Transcript PPT
Top-Down parsing LL(1) parsing Overview of Top-Down There are only two actions 1. Replace 2. Match Parsing stack Start-Symbol$ ... ... $ Input stack Input-Token$ ... ... $ Actions accept Overview of Top-Down e.g. with grammar S (S)S| S$ (S)S$ S)S$ )S$ S$ $ ( )$ ( )$ )$ )$ $ $ S (S)S match S match S accept S 1.replace ( S 2.match ) S 4.match 3.replace 5.replace LL(k) parsing L stands for left-to-right parse of input L stands for leftmost-derivation k stands for k-token look-ahead LL(1) Parsing At top of Parsing stack For Non-terminal Replace: a decision must be made, based on the current input token. For terminal Match: no decision is to be made but need to see if it is the same as the current input token, if not, an error occurs. LL(1) Parsing : First Sets First Sets Let X be a grammar symbol (a terminal or non-terminal) or ε. Then the set First(X) consisting of terminals, and possibly ε, is defined as follows 1. If X is a terminal or , then First(X )= X . 2. If X is a nonterminal, then for each production choice X X 1 X 2 ... X n , First(X ) contains First(X ) contains First(X 1 ) . If also for some i < n, all the sets First(X 1 ),..., First(X i ) contains , then First(X ) contains First(X i+1 ) . If all the sets First(X 1 ),...,First(X n ) contains , then First(X ) contains LL(1) Parsing : First Sets e.g. for the grammar S ( S ) S | S X1 X 2 X 3 X 4 | X 5 First(S) First(X 1 ) ( First(S) First(X 5 ) thus First(S) ( , LL(1) Parsing : Follow Sets Follow Sets Given a non-terminal A, the set Follow(A), consisting of terminals, and possibly $, is defined as follows. 1. If A is the start symbol, then $ is in Follow(A). 2. If there is a production B A , then First( )- is in Follow(A). 3. If there is a production B A such that is in First( ), then Follow(A) contains Follow(B). ε is never an element of Follow set LL(1) Parsing : Follow Sets e.g. for the grammar S (S)S | S is the start symbol , thus Follow(S) $ S ( S )S S S Follow(S) First( ) $ , ) S1 (S)S S1 S is in First( ) Follow(S) $ , ) Follow(S) contains Follow(S1 ) First & Follow set The First set and Follow set for the grammar S (S)S | is First(S) ( , Follow(S) $ , ) Non-terminal nullable First Follow S Yes ( $,) LL(1) Parsing table How to construct LL(1) parsing table For each production rule A 1. for each terminal t First( ) M[A,t] 2. if First( ) and t Follow(A) M[A,t] LL(1) Parsing table The First set and Follow set for the grammar Follow(S) $ , ) S (S)S | is First(S) ( , for production S (S)S ( First ( S ) S , thus M[ S , ( ] (S)S for production S First( ) and ) Follow(S) , thus M[ S , ) ] First( ) and $ Follow(S) , thus M[ S , $ ] M[N,T] ( ) $ S (S)S ε ε LL(1) Parsing table S (S)S| S$ (S)S$ S)S$ )S$ S$ $ ( )$ ( )$ )$ )$ $ $ S (S)S match S match S accept M[N,T] ( ) $ S (S)S ε ε LL(1) grammar A grammar is LL(1) if the following conditions are satisfied. 1. For every production A 1| 2 |...| n , First( i ) First( j ) is empty for all i and j, 1 i,j n, i j. 2. For every nontermianl A such that First(A) contains , First(A) Follow(A) is empty. That is the LL(1) parsing table has at most one production in each table entry. Mentioned issues Left Recursion removal Left Factoring References COMPILER CONSTRUCTION: Principles and Practice, Kenneth C. Louden Chapter 4 http://www.cs.sjsu.edu/faculty/louden/cm ptext/ http://www.course.com/isbn=0-53493972-4