CIS 400 LECTURE 7

Denotational semantics

Functional calculus

Machine state <memory, input, output>

Current binding to all identifiers in memory and registers

d_sem denotational semantic function (similar to parsing)

Arithmetic:

d_sem^ex: Ex C S®Z È {error}, for EX=all legal expressions, S=states, Z=integers

d_sem^ex (E, S₀) = error if S₀ = <mem, i, o> and mem(v) = undefined for some variable, v, in E. Otherwise:

d_sem^ex (E, S₀) = e_{value expression}

see accompanying handout for d_sem^as and d_sem^rd

Program p

Read (n)

fact := 1;

i := 1;

while i <= n do

fact := fact * i;

i := i + 1;

od;

write(fact);

recurrence relations;

sum(x) = 1 if x = 1

else

sum(x) = sum(x - 1) + 1

so:

sum[3] = sum[2] + 1

= [sum[(1) + 1] + 1]

= [1 + 1] + 1

= 3

Attribute grammars

· Associated with each grammar item-like symbol x-is a set of attributes (or variables) denoted A(x). There are two disjoint sub-sets of A(x).

v S(x), synthesis attributes

v I(x), inherited attributes

· Associated with each grammar rule is a set of semantic functions, (attribute computation functions) and predicate functions

Syntax rule: <assign>®<var> := <exp>

Semantics rule: <var>.<env> ¬ <assign>.env

<expr>.env ¬ <assign>.env

<assign>.lhs_type ¬ <var>.actual_type

<expr>.expected_type ¬ <assign>.lhs_type

Attributes:

actual_type

expected_type

lhs_type

env

Synthesized values:

Computed by semantic function

S(x₀) = f( A(x₁), …A(x_n))

I(x₀) = (x_j), 1 £ j £ n

Variable, expressions, statements

Variable-quadruple

· Name

· Attributes

· Reference, memory location

· Value

Pascal

Snobol: (aliasing)

It is very important to know the specific language protocol for aliasing

Aliasing:

· Equivalence-Fortran

· Define-PL/1

Bindings-association of a program element with a particular characteristic or property

(E.g. Once you declare int x; you can't use it as char x;)

Binding time-time during program formulation or processing when association occurs

· Writing program

· Compiling

· Linking module

· Loading program into memory

· Entry into sub-program

· Execution of statement

In the case of x := x + 10;

· What type is allowed for x?

· What type is x?

· What is representation for x? (binary, hex, etc.)

· What does "+" mean? (add, concatenate, etc.)

· When is it decoded?

When is binding times important?

· Many subtle differences in languages are binding time differences

· Early binding time languages are usually compiled and efficiency is important, (defined/ declared variables before use)

· Late binding languages have interpretive bindings, done at execution, flexibility is most important

Declaration

Explicit vs. implicit

(provides translator with info relative to type checking and storage management)

specifies:

· Data type

· Attributes of data object

· Value

· Name or placement within larger object

· Binding to storage location