's a CFG, called PY, representing a small Python-like language: (STMTS)→(STMT) (STMTS) | (STMT) (STMT)→(ID) = (EXPR) | if (EXPR): (STMT) else: (STMT) | print ((EXPR))| (EXPR) (EXPRS)→(EXPR),(EXPRS)|(EXPR) | ɛ (EXPR)→(ID)| (NUM)|(EXPR) == (EXPR) | (EXPR) + (EXPR) | (TUP) | lambda ((IDS)) : (EXPR)| (ID) ((EXPRS) ) (TUP)→| ((EXPRS) ) (NUM)→0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 (IDS)→(ID), (IDS)| (ID) | ɛ (ID)→a | b | c | ….. | x | y | z (Yes, real-world languages are much more complicated than textbook examples.) The variables of the CFG are all the names enclosed in angle brackets, e.g., (EXPR) is a variable name. All other symbols used in the rules are terminals. Note, however, that unlike Python, this grammar ignores whitespace (so your answers to this problem do not need to explicitly deal with whitespace).
Give a formal description of the grammar PY. You may assume that the given rules
are in a set called RULES.
Give parse trees for the following strings in the language of PY:
a. if x == 9: print ((a,b,c)) else: print (0)
b. a = 1 \n f = lambda (x) : x + a \n f (5)
Transcribed Image Text:Give a formal description of the grammar PY. You may assume that the given rules are in a set called RULES. Give parse trees for the following strings in the language of PY: a. if x == 9: print ((a,b,c)) else: print (0) b. a = 1 \n f = lambda (x) : x + a \n f (5)
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