Outline CS412/413. Administrivia. Review. Grammars. Left vs. Right Recursion. More tips forll(1) grammars Bottomup parsing LR(0) parser construction


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1 C12/1 Introduction to Compilers and Translators pring 00 Outline More tips forll1) grammars Bottomup parsing LR0) parser construction Lecture 5: Bottomup parsing Lecture 5 C 12/1 pring '00 Andrew Myers 2 Administrivia Programming Assignment 1 due next class Fray) should be well under way  leave time for testing, documentation do not need to construct DFA! All group assignments should have settled out Homework 2 due next Fray Reading: finish Chapter of Appel Lecture 5 C 12/1 pring '00 Andrew Myers Review Can make recursive descent parsers for LL1) grammars Natural language grammar LL1) grammar predictive parse table recursivedescent parser recursivedescent parser w/ AT generation How to perform this step? Lecture 5 C 12/1 pring '00 Andrew Myers Grammars Have been using grammar for language of sums with parentheses 1++))+5 imple grammar w/ left associativity: + E E E number ) LL1) grammar for same language: E ε + E number ) Lecture 5 C 12/1 pring '00 Andrew Myers 5 E ε + Left vs. Right Recursion + E E Right recursion : rightassociative E + E 1 + Lecture 5 C 12/1 pring '00 Andrew Myers Left recursion : leftassociative
2 Leftrecursive vs Rightrecursive Leftrecursive grammars don t work with topdown parsing: arbitrary amount of lookahead needed derived string lookahead read/unread E E + E E + E + E E + E + E + E E + E + E E + E E $ E E How to create an LL1) grammar Write a rightrecursive grammar E + E Leftfactor common prefixes, place suffix in new nonterminal E ε + Lecture 5 C 12/1 pring '00 Andrew Myers 7 Lecture 5 C 12/1 pring '00 Andrew Myers 8 EBNF Extended BackusNaur Form: allows some regular expression syntax on RH *, +, ),? operators Iota spec:? = [ ]) BNF: operator at top level E ε + E + E ) * )) + 5 EBNF version: no position on + associativity Lecture 5 C 12/1 pring '00 Andrew Myers Topdown parsing EBNF Recursivedescent code can directly implement the EBNF grammar: E + E ) * vo parse_ ) { // parses sequence of E + E + E... parse_e ); while true) { switch token) { case + : token = input.read); parse_e); break; case ) : case EOF: return; default: throw new ParseError); Lecture 5 C 12/1 pring '00 Andrew Myers 10 Building a leftassociative AT Expr parse_) { Expr result = parse_e); while true) { switch token) { case + : token = input.read); result = new Addresult, parse_e)); break; case ) : case EOF: return result; default: throw new ParseError); ummary Now have complete recipe for building a parser Language grammar LL1) grammar predictive parse table recursivedescent parser recursivedescent parser w/ AT generation Lecture 5 C 12/1 pring '00 Andrew Myers 11 Lecture 5 C 12/1 pring '00 Andrew Myers 12 2
3 Bottomup parsing A more powerful parsing technology LR grammars  more expressive than LL can handle leftrecursive grammars, virtually all programming languages More natural expression of programming language syntax hiftreduce parsers automatic parser generators e.g. yacc,cup) detect errors as soon as possible allows better error recovery Lecture 5 C 12/1 pring '00 Andrew Myers 1 Topdown parsing 1+2++))+5 +E E+E )+E +E)+E +E+E)+E E+E+E)+E 1+E+E)+E 1+2+E)+E... In leftmost derivation, entire tree above a token 2) has been expanded when encountered Must be able to predict productions! + E E E number ) + E E 5 ) + E + E ) E 2 + E 1 E Lecture 5 C 12/1 pring '00 Andrew Myers 1 Bottomup parsing Rightmost derivation  backward tart with the tokens End with the start symbol + E E E number ) 1+2++))+5 E+2++)) ))+5 +E++))+5 ++))+5 +E+))+5 ++))+5 ++E))+5 +))+5 +E)+5 )+5 E+5 +E Lecture 5 C 12/1 pring '00 Andrew Myers 15 rightmost derivation Progress of bottomup parsing 1+2++)) ))+5 E+2++)) )) )) ))+5 +E++)) ))+5 ++)) ))+5 +E+)) ))+5 ++)) ))+5 ++E)) ))+5 +)) ))+5 +E) ) )+5 ) ) )+5 E )) +5 +E 1+2++)) ))+5 Lecture 5 C 12/1 pring '00 Andrew Myers ))+5 E+2++)) ))+5 +E++))+5 Bottomup parsing + E E E number ) Advantage of bottomup parsing: can select productions based on more information + E E 5 ) + E +E ) E 2 + E 1 E Topdown vs. Bottomup Bottomup: Don t need to figure out as much of the parse tree for a given amount of input scanned unscanned Topdown scanned unscanned Bottomup Lecture 5 C 12/1 pring '00 Andrew Myers 17 Lecture 5 C 12/1 pring '00 Andrew Myers 18
4 hiftreduce parsing Parsing is a sequence of shift and reduce operations Parser state is a stack of terminals and nonterminals grows to the right) Unconsumed input is a string of terminals Current derivation step is always stack+input Derivation step stack unconsumed input 1+2++)) ))+5 E+2++))+5 E +2++)) )) ))+5 +E++))+5 +E ++))+5 Lecture 5 C 12/1 pring '00 Andrew Myers 19 hiftreduce parsing Parsing is a sequence of shifts and reduces hift  move lookahead token to stack stack input action 1+2++))+5 shift ))+5 Reduce  Replace symbols γ in top of stack with nonterminal symbol X, corresponding to production X γ pop γ, push X) stack input action +E ++))+5 reduce +E ++))+5 Lecture 5 C 12/1 pring '00 Andrew Myers 20 hiftreduce parsing derivation stack input stream action + E E E number ) 1+2++)) ))+5 shift 1+2++)) ))+5 shift 1+2++)) ))+5 reduce E num E+2++))+5 E +2++))+5 reduce E +2++)) ))+5 shift +2++)) ))+5 shift +2++)) ))+5 reduce E num +E++))+5 +E ++))+5 reduce +E ++))+5 ++))+5 shift ++))+5 + +))+5 shift ++))+5 + +))+5 shift ++))+5 + +))+5 reduce E num Lecture 5 C 12/1 pring '00 Andrew Myers 21 Problem How do we know which action to take  whether to shift or reduce, and which production? ometimes can reduce but shouldn t e.g., X εcan always be reduced ometimes can reduce in different ways Lecture 5 C 12/1 pring '00 Andrew Myers 22 Action election Problem Given stack σ and lookahead symbol b, should we shift b onto the stack making it σb) reduce some production X γassuming that stack has the form αγ making it αx) If stack has form αγ, should apply reduction X γdepending on what stack prefix α is  but α is different for different possible reductions, since γ s have different length. How to keep track? Lecture 5 C 12/1 pring '00 Andrew Myers 2 Parser tates Goal: know what reductions are legal at any given point Idea: summarize all possible stack prefixes α as a parser state Parser state is defined by a DFA that reads in the stack α Accept states of DFA: unique reduction! ummarizing discards information affects what grammars parser handles affects size of DFA number of states) Lecture 5 C 12/1 pring '00 Andrew Myers 2
5 LR0) parser Lefttoright scanning, Rightmost derivation, zero lookahead characters Too weak to handle most language grammars including this one) But will help us understand how to build better parsers An LR0) grammar: nonempty lists L ) L L L, x x,y) x, y,z), w) x)))) x, y, z, w))) Lecture 5 C 12/1 pring '00 Andrew Myers 25 Lecture 5 C 12/1 pring '00 Andrew Myers 26 LR0) states tart tate & Closure L ) L L, A state is a set of items An LR0) item is a production from the language with a separator. somewhere in the RH of the production E number. state E. ) item tuff before. already on stack beginnings of possible γ s to be reduced) tuff after. : what we might see next The prefixes α represented by state itself Lecture 5 C 12/1 pring '00 Andrew Myers 27 DFA start state closure. $. $ First step: augment grammar with prod n $ tart state of DFA: empty stack =. $ Closure of a state adds items for all productions whose LH occurs in an item in the state, just after. set of possible productions to be reduced next Added items have the. located at the beginning: no symbols for these items on the stack yet Lecture 5 C 12/1 pring '00 Andrew Myers 28. $ Applying symbols.. L ) L. L. L, L ) L L, In new state, include all items that have appropriate input symbol just after dot, and advance dot in those items and take closure.) Lecture 5 C 12/1 pring '00 Andrew Myers 29 Applying reduce actions. $.. L ) L. L. L, Pop RH off stack, replace with LH X X γ), rerun DFA e.g. x)) Lecture 5 C 12/1 pring '00 Andrew Myers 0 L states causing reductions L. ) L L., L. 5
6 1. $ Full DFA Appel p. 6). $ $ final state 2.. L ) L. L. L, L. 7 L L L,. L. ) L L., 6 L ). 8 9 L L,. Lecture 5 C 12/1 pring '00 Andrew Myers 1 ) 5 L ) L L, L ) Optimization: stack is labeled w/state L L, Let s try parsing x),y) derivation stack input action x),y) 1 x),y) shift, goto x),y) 1 x),y) shift, goto x),y) 1 x),y) shift, goto 2 x),y) 1 x 2 ),y) reduce ),y) 1 7 ),y) reduce L L),y) 1 L 5 ),y) shift, goto 6 L),y) 1 L 5 ) 6,y) reduce L),y) 1 7,y) reduce L L,y) 1 L 5,y) shift, goto 8 L,y) 1 L 5, 8 y) shift, goto 9 L,y) 1 L 5, 8 y 2 ) reduce L,) 1 L 5, 8 9 ) reduce L L, L) 1 L 5 ) shift, goto 6 L) 1 L 5 ) 6 reduce L) 1 $ done Lecture 5 C 12/1 pring '00 Andrew Myers 2 Bottomup parsing Grammars can be parsed bottomup using a DFA + stack tate construction converts grammar into states that capture information needed to know what action to take Next time: shiftreduce parsing tables LR, LR1) parsers, automatic parser generators Lecture 5 C 12/1 pring '00 Andrew Myers 6
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