1. Programming Language Concepts
Tree Generation
Programming Language Concepts
Lecture 8
Prepared by
Manuel E. Bermúdez, Ph.D.
Associate Professor
University of Florida

2. String-To-Tree Transduction
Can obtain derivation or abstract syntax tree.
Tree can be generated top-down, or bottom-up.
We will show how to obtain
Derivation tree top-down
AST for the original grammar, bottom-up.

3. Top-Down Generation of Derivation Tree
In each procedure, and for each alternative, write out the appropriate production AS SOON AS IT IS KNOWN

4. Top-Down Generation of Derivation Tree (cont’d)
proc S; {S → begin SL end
→ id := E; }
case Next_Token of
T_begin : Write(S → begin SL end);
Read(T_begin);
SL;
Read(T_end);

5. Top-Down Generation of Derivation Tree (cont’d)
T_id : Write(S → id :=E;);
Read(T_id);
Read (T_:=); E;
Read (T_;);
otherwise Error
end
end;

6. Top-Down Generation of Derivation Tree (cont’d)
proc SL; {SL → SZ}
Write(SL → SZ); S; Z;
end;
proc E; {E → TY}
Write(E → TY); T; Y;

7. Top-Down Generation of Derivation Tree (cont’d)
proc Z; {Z → SZ
→ }
case Next_Token of
T_begin, T_id: Write(Z → SZ); S; Z;
T_end: Write(Z → );
otherwise Error;
end
end;

8. Top-Down Generation of Derivation Tree (cont’d)
proc Y; {Y → +TY
→ }
if Next_Token = T_+ then
Write (Y → +TY);
Read (T_+); T; Y;
else Write (Y → );
end;

9. Top-Down Generation of Derivation Tree (cont’d)
proc T; {T → PX}
Write (T → PX); P; X
end;
proc X;{X → *T
→ }

10. Top-Down Generation of Derivation Tree (cont’d)
if Next_Token = T_* then
Write (X → *T);
Read (T_*); T;
else Write (X → );
end;

11. Top-Down Generation of Derivation Tree (cont’d)
proc P;{P → (E)
→ id }
case Next_Token of
T_(: Write (P → (E));
Read (T_(); E;
Read (T_));
T_id: Write (P → id);
Read (T_id);
otherwise Error;
end;

12. Notes
The placement of the Write statements is obvious precisely because the grammar is LL(1).
Can build the tree “as we go”, or have it built by a post-processor.

13. Example 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 →

15. Bottom-up Generation of the Derivation Tree
We could have placed the write statements at the END of each phrase, instead of the beginning. If we do, the tree will be generated bottom-up.
In each procedure, and for each alternative, write out the production A   AFTER  is parsed.

16. Bottom-up Generation of the Derivation Tree (cont’d)
proc S;{S → begin SL end
→ id := E; }
case Next_Token of
T_begin: Read (T_begin);
SL;
Read (T_end);
Write (S → begin SL end);
T_id: Read (T_id);
Read (T_:=); E;
Read (T_;);
Write (S → id:=E;);
otherwise Error;
end;

17. Bottom-up Generation of the Derivation Tree (cont’d)
proc SL; {SL → SZ} S; Z;
Write(SL → SZ);
end;
proc E; {E → TY} T; Y;
Write(E → TY);

18. Bottom-up Generation of the Derivation Tree (cont’d)
proc Z; {Z → SZ
→ }
case Next_Token of
T_begin, T_id: S; Z;
Write(Z → SZ);
T_end: Write(Z → );
otherwise Error;
end
end;

19. Bottom-up Generation of the Derivation Tree (cont’d)
proc Y; {Y → +TY
→ }
if Next_Token = T_+ then
Read (T_+); T; Y;
Write (Y → +TY);
else Write (Y → );
end;

20. Bottom-up Generation of the Derivation Tree (cont’d)
proc T; {T → PX } P; X;
Write (T → PX)
end;
proc X;{X → *T
→ }
if Next_Token = T_* then
Read (T_*); T;
Write (X → *T);
else Write (X → );
end

21. Bottom-up Generation of the Derivation Tree (cont’d)
proc P;{P → (E)
→ id }
case Next_Token of
T_(: Read (T_(); E;
Read (T_));
Write (P → (E));
T_id: Read (T_id);
Write (P → id);
otherwise Error;
end;

22. Notes The placement of the Write statements is still obvious.
The productions are emitted as procedures quit, not as they start.

23. Notes (cont’d)
Productions emitted in reverse order, i.e., the sequence of productions must be used in reverse order to obtain a right-most derivation.
Again, can built tree “as we go” (need stack of trees), or later.

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

26. Programming Language Concepts
Tree Generation
Programming Language Concepts
Lecture 8
Prepared by
Manuel E. Bermúdez, Ph.D.
Associate Professor
University of Florida