* 07/16/96 Plan for Today Shift-reduce parsing The problem with - PowerPoint PPT Presentation

* 07/16/96 Plan for Today Shift-reduce parsing – The problem with predictive top down parsing CS453 : Shift Reduce Parsing – LR parsing: bottom up Unambiguous Grammars LR(0) and SLR Parse Tables – Performs a right-most derivation in reverse – Parsing unambiguous grammars – LR parsing table and parsing algorithm CS453 Shift-reduce Parsing 1 CS453 Shift-reduce Parsing 2 LL ¡vs ¡LR ¡ Shift-reduce parsing in an LR parser LL(k) must predict which production to use when seeing k LR(k) parser • tokens of the rhs: – Left-to-right parse – Right-most derivation S à SS | (S) | ε – K-token look ahead is it S à SS or (S) when I see ((((……. ? produces the parse tree TOP DOWN LR parsing algorithm – Performs a shift-reduce parse LR(k) postpones the decision until all tokens of the rhs plus k – Look at state at top of stack and input symbol to find action in table • more tokens have been seen. It therefore is more powerful. – shift(n): advance input, push state n on stack – reduce(k): pop rhs of grammar rule k, look up state on top of stack and lhs for goto n, push lhs(k) and n onto stack It does this by parsing BOTTOM UP – accept: stop and success • – error: stop and fail CS453 Shift-reduce Parsing 3 CS453 Shift-reduce Parsing 4 1

* 07/16/96 LR ¡parsing ¡engine ¡ Example ¡LR ¡parse ¡ S à AB A à Aa | a B à Bb | b S’ à S $ The LR parsing engine uses an Explicit Stack (as opposed to • • the implicit stack of LL) and the input token string and performs two kinds of actions a aabb$ ß Aa abb$ ß Aa bb$ ß A b b$ ß ABb$ ß AB $ ß S$ ß S’ Shift push input token onto the stack Notice that this is the rightmost derivation • Reduce pop a rhs off the stack and push the corresponding lhs S’ à S$ à AB$ à ABb$ à Abb$ à Aabb$ à Aaabb$ à aaabb$ • on the stack in reverse! It accepts the string of tokens when the input is empty or LR(k) parsing scans the input Left to right and produces the $ (eof) and the stack contains the start symbol Rightmost derivation (looking k tokens ahead) in reverse. CS453 Shift-reduce Parsing 5 CS453 Shift-reduce Parsing 6 Simplified ¡example ¡LR ¡parsing ¡engine ¡ac5ons ¡ Shift reduce parsing applied to unambiguous grammars S à à AB A à à Aa | a B à à Bb | b S’ à à S $ [0] S à ( S ) Single parentheses nest [1] S ‘ à S $ Start symbol is S ’ Stack input action [2] S à ID aaabb$ S a aabb$ R : A à à a Stack input action A aabb$ S ((ID))$ S Aa abb$ R: A à à Aa ( (ID))$ S A abb$ S (( ID))$ S Aa bb$ R: A à à Aa ((ID ))$ R: S à Id A bb$ S ((S ))$ S Ab b$ R: B à à b ((S) )$ R: S à (S) AB b$ S (S )$ S ABb $ R: B à à Bb (S) $ R: S à (S) AB $ R: S à à AB S $ accept S $ accept CS453 Shift-reduce Parsing 7 CS453 Shift-reduce Parsing 8 2

* 07/16/96 Table ¡driven ¡LR ¡parse ¡algorithm ¡ LR(0) SLR LALR LR(k) The stack contains grammar symbols and states: Given the shift reduce machinery described, there are various after a symbol is pushed, the next state is pushed algorithms for creating the parse table. The actions can now be formulated as: These algorithms get more and more sophisticated, starting – Sn : push input token; push n (ie goto state n) from simple LR(0) – Rk : rule k: lhs à rhs pop rhs of rule k off the stack, this exposes a state s Parser generators such as java-cup use the more sophisticated look up in row s and column lhs the next state gn to goto LALR parse table creation algorithm push lhs; push n (ie goto state n) – a : stop parsing, report success – _ : stop parsing, report error CS453 Shift-reduce Parsing 9 CS453 Shift-reduce Parsing 10 Table ¡Driven ¡LR ¡Parsing ¡ Example LR(0) Parse Table, Single Parentheses Nest [0] S -> ( S ) [1] S ’ -> S $ [2] S -> ID The ¡parsing ¡engine ¡is ¡a ¡DFA ¡plus ¡a ¡stack: ¡a ¡determinis7c ¡ pushdown ¡automaton. ¡The ¡DFA ¡is ¡described ¡by ¡a ¡transi7on ¡table: ¡ Action Goto ¡Rows ¡are ¡states ¡ State ( ) $ ID S ¡Column s ¡are ¡Grammar ¡symbols ¡(terminals, ¡non-­‑terminals) ¡ 0 s3 s1 2 ¡ ¡ ¡terminals: ¡ ¡shiD ¡or ¡reduce ¡and ¡go ¡to ¡next ¡state ¡ 1 r2 r2 r2 r2 ¡ ¡ ¡non-­‑terminals: ¡decide ¡which ¡state ¡to ¡go ¡to ¡aDer ¡a ¡reduc7on ¡ 2 accept ¡ ¡So ¡there ¡are ¡five ¡kinds ¡of ¡ac7ons ¡ 3 s3 s1 4 ¡ ¡ ¡ ¡sn: ¡ ¡ ¡shiD ¡input ¡and ¡go ¡to ¡state ¡ ¡n ¡ ¡ ¡ ¡ ¡rk: ¡ ¡ ¡reduce ¡according ¡to ¡rule ¡k, ¡then ¡gn: ¡go ¡to ¡state ¡n ¡ 4 s5 ¡ ¡ ¡ ¡ ¡ ¡a: ¡ ¡accept ¡ 5 r0 r0 r0 r0 ¡ ¡ ¡ ¡ ¡ ¡_: ¡ ¡error ¡ ¡(indicated ¡by ¡blank ¡state) ¡ In LR(0) parse tables, reduce actions happen for all terminals, as the parser does not look ahead . CS453 Shift-reduce Parsing 11 CS453 Shift-reduce Parsing 12 3

* 07/16/96 LR(0) table construction Shift, reduce, goto actions in LR(0) table construction Example grammar for Lists: goto action: S’ à .S$ S’ à S.$ S à x. 0: S’ à à S$ 1: S à à ( L ) 2: S à à x 3: L à à S 4: L à à L , S Also in state 0 S à .x 3:V[S] 1:V[x] we could have S à .(L) We start with an empty stack and with a complete S$ sentence on input reduced to S 0:V[ ε ] We indicate this as follows: S’ à à . S$ S à (.L) shift action: this (a rule with a dot in it) is called an item, L à .L,S In state 1 we are at the end In state 0 we it indicates what is in the stack (left of .) of an item. This will give rise L à .S can shift an x and what is to be expected on input (right of .) S à .x to a reduce action or shift a ( The input can start with anything S can start with, eg an x or a ( S à .(L) We indicate this as follows: S’ à à .S$ 2:V[(] (we are making a DFA S à à .x Transitions: the shifts and goto-s explicitly connect the states. The throug another closure S à à .(S) reduces implicitly move to another state by popping the rhs off the remember the NFA à à DFA) stack, after which a goto with the lhs will produce a new next state We call this a state: state 0, the start state with an empty prefix (V[ ε ]) CS453 Shift-reduce Parsing 13 CS453 Shift-reduce Parsing 14 LR(0) Closure, Goto, State Diagram, Reduce LR(0) states and transitions Goto(I,X): // state I , symbol X Closure(I): // state I L à L,.S x x S if X==$ return {} // no gotos for $ repeat L à L,S. S’ à .S$ S à x. S à .x J = {} // new state for any item A à à α . X β S à .x 8:V[(L,S] 1:V[x] S à .(L) for any item A à à α . X β in I for any X à à γ S à .(L) 7:V[(L] , ( x J+= A à à α X . β I+= X à à . γ 0:V[ ε ] ( return Closure(J) // close it until I does not change S à (L.) S S à (.L) L List grammar State Diagram construction Reduce(T): ( L à L.,S L à .L,S 0: S’ à S$ T = Closure({ S’ à à .S$ } ); // states R = {} S’ à S.$ L à .S 1: S à ( L ) E = {} // edges (gotos and shifts) for each state I in T 3:V[S] 4:V[(L] S à .x 2: S à x repeat until no change in E or T for each item A à à α . S S à .(L) ) 3: L à S for each state I in T R += (I, A à à α ) 2:V[(] 4: L à L , S for each item A à à α . X β in I L à S. S à (L). J = Goto(I,X); 6:V[(S] 5:V[(L)] T+=J ; E += (X: (I,J)) // the edge (I,J) labeled X CS453 Shift-reduce Parsing 15 CS453 Shift-reduce Parsing 16 4