Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
4. Syntax-Directed Translation
Eva Rose
Kristoffer Rose
NYU Courant Institute
Compiler Construction (CSCI-GA.2130-001)
http://cs.nyu.edu/courses/fall14/CSCI-GA.2130-001/lecture-4.pdf
September 25, 2014
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September 25, 2014
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Introduction
SDT: Syntax-Directed Translation
1
Introduction
2
SDT: Syntax-Directed Translation
3
SDD: Syntax-Directed Definition
4
HACS
Review
S-attributed SDDs
Recursive Translation Schemes
Eva Rose, Kristoffer Rose
SDD: Syntax-Directed Definition
Compiler Construction (CSCI-GA.2130-001) 4. Syntax-Directed Translation
HACS
September 25, 2014
2 / 62
Introduction
SDT: Syntax-Directed Translation
1
Introduction
2
SDT: Syntax-Directed Translation
3
SDD: Syntax-Directed Definition
4
HACS
Review
S-attributed SDDs
Recursive Translation Schemes
Eva Rose, Kristoffer Rose
SDD: Syntax-Directed Definition
Compiler Construction (CSCI-GA.2130-001) 4. Syntax-Directed Translation
HACS
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
Context
source program
- Lexical Analysis
- Syntax Analysis
Tokens
Tree
Tree
IR
IR
IR
Eva Rose, Kristoffer Rose
Symbol
Table
- Semantic Analysis
- Intermediate Representation Generator
- Optimizer
- Code Generator
- Machine-Dependent Code Optimizer
target
machine code
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
The Trees
T REE
I NTERIOR NODES
G RAMMAR
parse tree
nonterminals
concrete syntax
abstract syntax tree programming constructs abstract syntax
Example (abstract syntax)
+
−
9
Eva Rose, Kristoffer Rose
2
E → E + E | E − E | digit
5
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
The Trees
T REE
I NTERIOR NODES
G RAMMAR
parse tree
nonterminals
concrete syntax
abstract syntax tree programming constructs abstract syntax
Example (abstract syntax)
+
−
9
Eva Rose, Kristoffer Rose
2
E → E + E | E − E | digit
5
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
Back to the introductory example...
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
From Abstract Syntax Tree (AST)
position = initial + rate * 60
parsed into abstract syntax tree:
=
hid, 1i
+
∗
hid, 2i
hid, 3i
Eva Rose, Kristoffer Rose
hnum, 60i
id
1
2
3
Compiler Construction (CSCI-GA.2130-001) 4. Syntax-Directed Translation
lexeme
position
initial
rate
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
. . . to Annotated AST. . .
= t = float
hid, 1i
t = float
+ t = float
∗ t = float
hid, 2i
t = float
hid, 3i
t = float
Eva Rose, Kristoffer Rose
id
1
2
3
lexeme
position
initial
rate
t
float
float
float
hnum, 60i
t = int
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
. . . to “Fixed” AST
= t = float
hid, 1i
t = float
+ t = float
∗ t = float
hid, 2i
t = float
hid, 3i
t = float
Eva Rose, Kristoffer Rose
id
1
2
3
lexeme
position
initial
rate
t
float
float
float
int-to-float t = float
hnum, 60i
t = int
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Introduction
SDT: Syntax-Directed Translation
1
Introduction
2
SDT: Syntax-Directed Translation
3
SDD: Syntax-Directed Definition
4
HACS
Review
S-attributed SDDs
Recursive Translation Schemes
Eva Rose, Kristoffer Rose
SDD: Syntax-Directed Definition
Compiler Construction (CSCI-GA.2130-001) 4. Syntax-Directed Translation
HACS
September 25, 2014
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
Syntax-Directed Translation
We have built a parse (or AST) tree, now what? How will this
tree and production rules help the translation?
Intuitively, we need to associate something with each
production and each tree node:
I
I
something that evaluates the meaning at each node,
something that emits the meaning as program fragments.
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
Syntax-Directed Translation
We have built a parse (or AST) tree, now what? How will this
tree and production rules help the translation?
Intuitively, we need to associate something with each
production and each tree node:
I
I
something that evaluates the meaning at each node,
something that emits the meaning as program fragments.
Eva Rose, Kristoffer Rose
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
Syntax-Directed Definition (SDD)
Attributes Each grammar symbol (terminal or nonterminal)
has an attribute (“meaning”) associated.
Semantic Rules Each production has semantic rules associated
for computing the attributes.
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
Example: SDD for Infix to Postfix Notation
Consider the grammar:
expr → expr + term
| expr − term
| term
term → 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9
expr has an attribute expr.t, term has an attribute term.t.
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
Example: SDD Infix to Postfix Notation
P RODUCTION
expr → expr1 + term2
expr → expr1 − term2
expr → term1
term → 0
term → 1
...
term → 9
− ||−
Eva Rose, Kristoffer Rose
S EMANTIC R ULE
expr.t = expr1 .t || term2 .t || 0 +0
expr.t = expr1 .t || term2 .t || 0 −0
expr.t = term1 .t
term.t =0 00
term.t =0 10
...
term.t =0 90
means concatenation, − 1 , − 2 disambiguates
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
Attribute Values in Parse Trees
expr.t = 9 5 − 2 +
expr.t = 9 5 −
expr.t = 9
term.t = 9
−
+
term.t = 2
term.t = 5
2
5
9
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
Translation Schemes
I
I
I
I
Equivalent mechanism.
Attaching program fragments to productions.
The program fragments are called semantic
actions/side-effects.
They “emit” the program fragments during “tree traversal”.
Example (rest → +term {print(0 +0 )} rest1 )
rest
+
Eva Rose, Kristoffer Rose
term
{print(0 +0 )}
rest1
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
Translation Schemes
I
I
I
I
Equivalent mechanism.
Attaching program fragments to productions.
The program fragments are called semantic
actions/side-effects.
They “emit” the program fragments during “tree traversal”.
Example (rest → +term {print(0 +0 )} rest1 )
rest
+
Eva Rose, Kristoffer Rose
term
{print(0 +0 )}
rest1
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
Semantic Action Table: Infix to Postfix Notation
PRODUCTIONS WITH SIDE - EFFECTS / ACTIONS
expr → expr1 + term2 {print(‘+0 )}
expr → expr1 − term2 {print(‘−0 )}
expr → term
term → 0 {print(‘00 )}
term → 1 {print(‘10 )}
term → 2 {print(‘20 )}
term → 3 {print(‘30 )}
term → 4 {print(‘40 )}
term → 5 {print(‘50 )}
term → 6 {print(‘60 )}
term → 7 {print(‘70 )}
term → 8 {print(‘80 )}
term → 9 {print(‘90 )}
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
Tree Traversal in Translation Schemes: Depth-First
◦
◦
◦
Eva Rose, Kristoffer Rose
_
◦
◦
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
Semantic Actions/Side-Effects in Parse Tree
expr
{print(0 +0 )}
expr
expr
−
+
{print(0 −0 )}
term
2
0 0
{print( 5 )}
term
{print(0 20 )}
term
5
0 0
{print( 9 )}
9
Input: 9 − 5 + 2. Output (print): 9 5 − 2 +. Single depth-first
traversal.
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
Semantic Actions/Side-Effects in Parse Tree
expr
{print(0 +0 )}
expr
expr
−
+
{print(0 −0 )}
term
2
0 0
{print( 5 )}
term
{print(0 20 )}
term
5
0 0
{print( 9 )}
9
Input: 9 − 5 + 2. Output (print): 9 5 − 2 +. Single depth-first
traversal.
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
Semantic Actions/Side-Effects in Parse Tree
expr
{print(0 +0 )}
expr
expr
−
+
{print(0 −0 )}
term
2
0 0
{print( 5 )}
term
{print(0 20 )}
term
5
0 0
{print( 9 )}
9
Input: 9 − 5 + 2. Output (print): 9 5 − 2 +. Single depth-first
traversal.
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
Summary
expr.t = 95 − 2+
expr.t = 95−
+
term.t = 2
−
term.t = 5
2
expr.t = 9
term.t = 9
attributes/semantic rules (HACS)
5
9
expr
{print(0 +0 )}
expr
+
{print(0 −0 )}
expr
−
term
2
{print(0 50 )}
term
{print(0 20 )}
semantic actions/side-effects (yacc)
term
5
{print(0 90 )}
9
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
Tree Traversal and Translation Schemes
When translation is defined in terms of semantic actions, the
tree traversal order, that is the order in which the nodes are
visited, becomes essential.
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
Exercise
Construct an SDD that generates an attribute t in prefix
notation for each expression expr, for arithmetic expressions.
(You only need to consider: ‘+’,’−’, and ’∗’ expressions). Prefix
notation is where the operator comes before its operands; e.g.,
− x y is the prefix notation for x − y.
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
Solution: SDD for Infix Notation into Prefix Notation
P RODUCTION
expr → expr1 + term2
expr → expr1 − term2
expr → expr1 ∗ term2
expr → term
term → 0
term → 1
...
term → 9
Eva Rose, Kristoffer Rose
S EMANTIC R ULE
expr.t = 0 +0 || expr1 .t || term2 .t
expr.t = 0 −0 || expr1 .t || term2 .t
expr.t = 0 ∗0 || expr1 .t || term2 .t
expr.t = term.t
term.t =0 00
term.t =0 10
...
term.t =0 90
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Introduction
SDT: Syntax-Directed Translation
1
Introduction
2
SDT: Syntax-Directed Translation
3
SDD: Syntax-Directed Definition
4
HACS
Review
S-attributed SDDs
Recursive Translation Schemes
Eva Rose, Kristoffer Rose
SDD: Syntax-Directed Definition
Compiler Construction (CSCI-GA.2130-001) 4. Syntax-Directed Translation
HACS
September 25, 2014
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
Syntax-Directed Definition (SDD)
Recall the key definition:
Grammar Given a context-free grammar.
Attributes Each grammar symbol (terminal or nonterminal)
has a set of attributes associated.
Semantic Rules Each production has a set of semantic rules
associated for computing the attributes.
If X is a symbol, a is an attribute, then X.a denotes the value of
a at node X.
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
Synthesized and Inherited Attributes
Synthesized attributes at node N are defined only in terms of
the attribute values of the children of N, and N itself.
Inherited attributes at node N is defined only in terms of
attribute values at N’s parent, N itself, and N’s
siblings.
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
Example: SDD for Desk Calculator
1.
2.
3.
4.
5.
6.
7.
P RODUCTION
L→E$
E → E1 + T
E→T
T → T1 ∗ F
T→F
F → (E)
F → digit
S EMANTIC R ULE
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
‘val’ and ‘lexval’ are synthesized attributes.
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
Characteristics of Desk Calculator
I
S-attributed (only synthesized attributes)
I
attribute grammar (without side-effects)
Order of attribute evaluation: any bottom-up traversal.
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
Tree Traversal: Depth-First
◦
◦
◦
◦
_
◦
Post-order (default). Pre-order. Binary trees: also in-order.
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
Exercise: Desk Calculator
Give annotated parse trees for the following expressions:
I
I
(3 + 4) ∗ (5 + 6) $
1 ∗ 2 ∗ 3 ∗ (4 + 5) $
(Parse trees showing attributes and their values)
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
Exercise: Mingling with Inherited Attributes. . .
1.
2.
3.
4.
P RODUCTION
T → F T0
T 0 → ∗ F T10
T0 → F → digit
S EMANTIC R ULES
T 0 .inh = F.val; T.val = T 0 .syn
T10 .inh = T 0 .inh × F.val; T 0 .syn = T10 .syn
T 0 .syn = T 0 .inh
F.val = digit.lexval
‘inh’ is inherited, and ‘val’, ‘syn’ are synthesized.
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
Dependency Graphs
Dependency graphs depicts the flow of information among
attributes.
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
Example: Attributes
Parse tree for 3 ∗ 5 based on SDD:
T
F
3O
val
digit 1 lexval
9 i val
inh
∗
F
'5
4O
T0
8 i syn
val
inh
digit 2 lexval
Eva Rose, Kristoffer Rose
Compiler Construction (CSCI-GA.2130-001) 4. Syntax-Directed Translation
7) 6
T0
;7
syn
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
Example: Attributes with Dependency Graph
Parse tree for 3 ∗ 5 based on SDD:
T
F
3O
val
digit 1 lexval
9 i val
inh
∗
F
'5
4O
T0
8 i syn
val
inh
digit 2 lexval
Eva Rose, Kristoffer Rose
Compiler Construction (CSCI-GA.2130-001) 4. Syntax-Directed Translation
7) 6
T0
;7
syn
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
Dependency Graphs
Central problem: Determining the efficient evaluation order for
the attribute instances in a given parse tree.
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
Calculating Attributes
Cycles possible!
P RODUCTION S EMANTIC R ULE
A→B
A.s = B.i; B.i = A.s + 1
When dependency graphs have cycles, evaluation is “stuck”!
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
Well-behaved SDD Classes
Given an SDD, hard to tell if there exists a parse tree whose
dependency graphs have cycles!
Safe way to go: use classes of SDDs that guarantee an
evaluation order:
S-Attributed Definitions all attributes are synthesized.
L-Attributed Definitions “left” restrictions on dependency
graph edges.
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
Well-behaved SDD Classes
Given an SDD, hard to tell if there exists a parse tree whose
dependency graphs have cycles!
Safe way to go: use classes of SDDs that guarantee an
evaluation order:
S-Attributed Definitions all attributes are synthesized.
L-Attributed Definitions “left” restrictions on dependency
graph edges.
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
L-Attributed Definitions
Suppose an attribute rule for A → X1 X2 . . . Xi . . . Xn produces
inherited Xi .a attribute. The rule may only use:
I inherited attributes associated with the head (A),
I inherited or synthesized attributes associated with the
occurences of symbols X1 , X2 , . . . , Xi−1 located left of Xi .
I Inherited or synthesized attributes associated with the
occurence of Xi itself, as long as not part of a dependency
graph cycle!
or, the produced attribute is synthesized.
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
Example: Mingling with Inherited Attributes. . .
Decide if the SDD is L-attributed and argue :
1.
2.
3.
4.
P RODUCTION
T → F T0
T 0 → ∗ F T10
T0 → F → digit
S EMANTIC R ULES
T 0 .inh = F.val; T.val = T 0 .syn
T10 .inh = T 0 .inh × F.val; T 0 .syn = T10 .syn
T 0 .syn = T 0 .inh
F.val = digit.lexval
‘inh’ is inherited, and ‘val’, ‘syn’ are synthesized.
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
Example: Mingling with Inherited Attributes. . .
Decide if the SDD is L-attributed and argue :
1.
2.
3.
4.
P RODUCTION
T → F T0
T 0 → ∗ F T10
T0 → F → digit
S EMANTIC R ULES
T 0 .inh = F.val; T.val = T 0 .syn
T10 .inh = T 0 .inh × F.val; T 0 .syn = T10 .syn
T 0 .syn = T 0 .inh
F.val = digit.lexval
‘inh’ is inherited, and ‘val’, ‘syn’ are synthesized.
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
Example: Mingling with Inherited Attributes. . .
Decide if the SDD is L-attributed and argue :
1.
2.
3.
4.
P RODUCTION
T → F T0
T 0 → ∗ F T10
T0 → F → digit
S EMANTIC R ULES
T 0 .inh = F.val; T.val = T 0 .syn
T10 .inh = T 0 .inh × F.val; T 0 .syn = T10 .syn
T 0 .syn = T 0 .inh
F.val = digit.lexval
‘inh’ is inherited, and ‘val’, ‘syn’ are synthesized.
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
Another example
The following SDD is NOT L-attributed. Why?
P RODUCTION S EMANTIC R ULES
A → BC
A.s = B.b
B.i = F(C.c, A.s)
where B.i is inherited, and A.s, C.c are synthesized.
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
Another example
The following SDD is NOT L-attributed. Why?
P RODUCTION S EMANTIC R ULES
A → BC
A.s = B.b
B.i = F(C.c, A.s)
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
Construction of Abstract Syntax Trees
T REE
I NTERIOR NODES
G RAMMAR
parse tree
nonterminals
concrete syntax
abstract syntax tree programming constructs abstract syntax
Example (abstract syntax)
+
−
9
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2
E → E + E | E − E | digit
5
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
Construction of AST
Example 1: S-attributed SDD for simple expresssions.
1.
2.
3.
4.
5.
6.
I
P RODUCTION
E → E1 + T2
E → E1 − T2
E→T
T → (E)
T → id
T → num
S EMANTIC R ULE
E.node = new Node(0 +0 , E1 .node, T2 .node)
E.node = new Node(0 −0 , E1 .node, T2 .node)
E.node = T.node
T.node = E.node
T.node = new Leaf (id, id.entry)
T.node = new Leaf (num, num.entry)
Show the AST for a − 4 + c
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
Construction of AST
Example 2: L-attributed SDD for simple expresssions.
I
1.
2.
P RODUCTION
E → T E0
E0 → + T E10
3.
E0 → − T E10
4.
5.
6.
7.
E0 → T → (E)
T → id
T → num
S EMANTIC R ULE
E.node = E0 .syn; E0 .inh = T.node
E10 .inh = new Node(0 +0 , E0 .node, T.node)
E0 .syn = E10 .syn
E10 .inh = new Node(0 −0 , E0 .node, T.node)
E0 .syn = E10 .syn
E0 .syn = E0 .inh
T.node = E.node
T.node = new Leaf (id, id.entry)
T.node = new Leaf (num, num.entry)
Show AST and dependency graph for a − 4 + c
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
Syntax-Directed Translation of Type Expressions
P RODUCTION
1 T → BC
2 B → int
3 B → float
4 C → [num]C1
5 C→
I
S EMANTIC R ULE
T.syn = C.syn
C.inh = B.syn
B.syn = integer
B.syn = integer
C.syn = array(num.val, C1 .syn)
C1 .inh = C.inh
C.syn = C.inh
Show AST and dependencies for int[2][3]
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Introduction
SDT: Syntax-Directed Translation
1
Introduction
2
SDT: Syntax-Directed Translation
3
SDD: Syntax-Directed Definition
4
HACS
Review
S-attributed SDDs
Recursive Translation Schemes
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SDD: Syntax-Directed Definition
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HACS
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
HACS Review: Lexical Specification
space [ \t\n] ;
token Int | hDigiti+ ;
token Float | hInti "." hInti ;
token fragment Digit | [0−9] ;
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
HACS Review: Parser Specification
E→E+T |T
T →T∗F |F
F → ( E ) | int | float
(4.1)
sort Exp | JhExp@1i + hExp@2iK@1
| JhExp@2i ∗ hExp@3iK@2
| JhIntiK@3 | JhFloatiK@3
| sugar J(hExp#1@1i)K@3 →Exp#1 ;
E → E + E | E ∗ E | int | float
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
HACS Review: Parser Specification
E→E+T |T
T →T∗F |F
F → ( E ) | int | float
(4.1)
sort Exp | JhExp@1i + hExp@2iK@1
| JhExp@2i ∗ hExp@3iK@2
| JhIntiK@3 | JhFloatiK@3
| sugar J(hExp#1@1i)K@3 →Exp#1 ;
E → E + E | E ∗ E | int | float
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
HACS Review: Parser Specification
E→E+T |T
T →T∗F |F
F → ( E ) | int | float
(4.1)
sort Exp | JhExp@1i + hExp@2iK@1
| JhExp@2i ∗ hExp@3iK@2
| JhIntiK@3 | JhFloatiK@3
| sugar J(hExp#1@1i)K@3 →Exp#1 ;
E → E + E | E ∗ E | int | float
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
This Week
I
S-attributed SDDs.
I
Recursive Translation Schemes.
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
S-attributed SDD
Only synthesized attributes.
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
Example: Type Synthesis SDD
P RODUCTION
E → E1 + E2
| E1 ∗ E2
| int
| float
Eva Rose, Kristoffer Rose
S EMANTIC R ULES
E.t = Unif(E1 .t, E2 .t)
E.t = Unif(E1 .t, E2 .t)
E.t = Int
E.t = Float
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(1)
(2)
(3)
(4)
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
Example: Type Synthesis HACS Sorts
sort Type | Int | Float;
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
Example: Type Synthesis HACS Unification Rules
sort Type | scheme Unif(Type,Type);
Unif(Int, Int) →Int;
Unif(Float, #) →Float;
Unif(#, Float) →Float;
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
Example: Type Synthesis SDD Rule (1)
E → E1 + E2
| E.t = Unif(E1 .t, E2 .t)
(1)
JhExp#1 ↑ type(#t1)i+hExp#2 ↑ type(#t2)iK ↑ type(Unif (#t1, #t2))
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
Example: Type Synthesis SDD Rule (1)
E → E1 + E2
| E.t = Unif(E1 .t, E2 .t)
(1)
JhExp#1 ↑ type(#t1)i+hExp#2 ↑ type(#t2)iK ↑ type(Unif (#t1, #t2))
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
Example: Type Synthesis SDD Rule (1)
E → E1 + E2
| E.t = Unif(E1 .t, E2 .t)
(1)
JhExp#1 ↑ type(#t1)i+hExp#2 ↑ type(#t2)iK ↑ type(Unif (#t1, #t2))
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
Example: Type Synthesis SDD Rule (1)
E → E1 + E2
| E.t = Unif(E1 .t, E2 .t)
(1)
JhExp#1 ↑ type(#t1)i+hExp#2 ↑ type(#t2)iK ↑ type(Unif (#t1, #t2))
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
Example: Type Synthesis SDD Rule (1)
E → E1 + E2
| E.t = Unif(E1 .t, E2 .t)
(1)
JhExp#1 ↑ type(#t1)i+hExp#2 ↑ type(#t2)iK ↑ type(Unif (#t1, #t2))
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
Example: Type Synthesis HACS
attribute ↑type(Type);
sort Exp; ↑type;
J
J
J
J
hExp#1 ↑type(#t1)i + hExp#2 ↑type(#t2)i K↑type(Unif(#t1,#t2));
hExp#1 ↑type(#t1)i ∗ hExp#2 ↑type(#t2)i K↑type(Unif(#t1,#t2));
hInt#i K↑type(Int);
hFloat#i K↑type(Float);
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
Recursive Translation Scheme
// New syntax for value conversion from Int to Float:
sort Exp | Jfloat hExpiK;
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
Recursive Translation Scheme (II)
// New scheme for inserting all needed int−to−float conversions:
sort Exp | scheme I2F(Exp);
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
Recursive Translation Scheme (III)
// Cases for +:
I2F(JhExp#1↑type(Int)i+hExp#2↑type(Int)iK↑type(#t))
→ JhExp I2F(#1)i + hExp I2F(#2)iK↑type(#t);
I2F(JhExp#1↑type(Float)i+hExp#2↑type(Int)iK↑type(#t))
→ JhExp I2F(#1)i + (floathExp I2F(#2)i)K↑type(#t);
I2F(JhExp#1↑type(Int)i+hExp#2↑type(Float)iK↑type(#t))
→ J(floathExp I2F(#1)i) + hExp I2F(#2)iK↑type(#t);
I2F(JhExp#1↑type(Float)i+hExp#2↑type(Float)iK↑type(#t))
→ JhExp I2F(#1)i + hExp I2F(#2)iK↑type(#t);
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
Recursive Translation Scheme (IV)
// Cases for *:
I2F(JhExp#1↑type(Int)i∗hExp#2↑type(Int)iK↑type(#t))
→ JhExp I2F(#1)i ∗ hExp I2F(#2)iK↑type(#t);
I2F(JhExp#1↑type(Float)i∗hExp#2↑type(Int)iK↑type(#t))
→ JhExp I2F(#1)i ∗ (floathExp I2F(#2)i)K↑type(#t);
I2F(JhExp#1↑type(Int)i∗hExp#2↑type(Float)iK↑type(#t))
→ J(floathExp I2F(#1)i) ∗ hExp I2F(#2)iK↑type(#t);
I2F(JhExp#1↑type(Float)i∗hExp#2↑type(Float)iK↑type(#t))
→ JhExp I2F(#1)i ∗ hExp I2F(#2)iK↑type(#t);
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
Recursive Translation Scheme (II)
// Cases for literals:
I2F(JhInt#1iK↑type(#t)) →JhInt#1iK↑type(#t);
I2F(JhFloat#1iK↑type(#t)) →JhFloat#1iK↑type(#t);
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Introduction
SDT: Syntax-Directed Translation
SDD: Syntax-Directed Definition
HACS
Questions?
[email protected]
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[email protected]
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