Lesson 11

CDT301 – Compiler Theory, Spring 2011Teacher: Linus Källberg

Outline

• Syntax-directed specifications of language semantics– Syntax-directed definitions– Syntax-directed translation schemes

• Semantic analysis– Focus on type analysis

SYNTAX-DIRECTED SPECIFICATIONS OF LANGUAGE SEMANTICS

Overview of syntax-directed specifications of semantics

• Semantics can be expressed by:– Attaching attributes to grammar symbols– Specifying how to compute those attributes:

• By adding semantic rules, we get a syntax-directed definition (SDD)

• By adding semantic actions, we get a syntax-directed translation scheme (SDT)

Examples of attributes:values of evaluated subtrees

Grammar:E → E + TE → TT → num

E

E + T

T

num

num

E.val = 7

E.val = 3

T.val = 3num.val = 4

num.val = 3String:

3 + 4

Examples of attributes:(line, column) in source file

Grammar:E → E + TE → TT → num

E

E + T

T

num

num

E.coord =(1,1) to (1,6)

E.coord =(1,1) to (1,2)

T.coord =(1,1) to (1,2)

num.coord =(1,5) to (1,6)

num.coord =(1,1) to (1,2)

String:

3 + 4❏ ❏

+.coord =(1,3) to (1,4)

Examples of attributes:data types

Grammar:E → E + TE → TT → num

E

E + T

T

num

num

E.type = int

E.type = int

T.type = intnum.type = int

num.type = intString:

3 + 4

SDDs vs. SDTs

SDDs• Do not specify any evaluation

order for the semantic rules• The rules appear at the end of

the production bodies• The semantic rules may only

have controlled side effects• Mostly useful for specification

SDTs• Explicitly specify an evaluation

order for the semantic actions• The actions may appear

anywhere in the production bodies

• The semantic actions may be arbitrary code fragments

• Mostly useful for implementation

Syntax-directed definitions

• SDD of values of evaluated subtrees:Production RulesE → E1 + T E.val = E1.val + T.val

E → T E.val = T.valT → num T.val = num.val• Each node has an attribute val holding the

value of its evaluated subtree

Types of attributes

• An attribute at a parse tree node N may be of two kinds:– Synthesized

• Computed in terms of attributes at the children of N and/or other attributes at N

– Inherited• Assigned to N at the parent of N

Annotated parse tree for “3 + 4”E.val = 7

E.val = 3

T.val = 3

num.val = 3

T.val = 4

num.val = 4

+

Inherited attributes

• After eliminating left recursion from the previous grammar:

Production RulesE → T E' E'.inh = T.val

E.val = E'.synE' → + T E'1 E'1.inh = E'.inh + T.val

E'.syn = E'1.syn

E' → ε E'.syn = E'.inhT → num T.val = num.val

Annotated parse tree for “3 + 4”

T.val = 3

E.val = 7

num.val = 3

E'.inh = 3E'.syn = 7

+ T.val = 4 E'.inh = 7E'.syn = 7

num.val = 4ε

Classes of SDDs

• S-attributed SDDs:– Only synthesized attributes

• L-attributed SDDs:– Inherited attributes depend on attributes of symbols

to the left in the production (including the head)– Attributes at a node N can also depend on other

attributes at N, if it does not introduce dependency cycles

• In the first lab, you used an L-attributed SDD• In the third lab, you will use an S-attributed SDD

L

S

Example of non-L-attributed SDD

Production Semantic rulesA → B C A.syn = B.syn;

B.inh = f(C.syn, A.syn)

Example SDD• Grammar for mathematical functions:

E → E + EE → E * EE → num | x | ( E )

• Goal: specify an SDD for the translation of an expression into its derivative (as a string), recalling the rules:

x’ = 1n’ = 0(f * g)’ = f’ * g + f * g’(f + g)’ = f’ + g’

Example SDDProduction RulesE → E1 + E2 E.expr = E1.expr || ”+” || E2.expr

E.der = ”(” || E1.der || ”+” || E2.der || ”)”

E → E1 * E2 E.expr = E1.expr || ”*” || E2. expr E.der = ”(” || E1.der || ”*” || E2. expr || ”+” || E1.expr || ”*” || E2.der || ”)”

E → x E.expr = ”x” E.der = ”1”

E → num E.expr = num.val E.der = ”0”

E → ( E1 ) E.expr = ”(” || E1.expr || ”)”E.der = E1.der

Where || is the string concatenation operator

Exercise (1)

Draw the parse tree for the string2*(x + x)

Then decorate it using the SDD on the previous slide.

Exercise (2)Complete the following SDD of values of evaluated subtrees.Production RulesE → T E‘ E'.inh = T.val

E.val = E'.synE' → + T E'1 E'1.inh = E'.inh + T.val

E'.syn = E'1.synE' → ε E'.syn = E'.inhT → F T' ?T' → * F T'1 ?

T' → ε ?F → num F.val = num.valF → ( E ) ?

SEMANTIC ANALYSIS

Semantic analysis

• Why?– Not all errors are lexical or syntactical– Needed to generate correct code

• When?– Can be done during parsing (semantic actions)– Easier in separate passes on some

intermediate program representation

Semantic analysis –name analysis

• Examples of name analyses from trac42:– Is a referenced variable declared?– Is a variable uniquely declared in the scope?– Is a called function declared/defined?

void my_func(void){

int x = y + 23 * my_fnuc();char x = ‘x’;

}

Semantic analysis –type analysis

• Examples of type analyses from trac42:– Is an operator applied to operands of the right types?– Is a function called with the right number of arguments?– Are the function arguments of the right types?

int my_func(int arg){

int x = arg * “bla bla bla”;int y = my_func(23, 78);return my_func(37.8);

}

More examples ofsemantic analyses

• Is a “break” statement enclosed in a loop or a switch? (C, C++, C#, Java…)

• From ADA: The beginning and end of blocks should be tagged with the same name

Static vs. dynamic checks

• Static checks are done during compilation– Static type checks requires type specifications by

the programmer or type inference by the compiler• Dynamic checks are done during runtime

– Dynamic type checks require type information to be carried with data objects. Examples:• A ” type” member in structs• Vpointers and vtables in OO languages

• Trac42 needs only static checks

Type analysis• Type information is gathered from:

– Declarations of variables and functionschar str[256];int some_func(float arg);

– Format of constantsx = 15.7f;c = ’a’;z = 98ul;

• A type system specifies how to assign type attributes to program parts– More on this in the next lecture

What is a type?

• Specification of:– The size needed to store a data object– How to interpret the stored data

• Examples:– Unsigned short: needs 16 bits and is

interpreted as a number from 0 to 65535– Signed short: needs 16 bits and is interpreted

as a number from -32768 to 32767

Using types for code generation

unsigned x;unsigned y = 24;unsigned z = 6;x = y / z;

…divl -8(%ebp)…

int x;int y = 24;int z = 6;x = y / z;

…idivl -8(%ebp)…

Type conversions

• Changes the type of a data object• Explicit:

int a = 12; float b = (float) a;void* p_v = (void*) &a; int* p_i = (int*) p_v;

• Implicit (coercions): inferred by the compiler:char a = 12; int b = a;float x = 17;

• Trac42 does not have type conversions

Representing types

• Type expressions:– Basic types, e.g., int, char, float

• void – No value• error – Erroneous type

– Type names– Type constructors. Examples:

• int* p; pointer(int)• int a[27]; array(27, int);• int f(char a, float b); char × float → int

Representing types –type constructors

• pointer(T)– Pointer to an object of type T

• array(I, T)– Array with I nr of elements of type T

• T1 × T2

– Product of types T1 and T2

Representing types –type constructors

• Records. Similar to products, but includes the member name.– Example:

struct A { int a; char b; };record((a x integer) x (b x char))

• T1 → T2

– Function taking the type T1 as argument and returning T2

– T1 is often a product type

Tree representation oftype expressions

• Example:– int* my_func(char a, char b);

– Type of my_func:char × char → pointer(int)

×

→

char char

pointer

int

Exercise (3)

Write the type expression and draw it as a tree for the functionchar** your_func(int a, char* b, float c);

Conclusion

• SDDs and SDTs are two similar ways to attach semantics to a grammar

• Attributes on grammar symbols can be synthesized or inherited

• Data types are needed to guard against errors and to generate correct code

• Types can be represented as type expressions

Next time

• More type analysis