Syntax Analysis - Part IV: Bottom-Up Parsing and LR Grammars, Study Guides, Projects, Research of Electrical and Electronics Engineering

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Syntax Analysis – Part IV Bottom-Up Parsing EECS 483 – Lecture 7 University of Michigan Wednesday, September 29, 2004 - 1 - Announcements: Turning in Project 1 Anonymous ftp to www.eecs.umich.edu » login: anonymous » pw: your email addr cd groups/eecs483 put uniquename.l put uniquename.y Note, you won’t be able to “get” or “rm” any files in the directory – try if you wish If you make a mistake, then put uniquename2.l and send Yuan mail Grading signup sheet available soon (Fri) - 4 - Bottom-Up Parsing (2) Right-most derivation – Backward » Start with the tokens » End with the start symbol » Match substring on RHS of production, replace by LHS S S + E | E E num | (S) (1+2+(3+4))+5 (E+2+(3+4))+5 (S+2+(3+4))+5 (S+E+(3+4))+5 (S+(3+4))+5 (S+(E+4))+5 (S+(S+4))+5 (S+(S+E))+5 (S+(S))+5 (S+E)+5 (S)+5 E+5 S+E S - 5 - Bottom-Up Parsing (3) S S + E ( S ) S + E E S + E 2E 1 ( S ) S + E 4E 3 S S + E | E E num | (S) 5(1+2+(3+4))+5 (E+2+(3+4))+5 (S+2+(3+4))+5 (S+E+(3+4))+5 Advantage of bottom-up parsing: can postpone the selection of productions until more of the input is scanned - 6 - Top-Down Parsing S S + E ( S ) S + E E S + E 2E 1 ( S ) S + E 4E 3 S S + E | E E num | (S) 5S S+E E+E (S)+E (S+E)+E (S+E+E)+E (E+E+E)+E (1+E+E)+E (1+2+E)+E ... In left-most derivation, entire tree above token (2) has been expanded when encountered - 9 - Shift-Reduce Parsing Parsing actions: A sequence of shift and reduce operations Parser state: A stack of terminals and non- terminals (grows to the right) Current derivation step = stack + input Derivation step stack Unconsumed input (1+2+(3+4))+5 (1+2+(3+4))+5 (E+2+(3+4))+5 (E +2+(3+4))+5 (S+2+(3+4))+5 (S +2+(3+4))+5 (S+E+(3+4))+5 (S+E +(3+4))+5 ... - 10 - Shift-Reduce Actions Parsing is a sequence of shifts and reduces Shift: move look-ahead token to stack Reduce: Replace symbols β from top of stack with non-terminal symbol X corresponding to the production: X β (e.g., pop β, push X) stack input action ( 1+2+(3+4))+5 shift 1 (1 +2+(3+4))+5 stack input action (S+E +(3+4))+5 reduce S S+ E (S +(3+4))+5 - 11 - Shift-Reduce Parsing S S + E | E E num | (S) derivation stack input stream action (1+2+(3+4))+5 (1+2+(3+4))+5 shift (1+2+(3+4))+5 ( 1+2+(3+4))+5 shift (1+2+(3+4))+5 (1 +2+(3+4))+5 reduce E num (E+2+(3+4))+5 (E +2+(3+4))+5 reduce S E (S+2+(3+4))+5 (S +2+(3+4))+5 shift (S+2+(3+4))+5 (S+ 2+(3+4))+5 shift (S+2+(3+4))+5 (S+2 +(3+4))+5 reduce E num (S+E+(3+4))+5 (S+E +(3+4))+5 reduce S S+E (S+(3+4))+5 (S +(3+4))+5 shift (S+(3+4))+5 (S+ (3+4))+5 shift (S+(3+4))+5 (S+( 3+4))+5 shift (S+(3+4))+5 (S+(3 +4))+5 reduce E num ... - 14 - LR Parsing Engine Basic mechanism » Use a set of parser states » Use stack with alternating symbols and states E.g., 1 ( 6 S 10 + 5 (blue = state numbers) » Use parsing table to: Determine what action to apply (shift/reduce) Determine next state The parser actions can be precisely determined from the table - 15 - LR Parsing Table Terminals Algorithm: look at entry for current state S and input terminal C » If Table[S,C] = s(S’) then shift: push(C), push(S’) » If Table[S,C] = X α then reduce: pop(2*|α|), S’= top(), push(X), push(Table[S’,X]) Non-terminals Next action and next state Next stateState Action table Goto table - 16 - LR Parsing Table Example We want to derive this in an algorithmic fashion Input terminal Non-terminals ( ) id , $ S L 1 s3 s2 g4 2 S id S id S id S id S id 3 s3 s2 g7 g5 4 accept 5 s6 s8 6 S (L) S (L) S (L) S (L) S (L) 7 L S L S L S L S L S 8 s3 s2 g9 9 L L,S L L,S L L,S L L,S L L,S St at e - 19 - Example LR(0) State An LR(0) item is a production from the language with a separator “.” somewhere in the RHS of the production Sub-string before “.” is already on the stack (beginnings of possible γ’s to be reduced) Sub-string after “.”: what we might see next E num . E ( . S) state item - 20 - Class Problem For the production, E num | (S) Two items are: E num . E ( . S ) Are there any others? If so, what are they? If not, why? - 21 - LR(0) Grammar Nested lists » S (L) | id » L S | L,S Examples » (a,b,c) » ((a,b), (c,d), (e,f)) » (a, (b,c,d), ((f,g))) Parse tree for (a, (b,c), d) S ( L ) L , S L , S ( S )S a L , S S b c d - 24 - The Goto Operation Goto operation = describes transitions between parser states, which are sets of items Algorithm: for state S and a symbol Y » If the item [X α . Y β] is in I, then » Goto(I, Y) = Closure( [X α Y . β ] ) S’ . S $ S . (L) S . id Goto(S, ‘(‘) Closure( { S ( . L) } ) - 25 - Class Problem E’ E E E + T | T T T * F | F F (E) | id 1. If I = { [E’ . E]}, then Closure(I) = ?? 2. If I = { [E’ E . ], [E E . + T] }, then Goto(I,+) = ?? - 26 - Goto: Terminal Symbols S’ . S $ S . (L) S . id S ( . L) L . S L . L, S S . (L) S . id S id . id id ( Grammar S (L) | id L S | L,S ( In new state, include all items that have appropriate input symbol just after dot, advance do in those items and take closure - 29 - Full DFA S’ . S $ S . (L) S . id S ( . L) L . S L . L, S S . (L) S . id S id .id ( id ( S (L . )L L L . , S L S . L L , . S S . (L) S . id L L,S . S (L) . S’ S . $ final state 1 2 8 9 6 3 7 S ) S $ id L , 5 S 4 Grammar S (L) | id L S | L,S - 30 - S (L) | id L S | L,SParsing Example ((a),b) derivation stack input action ((a),b) 1 ((a),b) shift, goto 3 ((a),b) 1(3 (a),b) shift, goto 3 ((a),b) 1(3(3 a),b) shift, goto 2 ((a),b) 1(3(3a2 ),b) reduce S id ((S),b) 1(3(3(S7 ),b) reduce L S ((L),b) 1(3(3(L5 ),b) shift, goto 6 ((L),b) 1(3(3L5)6 ,b) reduce S (L) (S,b) 1(3S7 ,b) reduce L S (L,b) 1(3L5 ,b) shift, goto 8 (L,b) 1(3L5,8 b) shift, goto 9 (L,b) 1(3L5,8b2 ) reduce S id (L,S) 1(3L8,S9 ) reduce L L,S (L) 1(3L5 ) shift, goto 6 (L) 1(3L5)6 reduce S (L) S 1S4 $ done - 31 - Reductions On reducing X β with stack αβ » Pop β off stack, revealing prefix α and state » Take single step in DFA from top state » Push X onto stack with new DFA state Example derivation stack input action ((a),b) 1 ( 3 ( 3 a),b) shift, goto 2 ((a),b) 1 ( 3 ( 3 a 2 ),b) reduce S id ((S),b) 1 ( 3 ( 3 S 7 ),b) reduce L S - 34 - LR(0) Summary LR(0) parsing recipe: » Start with LR(0) grammar » Compute LR(0) states and build DFA: Use the closure operation to compute states Use the goto operation to compute transitions » Build the LR(0) parsing table from the DFA This can be done automatically - 35 - Homework Problem Generate the DFA for the following grammar S E + S | E E num