LL Parsing: A piece of cake after LR

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1 LL Parsing: A piece of cake after LR Lecture 11 Dr. Sean Peisert ECS 142 Spring

2 LL Parsing Still specified using a CFG Still reads left-to-right (Lx) Now is leftmost derivation (xl) rather than rightmost (xr) Constructed from the top in the order that tokens appear in the token stream 2

3 Parsing Algorithms LL E E + E 2 + E 2 + E * E * E * 8 LR E 2 E 3 E E + E E 8 E E * E E E 3

4 LR vs. LL LR (bison/cup): harder to implement, but allows more grammars LL: easier to write, but less flexible in the grammars 4

5 Recursive Descent Parsing Consider the grammar: E T + E T T int int * T (E) Token stream is int5 * int2 Start with top-level non-terminal E Try the rules E in order 5

6 Recursive Descent Parsing E0 T1 + E2 Then try a rule for T1 (E3) But ( does not match the input token int 5 Try T1 int. Token matches. But + after T 1 does not match the input token * Try T1 int * T2 This will match but + after T 1 will be unmatched Have exhausted the choices for T 1 Backtrack to choice for E 0 6

7 Recursive Descent Parsing E0 T1 Follow same steps as before for T 1 And succeed with T1 int * T2 and T2 int E0 T1 int5 * T2 7 int2

8 Recursive Descent Parsing Parsing: given a string of tokens t1, t2, t3, t4, t5, find its parse tree Recursive descent parsing. Try all of the productions exhaustively: At a given moment, the finge of the parse tree is: t1, t2,... tk, A Try all the productions for A: if A BC is a production, the new finge is t1, t2,... tk, BC Backtrack where the finge doesn t match the string. Stop when there are no more non-terminals. 8

9 Construction of Decision Table for each rule X α for each a in First(α) table (X, a) = X α so if we see the very first symbol, match the rule if ε is in First(alpha) for each b in Follows(X) table(x, b) = X α That s it! 9

10 Non-LL Grammars There are a lot of non-ll grammars. The patterns to look for are: Left-Recursive rules (goes into an infinite loop) which must be rewritten as right-recursive Common prefix rules which must be rewritten to move the common prefix to one rule 10

11 Left Recursion A Aa A b For LL, First(A Aa) = b For LL, First(A b) = b this gives a conflict 11

12 Rewrite the Grammar A ba A aa A ε 12

13 Common Prefix X abc X abd This works for LR. For LL, the parser only looks at the First set of rules, not the entire rule. So the rules cause a conflict. 13

14 Rewritten Grammar X aby Y c Y d 14

15 Recursive Descent Simple and general, but unpopular (and slow) because of backtracking Often we can avoid backtracking (somewhat) 15

16 Predictive Parsing Like recursive-descent, but parser can predict which production to use By looking at the next few tokens No backtracking Predictive parsers accept LL(k) grammars 16

17 LL(1) Languages In recursive-descent, for each non-terminal and input token, there may be a choice of production LL(1) means that for each non-terminal and token, there is only one production that could lead to success. Can be specified as a 2D table 1 dim for curent non-terminal to expand 1 dim for next token A table entry contains one production 17

18 Example Grammar #1 Grammar: E T + E T T int int * T (E) Impossible to predict because T has two productions with int. For E it is not clear how to predict. Grammar must be left-factored 18

19 Left Factoring Grammar E T + E T T int int * T (E) Factor out common prefixes of productions: E T X X + E ε T (E) int Y Y * T ε 19

20 LL(1) Parse Table Example Left-Factored Grammar E T X X + E ε T (E) int Y Y * T ε The LL(1) parsing table ($ is a special end marker): int * + ( ) $ T int Y (E) E T X T X X + E ε ε Y * T ε ε ε 20

21 LL(1) Parse Table Consider the [E, int] entry: When current non-terminal is E and next input is int, use production E TX This production can generate an int in the first place Consider the [Y, +] entry: When current non-terminal is y and current token is +, get rid of Y We ll see later why this is so 21

22 LL(1) Parse Table Blank entries indicate error situtations E.g., consider the [E, *] entry There is no way to derive a string starting with * from non-terminal E 22

23 Using Parse Tables Similar to recursive descent, except: For each non-terminal S We look at the next token a And choose the production shown at [S,a] Use a stack to keep track of pending non-terminals Reject when we encounter an error state Accept when we encounter an end-to-input 23

24 LL(1) Parsing Algorithm initialize stack = <S, $> and next (pointer to tokens) repeat case stack of <X, rest> if T[X, *next] = Y1...Yn then stack Y1...Yn rest> ; else error(); <t, rest> if T == *next ++ then stack <rest> ; else error(); until stack == < > 24

25 LL(1) Parsing Example Stack Input Action E$ int * int $ TX TX$ int * int $ int Y int YX$ int * int * terminal YX$ *int$ *T *TX$ *int$ terminal TX$ int$ int Y int YX$ int$ terminal YX$ $ ε X$ $ ε $ $ ACCEPT 25

26 Example Grammar #2 D v L c T L L m i L i T r v = Var, L = IdList c = colon, T = type m = comma, i = id, r = REAL 26

27 After fixing L (which was right-recursive) D v L c T L i X X m i X X ε T r 27

28 Algorithm start with the start symbol on the stack repeat until done if top of stack == first char of input pop 1 of stack advance input else if top of stack == non-terminal T consult (T, input) if (T,input) == T α pop T push input in reverse order print T α reduce else if (T,input) == empty error - reject else if stack is empty and input is empty accept else if stack is empty and input is not empty reject 28

29 LL Decision Table v i m c r $ D D->vLcT L L->iX X X->miX X->e T T->r 29

30 stack input action D vimicr D, v=match D vlct, pop LHS(D), push RHS (vlct) in reverse order TcLv vimicr v, v = match so pop from stack, advance input TcL imicr L, i = match L ix pop L, push ix in reverse order TcXi imicr i, i = match, pop stack, advance TcX micr X, m = match X mix pop X, push mix in reverse order TcXim micr m, m = match pop stack, advance TcXi icr i, i = match pop stack, advance TcX cr X, c = match X ε, pop X, push in reverse order Tc cr c, c = match pop stack, advance T r T, r = match T r pop T, push r in reverse order r r r, r = match pop stack, advance 30

31 Done! Accept! 31

32 Status Project 2 Due Friday, Apr. 24, 11:55pm 32

Building a Parser III. CS164 3:30-5:00 TT 10 Evans. Prof. Bodik CS 164 Lecture 6 1

Building a Parser III. CS164 3:30-5:00 TT 10 Evans. Prof. Bodik CS 164 Lecture 6 1 Building a Parser III CS164 3:30-5:00 TT 10 Evans 1 Overview Finish recursive descent parser when it breaks down and how to fix it eliminating left recursion reordering productions Predictive parsers (aka