n Bottom-up (LR) parsing n Handle n LR item n Characteristic Finite State Machine (CFSM) n SLR(1) parsing tables n Conflicts in SLR(1)

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1 Aoucemets Quiz Hold o to paper, brig over at the ed HW due tomorrow (exteded 1 day) We have office hours -7pm today Dowload SWI Prolog! HW3 will be posted toight or tomorrow Prolog Due Fray, Sep 8 at pm Last Class Bottom-up (LR) parsig Hadle LR item Characteristic Fiite State Machie (CFSM) SLR(1) parsig tables Coflicts i SLR(1) Idivual assigmet 1 Fall 18 CSCI 30, A Milaova Today s Lecture Outlie The coclusio of bottom-up (LR) parsig Coflicts i SLR(1) LR parsig variats Logic Programmig Cocepts Prolog Laguage costructs: facts, rules, queries Programmig Laguage Sytax Bottom-up Parsig Logic Programmig ad Prolog Read: coclude Scott, Chapter. Scott, Chapter 1.1, 1. (begiig) Fall 18 CSCI 30, A Milaova 3 Fall 18 CSCI 30, A Milaova Model of the LR parser Stack: State Grammar Symbol s m X m s m-1 X m-1 s 0 Iput: a 1 a i a $$ Parsig table: LR Parser actio actio[s,a]: Do we shift or reduce? Fall 18 CSCI 30, A Milaova goto goto[s,a]: After reductio to otermial A, what state is pushed o top of the stack? 5 CFSM: Sets of LR items with Trasitios + Reduce by Labels 0 start expr expr expr+term expr term term term* term term 3 expr term reduce by term o $$,+,* 1 start expr expr expr +term accept o $$ expr term term term * + reduce by expr term o $$,+ * expr expr+ term term term * term term 6 expr expr+term term term * reduce by expr expr+term o $$,+ * 5 term term* term term* reduce by term term* o $$,+,* 7 6 1

2 From CFSM to SLR(1) Parsig Table state 1. expr expr + term 3. term term *. expr term. term + * $$ expr term 0 shift shift accept reduce shift 5 reduce 3 reduce reduce reduce shift shift 7 6 reduce 1 shift 5 reduce 1 7 reduce 3 reduce 3 reduce 3 White actio table Blue goto table 7 Coflicts i SLR(1): Shift-reduce Shift-reduce coflict i state k o a: State k cotais item A β ad a is i FOLLOW(A) ad State k cotais item A α aβ The parser does ot kow whether it is at the ed of productio A β ad thus should reduce by A β, or it is i the mdle of productio A αaβ ad thus should shift a ad cotiue lookig for β Fall 18 CSCI 30, A Milaova 8 Coflicts i SLR(1): Reduce-reduce Reduce-reduce coflict i state k o a: State k cotais item A β ad a is i FOLLOW(A) ad State k cotais item A β ad a is i FOLLOW(A ) The parser does ot kow whether it is at the ed of productio A β ad thus should reduce by A β, or whether it is at the ed of productio A β ad thus should reduce by A β Usually, a reduce-reduce coflict icates a serious problem with the grammar Fall 18 CSCI 30, A Milaova 9 Resolvig Coflicts i SLR(1) I some cases, it makes sese to use a o-slr(1) grammar (e.g., a ambiguous grammar) Iterestigly, we ca still esure desired behavior by choosig oe of the coflictig actios E.g., we ca resolve a shift-reduce coflict by determiistically choosig the shift or the reduce Popular techique with parsig tools: use of directives to choose shift or reduce Fall 18 CSCI 30, A Milaova 10 Exercise CFSM for Grammar start expr expr expr + expr start expr expr expr + expr Costruct the CFSM ad SLR(1) parsig table for above grammar This grammar is ambiguous ad as expected we have shift-reduce coflict(s) Resolve the coflict(s) so that + is leftassociative 0 start expr expr expr+expr expr expr reduce by expr o $$,+ expr 1 start expr expr expr +expr accept o $$ + expr expr+ expr expr expr+expr expr expr 3 expr expr+expr expr expr +expr reduce by expr expr+expr o $$,+ There is a shift-reduce coflict o + i state! + Fall 18 CSCI 30, A Milaova 11 1

3 From CFSM to SLR(1) Parsig Table 1. expr expr + expr. expr state + $$ expr 0 shift 1 1 shift 3 accept reduce reduce 3 shift shift 3 reduce 1 reduce 1 Shift-reduce coflict! White actio table Blue goto table LR Parsig Variats LR(0), SLR(1), LALR(1), LR(1), LR(k) LR(0), SLR(1), LALR(1) are most practical Use the same set of parsig states Differ i the hadlig of shift-reduce states (states with both a shift item ad a reduce item) LR(0) uses 0 tokes of lookahead Disallows shift-reduce states Our ruig example is ot LR(0) E.g., state : expr term term term * To force left associativity of + resolve coflict i favor of reduce! 13 1 LR Parsig Variats SLR(1) uses 1 toke of lookahead Resolves (some) shift-reduce states by peekig at oe toke ahead Adds labels reduce by A β o FOLLOW(A) to states cotaiig items A β. The FOLLOW sets serve as filters If after filterig by FOLLOW, there are o shift-reduce ad o reduce-reduce coflicts, the grammar is SLR(1) Is our ruig example SLR(1)? Yes. Filterig by FOLLOW resolves the shift-reduce issue i state : expr term term term * reduce by expr term o $$,+ Fall 18 CSCI 30, A Milaova 15 Parsig Variats LALR(1) Uses the same set of states as SLR(1) Costructs local, cotext-sesitive FOLLOW sets ad is able to avo more coflicts Mior challege: grammar i Problem 5 is LALR(1). Thik about why. A efficiecy hack Most commo parsers i practice LR(1) Uses a differet set of states More states, i order to keep paths disjoit 16 Hierarchy of Grammar Classes LL(0) < LL(1) < LL(k) LR(0) < SLR(1) < LALR(1) < LR(1) < LR(k) Also, LL(k) < LR(k) Questio: SLR(1) parsers are more powerful tha LL(1) oes? Why, what is the ituitio? Aswer: LL(1) predicts what productio to apply before it has see the strig. LR determies what productio to reduce by, after it has see the etire strig! 17 Exercise Coser the grammar: start expr expr expr + expr expr * expr Costruct the CFSM for this grammar First, costruct the sets of LR items with trasitios Secod, add reduce by labels Resolve the coflicts i such a way that the operators will behave ormally : + ad * are left-associative * has higher precedece tha + Fall 18 CSCI 30, A Milaova 18 3

4 Today s Lecture Outlie The coclusio of bottom-up (LR) parsig Coflicts i SLR(1) LR parsig variats Movig o: Logic Programmig Dowload ad istall SWI Prolog o laptop! Logic Programmig Cocepts Prolog Laguage costructs: facts, rules, queries Fall 18 CSCI 30, A Milaova 19 Fall 18 CSCI 30, A Milaova 0 Logic Programmig Logic programmig Logic programmig is declarative programmig Logic program states what (logic), ot how (cotrol) Programmer declares axioms I Prolog, facts ad rules Programmer states a theorem, or a goal I Prolog, a query Laguage implemetatio determies how to use the axioms to prove the goal Fall 18 CSCI 30, A Milaova 1 Logic Programmig Prolog Program: Java Program: raiy(seattle). raiy(rochester). cold(rochester). sowy(x):-raiy(x),cold(x).? - sowy(c). C = rochester HashSet raiy = ew HashSet(); HashSet cold = ew HashSet(); HashSet sowy = ew HashSet(); raiy.add( seattle ); raiy.add( rochester ); cold.add( rochester ); for (Iterator it=raiy.iterator(); it.hasnext();) { Strig city = (Strig) it.ext(); if (cold.cotais(city)) sowy.add(city); } for (Iterator it=sowy.iterator(); it.hasnext();) { System.out.pritl((Strig) it.ext()); } Fall 18 CSCI 30, A Milaova Logic Programmig Logic Programmig Cocepts Laguage iterpreter is a iferece egie Resolutio Uificatio, backward chaiig, backtrackig Logic programmig style is characterized by Database of facts ad rules that represet logical relatios. Computatio is modeled as search (queries) over this database Maipulatio of lists ad use of recursio, i which it is very similar to the fuctioal A Hor Clause is: H B 1,B,,B Atecedets (B s): cojuctio of zero or more terms i predicate calculus; this is the body of the hor clause Cosequet (H): a term i predicate calculus Meaig of a Hor clause: H is true if B 1, B,..., ad B are all true Whe the atecedets B i are all true, we deduce that cosequet H is true as well For example: tiger(hobbes). child(calvi). likes(calvi,hobbes) tiger(hobbes),child(calvi). programmig style 3

5 Logic Programmig Cocepts Resolutio Priciple If two Hor clauses A B 1,B,B 3,, B m C D 1,D,D 3,, D are such that A matches D 1, the we ca replace D 1 with B 1,B,B 3,, B m C B 1,B,B 3,, B m,d,d 3,, D For example: C A,B D C A D A,B,C Fall 18 CSCI 30, A Milaova 5 Hor Clauses i Prolog I Prolog, a Hor clause is writte h :- b 1,...,b. Hor Clause is called clause Cosequet is called goal or head Atecedets are called subgoals or tail Hor Clause with o tail is a fact E.g., raiy(seattle). Depeds o o other coditios Hor Clause with a tail is a rule sowy(x) :- raiy(x),cold(x). Fall 18 CSCI 30, A Milaova 6 Hor Clauses i Prolog Hor Clauses i Prolog Clause is composed of terms Costats Number, e.g., 13, etc. Atoms e.g., seattle, rochester, raiy, foo I Prolog, atoms begi with a lower-case letter! Variables X, Foo, My_var I Prolog, variables must begi with upper-case letter! Structures cosists of a atom, called a fuctor ad a list of argumets raiy(seattle), sowy(x) Variables may appear i the tail ad head of a rule: c(x) :- h(x,y). For all values of X, c(x) is true if there exist a value of Y such that h(x,y) is true Call Y a auxiliary variable. Its value will be boud to make cosequet true, but ot reported by Prolog, because it does ot appear i the head 7 Fall 18 CSCI 30, A Milaova 8 Prolog Facts Program has a database of clauses i.e., facts ad rules; the rules help derive more facts We add simple queries with costats, variables, cojuctios or disjuctios raiy(seattle). raiy(rochester). cold(rochester). sowy(x) :- raiy(x),cold(x).? - raiy(c).? sowy(c). perso(tom). fuctors costats The combiatio of the fuctor ad its arity (i.e., its umber of argumets) is called a predicate. Fall 18 CSCI 30, A Milaova 9 Fall 18 CSCI 30, A Milaova 30 5

6 Queries Questio query perso(tom). variable?-likes(al,eve).?-likes(al,who). true. Who=eve. aswer?-likes(al,pie).?-likes(eve,w). aswer with false. W=pie ; variable big?-likes(eve,al). W=tom ; false. W=eve. force search for more aswers?-likes(eve,w). W = pie ; W = tom ; W = eve. perso(tom). Prolog gives us the aswer precisely i this order: first W=pie the W=tom ad fially W=eve. Ca you guess why? Fall 18 CSCI 30, A Milaova 31 3 Harder Queries Harder Queries ad perso(tom). perso(tom). same big?-likes(al,v), likes(eve,v). V=eve.?-likes(eve,W), perso(w). W=tom?-likes(A,B). A=eve,B=pie ; A=al,B=eve ; A=eve,B=tom ; A=eve,B=eve.?-likes(D,D). D=eve. 33?-likes(eve,W),likes(W,V). W=eve,V=pie ; W=eve,V=tom ; W=eve,V=eve.?-likes(eve,W),perso(W),food(V). W=tom,V=pie ; W=tom,V=apple or?-likes(eve,v),(perso(v);food(v)). V=pie ; V=tom Fall 18 CSCI 30, A Milaova 3 Rules Rules Add a rule to the database: perso(tom). perso(tom). rule1 :- likes(eve,v),perso(v). rule(v) :- likes(eve,v),perso(v). rule1:-likes(eve,v),perso(v).?-rule1. true?-rule(h). H=tom?-rule(pie). false. rule1 ad rule are just like ay other predicate! Fall 18 CSCI 30, A Milaova 35 Fall 18 CSCI 30, A Milaova 36 6

7 Quee Victoria Example male(albert). male(edward). Put all clauses i file female(alice). family.pl female(victoria). parets(edward,victoria,albert). parets(alice,victoria,albert).?- [family]. Loads file family.pl true.?- male(albert). A query true.?- male(alice). false.?- parets(edward,victoria,albert). true.?- parets(bullwikle,victoria,albert). false. cf Clocksi ad Mellish Quee Victoria Example?-female(X). a query X = alice ; ; asks for more aswers X = victoria. Variable X has bee uified to all possible values that make female(x) true. Variables are upper-case, fuctors (predicates ad costats) are lower-case! Fall 18 CSCI 30, A Milaova 37 Fall 18 CSCI 30, A Milaova 38 Quee Victoria Example Facts aloe do ot make iterestig programs. We eed variables ad deductive rules. sister_of(x,y) :- female(x),parets(x,m,f), parets(y,m,f). Next class We ll cotiue with Prolog! Dowload SWI Prolog ad ru through the lecture examples!!!?- sister_of(alice, Y). Y = edward <eter>: ot askig for more aswers?- sister_of(alice, victoria). false. Fall 18 CSCI 30, A Milaova 39 Fall 18 CSCI 30, A Milaova 0 7