First and follow set
- 1. UNIVERSITY OF AZAD JAMMU & KASHMIR MUZAFFARABAD Dawood Faheem Abbasi BSCS-VI-05
- 2. FIRST AND FOLLOW SET Compiler Construction
- 3. FIRST & FOLLOW • The construction of a predictive parser is aided by two functions associated with a grammar G. • These functions, FIRST and FOLLOW, allow us to fill in the entries of a predictive parsing table for G, • Whenever possible. Sets of tokens yielded by the FOLLOW function can also be used as synchronizing tokens during panic-mode error recovery.
- 4. FIRST SET • If α is any string of grammar symbols, let FIRST(α) be the set of terminals that begin the strings derived from a. If a => Ɛ then Ɛ is also in FIRST(α). • To compute FIRST(X) for all grammar symbols X, apply the following rules until no more terminals or Ɛ can be added to any FIRST set.
- 5. RULES FOR FIRST SET 1. If X is terminal, then FIRST(X) is {X}. 2. If X => Ɛ is a production, then add Ɛ to FIRST(X). 3. If X is nonterminal and X => Y1 Y2 ... Yk. is a production, then place a in FIRST(X) if for some i, a is in FIRST(Yi), and Ɛ is in all of FIRST(Y1), ... , FIRST(Yi-1); that is, Y1, ... ,Yi-1 => Ɛ. If Ɛ is in FIRST(Yj) for all j = 1, 2, ... , k, then add Ɛ to FIRST(X). For example, everything in FIRST(Y1) is surely in FIRST(X). If Y1 does not derive Ɛ, then we add nothing more to FIRST(X), but if Y1 => Ɛ, then we add FIRST(Y2) and so on.
- 6. FOLLOW SET • Define FOLLOW(A), for nonterminal A, to be the set of terminals a that can appear immediately to the right of A in some sentential form, that is, the set of terminals a such that there exists a derivation of the form • S => α Aaβ for some α and β. Note that there may, at some time during the derivation, have been symbols between A and a, but if so, they derived Ɛ and disappeared. • If A can be the rightmost symbol in some sentential form, then $, representing the input right end marker, is in FOLLOW(A).
- 7. RULES FOR FOLLOW SET 1. Place $ in FOLLOW(S), where S is the start symbol and $ is the input right end marker. 2. If there is a production A => α Bβ, then everything in FIRST(β), except for Ɛ, is placed in FOLLOW(B). 3. If there is a production A => α B, or a production A => α Bβ where FIRST(β) contains Ɛ (i.e., β => Ɛ), then everything in FOLLOW(A) is in FOLLOW(B).
- 8. EXAMPLES E => T E’ E’=> + T E’ | Ɛ T => F T’ T’=> * F T’ | Ɛ F => ( E ) | id FIRST(E) = FIRST(T) = FIRST(F) = {( , id} FIRST(E’) = {+, Ɛ} FIRST(T’) = {*, Ɛ} FOLLOW(E) = FOLLOW(E’) = {) , $} FOLLOW(T) = FOLLOW(T’) = {+, ), $} FOLLOW(F) = {+, *, ), $}
- 9. EXAMPLE S => A a A => B D B => b | Ɛ D => d | Ɛ First(S) = {b, d, a} First(A) = {b, d, Ɛ} First(B) = {b, Ɛ} First(D) = {d, Ɛ } Follow(S) = {$} Follow(A) = {a} Follow(B) = {d, a} Follow(D) = {a}
- 10. EXAMPLE • C => P F class id X Y • P => public | Ɛ • F => final | Ɛ • X => extends id | j • Y => implements I | Ɛ • I => id j • J => , I | Ɛ
- 11. 1. C => P F class id X Y 2. P => public 3. P => Ɛ 4. F => final 5. F => Ɛ 6. X => extends id 7. X => Ɛ 8. Y => implements I 9. Y => Ɛ 10. I => id J 11. J => , I 12. J => Ɛ First(C) = {public, final, class} First(P) = {public, Ɛ } First(F) = {final, Ɛ } First(X) = {extends, Ɛ } First(Y) = {implements, Ɛ } First(I) = {id} First(J) = {‘,', Ɛ } Follow(C) = {$} Follow(P) = {final, class} Follow(F) = {class} Follow(X) = {implements, $} Follow(Y) = {$} Follow(I) = {$} Follow(J) = {$}
- 12. THANK YOU