Top-Down Parsing, Part II

Transcription

1 op-down Parsing, Part II

2 Announcements Programming Project 1 due Friday, 11:59PM Office hours every day until then. ubmission instructions will be ed out tonight.

3 Where We Are ource Code Lexical Analysis yntax Analysis emantic Analysis IR Generation IR Optimization Code Generation Optimization Machine Code

4 Review of LL1 Left-to-right scan, Leftmost derivation, 1 token lookahead. Predict which production to use based on the current nonterminal and the lookahead token. Build an LL1 parse table to make these lookups fast and streamlined.

5 Review of FIR ets he set FIRA is defined as the set of terminals that could be at the start of a string ultimately derived from A. Formally: FIRA = { t A * tv } Can compute iteratively: et FIRA = { t A tv } Keep computing FIRA = FIRA FIRB for all productions A wbv, where w is a string of nonterminals that can derive ε.

6 Review of FOLLOW ets he set FOLLOWA is defined as the set of terminals that could potentially follow a string produced from nonterminal A. Formally: FOLLOWA = { t B * uatv } Can also be computed iteratively: Initially, set FOLLOWA = FIRw {ε} for all rules C vaw. Keep computing FOLLOWA = FOLLOWA FOLLOWB for all rules B vaw where w is or can derive ε.

7 LL1 able Construction Compute FIRA and FOLLOWA for all nonterminals A. For each rule A w and for each terminal t in FIRw, set [A, t] = w. Note that ε is not a terminal! For each rule A w with ε in FIRw, set [A, t] = w for each t in FOLLOWA.

8 xample LL1 Construction

9 he Limits of LL1

10 A Grammar that is Not LL1 Consider the following left-recursive grammar: A Ab c FIRA = {c} However, we cannot build an LL1 parse table. Why? Cannot uniquely predict production! his is called a FIR/FIR conflict.

11 A Grammar that is Not LL1 Consider the following left-recursive grammar: A Ab c FIRA = {c} However, we cannot build an LL1 parse table. Why? A b c A Ab A c Cannot uniquely predict production! his is called a FIR/FIR conflict.

12 A Grammar that is Not LL1 Consider the following left-recursive grammar: A Ab c FIRA = {c} However, we cannot build an LL1 parse table. Why? A b c A Ab A c Cannot uniquely predict production! his is called a FIR/FIR conflict.

13 liminating Left Recursion In general, left recursion can be converted o right recursion by a mechanical transformation. Consider the grammar A Av w his will produce w followed by some number of v's. Can rewrite the grammar as A wb B ε vb

14 Another Non-LL1 Grammar Consider the following grammar: FIR = {, } FIR = {, } Why is this grammar not LL1?

15 Another Non-LL1 Grammar Consider the following grammar: FIR = {, } How do you predict which of these to use? FIR = {, } Why is this grammar not LL1?

16 Left-Factoring

17 ε Left-Factoring

18 ε ε Left-Factoring

19 Left-Factoring ε

20 Left-Factoring ε $

21 Left-Factoring FIR ε $

22 ε Left-Factoring FIR ε $

23 Left-Factoring ε FIR ε $

24 Left-Factoring ε FIR ε $

25 Left-Factoring ε FIR ε FOLLOW $

26 ε Left-Factoring $ $ FIR FOLLOW ε $

27 ε Left-Factoring $ $ FIR FOLLOW ε $

28 ε Left-Factoring $ $ FIR FOLLOW ε $ $

29 ε Left-Factoring $ $ FIR FOLLOW $ ε $ $

30 ε 6 Left-Factoring $ $ FIR FOLLOW $ $ ε $

31 ε 6 Left-Factoring $ $ FIR FOLLOW $ $ ε $

32 ε 6 Left-Factoring $ $ FIR FOLLOW $ $ ε $

33 ε 6 Left-Factoring $ $ FIR FOLLOW $ $ ε $

34 ε 6 Left-Factoring $ $ FIR FOLLOW $ $ ε $

35 ε 6 Left-Factoring $ $ FIR FOLLOW $ $ ε $

36 he trengths of LL1

37 LL1 is Realistic ome real-world programming languages are LL1-parsable or parsable with a minor modification on LL1. xamples: LIP Python Javacript

38 LL1 is traightforward Can be implemented quickly with a table-driven design. Can be implemented by recursive descent: Define a function for each nonterminal. Have these functions call each other based on the lookahead token. ee Handout #09 for more details.

39 LL1 is Fast Both table-driven LL1 and recursive-descentpowered LL1 are fast. Can parse in On fg time, where n is the length of the string and fg is some function of the size of the grammar usually a small constant.

40 ummary op-down parsing tries to derive the user's program from the start symbol. Leftmost BF is one approach to top-down parsing; it is mostly of theoretical erest. Leftmost DF is another approach to top-down parsing that is uncommon in practice. LL1 parsing scans from left-to-right, using one token of lookahead to find a leftmost derivation. FIR sets contain terminals that may be the first symbol of a production. FOLLOW sets contain terminals that may follow a nonterminal in a production. Left recursion and left factoring cause LL1 to fail and can be mechanically eliminated.