CSE443 Compilers Dr. Carl Alphonce alphonce@buffalo.edu 343 Davis - - PowerPoint PPT Presentation

CSE443 Compilers

• Dr. Carl Alphonce

alphonce@buffalo.edu 343 Davis Hall

Phases of a compiler

Figure 1.6, page 5 of text

Syntactic structure

Continuing from last time…

FIRST(X)

if X ∈ T then FIRST(X) = { X } if X ∈ N and X -> Y1 Y2 … Yk ∈ P for k≥1, then add a ∈ T to FIRST(X) if ∃i s.t. a ∈ FIRST(Yi) and 𝜁 ∈ FIRST(Yj) ∀ j < i ( i.e. Y1 Y2 … Yi-1 ⇒* 𝜁 ) if 𝜁 ∈ FIRST(Yj) ∀ j <= k add 𝜁 to FIRST(X) if X -> 𝜁 ∈ P, then add 𝜁 to FIRST(X)

FOLLOW(X)

Place $ in FOLLOW(S), where S is the start symbol ($ is an end marker) if A -> 𝛽B𝛾 ∈ P, then FIRST(𝛾) - {𝜁} is in FOLLOW(B) if A -> 𝛽B ∈ P or A -> 𝛽B𝛾 ∈ P where 𝜁 ∈ FIRST(𝛾), then everything in FOLLOW(A) is in FOLLOW(B)

Table-driven predictive parsing Algorithm 4.32 (p. 224)

INPUT: Grammar G = (N,T,P,S) OUTPUT: Parsing table M For each production A -> 𝛽 of G:

• 1. For each terminal a ∈ FIRST(𝛽), add A -> 𝛽 to

M[A,a]

• 2. If 𝜁 ∈ FIRST(𝛽), then for each terminal b in

FOLLOW(A), add A -> 𝛽 to M[A,b]

• 3. If 𝜁 ∈ FIRST(𝛽) and $ ∈ FOLLOW(A), add A -> 𝛽 to

M[A,$]

Example

G given by its productions: E -> T E' E' -> + T E' | 𝜁 T -> F T' T' -> * F T' | 𝜁 F -> ( E ) | id

For each production A -> 𝛽 of G: For each terminal a ∈ FIRST(𝛽), add A -> 𝛽 to M[A,a] If 𝜁 ∈ FIRST(𝛽), then for each terminal b in FOLLOW(A), add A -> 𝛽 to M[A,b] If 𝜁 ∈ FIRST(𝛽) and $ ∈ FOLLOW(A), add A -> 𝛽 to M[A,$]

FIRST SETS

FIRST(F) = { ( , id } FIRST(T) = FIRST(F) = { ( , id } FIRST(E) = FIRST(T) = FIRST(F) = { ( , id } FIRST(E') = { + , 𝜁 } FIRST(T') = { * , 𝜁 }

For each production A -> 𝛽 of G: For each terminal a ∈ FIRST(𝛽), add A -> 𝛽 to M[A,a] If 𝜁 ∈ FIRST(𝛽), then for each terminal b in FOLLOW(A), add A -> 𝛽 to M[A,b] If 𝜁 ∈ FIRST(𝛽) and $ ∈ FOLLOW(A), add A -> 𝛽 to M[A,$]

if X ∈ T then FIRST(X) = { X } if X ∈ N and X -> Y1 Y2 … Yk ∈ P for k≥1, then add a ∈ T to FIRST(X) if ∃i s.t. a ∈ FIRST(Yi) and 𝜁 ∈ FIRST(Yj) ∀ j < i (i.e. Y1 Y2 … Yk ⇒* 𝜁 ) if 𝜁 ∈ FIRST(Yj) ∀ j < k add 𝜁 to FIRST(X) E -> T E' E' -> + T E' | 𝜁 T -> F T' T' -> * F T' | 𝜁 F -> ( E ) | id

For each production A -> 𝛽 of G: For each terminal a ∈ FIRST(𝛽), add A -> 𝛽 to M[A,a] If 𝜁 ∈ FIRST(𝛽), then for each terminal b in FOLLOW(A), add A -> 𝛽 to M[A,b] If 𝜁 ∈ FIRST(𝛽) and $ ∈ FOLLOW(A), add A -> 𝛽 to M[A,$]

Place $ in FOLLOW(S), where S is the start symbol ($ is an end marker) if A -> 𝛽B𝛾 ∈ P, then FIRST(𝛾) - {𝜁} is in FOLLOW(B) if A -> 𝛽B ∈ P or A -> 𝛽B𝛾 ∈ P where 𝜁 ∈ FIRST(𝛾), then everything in FOLLOW(A) is in FOLLOW(B) E -> T E' E' -> + T E' | 𝜁 T -> F T' T' -> * F T' | 𝜁 F -> ( E ) | id

FOLLOW SETS

FOLLOW(E) = { ) , $ } FOLLOW(E') = FOLLOW(E) = { ) , $ } FOLLOW(T) = { + , ) , $ } FOLLOW(T') = FOLLOW(T) = { + , ) , $ } FOLLOW(F) = { + , * , ) , $ }