1. Top-down derivation tree generation
COP4620 – Programming Language Translators Dr. Manuel E. Bermudez

2. Tree generation Red: now Possibilities:
Derivation tree or Abstract Syntax Tree.
Top-down, or Bottom-up.
For original or modified grammar !
Leading up to:
AST, bottom-up, for the original grammar (“the one”).

3. Top-down derivation tree generation
In each procedure,
For each alternative,
Write out the selected production rule
AS SOON AS IT IS KNOWN

4. Top-down derivation tree generation
proc S;
case Next_Token of
T_begin : Write(S → begin SL end);
Read(T_begin);
SL();
Read(T_end);
T_id : Write(S → id :=E;);
Read(T_id);
Read(T_:=);
E();
Read(T_;);
otherwise Error;
end
end;

5. Top-down derivation tree generation
proc SL;
Write(SL → SZ);
S(); Z();
end;
proc Z;
case Next Token of
T_begin, T_id: Write(Z → SZ);
S();Z();
T_end: Write(Z → );
otherwise Error;

6. Top-down derivation tree generation
proc E;
Write(E → TY);
T(); Y();
end;
proc Y;
if Next Token = T_+ then
Write (Y → +TY);
Read(T_+); T(); Y();
else Write (Y → ) ; // new: else clause

7. Top-down derivation tree generation
proc T;
Write (T → PX);
P(); X();
end;
proc X;
if Next Token = T_* then
Write (X → *T);
Read(T_*); T();
else Write (X → ); // new: else clause
T: Could have checked for T_( and T_id..
X: Could have used a case statement.

8. Top-down derivation tree generation
proc P;
case Next Token of
T_(: Write (P → (E));
Read(T_();
E();
Read(T_));
T_id: Write (P → id);
Read(T_id);
otherwise Error;
end;

9. Input String: begin id := (id + id) * id; end Output:
Tree building
Input String:
begin id := (id + id) * id; end
Output:
S → begin SL end
SL → SZ
S → id :=E;
E → TY
T → PX
P → (E)
P → id
X →
Y → +TY
T → PX
P → id
X →
Y →
X → *T
Z →

10. Top-down derivation tree generation
Obvious locations of the Write() statements:
Locations where PT Lookups would take place.
Works because grammar is LL(1).
Two ways to build tree:
As parsing proceeds (“as we go”).
“Write(A->ω)” (or process A->ω) means:
Create tree nodes for ω under “current”;
Update current (complicated: need “current” for each procedure).
Yuck. Better way ? Yep: Bottom-up ! (Coming Soon …)
Build tree after parsing concludes.

11. summary Red: done Possibilities: Leading up to:
Derivation tree or Abstract Syntax Tree.
Top-down, or Bottom-up.
For original or modified grammar.
Leading up to:
AST, bottom-up, for the original grammar (“the one”).