Using the grammar for real-number constants discussed in class, write a set of rewrite rules for signed real-number constants that allow an optional sign at the front of the constants. Use signed-real-const as the new start symbol. You can reuse as much or as little of the real-number constant grammar rules as you deem appropriate. Examples of valid signed real-number constants are:

-3.56, +17.E09, 4.95

Using the following rewrite rules for Boolean expressions, give a derivation for the Boolean expression (NOT((F AND T)) OR F). Also draw a derivation tree corresponding to the derivation.

bool-exp → T |
→ F |
→ NOT ( bool-exp ) |
→ ( bool-exp AND bool-exp ) |
→ ( bool-exp OR bool-exp )
Using the following rewrite rules for Boolean expressions, find two different derivation trees for the Boolean expression NOT(T OR T AND F).

bool-exp → T |
→ F |
→ NOT ( bool-exp ) |
→ bool-exp AND bool-exp |
→ bool-exp OR bool-exp
Using the following rewrite rules for arithmetic expressions, draw a derivation tree for the expression 5*3+1+4.

expr → expr add-op term | term
term → term mult-op factor | factor
factor → ( expr ) | digit-seq
add-op → + | -
mult-op → * | DIV | MOD
digit-seq → digit digit-seq | digit
digit → 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9
Using the following rewrite rules for arithmetic expressions, draw a derivation tree for the expression 5*3+1+4.

expr → term { add-op term }
term → factor { mult-op factor }
factor → ( expr ) | digit-seq
add-op → + | -
mult-op → * | DIV | MOD
digit-seq → digit digit-seq | digit
digit → 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9
Note: A pair of new special symbols ('{' and '}') is used in the rewrite rules above. The meaning of {...} is that the string of nonterminal and terminal symbols appearing between { and } can be repeated 0 or more times. For instance, the first rewrite rule:

expr → term { add-op term }
is equivalent to the following (infinite) set of rewrite rules:

expr

→ term |

→ term add-op term |

→ term add-op term add-op term |

→ term add-op term add-op term add-op term |

→ ...