a calculus of untyped aspect-oriented programs paper by radha jagadeesan alan jeffrey james riely...

A Calculus of Untyped Aspect-Oriented Programs

Paper byRadha

JagadeesanAlan JeffreyJames Riely

Presented byShay Cohen

Contents Introduction A Class-based Language

Syntax Reduction

An Aspect-based Language Syntax Reduction

Weaving The Correctness of Weaving

Introduction - example

Aspects have emerged as a powerful tool

For example:

Introduction - intended

execution

The intended execution semantics is as follows: a call to foo() invokes the code

associated with the advice (the timer is started)

foo() method is invoked when control reaches proceed()

Upon termination of foo(), control returns to the advice

Introduction - Example

public aspect WeavingAspect {

before (String s): execution(void go(*)) && args(s){

System.out.println("before (String s): execution(void go(*)) && args(s) " + s); }

before (Object s): execution(void go(*)) && args(s){

System.out.println("before (Object s): execution(void go(*)) && args(s) " + s); }

}

Introduction- Problem

public class WeavingObject {

public static void main(String[] args) {WeavingObject obj = new

WeavingObject();

String s = null; obj.go(s);

System.out.println();

s = new String("String");obj.go(s);

}

public void go(Object s) {System.out.println("go(Object s) "

+ s); }

}

before (Object s): execution(void go(*)) && args(s) nullgo(Object s) null

before (String s): execution(void go(*)) && args(s) Stringbefore (Object s): execution(void go(*)) && args(s) Stringgo(Object s) String

Introduction- Conclusion

Knowing the aspects semantics is essential.

One cannot naively extend object-oriented reasoning to aspect-oriented programs.

Introduction Reductionism and a specification for

weaving: Advice looked as a primitive Only around advice No reflection Focusing on dynamics

At the end correctness of the weaving transformation will be shown

Weavability will be defined to exclude programs that cannot be woven statically

Contents Introduction A Class-based Language

Syntax Reduction

An Aspect-based Language Syntax Reduction

Weaving The Correctness of Weaving

A Class-based Language - Program

'P P

Transformation of a program

( )D HＴ

D

H

A program P has the form

is a set of declarations is a set of heap allocated threads and objects.

A Class-based Language – class, thread (table 1)

thrd p{new class c<:d {...};} class c<:d {...}

thrd p{ }

class c<:d {...m(x) {C}...}============= =

Superclass dA set of method declarations

thrd p{S}Controlling object pStack S

A Class-based Language – object (table 1)

obj o:c {... f =v ...} obj o:c {... f =v ...}

thrd p{let x=o.f;} thrd p{let x=v;}

obj o:c {... f =v ...}Actual class of the objectValue of fields

obj o:c {... f =u...} obj o:c {... f =v ...}

thrd p{set o.f =v;} thrd p{}

A Class-based Language – Syntax (table 1)

A Class-based Language cont.

Method calls may be dispatched dynamic type static type

let x=o.m(v)

let x=o.c::m(v)

Contents Introduction A Class-based Language

Syntax Reduction

An Aspect-based Language Syntax Reduction

Weaving The Correctness of Weaving

A Class-based Language – Reduction

Reduction proceeds via a standard substitution of parameters

A Class-based Language –Reduction example

c

c

(R -DYN-MSG) thrd p{let x=p{let z=b; let y=p.f; set p.f=z; return (y);};}

(R

-

VAL) th

thrd p{l

rd p{let x=p{let y=p.f; set p.

et x

f=b;

=p.m(b);

return )

}

y

(

c

c

c

c

;};}

(R -GET) thrd p{let x=p{let y=a; set p.f=b; return (y);};}

(R -VAL) thrd p{let x=p{set p.f=b; return (a);};}

(R -SET) thrd p{let x=p{return (a);};}

(R -RET

c

URN) thrd p{let x=a;}

(R -VAL) thrd p{}

class d <: Object {m(x) {let z=x; let y=p.f; set p.f=z; return (y);}}

obj p:d{f=a}

A Class-based Language –Dynamic message (table 2)

c

c

(R -DYN-MSG) thrd p{let x=p{let z=b; let y=p.f; set p.f=z; return

(R -VAL) thrd p{let

(y);}

x=p{le

thrd p{let

t y=p.f; se

;}

t

x=p.m(b

p.f=b;

);

re

tu y

}

rn ( )

c

c

c

c

;};}

(R -GET) thrd p{let x=p{let y=a; set p.f=b; return (y);};}

(R -VAL) thrd p{let x=p{set p.f=b; return (a);};}

(R -SET) thrd p{let x=p{return (a);};}

(R -RET

c

URN) thrd p{let x=a;}

(R -VAL) thrd p{}

class d <: Object {m(x) {let z=x; let y=p.f; set p.f=z; return (y);}}

obj p:d{f=a}

A Class-based Language –Value (table 2)

c

c

thrd p{let x=p{let z=b; let y=p.f; set p.f=z; return (y);};}

(R -VAL)

thrd p{let x

thrd p{let

=p.m(b);}

(

x=p{let y=p.f; set p.f=b; return (y

R -DY

)

N-MSG)

c

c

c

c

(R -GET) thrd p{let x=p{let y=a; set p.f=b; return (y);};}

(R -VAL) thrd p{let x=p{set p.f=b; return (a);};}

(R -SET) thrd p{let x=p{return (a);}

;}

(R -RE

}

T

;};

c

URN) thrd p{let x=a;}

(R -VAL) thrd p{}

class d <: Object {m(x) {let z=x; let y=p.f; set p.f=z; return (y);}}

obj p:d{f=a}

A Class-based Language –Get (table 2)

c

c

thrd p{let x=p.m(b);}

(R -DYN-MSG) thrd p{let x=p{let z=b; let y=p.f; set p.f=z; return (y);};}

thrd p{let x=p{let y=p.f; set p. f= (R -VAL b; return )) (y

c

c

c

c

(R -VAL) thrd p{let x=p{set p.f=b

(R -GET) thrd p{let x=p{

; return (a);};}

(

;};

R -SET

let y=a; se

) thrd p

t p.f=b; return (y

{let x=p{return (a

);};}

);};}

(

R

RE

}

- T

c

URN) thrd p{let x=a;}

(R -VAL) thrd p{}

class d <: Object {m(x) {let z=x; let y=p.f; set p.f=z; return (y);}}

obj p:d{f=a}

A Class-based Language – Set (table 2)

c

c

thrd p{let x=p.m(b);}

(R -DYN-MSG) thrd p{let x=p{let z=b; let y=p.f; set p.f=z; return (y);};}

(R -VAL) thrd p{let x

=p{let y=p.f; set p.f=b; retu

)

rn (y

c

c

c

c thrd p{let

;};}

x=p{set p.f=b;

(R -GET) thrd p{let x=p{let

return (a);};}

(R

y=a

-S

; set p.f=b; ret

ET) thrd p{le

urn (y);};

t x=p{retu

}

rn (a);};

}

(R -V

(R R T

A )

E

L

-

c

URN) thrd p{let x=a;}

(R -VAL) thrd p{}

class d <: Object {m(x) {let z=x; let y=p.f; set p.f=z; return (y);}}

obj p:d{f=b}

A Class-based Language –Return (table 2)

c

c

thrd p{let x=p.m(b);}

(R -DYN-MSG) thrd p{let x=p{let z=b; let y=p.f; set p.f=z; return (y);};}

(R -VAL) thrd p{let x=p{let y=p.f; set p.f=b; return (y)

c

c

c

c

;};}

(R -GET) thrd p{let x=p{let y=a; set p.f=b; return (y);};}

(R -VAL) thrd p{let x=p{set p.f=b; return (a);};}

(R thrd p{let x=p{return (a);};

-SET)

(R ET

}

-R

c

URN) thrd

(R -VAL)

p{let x=a

th {}

;}

rd p

class d <: Object {m(x) {let z=x; let y=p.f; set p.f=z; return (y);}}

obj p:d{f=b}

A Class-based Language -Reduction

c

c

thrd p{let x=p.m(b);}

(R -DYN-MSG) thrd p{let x=p{let z=b; let y=p.f; set p.f=z; return (y);};}

(R -VAL) thrd p{let x=p{let y=p.f; set p.f=b; return (y)

c

c

c

c

;};}

(R -GET) thrd p{let x=p{let y=a; set p.f=b; return (y);};}

(R -VAL) thrd p{let x=p{set p.f=b; return (a);};}

(R -SET) thrd p{let x=p{return (a);};}

(R -RET

c

URN) thrd p{let x=a;}

(R -VAL) thrd p{}

class d <: Object {m(x) {let z=x; let y=p.f; set p.f=z; return (y);}}

obj p:d{f=b}

A Class-based Language – This, Super (table 2)

(L -THIS)c

D class c<: _ {M, m(x) {C}}

D body(c::m) = (x)C

============= =

============= =Ｔ

(R -SUPER)c

D class c<:d {M}

M m(_) {_}

D body(d::m) = (x)C

D body(c::m) = (x)C

============= =

============= =Ｔ

Ｔ

A Class-based Language – Reduction summary

Rules Usage

(RC-LET), (RC-RETURN) and (RC-GARBAGE)

Deal with pushed frames

(RC-VALUE) Returned values to be substituted

(RC-DEC) and (RC-HEAP) Create new classes, objects and threads

(RC-GET) and (RC-SET) Manipulation of fields

(RC-DYN-MSG) and (RC-STC-MSG) Reduction on method calls

(LC-THIS) Method body to be retrieved

(LC-SUPER) Looks for a method in the superclass

Contents Introduction A Class-based Language

Syntax Reduction

An Aspect-based Language Syntax Reduction

Weaving The Correctness of Weaving

An Aspect-based Language – Example

Advised message

An Aspect-based Language – Aspect declaration (table 3)

adv a(x): {C}============= =

Aspect declaration Name – allows reference Command sequence – what to

execute Pointcut – when to execute

pointcuts are presented as elements of the Boolean algebra

An Aspect-based Language – Advice (table 3)

Advised method call Call advice set Execution advice set

let x=o.m[a ; b](v)

ab

let x=proceed(v);

Advice body new command

An Aspect-based Language – method (table 3)

Dynamically dispatched method changed We now have the static type as well Static type is needed for call advice

We ignore call advice for super calls

let x=o:c.m(v)

An Aspect-based Language – Advice creation

Given a method definition

class d <:c {...m(x) {C}...}============= =

class d <:c {...m[ ; cbl_d_m]...}

adv cbl_d_m(x):exec(d::m) {C[proceed/super.m]}

============= =

methods in the aspect calculus do not have any method bodies:

An Aspect-based Language – Aspect based syntax (table 3)

An Aspect-based Language – Semantics of pointcuts (table 4)

(S-EXTENDS)

D class c<:d {_}

D c<:d

Ｔ

(S-REFLEX)

D c<:c Ｔ

(S-TRANS)

D c<:d

D d <:e

D c<:e

Ｔ

Ｔ

Ｔ

An Aspect-based Language – Semantics of pointcuts (table 4)

(PC-EXEC)

D c<:d

D c::m execadv(exec(d::m))

Ｔ

Ｔ

(PC-CALL)

D c<:d

D c::m calladv(call(d::m))

Ｔ

Ｔ

An Aspect-based Language – Semantics of pointcuts (table 4)

An Aspect-based Language – Semantics of pointcuts (table 4)

Contents Introduction A Class-based Language

Syntax Reduction

An Aspect-based Language Syntax Reduction

Weaving The Correctness of Weaving

An Aspect-based Language – Reduction example

A

A

A

(R -DYN-MSG) thrd p{let x=o.m[ca ; cb]();}

(R -ADV-MSG2) thrd p{let x=p

{let y=o.m[ ; cb]();return

();

thrd p{let x=o:c.m();}

};}

(R -ADV-MSG1) thrd p{let x=p

A

A

A

A

{let y=o{return ();};return ();};}

(R -RETURN) thrd p{let x=p{let y=();return ();};}

(R -VAL) thrd p{let x=p{return ();};}

(R -RETURN) thrd p{let x=();}

(R -VAL) th

rd p{}

obj p:Main {}

class Main{m[ ; ma]}

adv ma():exec(Main::m) {let x=o:c.m();return ();}

obj o:c {}

class c{m[ca ; cb]}

adv ca():call(c::m) {let y=proceed();return ();}

adv cb():exec(c::m) {return ();}

An Aspect-based Language – Dynamic message (table 5)

A

A

A

(R -DYN-MSG) thrd p{let x=o.m[ca ; cb]

(R -ADV-MSG2) thrd p{l

thr

et

x=p{let y=o.m[ ; cb]();return ()

d p

;};

{let x

}

(R -

ADV-

=o:c.m(

MSG1) thrd p{let x

();

=

}

p

);}

A

A

A

A

{let y=o{return ();};return ();};}

(R -RETURN) thrd p{let x=p{let y=();return ();};}

(R -VAL) thrd p{let x=p{return ();};}

(R -RETURN) thrd p{let x=();}

(R -VAL) th

rd p{}

obj p:Main {}

class Main{m[ ; ma]}

adv ma():exec(Main::m) {let x=o:c.m();return ();}

obj o:c {}

class c{m[ca ; cb]}

adv ca():call(c::m) {let y=proceed();return ();}

adv cb():exec(c::m) {return ();}

An Aspect-based Language – Advice message (call) (table 5)

A

A

A

thrd p{let x=o.m[ca ; cb]

(R -ADV-MSG2)

thrd p{let x=p{let y=o.m[ ; cb

thrd p{let x

]();return (

=o:c.m();}

(R -DYN-MSG

(R -ADV-MSG

)

1

);

)

(

thrd p{let x

)

};

}

p

;}

=

A

A

A

A

{let y=o{return ();};return ();};}

(R -RETURN) thrd p{let x=p{let y=();return ();};}

(R -VAL) thrd p{let x=p{return ();};}

(R -RETURN) thrd p{let x=();}

(R -VAL) th

rd p{}

obj p:Main {}

class Main{m[ ; ma]}

adv ma():exec(Main::m) {let x=o:c.m();return ();}

obj o:c {}

class c{m[ca ; cb]}

adv ca():call(c::m) {let y=proceed();return ();}

adv cb():exec(c::m) {return ();}

An Aspect-based Language – Advice message (execution) (table 5)

A

A

A

thrd p{let x=o:c.m();}

(R -DYN-MSG) thrd p{let x=o.m[ca ; cb]

thrd p{let x=p{let y=o.

m[ ; cb]();re

();}

(R -ADV-MSG turn ();

(

R

2)

-

ADV-MSG1) th

};}

rd

p

{let x=

p

A

A

A

A

(R -RETURN) thrd p{let x=p{let y=();return ();};}

(R -VAL) thrd p{let x=p{return ();};}

(R -RETURN) thrd

{let y=o{return ();};return

p{let x=();}

(R

();};}

-VAL) h

t

rd p{}

obj p:Main {}

class Main{m[ ; ma]}

adv ma():exec(Main::m) {let x=o:c.m();return ();}

obj o:c {}

class c{m[ca ; cb]}

adv ca():call(c::m) {let y=proceed();return ();}

adv cb():exec(c::m) {return ();}

An Aspect-based Language – Reduction

A

A

A

thrd p{let x=o:c.m();}

(R -DYN-MSG) thrd p{let x=o.m[ca ; cb]();}

(R -ADV-MSG2) thrd p{let x=p{let y=o.m[ ; cb]();return ();};}

(R -ADV-MSG1) thrd p{let x=p

A

A

A

A

{let y=o{return ();};return ();};}

(R -RETURN) thrd p{let x=p{let y=();return ();};}

(R -VAL) thrd p{let x=p{return ();};}

(R -RETURN) thrd p{let x=();}

(R -VAL) th

rd p{}

obj p:Main {}

class Main{m[ ; ma]}

adv ma():exec(Main::m) {let x=o:c.m();return ();}

obj o:c {}

class c{m[ca ; cb]}

adv ca():call(c::m) {let y=proceed();return ();}

adv cb():exec(c::m) {return ();}

An Aspect-based Language – Aspect based Reduction (table 5)

An Aspect-based Language – Reduction summary

Rules Purpose

(RA-DYN-MSG) and (RA-STC-MSG) Rely on the advice sets declared by methods.

(LA-TOP) Ensure that (RA-DYN-MSG)always succeeds

(RA-DYN-MSG) Call and execution advice

(RA-ADV-MSG1) Reduction of execution advice.

(RA-ADV-MSG2) Reduction of call advice

An Aspect-based Language – Coherence

advice that appears in a method declaration must be consistent with that which is attached to a pointcut

A collection of declarations D is coherent (resp. semicoherent)

if whenever D adv b(_): {_} and D class c<:_ {...m[a ; a']...} then

b a iff (resp

DEFINITION 1

. implies) D

(COHERENCE)

c::m ca

.

lladv(

Ｔ )

and b a' iff (resp. implies) D c::m execadv( ) Ｔ

An Aspect-based Language – Close

(C-FIX)

We define the function close(D),

which saturates class

declarations with

DEF

advice:

D is coh

INITION 2 (C

erent

close(D

LOSE).

) = D

(C-CALL)

(C-EXEC)

D adv a(_): {_}

D c::m calladv( )

D = E, class c<:d {M, m[a ; b]}

close(D) = close(E, class c<:d {M, m[a, a; b]})

D adv b(_): {_}

D c::m execadv( )

D= E, class c<:d {M, m[a ; b]}

close

Ｔ

Ｔ

(D) = close(E, class c<:d { M, m[a; b, b]})

An Aspect-based Language – Lemma

If D is semi-coherent, then close(

LEMMA 1

D) is co

(

h

CLOSE).

erent.

Cohe

LEMMA

rence

2 (COHERE

is preser

NCE PRESE

ved by re

RVATIO

duc

N).

tion.

Note that any program where each class declaration is taken

from the class-based language is semi-coherent by construction.

Contents Introduction A Class-based Language

Syntax Reduction

An Aspect-based Language Syntax Reduction

Weaving The Correctness of Weaving

Weaving – Requirements

Correctness is formalized by demanding that the following diagram can be completed

We also expect that a woven program not have spurious new reductions.

Weaving – Macro expansion

Weaving as Macro Expansion The body of a method is determined

by selecting the body of the first advice named in the advice list.

The rule is applied again, after substituting the remaining advice through for proceed.

Weaving – New methods

Weaving by Introducing New Methods given a method m affected by advice

, we create an auxiliary method for each suffix of the list .

Call advised methods are placed in the class of the caller, whereas execution advised methods are placed in the class of the callee.

a

a

Weaving – Advice weaving (table 6)

Weaving – Advice weaving (table 6)

Weaving – Advice weaving, execution, call (table 6, 7)

Contents Introduction A Class-based Language

Syntax Reduction

An Aspect-based Language Syntax Reduction

Weaving The Correctness of Weaving

The Correctness of Weaving – Weavability

Weaving is not correct for all programs. Weaving does not support the dynamic

loading of advice Controlling object of all threads must be

defined All advised messages m[ ; ] in a thread with

controlling object p should arise no dangling references

We formalize these intuitions as Weavability.

The Correctness of Weaving – Weavability definition

We define D; H ; n weavable(·) on stacks in Table 8.

Extend the definition to programs and advice declarations as follows:

D; H; bn(H) weava

DEFINITION 3 (W

ble(D)

D; H; bn(

EAVA

H) weavable(H

BILITY).

Ｔ

Ｔ

Ｔ )

weavable(D H)

D; H; n, x, this, target weavable(this{C})

D; H; n weavable(adv a(x): {C})

============= =

============= =

Ｔ

Ｔ

Ｔ

The Correctness of Weaving – Weavability of stacks (table 8)

The Correctness of Weaving – Lemma

Weavability is preserved by red

LEMMA 3.

uction.

The Correctness of Weaving – Name equivalence

Let be the equivalence on class-based commands generated by:

H obj o:d {_}

D advice(d::m) = [_; b]

D; H let x=o.m(v); let x=o

DEFINITION 4 (NAME EQUIV

.exec_b(v);

D advic

ALENCE)

e(c::m) = b]

.

[_;

Ｔ

Ｔ

Ｔ

D; H let x=o.c::m(v); let x=o.exec_b(v);

C is not a method call

D; H C C

Extend the definition to all other program constructs homorphically using conjunction.

Let P = (D H) and P' = (D' H')

Ｔ

Ｔ

Ｔ Ｔ . We write "P P0" when D; H P P' and

D'; H' P P'.

Ｔ

Ｔ

The Correctness of Weaving – Theorem

Suppose that an aspect-based program P is coherent and weavable, and

that P P'. Then there exists some Q', such that weave(P) Q' and Q' weave(P').

Suppose that an aspect-based p

THEOREM 1

rogram P c

.

is

oherent and weavable, and that weave(P) Q'.

Then there exists some P', such that P P' and P' weave(Q').

The end

Table 1

Table 2

Table 3

Table 4

Table 5

Table 6

Table 7

Table 8