TopDown Parsing

1
Top-Down Parsing

• Based On Grammar
• E-gt vT
• E-gt P(E)
• P-gt l
• P-gt f
• T-gtE
• T-gtl
• Leftmost Derivation f(vv)
• E-gtP(E)
• -gtf(E)
• -gtf(vT)
• -gtf(vE)
• -gtf(vvT)
• -gtf(vv)

2
Parse Tree for Grammar
3
Attempting to form the Parse Tree automatically
in Production order precedence
4
LL(1) Terminology

• LL(1) Parsing
• Left to Right
• Leftmost Derivation
• 1 Token Look-ahead
• Pseudocode for LL(1) Parsing
• At Each Stage
• Identify next VN for Parsing
• If more then 1 Production Rule with VN LHS
• ID set of next (Leftmost) possible VTs for each
  rule
• From look-ahead VT, and input-stream look-ahead,
  decide which of these Production Rules to go for

5
Top-Down Parsing

• Based On Grammar
• E-gt vT
• E-gt P(E)
• P-gt l
• P-gt f
• T-gtE
• T-gtl
• Leftmost Derivation f(vv)
• Start by breaking down the E
• Rule 1 we expect a v next
• Rule 2 we expect a P next
• Means that we can really expect an f as our next
  token if P broken down by rule 4
• Means we can expect a ( next if P broken down
  to nothing by rule 3. The ( follows P in rule
  2.
• Given that our look-ahead is f, we select a
  breakdown by rule 2

6
LL(1) Parsing

• Formalize What could possibly be the 1st
  (leftmost ) VT on RHS of each production with
  LHS VN?
• Knowing this set for each production rule for VN,
  and knowing what the next VT we will come across
  is, we can match the next VT in the input to one
  of these sets and thus pick the correct
  production rule for VN breakdown.
• Production Rule A-gt X1 X2XM
• Want to see the set of tokens that could be the
  first token when we transform A-gt(X1 X2..XM)
• We call this set of tokens FIRST(X1 X2..XM)
• Rules
• If (X1 e VT)
• FIRST(X1 X2XM)X1
• If (X1 e VN)
• Look at each production where X1 LHS
• Include FIRST(RHS) for each
• If(X1 can Reduce to l)
• Then must consider FIRST(X2.XM)

7
FOLLOW(A)

• Say we are parsing AB and
• A-gt(X1 X2. XM)
• B-gt(Y1 Y2. YM)
• We look at the FIRST(A) and (X1 X2 XM) can all
  reduce to l!
• Then we become interested in the FIRST(B). In the
  general case FIRST(B) is termed FOLLOW(A) (it may
  not be B following A!)
• So Set of Look-ahead tokens or PREDICT()
• PREDICT(A-gtX1 X2 XM)
• IF l e FIRST(X1 X2XM)
• (FIRST(X1 X2 XM)-l) U FOLLOW(A)
• ELSE
• FIRST(X1 X2XM)

8
So, calculate the Predict set for the Grammar

• Based On Grammar
• E-gt vT
• E-gt P(E)
• P-gt l
• P-gt f
• T-gtE
• T-gtl

9
So, calculate the Predict set for the Grammar

• Based On Grammar
• E-gt vT v
• E-gt P(E) f, (
• P-gt l (
• P-gt f f
• T-gtE
• T-gtl EOF