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Compiler Designs and Constructions. Chapter 6: Top-Down Parser Objectives: Types of Parsers Backtracking Vs. Non-backtracking PDA Dr. Mohsen Chitsaz. Definition :. Alphabet: Set of Char (token) Language : Set of Token Sentence : a group of token
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Compiler Designs and Constructions Chapter 6: Top-Down Parser Objectives: Types of Parsers Backtracking Vs. Non-backtracking PDA Dr. Mohsen Chitsaz Chapter 6: Top-Down Parser
Definition: • Alphabet: Set of Char (token) • Language: Set of Token • Sentence: a group of token • Grammar: a set of (productions) that control the order of the occurrence of words • Syntax: a set of rules • Parser: software to check the syntax • Parsing: Process of breaking down the lexemes Chapter 6: Top-Down Parser
Types of Parser • Universal Parsing Method example: Cocke-Younger-Kasami Algorithm • Can parse any grammar • too inefficient to use in compiler production • Top-Down Parsing • Left most derivation • Bottom-up Parsing • Right most derivation Chapter 6: Top-Down Parser
Top-Down Parsing Non-backtracking Vs. Backtracking Large Plant Green Plant • Recursive Descent Parsing (Predictive Parser) • We execute a set of recursive procedures to process the input • There is one procedure associated with each non-terminal of a grammar Chapter 6: Top-Down Parser
Example • <type> <simple> • <type> ^id • <type> array [<simple>] of <type> <simple> integer • <simple> char • <simple> num .. num Chapter 6: Top-Down Parser
Procedure Match (T:token); Begin If LookaHead==T then LookaHead==NextToken Else Error(); End; Chapter 6: Top-Down Parser
Procedure Type( ); Begin If LookaHead in {integer, char, num} then Simple(); Else If LookaHead == ‘^’ then Begin Match (‘^’); Match (id); End Else If LookaHead == array then Chapter 6: Top-Down Parser
Begin Match (array); Match (‘[‘); Simple(); Match (‘]’); Match (of); Type(); End Else Error(); End; Chapter 6: Top-Down Parser
Procedure Simple(); Begin If LookaHead == integer then Match (integer) Else If LookaHead == char then Match (char) Else If LookaHead == num then Begin Match (num); Match (‘..’); Match (num); End Else Error(); End; Chapter 6: Top-Down Parser
Example • <type> <simple> • <type> ^id • <type> array [<simple>] of <type> <simple> integer • <simple> char • <simple> num .. num Chapter 6: Top-Down Parser
Example • Which production should we use? integer • <type> ^id <type> <simple> <simple> integer <simple> char Chapter 6: Top-Down Parser
Example • First (simple) = {integer, char, num} First (^id) = {^} First (array [<simple>] of type = {array}) First (type) = {^, array, integer, char, num} Chapter 6: Top-Down Parser
Definition: • A ab • First (A) = a • A • A • First of & must be disjoint Chapter 6: Top-Down Parser
Push Down Automata(Non-recursive predictive Parsing) Chapter 6: Top-Down Parser
Push Down Automata(Non-recursive predictive Parsing) • PDA = {Q, , H,, q0, Z, F} • Q = finite set of States • =set of input alphabet • H = set of stack symbols • = transition function (q, a, z) • q0 = starting state • Z = starting stack • F = final states Chapter 6: Top-Down Parser
Operation on • state operation change() stay() • stack operation push() pop() replace() none() • input operation • advance() • retain() Chapter 6: Top-Down Parser
Example: INPUT • = { (, ), -| } • H = {A, $} • q0 = {S} • Z = {$} S T A R T Chapter 6: Top-Down Parser
If input is (())-| • StackInput $ (())-| $A ())-| $AA ))-| $A )-| $ -| Chapter 6: Top-Down Parser
Derivation Tree • S (S) | Chapter 6: Top-Down Parser
LL(1) Grammar (push down machine) Scan from Left (L), Leftmost derivation (L), Look a head 1 Token Chapter 6: Top-Down Parser
Definition: • A production is called NULL if the RHS of that production is Ø A • A production is call NULLABLE if the RHS can be reduced to Ø • B A • A Chapter 6: Top-Down Parser
Example of LL(1) Grammar: 1- S AbB-| First(AbB-|) ={a,e,g, } 2- S d First(d) = {d} 3- A C Ab First(C Ab) = {a,e} 4- A B First(B) = {g, } 5- B gSd First(gSd) = {g} 6- B First (Ø) = {} 7- C a First (a) = {a} 8- C ed First (ed) = {e} Chapter 6: Top-Down Parser
First () = {a| =>*a} • Set of terminal symbols that occur at the beginning of string derived from Chapter 6: Top-Down Parser
Follow ()= Set of input symbols that can immediately follow Follow (A) = {b} Follow (B) = {-|, b, d} 14 • S --->AbB --->BbB 1 5 1 • S --->AbB --->AbgSd --->AbgAbBd Chapter 6: Top-Down Parser
SELECT (PREDICT): • SELECT (A->) = {First () If = Ø; First () U Follow (A)} • SELECT (1) = {a,e,g} U Follow(A)={a, e, g ,b} • SELECT (2) = {d} • SELECT (3) = {a,e} • SELECT (4) = First(4) U Follow (A) = {g,b} • SELECT (5) = {g} • SELECT (6) = First(6) U Follow (B) = {-|,b,d} • SELECT (7)={a} • SELECT (8) = {e} Chapter 6: Top-Down Parser
Is this grammar LL(1)? • S SELECT (1) SELECT (2) ={a,e,g,b} {d}= Ø • A SELECT (3) SELECT (4) ={a,e} {g,b}= Ø • B SELECT (5) SELECT (6) = {g} {-|,b,d}= Ø • C SELECT (7) SELECT (8) = {a} {e}= Ø • Def: Grammar is LL(1), IIF production with the same LHS have disjoint prediction set. Chapter 6: Top-Down Parser
Creating the Table: • Stack symbols=rows • Input symbols=columns • A b For row A, column b =REPLACE(r), ADVANCE • A For row A, column(selection set) =REPLACE (r), RETAIN • Ab For row A, column b =POP, ADVANCE Chapter 6: Top-Down Parser
Creating the Table: • Row b, column b = POP, ADVANCE • Row Δ, column -|=ACCEPT • All other are ERROR Chapter 6: Top-Down Parser
Parsed Table Chapter 6: Top-Down Parser
1- Replace (Δ B b A), Retain 2- Pop, Advance 3- Replace (bAC), Retain 4- Replace (B), Retain 5- Replace (dS), Advance 6- Pop, Retain 7- Pop, Advance 8- Replace(d), Advance Chapter 6: Top-Down Parser
Input: b g d d -| Chapter 6: Top-Down Parser
Parse Tree Chapter 6: Top-Down Parser
Recovery in a Top-Down Parser • Advantage of TDP is efficient error recovery. • Error: If Top of stack (token) is not the same as Look a Head (token) • Recovery: • Pop stack until Top: Synchronization Token (ST) ST: is a token that can end blocks of codes Read input symbol until current LookaHead symbol matches the symbol at the top of the stack or reaches the end of input • If not end of input you are recovered Chapter 6: Top-Down Parser
LL(1) Grammars & Parser: • facts: • CFG • Leftmost Parser • Unambiguous • O(n) • Can be used for automatically generated parser Chapter 6: Top-Down Parser
Making Grammar: LL(1) • 1-Remove Common Prefixed (Left Factor) • S --> aBCd S --> aBD • S --> aB D --> • D --> Cd • <s> --> if <exp> then <action> endif; • <s> --> if <exp> then <action> else <action> endif; • <s> --> if <exp> then <action> <rest> • <rest> --> endif; • <rest> --> else <action> endif; Chapter 6: Top-Down Parser
2-Remove Left Recursion:E • E --> E + TE --> TT --> id • A--> AA-->B • A-->A1 A2A1-->BA2-->A2A2--> • E-->E1E2 E1-->T E2-->+T E2 T-->id E2--> Chapter 6: Top-Down Parser
3-Remove Unreachable Products • S-->a S -->a • B-->S Chapter 6: Top-Down Parser
4-Corner Substitution • S --> a • S --> AS • A --> ab • A --> cA • S --> aB • B --> • B --> bS • A --> ab • A --> cA • S --> cAS • S --> AB • B -->1 • B -->2 • B -->3 • S --> A1 • S --> A2 • S --> A3 Chapter 6: Top-Down Parser
5-Singleton Substitution • S-->B • S--> S'S'--> B • <S> --> <LABEL> <UNLABLE> <LABEL> --> id: <LABEL> --> <UNLABLE> --> id:= <EXP>; Chapter 6: Top-Down Parser
Singleton Substitution • -<S> --> id: <UNLABLE> <S> --> <UNLABLE> <UNLABLE> --> id:=<EXP>; • -<S> --> id:<UNLABLE> <S> --> id:= <EXP>; <UNLABLE> --> id:= <EXP>; • -<S> --> id <id-rest> <id-rest> --> : <UNLABLE> <id-rest> --> := <EXP> <UNLABLE> --> id := <EXP> Chapter 6: Top-Down Parser
Some Grammars Can Not be LL(1) • *If _ Then _ Else If <exp> then <action> If <exp> then <action> else <action> • *S --> aBcS S --> aBcSeS B --> d S --> b Chapter 6: Top-Down Parser
Q-Grammar: • A --> a1 • A --> b1 • A --> • S-Grammar: • A --> a1 • A --> b2 • A and S grammar are a LL(1) and we can make a push down Machine Chapter 6: Top-Down Parser