CS415 Compilers. LR Parsing & Error Recovery


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1 CS415 Compilers LR Parsing & Error Recovery These slides are based on slides copyrighted by Keith Cooper, Ken Kennedy & Linda Torczon at Rice University
2 Review: LR(k) items The LR(1) table construction algorithm uses LR(1) items to represent valid configurations of an LR(1) parser An LR(k) item is a pair [P, δ], where P is a production A β with a at some position in the rhs δ is a lookahead string of length k (words or EOF) The in an item indicates the position of the top of the stack LR(1): [A βγ,a] means that the input seen so far is consistent with the use of A βγ immediately after the symbol on top of the stack [A β γ,a] means that the input seen so far is consistent with the use of A βγ at this point in the parse, and that the parser has already recognized β. [A βγ,a] means that the parser has seen βγ, and that a lookahead symbol of a is consistent with reducing to A. Lecture 13 2
3 Review  Computing Closures Closure(s) adds all the items implied by items already in s Any item [A β Bδ,a] implies [B τ,x] for each production with B on the lhs, and each x FIRST(δa) for LR(1) item The algorithm Closure( s ) while ( s is still changing ) items [A β Bδ,a] s productions B τ P b FIRST(δa) // δ might be ε if [B τ,b] s then add [B τ,b] to s Ø Classic fixedpoint method Ø Halts because s ITEMS Closure fills out a state 3
4 Review  Computing Gotos Goto(s,x) computes the state that the parser would reach if it recognized an x while in state s Goto( { [A β Xδ,a] }, X ) produces [A βx δ,a] (easy part) Should also includes closure( [A βx δ,a] ) (fill out the state) The algorithm Goto( s, X ) new Ø items [A β Xδ,a] s new new [A βx δ,a] return closure(new) Ø Not a fixedpoint method! Ø Straightforward computation Ø Uses closure ( ) Goto() moves forward 4
5 Review  Building the Canonical Collection Start from s 0 = closure( [S S,EOF ] ) Repeatedly construct new states, until all are found The algorithm cc 0 closure ( [S S, EOF] ) CC { cc 0 } while ( new sets are still being added to CC) for each unmarked set cc j CC mark cc j as processed for each x following a in an item in cc j temp goto(cc j, x) if temp CC then CC CC { temp } record transitions from cc j to temp on x Ø Fixedpoint computation (worklist version) Ø Loop adds to CC Ø CC 2 ITEMS, so CC is finite 5
6 Review LR(1) Table Construction Highlevel overview 1 Build the canonical collection of sets of LR(1) Items, I a Begin in an appropriate state, s 0 Assume: S S, and S is unique start symbol that does not occur on any RHS of a production (extended CFG  ECFG) [S S,EOF], along with any equivalent items Derive equivalent items as closure( s 0 ) b Repeatedly compute, for each s k, and each X, goto(s k,x) If the set is not already in the collection, add it Record all the transitions created by goto( ) This eventually reaches a fixed point 2 Fill in the table from the collection of sets of LR(1) items The canonical collection completely encodes the transition diagram for the handlefinding DFA 6
7 Review: Example (building the collection) 1: Goal Expr 2: Expr Term Expr 3: Expr Term 4: Term Factor * Term 5: Term Factor 6: Factor ident Initialization Step Symbol FIRST Goal { ident } Expr { ident } Term { ident } Factor { ident } { } * { * } ident { ident } s 0 closure( { [Goal Expr, EOF] } ) = {[Goal Expr, EOF], [Expr à Term Expr, EOF], [Expr à Term, EOF], [Term à Factor * Term, ], [Term à Factor, ], [Term à Factor * Term, EOF], [Term à Factor, EOF], [Factor à ident, *], [Factor à ident, ], [Factor à ident, EOF]} S { S 0 } 7
8 Example (building the collection) s 0 closure( { [Goal Expr, EOF] } ) { [Goal Expr, EOF], [Expr Term Expr, EOF], [Expr Term, EOF], [Term Factor * Term, EOF], [Term Factor * Term, ], [Term Factor, EOF], [Term Factor, ], [Factor ident, EOF], [Factor ident, ], [Factor ident, *] } Iteration 1 s 1 goto(s 0, Expr) s 2 goto(s 0, Term) s 3 goto(s 0, Factor) s 4 goto(s 0, ident ) 8
9 Example (building the collection) s 0 closure( { [Goal Expr, EOF] } ) { [Goal Expr, EOF], [Expr Term Expr, EOF], [Expr Term, EOF], [Term Factor * Term, EOF], [Term Factor * Term, ], [Term Factor, EOF], [Term Factor, ], [Factor ident, EOF], [Factor ident, ], [Factor ident, *] } Iteration 1 s 1 goto(s 0, Expr) = { [Goal Expr, EOF] } s 2 goto(s 0, Term) = { [Expr Term Expr, EOF], [Expr Term, EOF] } s 3 goto(s 0, Factor) = { [Term Factor * Term, EOF],[Term Factor * Term, ], [Term Factor, EOF], [Term Factor, ] } s 4 goto(s 0, ident ) = { [Factor ident, EOF],[Factor ident, ], [Factor ident, *] } 9
10 Example (building the collection) Iteration 1 s 1 goto(s 0, Expr) = { [Goal Expr, EOF] } s 2 goto(s 0, Term) = { [Expr Term Expr, EOF], [Expr Term, EOF] } s 3 goto(s 0, Factor) = { [Term Factor * Term, EOF],[Term Factor * Term, ], [Term Factor, EOF], [Term Factor, ] } s 4 goto(s 0, ident ) = { [Factor ident, EOF],[Factor ident, ], [Factor ident, *] } Iteration 2 s 5 goto(s 2, ) s 6 goto(s 3, * ) 10
11 Example (building the collection) Iteration 1 s 1 goto(s 0, Expr) = { [Goal Expr, EOF] } s 2 goto(s 0, Term) = { [Expr Term Expr, EOF], [Expr Term, EOF] } s 3 goto(s 0, Factor) = { [Term Factor * Term, EOF],[Term Factor * Term, ], [Term Factor, EOF], [Term Factor, ] } s 4 goto(s 0, ident ) = { [Factor ident, EOF],[Factor ident, ], [Factor ident, *] } Iteration 2 s 5 goto(s 2, ) = { [Expr Term Expr, EOF], [Expr Term Expr, EOF], [Expr Term, EOF], [Term Factor * Term, ], [Term Factor, ], [Term Factor * Term, EOF], [Term Factor, EOF], [Factor ident, *], [Factor ident, ], [Factor ident, EOF] } s 6 goto(s 3, * ) = see next page 11
12 Example (building the collection) Iteration 2 s 5 goto(s 2, ) = { [Expr Term Expr, EOF], [Expr Term Expr, EOF], [Expr Term, EOF], [Term Factor * Term, ], [Term Factor * Term, EOF], [Term Factor, ], [Term Factor, EOF], [Factor ident, *], [Factor ident, ], [Factor ident, EOF] } s 6 goto(s 3, * ) = { [Term Factor * Term, EOF], [Term Factor * Term, ], [Term Factor * Term, EOF], [Term Factor * Term, ], [Term Factor, EOF], [Term Factor, ], [Factor ident, EOF], [Factor ident, ], [Factor ident, *] } Iteration 3 s 7 goto(s 5, Expr ) = {? } s 8 goto(s 6, Term ) = {? } s 2 goto(s 5, Term), s 3 goto(s 5, factor), s 4 goto(s 5, ident), s 3 goto(s 6, Factor), s 4 goto(s 6, ident) 12
13 Example (building the collection) Iteration 2 s 5 goto(s 2, ) = { [Expr Term Expr, EOF], [Expr Term Expr, EOF], [Expr Term, EOF], [Term Factor * Term, ], [Term Factor * Term, EOF], [Term Factor, ], [Term Factor, EOF], [Factor ident, *], [Factor ident, ], [Factor ident, EOF] } s 6 goto(s 3, * ) = { [Term Factor * Term, EOF], [Term Factor * Term, ], [Term Factor * Term, EOF], [Term Factor * Term, ], [Term Factor, EOF], [Term Factor, ], [Factor ident, EOF], [Factor ident, ], [Factor ident, *] } Iteration 3 s 7 goto(s 5, Expr ) = { [Expr Term Expr, EOF] } s 8 goto(s 6, Term ) = { [Term Factor * Term, EOF], [Term Factor * Term, ] } 13
14 Example (Summary) S 0 : { [Goal Expr, EOF], [Expr Term Expr, EOF], [Expr Term, EOF], [Term Factor * Term, EOF], [Term Factor * Term, ], [Term Factor, EOF], [Term Factor, ], [Factor ident, EOF], [Factor ident, ], [Factor ident, *] } S 1 : { [Goal Expr, EOF] } S 2 : { [Expr Term Expr, EOF], [Expr Term, EOF] } S 3 : { [Term Factor * Term, EOF],[Term Factor * Term, ], [Term Factor, EOF], [Term Factor, ] } S 4 : { [Factor ident, EOF],[Factor ident, ], [Factor ident, *] } S 5 : { [Expr Term Expr, EOF], [Expr Term Expr, EOF], [Expr Term, EOF], [Term Factor * Term, ], [Term Factor, ], [Term Factor * Term, EOF], [Term Factor, EOF], [Factor ident, *], [Factor ident, ], [Factor ident, EOF] } 14
15 Example (Summary) S 6 : { [Term Factor * Term, EOF], [Term Factor * Term, ], [Term Factor * Term, EOF], [Term Factor * Term, ], [Term Factor, EOF], [Term Factor, ], [Factor ident, EOF], [Factor ident, ], [Factor ident, *] } S 7 : { [Expr Term Expr, EOF] } S 8 : { [Term Factor * Term, EOF], [Term Factor * Term, ] } 15
16 Example (DFA) term s 1 s 2 s 7 term  expr expr ident ident s 0 s 4 s 5 term ident factor s 6 * s 3 s 8 factor factor The State Transition Table State Ident  * Expr Term Factor
17 Example (DFA) term s 1 s 2 s 7 term  expr expr ident ident s 0 s 4 s 5 term ident factor s 6 * s 3 s 8 factor factor The State Transition Table State Ident  * Expr Term Factor
18 Filling in the ACTION and GOTO Tables The algorithm set s x S item i s x if i is [A β ad,b] and goto(s x,a) = s k, a T then ACTION[x,a] shift k else if i is [S S,EOF] then ACTION[x, EOF] accept else if i is [A β,a] then ACTION[x,a] reduce A β n NT if goto(s x,n) = s k then GOTO[x,n] k Many items generate no table entry 18
19 Example (Filling in the tables) The algorithm produces LR(1) parse table ACTION GOTO Ident  * EOF Expr Term Factor 0 s acc 2 s 5 r 3 3 r 5 s 6 r 5 4 r 6 r 6 r 6 5 s s r 2 8 r 4 r 4 Plugs into the skeleton LR(1) parser Remember the state transition table? State Ident  * Expr Term Factor
20 An Example for Table Filling Practice A Parse Table Filling Example For pdf lecture notes readers, see attached LR(1) parse table example file Lecture 15 20
21 What can go wrong? What if set s contains [A β aγ,b] and [B β,a]? First item generates shift, second generates reduce Both define ACTION[s,a] cannot do both actions This is a fundamental ambiguity, called a shift/reduce error Modify the grammar to eliminate it (ifthenelse) What if set s contains [A γ, a] and [B γ, a]? Each generates reduce, but with a different production Both define ACTION[s,a] cannot do both reductions This fundamental ambiguity is called a reduce/reduce error Modify the grammar to eliminate it In either case, the grammar is not LR(1) EaC includes a worked example 21
22 Shrinking the Tables Three options: Combine terminals such as number & identifier, + & , * & / Directly removes a column, may remove a row For expression grammar, 198 (vs. 384) table entries Combine rows or columns Implement identical rows once & remap states Requires extra indirection on each lookup Use separate mapping for ACTION & for GOTO Use another construction algorithm Both LALR(1) and SLR(1) produce smaller tables Implementations are readily available (table compression) 22
23 LR(0) versus SLR(1) versus LR(1) LR(0)?  set of LR(0) items as states LR(1)?  set of LR(1) items as states, different states compared to LR(0) SLR(1)?  LR(0) items and canonical sets, same as LR(0) SLR(1): add FOLLOW(A) to each LR(0) item [A γ ] as its second component: [A γ, a], a FOLLOW(A) 23
24 LR(0) versus SLR(1) versus LR(1) Example: S S S S ; a a LR(0)? LR(1)? SLR(1)? Lecture 15 24
25 LR(0) versus LR(1) versus SLR(1) LR(0) States s0 = Closure({[S.S]}) = {[S >.S], [S >.S; a], [S >.a] } s1 = Closure( GoTo (s0, S)) = {[S S. ], [S S.; a] } s2 = Closure( GoTo (s0, a)) = {[S a.]} s3 = Closure( GoTo (s1, ;)) = {[S S;. a]} LR(1) States s4 = Closure( GoTo (s3, a)) = {[S S;a.] } s0 = Closure({[S.S,eof]}) = {[S >.S,eof], [S >.S; a,eof], [S >.a,;] } s1 = Closure( GoTo (s0, S)) = {[S S. eof], [S S.; a,eof] } s2 = Closure( GoTo (s0, a)) = {[S a.,;]} s3 = Closure( GoTo (s1, ;)) = {[S S;. a,eof]} s4 = Closure( GoTo (s3, a)) = {[S S;a., eof] } Grammar is not LR(0), but LR(1) and SLR(1) Lecture 15 25
26 LALR(1) versus LR(1) LALR(1)? LR(1) items, State > Grouped LR(1) states LALR(1): Merge two sets of LR(1) items (states), if they have the same core. core of set of LR(1) items: set of LR(0) items derived by ignoring the lookahead symbols FACT: collapsing LR(1) states into LALR(1) states cannot introduce shift/reduce conflicts 26
27 LALR(1) versus LR(1) s0 = Closure({[S.S, eof]}) s1 = Closure( GoTo (s0, a)) = {[S a. Ad, eof], [S a. Be, eof], [A.c, d], [ B.c, e]} s2 = Closure( GoTo (s0, b)) = {[S b. Ae, eof], [S b. Bd, eof], [A.c, e], [B.c, d]} s3 = Closure( GoTo (s1, c)) = {[A c., d], [B c., e]} s4 = Closure( GoTo (s2, c)) = {[A c., e], [B c., d]} There are other states that are not listed here! Grammar is LR(1), but not LALR(1), since collapsing s3 and s4 (same core) will introduce reducereduce conflict. Lecture 15 27
28 Hierarchy of ContextFree Grammars FloydEvans Parsable Contextfree grammars Unambiguous CFGs Operator Precedence Operator precedence includes some ambiguous grammars LL(1) is a subset of SLR(1) LR(k) LR(1) LALR(1) LL(k) The inclusion hierarchy for contextfree grammars SLR(1) LR(0) LL(1) Ref Book: Michael Sipser, Introduction to the Theory of Computation, 3 rd Edition Lecture 16 28
29 Error Recovery in ShiftReduce Parsers The problem: parser encounters an invalid token Goal: Want to parse the rest of the file Basic idea (panic mode): Assume something went wrong while trying to find handle for nonterminal A Pretend handle for A has been found; pop handle, skip over input to find terminal that can follow A Restarting the parser (panic mode): find a restartable state on the stack (has transition for nonterminal A) move to a consistent place in the input (token that can follow A) perform (error) reduction (for nonterminal A) print an informative message Lecture 15 29
30 Error Recovery in YACC Yacc s (bison s) error mechanism (note: version dependent!) designated token error used in error productions of the form A error α // basic case α specifies synchronization points When error is discovered pops stack until it finds state where it can shift the error token resumes parsing to match α special cases: α = w, where w is string of terminals: skip input until w has been read α = ε : skip input until state transition on input token is defined error productions can have actions Lecture 15 30
31 Error Recovery in YACC cmpdstmt: BEG stmt_list END stmt_list : stmt stmt_list ; stmt error { yyerror( \n***error: illegal statement\n );} This should throw out the erroneous statement synchronize at ; or end (implicit: α = ε) writes message ***Error: illegal statement to stderr Example: begin a & 5 hello ; a := 3 end resume parsing ***Error: illegal statement Lecture 15 31
32 Project #2 (see lex & yacc, Levine et al., O Reilly) You do have to (slightly) change the scanner (scan.l) How to specify and use attributes in YACC? Define attributes as types in attr.h typedef struct info_node {int a; int b} infonode; Include type attribute name in %union in parse.y %union {tokentype token; infonode myinfo; } Assign attributes in parse.y to Terminals: %token <token> ID ICONST Nonterminals: %type <myinfo> block variables procdecls cmpdstmt Accessing attribute values in parse.y use $$, $1, $2 etc. notation: block : variables procdecls {$2.b = $1.b + 1;} cmpdstmt { $$.a = $1.a + $2.a + $3.b;} Lecture 16 32
33 YACC : parse.y parse.y : %{ #include <stdio.h> #include "attr.h" int yylex(); void yyerror(char * s); #include "symtab.h" %} %union {tokentype token; } Will be included verbatim in parse.tab.c List and assign attributes %token PROG PERIOD PROC VAR ARRAY RANGE OF %token INT REAL DOUBLE WRITELN THEN ELSE IF %token BEG END ASG NOT %token EQ NEQ LT LEQ GEQ GT OR EXOR AND DIV NOT %token <token> ID CCONST ICONST RCONST %start program %% program : PROG ID ';' block PERIOD { } ; block : BEG ID ASG ICONST END { } ; %% void yyerror(char* s) { fprintf(stderr,"%s\n",s); } int main() { printf("1\t"); yyparse(); return 1; } Rules with semantic actions Main program and helper functions; may contain initialization code of global structures. Will be included verbatim in parse.tab.c Lecture 16 33
34 Project #2 : Things to do Learn/Review the C programming language Add error productions (syntax errors) Define and assign attributes to nonterminals Implement singlelevel symbol table Perform type checking and produce required error messages; note: actions may occur at any location on righthand side (implicit use of marker productions) Lecture 16 34
35 Next two classes Adhoc, syntax directed translation schemes,type checking Read EaC: Chapters Lecture 15 35
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