Symbol Table

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Symbol Table

ASU Textbook Chapter 7.6, 6.5 and 6.3

Tsan-sheng Hsu

tshsu@iis.sinica.edu.tw

http://www.iis.sinica.edu.tw/~tshsu

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Definition

Symbol table: A data structure used by a compiler to keep track of semantics of names.

• Data type.

• When is used: scope.

. The effective context where a name is valid.

• Where it is stored: storage address.

Operations:

• Search: whether a name has been used.

• Insert: add a name.

• Delete: remove a name when its scope is closed.

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Some possible implementations

Unordered list:

. for a very small set of variables;

. coding is easy, but performance is bad for large number of variables.

Ordered linear list:

. use binary search;

. insertion and deletion are expensive;

. coding is relatively easy.

Binary search tree:

. O(log n) time per operation (search, insert or delete) for n variables;

. coding is relatively difficult.

Hash table:

. most commonly used;

. very efficient provided the memory space is adequately larger than the number of variables;

. performance maybe bad if unlucky or the table is saturated;

. coding is not too difficult.

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Hash table

Hash function h(n): returns a value from 0, . . . , m − 1, where n is the input name and m is the hash table size.

• Uniformly and randomly.

Many possible good designs.

• Add up the integer values of characters in a name and then take the remainder of it divided by m.

• Add up a linear combination of integer values of characters in a name, and then take the remainder of it divided by m.

Resolving collisions:

• Linear resolution: try (h(n) + 1) mod m, where m is a large prime number, and then (h(n) + 2) mod m, . . ., (h(n) + i) mod m.

• Chaining: most popular.

. Keep a chain on the items with the same hash value.

. Open hashing.

• Quadratic-rehashing:

. try (h(n) + 1²) mod m, and then

2

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Performance of hash table

Performance issues on using different collision resolution schemes.

Hash table size must be adequately larger than the maximum number of possible entries.

Frequently used variables should be distinct.

• Keywords or reserved words.

• Short names, e.g., i, j and k.

• Frequently used identifiers, e.g., main.

Uniformly distributed.

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Contents in a symbol table

Possible entries in a symbol table:

• Name: a string.

• Attribute:

. Reserved word . Variable name . Type name

. Procedure name . Constant name . · · ·

• Data type.

• Storage allocation, size, . . .

• Scope information: where and when it can be used.

• · · ·

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How names are stored

Fixed-length name: allocate a fixed space for each name allocated.

• Too little: names must be short.

• Too much: waste a lot of spaces.

NAME ATTRIBUTES STORAGE ADDR ...

s o r t

a

r e a d a r r a y

i 2

Variable-length name:

• A string of space is used to store all names.

• For each name, store the length and starting index of each name.

NAME ATTRIBUTES STORAGE ADDR ...

index length

0 5

5 2

7 10

17 3

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

s o r t $ a $ r e a d a r r a y $ i 2 $

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Handling block structures

main() /* C code */

{ /* open a new scope */

int H,A,L; /* parse point A */

...

{ /* open another new scope */

float x,y,H; /* parse point B */

...

/* x and y can only be used here */

/* H used here is float */

...

} /* close an old scope */

...

/* H used here is integer */

...

{ char A,C,M; /* parse point C */

...

} }

Nested blocks mean nested scopes.

Two major ways for implementation:

• Approach 1: multiple symbol tables in one stack.

• Approach 2: one symbol table with chaining.

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Multiple symbol tables in one stack

An individual symbol table for each scope.

• Use a stack to maintain the current scope.

• Search top of stack first.

• If not found, search the next one in the stack.

• Use the first one matched.

• Note: a popped scope can be destroyed in a one-pass compiler, but it must be saved in a multi-pass compiler.

main()

...

} }

H, A, L S.T. for

H, A, L S.T. for S.T. for x,y,H

H, A, L S.T. for S.T. for A,C,M

parse point A parse point B parse point C

searching direction

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Pros and cons for multiple symbol tables

Advantage:

• Easy to close a scope.

Disadvantage: Difficulties encountered when a new scope is opened .

• Need to allocate adequate amount of entries for each symbol table if it is a hash table.

. Waste lots of spaces.

. A block within a procedure does not usually have many local variables.

. There may have many global variables, and many local variables when a procedure is entered.

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One symbol table with chaining (1/2)

A single global table marked with the scope information.

. Each scope is given a unique scope number.

. Incorporate the scope number into the symbol table.

Two possible codings (among others):

• Hash table with chaining.

. Chaining at the front when names hashed into the same location.

main()

...

} }

H(1) L(1)

A(1) H(2)

symbol table:

hash with chaining

H(1) L(1)

A(1)

parse point B parse point C

x(2) y(2)

C(3) M(3) A(3)

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One symbol table with chaining (2/2)

A second coding choice:

• Binary search tree with chaining.

. Use a doubly linked list to chain all entries with the same name.

main()

...

} }

H(1)

L(1) A(1)

H(2)

parse point B parse point C

x(2) y(2)

H(1) A(1) A(3) L(1)

C(3) M(3)

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Pros and cons for a unique symbol table

Advantage:

• Does not waste spaces.

• Little overhead in opening a scope.

Disadvantage: It is difficult to close a scope.

• Need to maintain a list of entries in the same scope.

• Using this list to close a scope and to reactive it for the second pass if needed.

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Records and fields

The “with” construct in PASCAL can be considered an additional scope rule.

• Field names are visible in the scope that surrounds the record declaration.

• Field names need only to be unique within the record.

Another example is the “using namespace” directive in C++.

Example (PASCAL code):

A, R: record

A: integer X: record

A: real;

C: boolean;

end end

...

R.A := 3; /* means R.A := 3; */

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Implementation of field names

Two choices for handling field names:

• Allocate a symbol table for each record type used.

A record

record R

main symbol table

A integer

record X

A real

boolean C

another symbol table

A integer

record X

A real

boolean C

another symbol table

• Associate a record number within the field names.

. Assign record number #0 to names that are not in records.

. A bit time consuming in searching the symbol table.

. Similar to the scope numbering technique.

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Locating field names

Example:

with R do begin

A := 3;

with X do A := 3.3 end

If each record (each scope) has its own symbol table,

• then push the symbol table for the record onto the stack.

If the record number technique is used,

• then keep a stack containing the current record number;

• During searching, succeed only if it matches the name and the current record number.

• If fail, then use next record number in the stack as the current record number and continue to search.

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Overloading (1/3)

A symbol may, depending on context, have more than one semantics.

Examples.

• operators:

. I := I + 3;

. X := Y + 1.2;

• function call return value and recursive function call:

. f := f + 1;

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Overloading (2/3)

Implementation:

• Link together all possible definitions of an overloading name.

• Call this an overloading chain.

• Whenever a name that can be overloaded is defined:

. if the name is already in the current scope, then add the new definition in the overloading chain;

. if it is not already there, then enter the name in the current scope, and link the new entry to any existing definitions;

. search the chain for an appropriate one, depending on the context.

• Whenever a scope is closed, delete the overloading definitions defined in this scope from the head of the chain.

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Overloading (3/3)

Example: PASCAL function name and return variable.

• Within the function body, the two definitions are chained.

. i.e., function call and return variable.

• When the function body is closed, the return variable definition disap- pears.

[PASCAL]

function f: integer;

begin

if global > 1 then f := f +1;

return end

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Forward reference

Definition:

• A name that is used before its definition is given.

• To allow mutually referenced and linked data types, names can some- times be used before thet are declared.

Possible implementations:

• Multi-pass compiler.

• Back-patching.

. Avoid resolving a symbol until all possible places where symbols can be declared have been seen.

. In C, ADA and languages commonly used today, the scope of a declaration extends only from the point of declaration to the end of the containing scope.

If names must be defined before their usages, then one-pass compiler with normal symbol table techniques suffices.

Some possible usages for forward referencing:

• GOTO labels.

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GOTO labels

Some language like C uses labels without declarations.

• Implicit declaration.

Example:

[C]

L0:

...

goto L0;

...

goto L1;

...

L1:

...

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Recursively defined pointer types

Determine the element type if possible;

Chaining together all references to unknown type names until the end of the type declaration;

All type names can then be looked up and resolved.

• Names that are unable to resolved are undeclared type names.

Example:

[PASCAL]

type link = ^ cell;

cell = record

info: integer;

next: link;

end;

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Mutually or recursively called procedures

Need to know the specification of a procedure before its definition.

• Some languages require prototype definitions.

Example:

procedure A() {

...

call B();

...

} ...

procedure B() {

...

call A();

...

}

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Type equivalent and others

How to determine whether two types are equivalent?

• Structural equivalence.

. Express a type definition via a directed graph where nodes are the elements and edges are the containing information.

. Two types are equivalent if and only if their structures (labeled graphs) are the same.

. A difficult job for compilers.

entry = record [entry]

info : real; +---> [info] <real>

coordinates : record +---> [coordinates]

x : integer; +----> [x] <integer>

y : integer; +----> [y] <integer>

end end

• Name equivalence.

. Two types are equivalent if and only if their names are the same.

. An easy job for compilers, but the coding takes more time.

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Usage of symbol table in YACC

Define symbol table routines:

• Find in symbol table(name,scope): check whether a name within a particular scope is currently in the symbol table or not.

. Return not found or

. an entry in the symbol table;

• Insert into symbol table(name,scope)

. Return the newly created entry.

• Delete from symbol table(name,scope)

For interpreters:

• Use the attributes associated with the symbols to hold temporary values.

• Use a structure with maybe some unions to record all attributes.

struct YYTYPE {

char type; /* data type of a variable */

int value;

int addr;

char * namelist; /* list of names */

}

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Hints on YACC coding (1/2)

Declaration:

• D → T L

. { insert each name in $2.namelist into symbol table, i.e., use Find in symbol table to check for possible duplicated names;

. use Insert into symbol table to insert each name in the list with the type $1.type;

. allocate sizeof ($1.type) bytes;

. record the storage address in the symbol table entry;}

• T → int

. {$$.type = int;}

• L → L, id

. {insert the new name yytext into $1.namelist;

. return $$.namelist as $1.namelist;}

| id

. {the variable name is in yytext;

. create a list of one name, i.e., yytext, $$.namelist;}

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Hints on YACC coding (2/2)

Usage of variables:

• Assign S → L var := Expression;

. {$1.addr is the address of the variable to be stored;

. $3.value is the value of the expression;

. generate code for storing $3.value into $1.addr;}

• L var → id

. { use Find in symbol table to check whether yytext is already declared;

. $$.addr = storage address;}

• Expression → Expression + Expression

. {$$.value = $1.value + $3.value;}

| Expression − Expression

. {$$.value = $1.value − $3.value;}

· · ·

| id

. { use Find in symbol table to check whether yytext is . already declared;

. if yes, error ...

. if not, $$.value = the value of the variable yytext}