Compilers

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Compilers

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Machine Code
Program
Add v,v,0 cmp v,5 jmplt ELSE THEN add x,
12,v ELSE WHILE cmp x,3 ...
v 5 if (vgt5) x 12 v while (x !3)
x x - 3 v 10 ......
Compiler
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Compiler
Lexical analyzer
parser
input
output
machine code
program
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A parser knows the grammar of the programming
language
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Parser
PROGRAM STMT_LIST STMT_LIST STMT
STMT_LIST STMT STMT EXPR IF_STMT
WHILE_STMT
STMT_LIST EXPR EXPR EXPR EXPR - EXPR
ID IF_STMT if (EXPR) then STMT
if (EXPR) then STMT else STMT WHILE_STMT
while (EXPR) do STMT
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The parser finds the derivation of a particular
input
derivation
Parser
input
E gt E E gt E E E gt 10 EE gt
10 2 E gt 10 2 5
E -gt E E E E INT
10 2 5
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derivation tree
derivation
E
E gt E E gt E E E gt 10 EE gt
10 2 E gt 10 2 5

E
E
10
E
E

2
5
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derivation tree
E
machine code

E
E
mult a, 2, 5 add b, 10, a
10
E
E

2
5
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Parsing

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Parser
input string
derivation
grammar
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Example
Parser
derivation
input
?
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Exhaustive Search
Phase 1
Find derivation of
All possible derivations of length 1
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(No Transcript)
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Phase 2
Phase 1
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Phase 2
Phase 3
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Final result of exhaustive search
(top-down parsing)
Parser
input
derivation
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Time complexity of exhaustive search
Suppose there are no productions of the form
Number of phases for string
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For grammar with rules
Time for phase 1
possible derivations
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Time for phase 2
possible derivations
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Time for phase
possible derivations
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Total time needed for string
phase 1
phase 2w
phase 2
Extremely bad!!!
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There exist faster algorithms for specialized
grammars
S-grammar
symbol
string of variables
appears once
Pair
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S-grammar example
Each string has a unique derivation
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For S-grammars
In the exhaustive search parsing there is only
one choice in each phase
Time for a phase
Total time for parsing string
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For general context-free grammars
There exists a parsing algorithm that parses a
string in time
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Simplifications of Context-Free Grammars

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A Substitution Rule
Equivalent grammar
Substitute B
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In general
Substitute B
equivalent grammar
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Useless Productions
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Another grammar
Not reachable from S
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In general
If
Then variable is useful
Otherwise, variable is useless
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A production is useful if all its
variables are useful
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Removing Useless Productions
Example Grammar
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First
find all variables that produce strings with only
terminals
Round 1
Round 2
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Keep only the variables that produce terminal
symbols
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Second
Find all variables reachable from
Dependency Graph
not reachable
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Keep only the variables reachable from S
Final Grammar
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Nullable Variables
Nullable Variable
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Removing Nullable Variables
Example Grammar
Nullable variable
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Final Grammar
Substitute
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Unit-Productions
Unit Production
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Removing Unit Productions
Observation
Is removed immediately
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Example Grammar
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Substitute
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Remove
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Substitute
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Remove repeated productions
Final grammar
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Removing All

• Step 1 Remove Nullable Variables
• Step 2 Remove Unit-Productions
• Step 3 Remove Useless Variables