Programming Language Principles Tree Generation Programming Language Principles Lecture 5 Prepared by Manuel E. Bermúdez, Ph.D. Associate Professor University of Florida

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.

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

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);

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;

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;

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;

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;

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

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

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;

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.

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 →

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.

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;

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);

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;

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;

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

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;

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

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.

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

Programming Language Principles Tree Generation Programming Language Principles Lecture 5 Prepared by Manuel E. Bermúdez, Ph.D. Associate Professor University of Florida