1

Syntax Directed Definition and

Syntax directed Translation

2

Compilation in a Nutshell 1

Source code(character stream)

Lexical analysis

Parsing

Token stream

Abstract syntax tree(AST)

Semantic Analysis

if (b == 0) a = b;

if ( b ) a = b ;0==

if==

b 0

=

a b

if

==

int b int 0

=

int alvalue

int b

boolean

Decorated ASTint

;

;

3

Compilation in a Nutshell 2

Intermediate Code Generation

Optimization

Code generation

if

==

int b int 0

=

int alvalue

int b

boolean int;

CJUMP ==

MEM

fp 8

+

CONST MOVE

0 MEM MEM

fp 4 fp 8

NOP

+ +

CJUMP ==

CONST

MOVE

0 DX

CX

NOP

CX CMP CX, 0

CMOVZ 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: EE1+T E.code=E1.code |T.code|’+’

– More readable– Useful for specification

• Syntax-directed translation (Translation Scheme)– Productions with semantic actions

• Ex: EE1+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

• EE1+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

• TF T’ T’.inh=F.val T.val=T’.syn

• Terminals can have synthesized attributes, but not inherited attributes

7

Example

Production Semantic Rules

1) LE n2) EE1+T3) ET4) TT1*F5) TF6) F(E)7) Fdigit

L.val=E.valE.val=E1.val+T.valE.val=T.valT.val=T1.val*F.valT.val=F.valF.val=E.valF.val=digit.lexval

8

Annotated Parse Tree for 3*5+4 n

digit.lexval=3

F.val=3

T.val=3 *

digit.lexval=5

F.val=5

T.val=15

E.val=15 +

digit.lexval=4

F.val=4

T.val=4

E.val=19 n

L

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

9

Class Exercise

S (L)|aL 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 grammarExample attribute grammar

A grammar to evaluate signed binary numbersProduction Semantic Rules

1 NUM ::= SIGN LIST LIST.pos 0NUM.val if SIGN.neg then -LIST.val else LIST.val

2 SIGN ::= + SIGN.neg false3 SIGN ::= - SIGN.neg true4 LIST ::= BIT BIT.pos LIST.pos

LIST.val BIT.val5 LIST0 ::= LIST1 BIT LIST1.pos LIST0.pos + 1

BIT.pos LIST0.posLIST0.val LIST1.val + BIT.val

6 BIT ::= 0 BIT.val 07 BIT ::= 1 BIT.val 2BIT.pos

POS, VAL, and NEG are attributes of the non-terminal (node) they are attached to

POS, VAL, and NEG are attributes of the non-terminal (node) they are attached to

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ExampleExampleProduction Semantic Rules

5 LIST0 ::= LIST1 BIT LIST1.pos LIST0.pos + 1BIT.pos LIST0.posLIST0.val LIST1.val + BIT.val

pos

pos

pos

valval

val

LIST0

LIST1BIT

Note:• semantic rules define a partial dependency graph• structure can be used to derive characteristics of generated total dependency graphs

13

Attribute grammarsAttribute grammarsThe attribute dependency graph

• 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 rulesThis order depends on both the grammar and the

input string

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Example attribute grammarExample attribute grammarExample Parse tree for -101

NUM

LIST

BIT

val

LIST

LIST BIT

BIT

negposval

posval

posval

posval

posval

posval

SIGN

- 1 0 1

15

Example grammar Example grammar dependency graphdependency graph

• val and neg are synthesized attributes• pos is an inherited attribute

LIST0.pos is an inherited attribute with an empty dependency set.

NUM

LIST0

BIT2

val

LIST1

LIST2BIT1

BIT0

negposvalSIGN

- 1 0 1

posval

posval

posval

posval

posval

0

16

Attribute grammarsAttribute grammarsA topological order for the example

1. SIGN.neg2. 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.val14. NUM.val

Evaluate in this orderYields NUM.val: -5

NUM

LIST0

BIT2

val

LIST1

LIST2BIT1

BIT0

negposvalSIGN

- 1 0 1

posval

posval

posval

posval

posval

0

17

Example grammar final Example grammar final resultresult

NUM

LIST0

BIT2

val :-5

LIST1

LIST2BIT1

BIT0

neg : TSIGN

- 1 0 1

pos: 2

val: 4

0

pos: 2

val: 4

pos: 1

val: 4

pos: 1

val: 0

pos: 0val: 5

pos: 0val: 1

The evaluation process is also called

decorating theparse tree

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 AX1X2…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) TF T’

2) T’*F T1’

3) T’

4) Fdigit

T’.inh=F.valT.val=T’.synT1’.inh=T.inh*F.valT’.syn=T1’.synT’.syn=T’.inh

F.val=digit.lexval

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Example: Annotated parse tree for 3*5

T.val=15

F.Val=3 T’.inh=3T’.syn=15

F.val=5 T1’.inh=15T1’.syn=15

digit.lexval=5

*digit.lexval=3

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)

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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

++ 5

1 +

2 +

3 4

(1 + 2 + (3 + 4)) + 5S

E + S

( S ) E

E + S 5

E + S1

2 E

( S )

E + S

E3 4

27

Construction of AST-- Example: S-Attributed

GrammarProduction Semantic Rules1) EE1+T2) EE1-T3) ET4) T(E)5) Tid6) Tnum

E.node=new Node(‘+’, E1.node, T.node)E.node=new Node(‘-’, E1.node, T.node)E.node=T.nodeT.node=E.nodeT.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 T nptr

E nptr

To entry for a

E

T nptr

id

- T nptr id

id-

id num 4

+

To entry for c

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:

• LE n { print(E.val); }EE1+T { E.val=E1.val+T.val; }ET { E.val=T.val; }TT1*F { T.val=T1.val*F.val; }TF { T.val=F.val; }F(E) { F.val=E.val; }Fdigit { 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– BX {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– BB1B2|B1 sub B2|(B1)|text

38

SDD for Typesetting Boxes

Production Semantic Rules1) SB2) BB1B2

3) BB1 sub B2

4) B(B1)

5) B text

B.ps=10B1.ps=B.ps,B2.ps=B.psB.ht=max(B1.ht,B2.ht)B.dp=max(B1.dp,B2.dp)

B1.ps=B.ps,B2.ps=0.7*B.psB.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