Compiler Structures

241-437 Compilers: Attr. Grammars/8 1

Compiler Structures

• Objective– describe semantic analysis with attribute

grammars, as applied in yacc and recursive descent parsers

241-437, Semester 1, 2011-2012

8. Attribute Grammars


Overview

1. What is an Attribute Grammar?

2. Parse Tree Evaluation

3. Attributes

4. Attribute Grammars and yacc

5. A Grid Grammar

6. Recursive Descent and Attributes


In this lecture

Source Program

Target Lang. Prog.

Semantic Analyzer

Syntax Analyzer

Lexical Analyzer

FrontEnd

Code Optimizer

Target Code Generator

BackEnd

Int. Code Generator

Intermediate Codeconcentratingon attribute grammars


1. What is an Attribute Grammar?

• An attribute grammar is a context free grammar with semantic actions attached to some of the productions– semantic = meaning

• An action specifies the meaning of a production in terms of its body terminals and nonterminals.


Example Attribute Grammar

L EE E + TE TT T * FT FF ( E )F num

printf(Ebody.val)E.val := Ebody.val + Tbody.valE.val := Tbody.valT.val := Tbody.val * Fbody.valT.val := Fbody.valF.val := Ebody.valF.val := value(num)

Production Semantic Action


2. Parse Tree Evaluation

• One way of understanding semantic actions is as extra information (attributes) attached to the nodes of the parse tree for the input.

• The semantic action specifies the parent node attribute in terms of the attributes of its children.


Basic Parse Tree Input: 9 * 5 + 2

L EE E + TE TT T * FT FF ( E )F num

L

E

TE +

*T

F

9

F

5

F

2

T


Adding Meaning to the Tree

• What is the meaning of "9 * 5 + 2"?– the answer is to evaluate it, to get 47

• Add attributes to the tree, starting from the leaves and working up to the root– use the semantic actions to get the attribute

values


Parse Tree with Actions

L

E

TE +

*T

F

9

F

5

F

2

T

printf(Ebody.val)E.val := Ebody.val + Tbody.valE.val := Tbody.valT.val := Tbody.val * Fbody.valT.val := Fbody.valF.val := Ebody.valF.val := value(num) 9

9

45

45

47

47printf

2

2

evaluatebottom-up

5


3. Attributes

• Attribute values can be– numbers, strings, any data structures,

code, assembly language instructions

• It's not always necessary to build a parse tree in order to evaluate the grammar's action.


Kinds of Attribute

• There are two main kinds of attribute evaluation:– synthesized and inherited attributes

• The value of a synthesized attribute is calculated by using its body values– as in the previous example


Synthesized Attributes in a Tree

• Example:Production Semantic Action

T T * F T.val := Tbody.val * Fbody.val

*T F

T

9

45

5 evaluatebottom-up


Inherited Attributes

• An inherited attribute for a body symbol (i.e. terminal, non-terminal) gets its value from the other body symbols and the parent value– often used for evaluating more complex

programming language features


Inherited Attributes in a Tree

X.x := function(A.a, Y.y)

Y.y := function(A.a, X.x)

A.a

X.x Y.y

A.a

X.x Y.y

Direction of

evaluation

• Two examples:


4. Attribute Grammars and yacc

• yacc supports (synthesized) attribute grammars– yacc actions are semantic actions– no parse tree is needed, since yacc evaluates the

actions using the parser's built-in stack


expr.y Again%token NUMBER

%%

exprs: expr '\n' { printf("Value = %d\n", $1); }

| exprs expr '\n' { printf("Value = %d\n", $2); }

;

expr: expr '+' term { $$ = $1 + $3; }

| expr '-' term { $$ = $1 - $3; }

| term { $$ = $1; }

;

continued

declarations

actions

attributes


term: term '*' factor { $$ = $1 * $3; }

| term '/' factor { $$ = $1 / $3; } /* integer division */

| factor

;

factor: '(' expr ')' { $$ = $2; }

| NUMBER

;

continued

more actions


$$#include "lex.yy.c"

int yyerror(char *s){ fprintf(stderr, "%s\n", s); return 0;}

int main(void){ yyparse(); // the syntax analyzer return 0;}

c code


Evaluation in yaccStack$$ 3$ F$ T$ T *$ T * 5$ T * F$ T$ E$ E +$ E + 4$ E + F$ E + T$ E$ E \n$ Es

Input3*5+4\n$

*5+4\n$*5+4\n$*5+4\n$

5+4\n$+4\n$+4\n$+4\n$

+4\n$ 4\n$

\n$\n$\n$\n$

$$

Stack Actionshiftreduce F numreduce T Fshiftshiftreduce F num reduce T T * Freduce E T shiftshiftreduce F num reduce T F reduce E E + T shiftreduce Es E \naccept

val_3333 3 53 5151515 15 415 415 41919 19

Semantic Action

$$ = $1 (implicit)$$ = $1 (implicit)

$$ = $1 (implicit)$$ = $1 * $3$$ = $1 (implicit)

$$ = $1 (implicit)

$$ = $1 (implicit)$$ = $1 + $3

printf $1

Input: 3 * 5 + 4\n


5. A Grid Grammar

• A robot starts at (0,0) on a grid, and is given compass directions:– n = north, s = south, e = east, w = west

• Evaluate the sequence of directions to work out the final position of the robot.


Example

• The robot receives the directions:– n e e n n w– what is the 'meaning' (semantics) of the

directions?– the 'meaning' is the final robot position, (1,3)

start

final

n

ew

s


5.1. Grid Grammar Input: n w s s

robot pathpath path step | step e | w | s | n

robot

path

path step

spath step

spath step

wpath step

n


Grid Attribute Grammar

robot path

path path step

path

step estep wstep sstep n

printf( pathbody.(x,y) )

path.x := pathbody.x + stepbody.dxpath.y := pathbody.y + stepbody.dypath.(x,y) = (0,0)

step.(dx,dy) := (1,0)step.(dx,dy) := (-1,0)step.(dx,dy) := (0,-1)step.(dx,dy) := (0,1)

Production Semantic Actions


Data Types

• The path rules use (x,y), the position of the robot.

• The step rules use (dx,dy), the step taken by the robot.

• Implementing these data types requires new features of yacc.

(x,y)

dx,dy


Parse Tree with Actions Input: n w s s

robot

path

path step

spath step

spath step

wpath step

n

(0,0)

(0,1)

(-1,1)

(-1,0)

(-1,-1)

0,1

-1,0

0,-1

0,-1

printf (-1,-1)

evaluatebottom-up


5.2. Non-integer Yacc Attributes

• The default yacc attributes (e.g. $$, $1, etc) are integers.

• We want data structures for (x,y) and (dx,dy), coded as two struct types.


Defining New Types

• The new types are collected together inside a %union in the yacc definitions section:

%union{ type1 name1; type2 name2; . . .}

• For the grid:%union{ struct (int x, int y; } pos; struct (int dx, int dy; } offset;}


• The non-terminals that return the new types must be listed.

• Any tokens that use the types must be listed.

• For the grid:% type <offset> step% type <pos> path

Using the Types

these non-terminals returnvalues of the specified type


Using Typed Variables

• If an attribute (variable) is a record, then dotted-name notation is used to refer to its fields– e.g. $$.dx, $1.y

• The default action ($$ = $1) will cause an error if $$ and $1 are not the same type.


5.3. Grid Compiler

$ flex grid.l$ bison grid.y$ gcc grid.tab.c -o gridEval

grid.l,

a flex file

grid.y,

a bison file

bison

flex lex.yy.c

grid.tab.c

gccgridEval,

c executable

#include


Usage

$ ./gridEvalnwssRobot is at (-1,-1)$ ./gridEvaln n n w w w s eRobot is at (-2,2)$

I typed these lines.

I typed ctrl-D


grid.l%%

[nN] {return NORTH;}[sS] {return SOUTH;}[eE] {return EAST;}[wW] {return WEST;}

[ \n\t] ;

%%

int yywrap(void) { return 1; }


grid.y

%union{ struct { int x; int y; } pos; struct { int dx; int dy; } offset;}

%token EAST WEST NORTH SOUTH

%type <offset> step%type <pos> path

%%

continued

typedefinitions

types use by thenon-terminals


robot: path { printf("Robot is at (%d,%d)\n", $1.x, $1.y); }

;

path: path step {$$.x = $1.x + $2.dx; $$.y = $1.y + $2.dy;}

| {$$.x = 0; $$.y = 0;} ;

step: EAST {$$.dx = 1; $$.dy = 0;} | WEST {$$.dx = -1; $$.dy = 0;} | SOUTH {$$.dx = 0; $$.dy = -1;} | NORTH {$$.dx = 0; $$.dy = 1;} ;

%%

continued


#include "lex.yy.c"

int yyerror(char *s){ fprintf(stderr, "%s\n", s); return 0;}

int main(void){ yyparse(); return 0;}


6. Recursive Descent and Attributes

• It is easy to add semantic actions to a recursive descent parser– in many cases, there's no need for the parser to

build a parse tree in order to evaluate the attributes

• The basic translation strategy:– each production becomes a function

continued


• The function (e.g. f()) calls other functions representing its body non-terminals– those functions return values (attributes) to f()– f() combines the values, and returns a value

(attribute)


6.1. The Expressions Parser Again

• The basic LL(1) grammar:Stats => ( [ Stat ] \n )*

Stat => let ID = Expr | Expr

Expr => Term ( (+ | - ) Term )*

Term => Fact ( (* | / ) Fact ) *

Fact => '(' Expr ')' | Int | Id


An Expressions Program (test3.txt)

5 + 6 give answerlet x = 2 declare

variable3 + ( (x*y)/2) // comments// ylet x = 5let y = x /0 error

// comments


• exprParse1.c is a recursive descent parser using the expressions language.

• It differs from exprParse0.c by having semantic actions attached to its productions– these actions evaluate the expressions, and

assign values to expression variables

6.2. Parsing with Actions


Grammar with Actions

• Productions ActionsStats => ( [ Stat ] \n )* ---

Stat => let ID = Expr add id to symbol table;id.val = expr.val;print( id.val );

Stat => Expr print( expr.val );

continued


Expr => Term ( (+ | - ) Term )*

return term1.val (+| -)term2.val (+| -) ...termn.val;

Term => Fact ( (* | / ) Fact ) *

return fact1.val (*| /)fact2.val (*| /) ...factn.val;

continued


Fact => '(' Expr ') return expr.val;

Fact => Int return int.val;

Fact => Id lookup id;if not found then add (id, 0) to table;

return id.val;


The Symbol Table

• The symbol table is a data structure used to store expression variables and their values.

• In exprParse1.c, it's an array of structs, with each struct holding the name of the variable and its current integer value.

. . . .idvalue

syms[]


6.3. Usage

$ gcc -Wall -o exprParse1 exprParse1.c$ ./exprParse1 < test3.txt== 11x being declaredx = 2y being declared== 3x = 5Error: Division by zero; using 1 insteady = 5$


6.4. exprParse1.c Callgraphsame as in exprParse0.c

symboltable (new)

generated fromgrammar (nowwith actions)


6.5. Symbol Table Data Structures

#define MAX_SYMS 15 // max no of variables

typedef struct SymInfo { char *id; // name of variable int value; // value (an integer)} SymbolInfo;

int symNum = 0; // number of symbols storedSymbolInfo syms[MAX_SYMS];

. . . .idvalue

syms[]

0 1 2 14


Symbol Table FunctionsSymbolInfo *getIDEntry(void)/* find _OR_ create symbol table entry for

current tokString; return a pointer to it */{ SymbolInfo *si = NULL; if ((si = lookupID(tokString)) != NULL)

// already declared return si;

// add id to table printf("%s being declared\n", tokString); return addID(tokString, 0); //0 is default value} // end of getIDEntry()


SymbolInfo *lookupID(char *nm)/* is nm in the symbol table? return pointer to struct or NULL */{ int i; for(i=0; i<symNum; i++) if (!strcmp(syms[i].id, nm)) return &syms[i]; return NULL;} // end of lookupID()


SymbolInfo *addID(char *nm, int value)/* add nm and value to the symbol table;

return pointer to struct */{ if (symNum == MAX_SYMS) { printf("Symbol table full; cannot add %s\n", nm); exit(1); }

syms[symNum].id = (char *) malloc(strlen(nm)+1); strcpy(syms[symNum].id, nm); syms[symNum].value = value; SymbolInfo *si = &syms[symNum]; symNum++;

return si;} // end of addID()


Using the Symbol Table• The grammar functions use the symbol table via the

matchID() function.

SymbolInfo *matchId(void)// checks current ID with symbol table{ SymbolInfo *si; dprint("Parsing ident\n"); if ((si = getIDEntry()) == NULL) { printf("Error: id is NULL on line %d\n",lineNum); exit(1); } match(ID); // ok, so consume ID token return si;} // end of matchId()


6.6. Translating the Grammar Rules

• The same translation is carried out as before, but the code is augmented with actions.

• The semantic actions are translated into extra C code in the grammar functions.


The Grammar Functions

• main() and statements() are unchanged from exprParse0.c since they don't have any semantic actions.

• Functions with extra actions:– statement(), expression(), term(), factor()


int main(void){ nextToken(); statements(); match(SCANEOF); return 0;}

void statementsvoid statements((voidvoid))// // statements statements ::= ::= { { // // [ [ statementstatement] ] '\n' }'\n' }{{ dprintdprint("("Parsing Parsing

statements\n statements\n")");; while while ((currToken currToken != !=

SCANEOF SCANEOF) ) {{ if if ((currToken currToken != != NEWLINENEWLINE)) statementstatement()();; matchmatch((NEWLINENEWLINE));; }}} } // // end of statementsend of statements()()

Unchanged Functions


statement() Before and After

void statement(void)// statement ::= ( 'let' ID '=' EXPR ) | EXPR{ if (currToken == LET) { match(LET); match(ID); match(ASSIGNOP); expression(); } else expression();} // end of statement()

with no semantic actions


void statement(void)// statement ::= ( 'let' ID '=' EXPR ) | EXPR{ SymbolInfo *si; int value; dprint("Parsing statement\n"); if (currToken == LET) { match(LET); si = matchId(); // was match(ID); match(ASSIGNOP); value = expression(); si->value = value; printf("%s = %d\n", si->id, value); } else { // expression value = expression(); printf("== %d\n", value); }}

Actions: add id to table; id.val = expr.val; print( id.val );or print( expr.val );


expression() Before and After

void expression(void)// expression ::= term ( ('+'|'-') term )*{ term(); while((currToken == PLUSOP) ||

(currToken == MINUSOP)) { match(currToken); term(); }} // end of expression()



int expression(void)// expression ::= term ( ('+'|'-') term )*{ int result, v2; int isAddOp;

dprint("Parsing expression\n"); result = term(); while((currToken == PLUSOP) || (currToken == MINUSOP)) { isAddOp = (currToken == PLUSOP) ? 1 : 0; match(currToken); v2 = term(); if (isAddOp == 1) // addition result += v2; else // subtraction result -= v2; } return result;} // end of expression()

Action: return term1.val (+| -) term2.val (+| -) ... termn.val;


term() Before and After

void term(void)// term ::= factor ( ('*'|'/') factor )*{ factor(); while((currToken == MULTOP) ||

(currToken == DIVOP)) { match(currToken); factor(); }} // end of term()



int term(void)// term ::= factor ( ('*'|'/') factor )*{ int result, v2; int isMultOp; dprint("Parsing term\n"); result = factor(); while((currToken == MULTOP) || (currToken == DIVOP)) { isMultOp = (currToken == MULTOP) ? 1 : 0; match(currToken); v2 = factor(); if (isMultOp == 1) // multiplication result *= v2; else { // division if (v2 == 0) printf("Error: Division by zero; using 1 instead\n"); else result = result / v2; } } return result;} // end of term()

Action: return fact1.val (*| / ) fact2.val (*| / ) ... factn.val;


factor() Before and After

void factor(void)// factor ::= '(' expression ')' | INT | ID{ if(currToken == LPAREN) { match(LPAREN); expression(); match(RPAREN); } else if(currToken == INT) match(INT); else if (currToken == ID) match(ID); else syntax_error(currToken);} // end of factor()



int factor(void)// factor ::= '(' expression ')' | INT | ID{ int result = 0; dprint("Parsing factor\n"); if(currToken == LPAREN) { match(LPAREN); result = expression(); match(RPAREN); } else if(currToken == INT) { match(INT); result = currTokValue; } else if (currToken == ID) { SymbolInfo *si = matchId(); result = si->value; } else syntax_error(currToken); return result;} // end of factor()

Actions: return expr.val;or return int.val;or add id to table (if new); return id.val;

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