1. Syntax Directed Definition and Syntax directed Translation

2. Compilation in a Nutshell 1
Source code
(character stream)
if (b == 0) a = b;
Lexical analysis
Token stream if ( b == ) a = b ;
Parsing if == = ;
Abstract syntax tree
(AST) b a b if
Semantic Analysis
boolean
int == = ;
Decorated AST
int b
int 0
int a
lvalue
int b

3. Compilation in a Nutshell 2if
boolean
int == = ;
int b
int 0
int a
lvalue
int b
Intermediate Code Generation
CJUMP ==
MEM
CONST
MOVE
NOP
Optimization +
MEM
MEM fp 8 + + fp 4 fp 8
CJUMP ==
Code generation CX
CONST
MOVE
NOP
CMP CX, 0
CMOVZ DX,CX DX CX

4. Outline Syntax-Directed Definitions Evaluation Orders for SDD’s
Applications of Syntax-Directed Definition
Syntax-Directed Translation

5. Definitions Syntax-directed definition (Attribute Grammar)
Productions with semantic rules
Ex: EE1+T E.code=E1.code |T.code|’+’
More readable
Useful for specification
Syntax-directed translation (Translation Scheme)
Productions with semantic actions
Ex: EE1+T { print ’+’ }
More efficient
Useful for implementation

6. Syntax-Directed Definitions
SDD: a context-free grammar with attributes and rules
Attributes: for grammar symbols
Rules: for productions
Attributes for nonterminals
Synthesized attribute: attributes that are passed up a parse tree, i.e., the LHS attribute is computed from the RHS attributes in the production rules
EE1+T E.val=E1.val+T.val
Inherited attribute: attributes that are passed down a parse tree, i.e., the RHS attributes are derived from its LHS attributes or other RHS attributes in the production rules
TF T’ T’.inh=F.val T.val=T’.syn
Terminals can have synthesized attributes, but not inherited attributes

7. Example Production Semantic Rules
1) LE n 2) EE1+T 3) ET 4) TT1*F 5) TF 6) F(E) 7) Fdigit
L.val=E.val E.val=E1.val+T.val E.val=T.val T.val=T1.val*F.val T.val=F.val F.val=E.val F.val=digit.lexval

8. Annotated Parse Tree for 3*5+4 n
Prod Semantic Rules
L→En print(E.val)
E→E1+T E.val := E1.val+T.val
E→T E.val :=T.val
T→T1*F T.val :=T1.val* F.val
T→F T.val :=F.val
F→ (E) F.val :=E.val
F→digit F.val :=digit.lexval
Annotated Parse Tree for 3*5+4 n L
E.val=19 n
E.val=15 +
T.val=4
T.val=15
F.val=4
T.val=3
F.val=5
digit.lexval=4 *
F.val=3
digit.lexval=5
digit.lexval=3

9. Class Exercise S (L)|a L L,S|S
Write an SDD to print the number of parenthesis pair for an input string.
Write an SDD to print the maximum parenthesis depth.

10. Outline Syntax-Directed Definitions Evaluation Orders for SDD’s
Applications of Syntax-Directed Definition
Syntax-Directed Translation

11. Example attribute grammar
A grammar to evaluate signed binary numbers
POS, VAL, and NEG are attributes of the non-terminal (node) they are attached to

12. Example LIST0 BIT LIST1 Note:
pos
val
LIST0
LIST1
BIT
Note:
semantic rules define a partial dependency graph
structure can be used to derive characteristics of generated
total dependency graphs

13. Attribute grammars The attribute dependency graph Evaluation order
nodes represent attributes
edges represent the flow of values
graph is specific to parse tree
size is related to parse tree's size
can be built alongside parse tree
The dependency graph must be acyclic
Evaluation order
Topological sort of the dependency graph to order attributes
Topological order: a linear ordering of the nodes of a directed acyclic graph such that each node comes before all nodes to which it has outbound edges
using this order, evaluate the rules
This order depends on both the grammar and the input string

14. Example attribute grammar
Example Parse tree for -101
NUM
val
SIGN
pos
val
LIST
neg
pos
val
pos
val
LIST
BIT
pos
val
LIST
BIT
pos
val
pos
val
BIT - 1 1

15. Example grammar dependency graph
NUM
val
SIGN
pos
val
LIST0
neg
pos
val
pos
val
LIST1
BIT2
val and neg are synthesized attributes
pos is an inherited attribute
LIST0.pos is an inherited attribute with an empty dependency set.
pos
val
pos
val
LIST2
BIT1
pos
val
BIT0 - 1 1

16. Attribute grammars - Evaluate in this order Yields NUM.val: -5
A topological order for the example
1. SIGN.neg
2. LIST0.pos
3. LIST1.pos
4. LIST2.pos
5. BIT0.pos
6. BIT1.pos
7. BIT2.pos
8. BIT0.val
9. LIST2.val
10. BIT1.val
11. LIST1.val
12. BIT2.val
13. LIST0.val
14. NUM.val
NUM
val
SIGN
pos
val
LIST0
neg
pos
val
pos
val
LIST1
BIT2
pos
val
pos
val
LIST2
BIT1
pos
val
BIT0 - 1 1
Evaluate in this order
Yields NUM.val: -5

17. Example grammar final result
NUM
val :-5
pos: 0
val: 5
SIGN
LIST0
neg : T
LIST1
pos: 1
val: 4
pos: 0
val: 1
BIT2
pos: 2
val: 4
LIST2
BIT1
pos: 1
val: 0
BIT0
pos: 2
val: 4
The evaluation process is also called decorating the
parse tree - 1 1

18. S-Attributed SDD
An SDD is S-attributed if every attribute is synthesized
We can evaluate its attributes in any bottom-up order of the nodes of the parse tree
A postorder traversal
Postorder(N) { for (each child C of N, from the left) postorder(C); evaluate the attributes associated with node N; }

19. L-Attributed SDD
L: dependency-graph edges can go from left to right, but not from right to left
Each attribute must be either:
Synthesized, or
Inherited, but with the rules limited as follows. Suppose production AX1X2…Xn and inherited attribute Xi.a computed by a rule which may only use:
Inherited attributes associated with head A
Either inherited or synthesized attributes associated with X1X2…Xi-1
Either inherited or synthesized attributes associated with Xi, in a way that there’s no cycle

20. L-Attributed example Production Semantic Rules
1) TF T’ 2) T’*F T1’ 3) T’ 4) Fdigit
T’.inh=F.val T.val=T’.syn T1’.inh=T.inh*F.val T’.syn=T1’.syn T’.syn=T’.inh F.val=digit.lexval

21. Example: Annotated parse tree for 3*5
T.val=15
F.Val=3
T’.inh=3 T’.syn=15
digit.lexval=3
T1’.inh=15 T1’.syn=15 *
F.val=5
digit.lexval=5 

22. L-Attributed example
Any SDD containing the following production and rules cannot be L-attributed.
A  B C A.s = B.b;
B.i = f(C.c, A.s)

23. Outline Syntax-Directed Definitions Evaluation Orders for SDD’s
Applications of Syntax-Directed Definitions
Syntax-Directed Translation

24. Applications of Syntax-Directed Definitions
Type checking
Intermediate-code generation
Construction of abstract syntax trees

25. Abstract Syntax Tree
An abstract syntax tree is the procedure’s parse tree with the nodes for most non-terminal symbols removed
E.g., “a + 3 * b”

26. Creating the AST (1 + 2 + (3 + 4)) + 5 S E + S ( S ) E + + 5 E + S 5 1

27. Construction of AST -- Example: S-Attributed Grammar
Production
Semantic Rules
1) EE1+T 2) EE1-T 3) ET 4) T(E) 5) Tid 6) Tnum
E.node=new Node(‘+’, E1.node, T.node) E.node=new Node(‘-’, E1.node, T.node) E.node=T.node T.node=E.node T.node=new Leaf(id, id.entry) T.node=new Leaf(num, num.val)
Ex: a-4+c

28. a－4＋c AST construction E nptr E nptr T nptr T nptr E - id T nptr id +
To entry for c id
num 4 id
To entry for a

29. Class Exercise
Build the parse tree and abstract parse tree for ((a)+(b))

30. Outline Syntax-Directed Definitions Evaluation Orders for SDD’s
Applications of Syntax-Directed Definition
Syntax-Directed Translation

31. Syntax-Directed Translation
SDT: a context-free grammar with semantic actions embedded with production bodies
Complementary to SDD
Actions performed by a preorder traversal of the parse tree
Can be used to implement two classes of SDD’s
LR-parsable grammar: S-attributed SDD
LL-parsable grammar: L-attributed SDD

32. Postfix Translation
Postfix SDT’s: SDT’s with all actions at the right ends of the production bodies
Ex:
LE n { print(E.val); } EE1+T { E.val=E1.val+T.val; } ET { E.val=T.val; } TT1*F { T.val=T1.val*F.val; } TF { T.val=F.val; } F(E) { F.val=E.val; } Fdigit { F.val=digit.lexval; }

33. Parser-Stack Implementation of Postfix SDT’s
Postfix SDT’s can be implemented during LR parsing by executing the actions when reductions occur
To place the attributes along with the grammar symbols on the stack (Fig. 5.19)

34. 5.4.2 Parser-Stack Implementation of Postfix SDT’s
Example 5.15:
Rewrite the actions of the desk-calculator so that they manipulate the parser stack explicitly.

35. SDT’s with Actions inside Productions
Actions may be placed at any position in the body of productions
They are performed immediately after all symbols to its left are processed
BX {a} Y
a is done after we have recognized X
In bottom-up parse, perform a as soon as X appears on top of the stack
In top-down parse, perform a just before we expand Y

36. SDT’s for L-Attributed SDD
Rules for turning L-attributed SDD into SDT
Embed the actions that computes the inherited attributes for nonterminal A immediately before A in the body of production
Place the actions that computes a synthesized attribute for the head of a production at the end of the body

37. Example Ex: grammar for boxes in typesetting language Eqn
BB1B2|B1 sub B2|(B1)|text

38. SDD for Typesetting Boxes
Production
Semantic Rules
1) SB 2) BB1B2 3) BB1 sub B ) B(B1) 5) B text
B.ps=10 B1.ps=B.ps,B2.ps=B.ps B.ht=max(B1.ht,B2.ht) B.dp=max(B1.dp,B2.dp) B1.ps=B.ps,B2.ps=0.7*B.ps B.ht=max(B1.ht,B2.ht-0.25*B.ps) B.dp=max(B1.dp,B2.dp+0.25*B.ps) B1.ps=B.ps, B.ht=B1.ht, B.dp=B1.dp B.ht=getHt(B.ps,text.lexval) B.dp=getDp(B.ps,text.lecval)

39. SDT for Typesetting Boxes