12 <= rm <digit> 2 <= rm <no> 2 <= rm <no> <digit> <= rm <no> <= rm <number>
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1 DDD16 Compilers nd Interpreters DDB44 Compiler Construction R Prsing Prt 1 R prsing concept Using prser genertor Prse ree Genertion Wht is R-prsing? eft-to-right scnning R Rigthmost derivtion in reverse i.e. ottom-up prsing 12 <= rm <digit> 2 <= rm <no> 2 <= rm <no> <digit> <= rm <no> <= rm <numer> R(1) R prsing with 1 token lookhed R(k) R prsing with k tokens lookhed R-prsing is the most generl noncktrcking shift-reduce prsing method known An R-prser detects syntctic error s soon s possile Peter ritzson Christoph Kessler IDA inköpings universitet DDD16/DDB44 Compiler Construction 2010 R-Grmmr Definition A grmmr for which unique R-tle cn e constructed is clled n R grmmr (R(0) SR(1) AR(1) R(1)...). R-Prsing is Bottom-up Prsing (from ecture 5) xmple: Bottom-up prsing with input: 3-6 * 2 - * Integer ( ) No miguous grmmrs re R grmmrs. here re unmiguous grmmrs which h re not R grmmrs. 3 - => 3-6 => he stte t the top of the stck contins ll the informtion we need. 3-6 => 3-6 => 3-6 * => 3-6 * 2 => 3 DDD16/DDB44 Compiler Construction DDD16/DDB44 Compiler Construction 2010 Bottom-up Prsing cont. Pushdown Automton for R-Prsing 110 inite-stte pushdown utomton Stck contins lterntingly sttes nd symols in NU (w.l.o.g.) input tpe strem of tokens := + c red-only hed O token end of file/input 3-6 * 2 => 3-6 * 2 => 3-6 * 2 5 DDD16/DDB44 Compiler Construction 2010 current stte stck of sttes nd grmmr symols s 3 X 1 s 3 push pop current stte Stck-Bottom mrker finite s 0 control s 4 s3 s 1 s 2 rnsition tle 2 sorts of trnsitions: Actions (shift reduce ccept error) Goto s ( -trnsitions to find new stte fter reductions) 6 DDD16/DDB44 Compiler Construction
2 Configurtions of the R-Prser Configurtion = ( stck contents remining input ) = (s 0 X 1 s 1... X m-1 s m-1 X m s m i i+1... n ) current stte (opofstck) Shift: red current input symol i nd push it with new stte s: (s 0 X 1 s 1... X m-1 s m-1 X m s m i s i+1... n ) Reduce: red pop 2r stck symols for hndle X m-r+1...x m push HS nonterminl + new stte (see elow) Invrints: Nonterminls on stck + remining input (X 1... X m-1 X m i i+1... n ) is rightmost-derived sententil form of G. Stte on top of stck represents vile prefix of G Needs to e reconstructed fter reduce using the GOO tle 7 DDD16/DDB44 Compiler Construction 2010 xmple: An SR(1) Grmmr erminls: Nonterminls: <list> (or ) (is lso the strt symol) <element> (or ) Productions: 1. <list> <list> <element> 2. <element> 3. <element> DDD16/DDB44 Compiler Construction 2010 xmple (cont.): xtend Grmmr with new strt symol erminls: (end-of-input symol) 112 Nonterminls: <SYS> (or S ) (new strt symol) <list> (or ) <element> (or ) Productions: 0. <SYS> <list> 1. <list> <list> <element> 2. <element> 3. <element> 9 DDD16/DDB44 Compiler Construction 2010 xmple: les (given); Step Stck Input le entries ACION[ 0 ] = S4 1. -> > S = Shift 4 = successor stte ACION tle: GOO tle: stte 10 DDD16/DDB44 Compiler Construction 2010 xmple: les (given); 1. -> > Step Stck Input le entries ACION[ 0 ] = S ACION[ 4 ] = R3 ( -> ) R = Reduce 3 = production rule (comment) ACION tle: GOO tle: stte 11 DDD16/DDB44 Compiler Construction 2010 xmple: les (given); 1. -> > Step Stck Input le entries ACION[ 0 ] = S ACION[ 4 ] = R3 ( -> ) GOO[ 0 ] = 6 Reconstruct successor stte fter Reduce from top stck items vi the GOO tle ACION tle: GOO tle: stte 12 DDD16/DDB44 Compiler Construction
3 xmple: les (given); 1. -> > Step Stck Input le entries ACION[ 0 ] = S ACION[ 4 ] = R3 ( -> ) GOO[ 0 ] = ACION[ 6 ] = R2 ( -> )... nd so on... ACION tle: GOO tle: stte 13 DDD16/DDB44 Compiler Construction 2010 xmple: les (given); 1. -> 2. Step Stck Input le entries 3. -> ACION[ 0 ] = S ACION[ 4 ] = R3 ( -> ) GOO[ 0 ] = ACION[ 6 ] = R2 ( -> ) GOO[ 0 ] = ACION[ 1 ] = S ACION[ 2 ] = S ACION[ 5 -- ] = R4 ( -> ) GOO[ 2 ] = ACION[ 3 -- ] = R1 ( ->) GOO[ 0 ] = ACION[ 1 -- ] = A (ccept) ACION tle: GOO tle: stte 14 DDD16/DDB44 Compiler Construction 2010 Smll xercise on R-prsing Rightmost Derivtion Hndle (from ecture 3) Reverse rightmost derivtion 12 <= rm <digit> 2 <= rm <no> 2 <= rm <no> <digit> <= rm <no> <= rm <numer> Hndles Consist of two prts: 1. A production A β 2. A position 1. <numer> <no> 2. <no> <no> <digit> 3. <digit> 4. digit> If S * rm α A w rm α β w the production A β together with the position fter α is hndle of α β w. xmple: he hndle of <no> 2 is the production <digit> 2 nd the position fter <no> ecuse: <numer> rm <no> rm <no> <digit> rm <no> 2 rm <digit> 2 rm DDD16/DDB44 Compiler Construction 2010 Informlly: hndle is wht we reduce to wht nd where to get the previous sententil form in rightmost derivtion. 16 DDD16/DDB44 Compiler Construction 2010 Hndle Vile Prefix Recognizing Hndles Consider rightmost derivtion S * rm Xu rm u for context-free grmmr G. is clled hndle of the right sententil form u ssocited with the rule X rm ch prefix of is clled vile prefix of G. xmple: Grmmr G with productions { S -> S c } Right sententil forms: e.g. c c S S... or c: Hndle: c Vile prefixes: c or c: Hndle: c c or S: Hndle: S S S or S: Hndle: S... S S 17 DDD16/DDB44 Compiler Construction 2010 How to recognize if hndle ppers s the top elements on the stck? Nive pproch: xmine the entire stck (e.g. from top to ottom or vice vers) t every step eds to unnecessrily long worst-cse prsing time Need to ctully store grmmr symols on stck Ide: Incrementl hndle recognition Keep informtion out prtilly recognized hndles (= vile prefixes) on top of stck encoded in stte Chrcteristic utomton (NA) to recognize vile pr. DA y suset construction with -closure Prser tles (ACION / GOO) 18 DDD16/DDB44 Compiler Construction
4 A NA Recognizing Vile Prefixes A.k.. the chrcteristic finite utomton for grmmr G Sttes: R(0) items (= context-free items) of extended grmmr Input strem: he grmmr symols on the stck Strt stte: [S.S ] inl stte: [S S.] rnsitions: move dot cross symol if symol found next on stck: A.B to A B. A. to A. -trnsitions to R(0)-items for nonterminl productions from items where the dot precedes tht nonterminl: A.B to B. (xmple nd construction of DA lter in ecture 7) 19 DDD16/DDB44 Compiler Construction 2010 DDD16 Compilers nd Interpreters DDB44 Compiler Construction Using Prser Genertor Peter ritzson Christoph Kessler IDA inköpings universitet Using Prser Genertor xmple: UNIX Ycc GNU Bison for AR(1) grmmrs ycc mygrmmr.y Report y.output gcc ly y.t.c.out < input stdin Ycc Grmmr mygrmmr.y Prser source code y.t.c Prser xecutle.out Grmmr specifiction (terminls nonterminls productions with inline-c for semntic ctions) + Additionl C code for uxiliry functions e.g. scnner error hndler stdout stderr other source files nd lirries for the compiler 21 DDD16/DDB44 Compiler Construction 2010 xmple Grmmr for Ycc %{ #include <ctype.h> #include <stdio.h> #define YYSYP chr /* chr type for Ycc stck */ %} %token '' %token '' %token '' %% list : list '' element { printf( /%c" $3); } element { printf("%c" $1); } ; element : '' { $$ = 'A'; } '' { $$ = 'B'; } ; %% yylex() { /* hnd-crfted scnner for toy exmple */ chr c; while (1) switch (c = getchr()) { cse '': cse '': cse '': return c; cse '\n': cse O: return O; defult: continue; /* et whitespce */ } P. ritzson } C. Kessler IDA inköpings universitet. xtr dt field for ech stck entry. Cn e used to store vlues (e.g. in n interpreter s here) or pointers to tree nodes to construct n explicit tree representtion (see Slides ). Semntic ctions: C code to e psted into the prser nd executed when reducing for production. Cn ccess the extr dt field of the production s stcked grmmr symols y $$ $1 $ DDD16/DDB44 Compiler Construction 2010 xmple (cont.) Ycc Report DDD16 Compilers nd Interpreters DDB44 Compiler Construction stte 0 $ccept : _list $end shift 3 shift 4 list goto 1 element goto 2 stte 1 $ccept : list_$end list : list_ element $end ccept shift 5 stte 2 list : element_ (2). reduce 2 stte 3 element : _ (3). reduce 3 stte 4 element : _ (4). reduce 4 stte 5 list : list _element shift 3 shift 4 element goto 6 stte 6 list : list element_ (1). reduce 1 5/127 terminls 2/600 nonterminls 5/300 grmmr rules 7/1000 sttes 0 shift/reduce 0 reduce/reduce conflicts reported 5/601 working sets used memory: sttesetc. 18/2000 prser 2/4000 3/3001 distinct lookhed sets 0 extr closures 5 shift entries 1 exceptions 3 goto entries 0 entries sved y goto defult Optimizer spce used: input 16/2000 output 10/ tle entries 4 zero mximum spred: 98 mximum offset: DDD16/DDB44 Compiler Construction 2010 Prse ree Construction in n R-Prser using the Semntic Stck Step Stck Input le entries Semntic stck now stores pointers to prse tree nodes Peter ritzson Christoph Kessler IDA inköpings universitet
5 Construction of prse tree (Bottom-up) Shift opertions: Crete one-node tree contining the shifted symol. Reduce opertions: When reducing hndle β to A (s in A β) crete new node A whose children re those nodes tht were creted in the hndle. During the nlysis we hve forest of su-trees. ch entry in the stck points to its corresponding su-tree. When we ccept the whole prse tree is completed. 25 DDD16/DDB44 Compiler Construction 2010 Prse ree Construction 1. -> > Step Stck Input le entries ACION[ 0 ] = S ACION[ 4 ] = R3 ( -> ) Shift: Crete one-node tree contining the shifted symol. ACION tle: GOO tle: stte 26 DDD16/DDB44 Compiler Construction 2010 Prse ree Construction 1. -> > Step Stck Input le entries ACION[ 0 ] = S ACION[ 4 ] = R3 ( -> ) GOO[ 0 ] = 6 Reduce [X.]: Crete new tree node for X whose children re those former root nodes pointed to from the hndle elements semntic stck fields (in Ycc: $1 $2...) ACION tle: Prse ree Construction 1. -> > ACION tle: Step Stck Input le entries ACION[ 1 ] = S ACION[ 2 ] = S ACION[ 5 -- ] = R4 ( -> ) GOO[ 2 ] = ACION[ 3 -- ] = R1 ( ->) During prsing: orest of sutrees roots pointed from the semntic stck 27 DDD16/DDB44 Compiler Construction DDD16/DDB44 Compiler Construction 2010 Prse ree Construction 1. -> > Step Stck Input le entries ACION[ 3 -- ] = R1 ( ->) GOO[ 0 ] = 1 ACION tle: Smll xercise on Prse ree Construction At ccept [S S. --]: mit the prse tree computed for S. 29 DDD16/DDB44 Compiler Construction DDD16/DDB44 Compiler Construction
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