Tree Generation

1
Tree Generation
Programming Language Principles Lecture 5

• 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

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Top-Down Generation of Derivation Tree (contd)

• 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)

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Top-Down Generation of Derivation Tree (contd)

• T_id Write(S ? id E)
• Read(T_id)
• Read (T_)
• E
• Read (T_)
• otherwise Error
• end
• end

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Top-Down Generation of Derivation Tree (contd)

• proc SL SL ? SZ
• Write(SL ? SZ)
• S
• Z
• end
• proc E E ? TY
• Write(E ? TY)
• T
• Y
• end

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Top-Down Generation of Derivation Tree (contd)

• 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

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Top-Down Generation of Derivation Tree (contd)

• proc Y Y ? TY
• ?
• if Next_Token T_ then
• Write (Y ? TY)
• Read (T_)
• T
• Y
• else Write (Y ? )
• end

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Top-Down Generation of Derivation Tree (contd)

• proc T T ? PX
• Write (T ? PX)
• P
• X
• end
• proc XX ? T
• ?

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Top-Down Generation of Derivation Tree (contd)

• if Next_Token T_ then
• Write (X ? T)
• Read (T_)
• T
• else Write (X ? )
• end

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Top-Down Generation of Derivation Tree (contd)

• proc PP ? (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

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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.

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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) E ? TY T ? PX P ? id X ?
Y ? TY T ? PX P ? id X ? Y ? X ? T T ? PX P ?
id X ? Y ? Z ?
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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.

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Bottom-up Generation of the Derivation Tree
(contd)

• proc SS ? 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 ? idE)
• otherwise Error
• end

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Bottom-up Generation of the Derivation Tree
(contd)

• proc SL SL ? SZ
• S
• Z
• Write(SL ? SZ)
• end
• proc E E ? TY
• T
• Y
• Write(E ? TY)
• end

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Bottom-up Generation of the Derivation Tree
(contd)

• 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

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Bottom-up Generation of the Derivation Tree
(contd)

• proc Y Y ? TY
• ?
• if Next_Token T_ then
• Read (T_)
• T
• Y
• Write (Y ? TY)
• else Write (Y ? )
• end

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Bottom-up Generation of the Derivation Tree
(contd)

• proc T T ? PX
• P
• X
• Write (T ? PX)
• end
• proc XX ? T
• ?
• if Next_Token T_ then
• Read (T_)
• T
• Write (X ? T)
• else Write (X ? )
• end

21
Bottom-up Generation of the Derivation Tree
(contd)

• proc PP ? (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

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Notes

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

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Notes (contd)

• 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.

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Example

• Input String
• begin id (id id) id end
• Output

P ? id X ? T ? PX P ? id X ? T ? PX Y ? Y ?
TY E ? TY P ? (E)
P ? id X ? T ? PX X ? T T ? PX Y ? E ? TY S ?
idE Z ? SL ? SZ S ? begin SL end
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Tree Generation
Programming Language Principles Lecture 5

• Prepared by
• Manuel E. Bermúdez, Ph.D.
• Associate Professor
• University of Florida