Topic #5: Translations

Topic #5: Translations

EE 456 – Compiling Techniques

Prof. Carl Sable

Fall 2003

Syntax-Directed Translations

• Translation of languages guided by CFGs• Information associated with programming

language constructs– Attributes attached to grammar symbols– Values of attributes computed by “semantic rules”

associated with grammar productions

• Two notations for associating semantic rules– Syntax-directed definitions– Translation schemes

Semantic Rules

• Semantic rules perform various activities:– Generation of code– Save information in a symbol table– Issue error messages– Other activities

• Output of semantic rules is the translation of the token stream

Conceptual View

• Implementations do not need to follow outline literally

• Many “special cases” can be implemented in a single pass

Attributes

• Each grammar symbol (node in parse tree) has attributes

• Synthesized attributes based on children• Inherited attributes based on siblings and parent• A dependency graph represents dependencies

between attributes• A parse tree showing the values of attributes at

each node is an annotated parse tree

Semantic Rules

• Each semantic rule for production A -> α has the form b := f(c1, c2, …, ck)– f is a function– b may be a synthesized attribute of A– b may be an inherited attribute of a grammar symbol

on the right side of the production

– c1, c2, …, ck are attributes belonging to grammar symbols of production

• An attribute grammar is one in which the functions do not have side effects

S-attributed Definitions

• Synthesized attributes are used extensively in practice

• S-attributed definition: A syntax-directed definition using only synthesized attributes

• Parse tree can be annotated by evaluation nodes during a single bottom up pass

S-attributed Definition Example

Production Semantic Rules

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

Annotated Parse Tree Example

Inherited Attributes

• Inherited Attributes:– Value at a node in a parse tree depends on

attributes of parent and/or siblings– Convenient for expressing dependencies of

programming language constructs on context

• It is always possible to avoid inherited attributes, but they are often convenient

Inherited Attributes Example

Production Semantic Rules

D T L L.in := T.type

T int T.type := integer

T real T.type := real

L L1, idL1.in := L.in

addtype(id.entry, L.in)

L id addtype(id.entry, L.in)

Annotated Inherited Attributes

Dependency Graphs

• Dependency graph:– Depicts interdependencies among

synthesized and inherited attributes– Includes dummy nodes for procedure calls

• Numbered with a topological sort– If mi mj is an edge from mi to mj, then mi

appears before mj in the ordering

– Gives valid order to evaluate semantic rules

Creating a Dependency Graph

for each node n in parse tree for each attribute a of grammar symbol at n construct a node in dependency graph for afor each node n in parse tree for each semantic rule b := f(c1, c2, …, ck) associated with production used at n for i := 1 to k construct edge from node for ci to node for b

Dependency Graph Example

Syntax Trees

• (Abstract) Syntax Trees– Condensed form of parse tree– Useful for representing language constructs– Operators and keywords appear as internal

nodes

• Syntax-directed translation can be based on syntax trees as well as parse trees

Syntax Tree Examples

Implementing Syntax Trees

• Each node can be represented by a record with several fields

• Example: node representing an operator used in an expression:– One field indicates the operator and others point to

records for nodes representing operands– The operator is referred to as the “label” of the node

• If being used for translation, records can have additional fields for attributes

Syntax Trees for Expressions

• Functions will create nodes for the syntax tree– mknode (op, left, right) – creates an

operator node with label op and pointers left and right which point to operand nodes

– mkleaf(id, entry) – creates an identifier node with label id and a pointer to the appropriate symbol table entry

– Mkleaf(num, val) – creates a number node with label num and value val

• Each function returns pointer to created node

Example: a - 4 + c

p1 := mkleaf(id, pa);P2 := mkleaf(num, 4);p3 := mknode('-', p1, p2);p4 := mkleaf(id, pc);p5 := mknode('+', p3, p4);

Constructing Trees for Expressions

Production Semantic Rules

E E1 + T E.np := mknode('+', E1.np, T.np)

E E1 – T E.np := mknode('-', E1.np, T.np)

E T E.np := T.np

T (E) T.np := E.np

T id T.np := mkleaf(id, id.entry)

T num T.np := mkleaf(num, value)

Directed Acyclic Graphs

• Called a dag for short• Convenient for representing expressions• As with syntax trees:

– Every subexpression will be represented by a node– Interior nodes represent operators, children represent

operands

• Unlike syntax trees, nodes may have more than one parent

• Can be created automatically (discussed in textbook)

Example: a + a * (b – c) + (b – c) * d

Bottom-Up Evaluation

• Synthesized attributes can be evaluated with single bottom-up pass

• Parser keeps values of synthesized attributes on stack

• With each reduction, new synthesized attributes computed based on those at top of stack

Bottom-Up Evaluation Example (1)

Production Code Fragment(1) L E \n val[ntop] := val[top-1]

(2) E E1 + t val[ntop] := val[top-2] + val[top]

(3) E T

(4) T T1 * F val[ntop] := val[top-2] * val[top]

(5) T F

(6) F (E) val[ntop] := val[top-1]

(7) F digit

Bottom-Up Evaluation Example (2)

Input State Val Rule

3*5+4\n --- ---

*5+4\n 3 3

*5+4\n F 3 (7)

*5+4\n T 3 (5)

5+4\n T* 3_

+4\n T*5 3_5

+4\n T*F 3_5 (7)

+4\n T 3_5 (4)

…

Input State Val Rule

…

+4\n E 15 (3)

4\n E+ 15_

\n E+4 15_4

\n E+F 15_4 (7)

\n E+T 15_4 (5)

\n E 19 (2)

E\n 19_

L 19 (1)

Evaluating Attributes

• Possible evaluation orders depend on order that nodes are created by parser

• Depth-first search is very common evaluation order

• L-attributed definitions use this technique

• Information appears to flow left-to-right

• Can handle all synthesized and some inherited attributes

Depth-First Evaluation

procedure dfvisit(n: node);begin for each child m of n, from left to right begin evaluate inherited attributes of m dfvisit(m) end; evaluate synthesized attributes of nend

L-attributed Definitions

• A syntax-directed definition is L-attributed:– If each inherited attribute of Xj, for production A X1X2…Xn (1 <= j <= n), depends on:•X1, X2, …, Xj-1 in the production

• The inherited attributes of A

– Any synthesized attribute is OK

• All S-attributed definitions are, by this definition, L-attributed

Non-L-Attributed Example

Production Semantic Rule

A L M

L.i := l(A.i)

M.i := m(L.s)

A.s := f(M.s)

A Q R

R.i := r(A.i)

Q.i := q(R.s)

A.s := f(q.s)

Translation Schemes

• Semantic actions are inserted within the right side of productions

• Placement indicates order of evaluation• If we are dealing with both inherited and

synthesized attributes:– Each inherited attribute must be computed by action

before symbol appears on right side of production– No action may refer to a synthesized attribute of a

symbol to the right of the action– Any synthesized attribute of nonterminal on left must

be computed after computing all referenced attributes

Typesetting Example (1)

Production Semantic Rules

S BB.ps := 10

S.ht := B.ht

B B1 B2

B1.ps := B.ps

B2.ps := B.ps

B.ht := max(B1.ht, B2.ht)

B B1 sub B2

B1.ps := B.ps

B2.ps := shrink(B.ps)

B.ht := disp(B1.ht, B2.ht)

B text B.ht := text.h * B.ps

Typesetting Example (2)

S {B.ps := 10}B {S.ht := B.ht}

B {B1.ps := B.ps}B1 {B2.ps := B.ps}B2 {B.ht := max(B1.ht, B2.ht)}

B {B1.ps := B.ps}B1

sub {B2.ps := shrink(B.ps)}B2 {B.ht := disp(B1.ht, B2.ht)}

B text {B.ht := text.h * B.ps}

Eliminating Left Recursion

• Have seen simple and general solution for CFGs• Now we must take semantic actions and

attributes into account as well• First we will examine synthesized attributes

A A1 Y {A.a := g(A1.a, Y.y)A X {A.a := f(X.x)}

A X {R.i := f(X.x)} R {A.a := R.s}R Y {R1.i := g(R.i, Y.y)} R1 {R.s := R1.s} | ε {R.s := R.i}

Evaluating Expressions Example

E E1 + T {E.val := E1.val + T.val}E E1 – T {E.val := E1.val – T.val}E T {E.val := T.val}T (E) {T.val := E.val}T num {T.val := num.val}

E T {R.i := T.val} R {E.val := R.s}R + T {R1.i := R.i + T.val} R1 {R.s := R1.s} | - T {R1.i := R.i + T.val} R1 {R.s := R1.s} | ε {R.s := R.i}T (E) {T.val := E.val}T num {T.val := num.val}

Creating Syntax Tree ExampleE E1 + T {E.np := mknode('+', E1.np, T.np)}E E1 – T {E.np := mknode('-', E1.np, T.np)}E T {E.np := T.np}T (E) {T.np := E.np}T id {T.np := mkleaf(id, id.entry)}T num {T.np := mkleaf(num, value)}

E T {R.i := T.np} R {E.np R.S}R + T {R1.i := mknode('+', R.i, T.np)} R1 {R.s := R1.s}R - T {R1.i := mknode(‘-', R.i, T.np)} R1 {R.s := R1.s}R ε {R.s := R.i}T (E) {T.np := E.np}T id {T.np := mkleaf(id, id.entry)}T num {T.np := mkleaf(num, value)}

Designing a Predictive Parser

• LL(1) Grammars can be implemented using relatively simple top-down parsing techniques

• For each nonterminal A, construct function:– Parameter for each inherited attribute– Returns synthesized attribute (or attributes)

• Code decides which production to use based on next input symbol

• Right side of production considered left to right:– For token X with synthesized attribute x, store X.x– For nonterminal B, generate c := B(b1,b2,…,bk)

with call to function for B– Copy other actions into the parser

Syntax Tree Code Examplefunction R(i:↑syntax_tree_node):↑syntax_tree_node;

var np, i1, s1, s: ↑syntax_tree_node;begin

if lookahead = '+' then begin/* Case for R + T R */match('+');np := T;i1 := mknode('+', i, np);s1 := R(il)s := s1;

endelse if lookahead = '-' then begin

/* Case for R - T R */…

else s := i; /* Case for R ε */return s

end

Generalized Bottom-Up Evaluation

• Can handle:– All synthesized attributes– All L-attributed definitions based on an LL(1)

grammar

• Can handle some L-attributed definitions based on LR(1) grammars

• Relies on use of copy rules and markers

Copy Rules

• Consider reduction: A X Y• Suppose X has synthesized attribute X.s• X.s will already be on stack before any

reductions take place in subtree below Y• Therefore, this value can be inherited by Y• Define attribute Y.i using a copy rule: Y.i = X.s

Copy Rule Example (1)

D T {L.in := T.type} LT int {T.type := integer}T real {T.type := real}L {L1.in := L.in} L1, id {addtype(id.entry, L.in)}L id {addtype(id.entry, L.in)}

Copy Rule Example (2)

Input State Production Used

real p, q, r ---

p, q, r real

p, q, r T T real

,q, r T id

,q, r T L L id

q, r T L ,

, r T L , id

, r T L L L , id

r T L ,

T L , id

T L L L , id

D D T L

Copy Rule Example (3)

Production Code Fragment

D T L ;

T int val[ntop] := integer

T real val[ntop] := real

L L, id addtype(val[top], val[top-3])

L id addtype(val[top], val[top-1])

Limitation of Copy Rules

• Reaching into stack for an attribute value only works if the position of the value is predictable

• Here, C inherits synthesized attribute A.s– There may or may not be a B between A and C– C.i may be in either val[top-1] or val[top-2]

Production Semantic Rules

S aAC C.i := A.s

S bABC C.i := A.s

C c C.s := g(C.i)

Markers

• Marker nonterminals generating ε are inserted into the grammar

• Each embedded action is replaced by a marker with the action attached

• Actions in the transformed translation scheme terminate productions

• Markers can often be used to move all actions to the right side of productions

Markers Example

E T RR + T {print('+')} R | - T {print('-')} R | εT num {print(num.val)}

E T RR + T M R | - T N R | εM ε {print('+')}N ε {print('+')}T num {print(num.val)}

Using Markers and Copy Rules

Production Semantic Rules

S aAC C.i := A.s

S bABC C.i := A.s

C c C.s := g(C.i)

Production Semantic Rules

S aAC C.i := A.s

S bABMC M.i := A.s; C.i := M.s

M ε M.s := M.i

C c C.s := g(C.i)

Using Markers for Other Rules

Production Semantic Rules

S aAC C.i := f(A.s)

Production Semantic Rules

S aANC N.i := A.s; C.i := N.s

N ε N.s := f(N.i)

Avoiding Inherited Attributes

• It is sometimes possible to avoid inherited attributes by rewriting the underlying grammar

• The goal is to replace inherited attributes with synthesized attributes

D L : TT integer | realL L, id | id

D id LL , id L | : TT integer | real