Structured Concurrent Programming Jayadev Misra Department of - - PowerPoint PPT Presentation

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Structured Concurrent Programming Jayadev Misra Department of - - PowerPoint PPT Presentation

D EPARTMENT OF C OMPUTER S CIENCES Structured Concurrent Programming Jayadev Misra Department of Computer Science University of Texas at Austin Email: misra@cs.utexas.edu web: http://www.cs.utexas.edu/users/psp Collaborators: William Cook,


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DEPARTMENT OF COMPUTER SCIENCES

Structured Concurrent Programming

Jayadev Misra Department of Computer Science University of Texas at Austin Email: misra@cs.utexas.edu web: http://www.cs.utexas.edu/users/psp

Collaborators: William Cook, David Kitchin

UNIVERSITY OF TEXAS AT AUSTIN

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DEPARTMENT OF COMPUTER SCIENCES

Example: Airline

Contact two airlines simultaneously for price quotes. Buy ticket from either airline if its quote is at most $300. Buy the cheapest ticket if both quotes are above $300. Buy any ticket if the other airline does not provide a timely quote. Notify client if neither airline provides a timely quote.

UNIVERSITY OF TEXAS AT AUSTIN 1

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DEPARTMENT OF COMPUTER SCIENCES

Wide-area Computing

Acquire data from remote services. Calculate with these data. Invoke yet other remote services with the results. Additionally Invoke alternate services for failure tolerance. Repeatedly poll a service. Ask a service to notify the user when it acquires the appropriate data. Download an application and invoke it locally. Have a service call another service on behalf of the user.

UNIVERSITY OF TEXAS AT AUSTIN 2

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DEPARTMENT OF COMPUTER SCIENCES

The Nature of Distributed Applications

Three major components in distributed applications: Persistent storage management databases by the airline and the hotels. Specification of sequential computational logic does ticket price exceed $300? Methods for orchestrating the computations We look at only the third problem.

UNIVERSITY OF TEXAS AT AUSTIN 3

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DEPARTMENT OF COMPUTER SCIENCES

Overview of Orc

Orchestration language.

– Invoke services by calling sites – Manage time-outs, priorities, and failures

A Program execution

– calls sites, – publishes values.

Simple

– Language has only 3 combinators. – Semantics described by labeled transition system and traces. – Combinators are (monotonic and) continuous.

UNIVERSITY OF TEXAS AT AUSTIN 4

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DEPARTMENT OF COMPUTER SCIENCES

Structure of Orc Expression

Simple: just a site call, CNN (d)

Publishes the value returned by the site.

composition of two Orc expressions:

do

f and g in parallel f j g

Symmetric composition for all

x from f do g f > x > g

Piping for some

x from g do f f where x:2 g

Asymmetric composition

UNIVERSITY OF TEXAS AT AUSTIN 5

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DEPARTMENT OF COMPUTER SCIENCES

Symmetric composition:

f j g CNN j B B C : calls both CNN and B B C simultaneously.

Publishes values returned by both sites. (

0, 1 or 2 values) Evaluate f and g independently. Publish all values from both. No direct communication or interaction between f and g.

They may communicate only through sites.

UNIVERSITY OF TEXAS AT AUSTIN 6

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DEPARTMENT OF COMPUTER SCIENCES

Pipe:

f > x > g

For all values published by

f do
  • g. Publish only the values from
g.
  • CNN
> x > E mail (addr ess; x)

Call

CNN . Bind result (if any) to
  • x. Call
E mail (addr ess; x).

Publish the value, if any, returned by

E mail.
  • (C
N N j B B C ) > x > E mail (addr ess; x)

May call

E mail twice. Publishes up to two values from E mail.

UNIVERSITY OF TEXAS AT AUSTIN 7

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DEPARTMENT OF COMPUTER SCIENCES

Notation

Write

f
  • g for
f > x > g if x unused in g.

Precedence:

f > x > g j h > y > u (f > x > g ) j (h > y > u)

UNIVERSITY OF TEXAS AT AUSTIN 8

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DEPARTMENT OF COMPUTER SCIENCES

Schematic of piping

f g1 g0 g2

Figure 1: Schematic of

f > x > g

UNIVERSITY OF TEXAS AT AUSTIN 9

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DEPARTMENT OF COMPUTER SCIENCES

Asymmetric parallel composition:

(f where x:2 g )

For some value published by

g do f . Publish only the values from f . E mail (addr ess; x) where x:2 (CNN j B B C )

Binds

x to the first value from CNN j B B C . Evaluate f and g in parallel.

Site calls that need

x are suspended; other site calls proceed. (M j N (x)) where x:2 g When g returns a value, assign it to x and terminate g.

Resume suspended calls.

Values published by f are the values of (f where x:2 g ).

UNIVERSITY OF TEXAS AT AUSTIN 10

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DEPARTMENT OF COMPUTER SCIENCES

Some Fundamental Sites

0: never responds. l et(x; y ;
  • ): returns a tuple of its argument values.
if (b): boolean b,

returns a signal if

b is true; remains silent if b is false. S ig nal returns a signal immediately. Same as if (true ). R timer (t): integer t, t
  • 0, returns a signal
t time units later.

UNIVERSITY OF TEXAS AT AUSTIN 11

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DEPARTMENT OF COMPUTER SCIENCES

Centralized Execution Model

An expression is evaluated on a single machine (client). Client communicates with sites by messages. All fundamental sites are local to the client.

All except

R timer respond immediately. Concurrent and distributed executions are derived from an expression.

UNIVERSITY OF TEXAS AT AUSTIN 12

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DEPARTMENT OF COMPUTER SCIENCES

Expression Definition

MailOn e (a)
  • E
mail (a; m) where m:2 (CNN j BBC ) MailL
  • p
(a; t)
  • MailOn
e (a)
  • R
timer (t)
  • MailL
  • p
(a; t) Expression is called like a procedure.

May publish many values.

MailL
  • p does not publish a value.
Site calls are strict; expression calls non-strict.

UNIVERSITY OF TEXAS AT AUSTIN 13

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DEPARTMENT OF COMPUTER SCIENCES

Metronome

Publish a signal at every time unit.

Metr
  • nome
  • S
ig nal j (R timer (1)
  • Metr
  • nome
)

S R S R

Publish

n signals. BM (0)
  • BM
(n)
  • S
ig nal j (R timer (1)
  • BM
(n
  • 1))

UNIVERSITY OF TEXAS AT AUSTIN 14

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DEPARTMENT OF COMPUTER SCIENCES

Example of Expression call

Site Quer y returns a value (different ones at different times). Site A ept(x) returns x if x is acceptable;

it is silent otherwise.

Produce all acceptable values by calling Quer y at unit intervals

forever.

Metr
  • nome
  • Quer
y > x > A ept(x)

UNIVERSITY OF TEXAS AT AUSTIN 15

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DEPARTMENT OF COMPUTER SCIENCES

Time-out

Publish

M ’s response if it arrives before t, and 0 otherwise. l et(z )

where

z :2 M j R timer (t)
  • l
et(0)

UNIVERSITY OF TEXAS AT AUSTIN 16

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DEPARTMENT OF COMPUTER SCIENCES

Fork-join parallelism

Call

M and N in parallel.

Return their values as a tuple after both respond.

l et(u; v )

where

u:2 M v :2 N

This stands for:

(l et(u; v )

where

u:2 M )

where

v :2 N

UNIVERSITY OF TEXAS AT AUSTIN 17

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DEPARTMENT OF COMPUTER SCIENCES

Recursive definition with time-out

Call a list of sites. Count the number of responses received within 10 time units.

tal l y ([ ℄)
  • l
et(0) tal l y (M : M S )
  • u
+ v

where

u:2 (M
  • l
et(1)) j (R timer (10)
  • l
et(0)) v :2 tal l y (M S )

UNIVERSITY OF TEXAS AT AUSTIN 18

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DEPARTMENT OF COMPUTER SCIENCES

Barrier Synchronization in

M
  • f
j N
  • g
f and g start only after both M and N complete.

(

l et(u; v )

where

u:2 M v :2 N )
  • (f
j g )

UNIVERSITY OF TEXAS AT AUSTIN 19

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DEPARTMENT OF COMPUTER SCIENCES

Arbitration

In CCS/ Pi-Calculus:

  • :P
+
  • :Q

In Orc:

if (b )
  • P
j if (:b )
  • Q

where

b :2 (Al pha
  • l
et(true )) j (B eta
  • l
et(false ))

Orc does not permit non-deterministic internal choice.

UNIVERSITY OF TEXAS AT AUSTIN 20

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DEPARTMENT OF COMPUTER SCIENCES

Priority

Publish N ’s response asap, but no earlier than 1 unit from now. D el ay
  • (R
timer (1)
  • l
et(u)) where u:2 N Call M , N together.

If

M responds within one unit, take its response.

Else, pick the first response.

l et(x) where x:2 (M j D el ay )

UNIVERSITY OF TEXAS AT AUSTIN 21

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DEPARTMENT OF COMPUTER SCIENCES

Interrupt

f

Evaluation of

f can not be directly interrupted.

Introduce two sites:

  • Interrupt
:set: to interrupt f
  • Interrupt
:g et: responds after Interrupt :set has been called.

Instead of

f , evaluate l et(z ) where z :2 (f j Interrupt :g et)

UNIVERSITY OF TEXAS AT AUSTIN 22

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DEPARTMENT OF COMPUTER SCIENCES

Parallel or

Sites

M and N return booleans. Compute their parallel or. ift (b)
  • if
(b)
  • l
et(true ): returns true if b is true; silent otherwise. ift (x) j ift (y ) j
  • r
(x; y )

where

x:2 M ; y :2 N

To return just one value:

l et(z )

where

z :2 ift (x) j ift (y ) j
  • r
(x; y ) x:2 M y :2 N

UNIVERSITY OF TEXAS AT AUSTIN 23

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DEPARTMENT OF COMPUTER SCIENCES

Airline quotes: Application of Parallel or

Contact airlines

A and B.

Return any quote if it is below

as soon as it is available,
  • therwise return the minimum quote.
thr eshold (x) returns x if x < ; silent otherwise. Min (x; y ) returns the minimum of x and y. l et(z )

where

z :2 thr eshold (x) j thr eshold (y ) j Min (x; y ) x:2 A y :2 B

UNIVERSITY OF TEXAS AT AUSTIN 24

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DEPARTMENT OF COMPUTER SCIENCES

Sequential Computing

  • (S
; T ) is (S
  • T
)
  • if
b then S

else

T

is

if (b )
  • S
j if (:b )
  • T
  • while
B (x) do x:= S (x) l
  • op(x)
  • B
(x) > b > (if (b )
  • S
(x) > y > l
  • op(y
) j if (:b )
  • l
et(x))

UNIVERSITY OF TEXAS AT AUSTIN 25

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DEPARTMENT OF COMPUTER SCIENCES

Angelic vs. Demonic non-determinism

for all x from f do g: implements angelic non-determinism.

All paths of computation are explored.

for some x from f do g: implements demonic non-determinism.

Some selected path of computation is explored.

UNIVERSITY OF TEXAS AT AUSTIN 26

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DEPARTMENT OF COMPUTER SCIENCES

Backtracking: Eight queens

... ...

Row 1 Row 2 Row 3 x

...

x x 1 x 1 1 7 7 7 7 x

... ...

x x 1 1 7

Figure 2: Backtrack Search for Eight queens

UNIVERSITY OF TEXAS AT AUSTIN 27

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DEPARTMENT OF COMPUTER SCIENCES

Eight queens; contd.

configuration: placement of queens in the last i rows. Represented

by a list of

i values from 0::7 Valid configuration: no queen captures another. v al id(z ) returns z if configuration z is valid; silent otherwise. Produce all valid extensions of z by placing n additional queens: extend(z ; 1)
  • v
al id(0: z ) j v al id(1: z ) j
  • j
v al id(7: z ) extend(z ; n)
  • extend(z
; 1) > y > extend(y ; n
  • 1)
Solve the original problem by calling extend([ ℄; 8).

UNIVERSITY OF TEXAS AT AUSTIN 28

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DEPARTMENT OF COMPUTER SCIENCES

Processes

Processes typically communicate via channels. For channel , treat :put and :g et as site calls. In our examples, :g et is blocking and :put is non-blocking. Other kinds of channels can be programmed as sites.

UNIVERSITY OF TEXAS AT AUSTIN 29

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DEPARTMENT OF COMPUTER SCIENCES

Typical Iterative Process

Forever: Read

x from channel , compute with x, output result on e: P ( ; e)
  • :g
et > x > Compute (x) > y > e:put(y )
  • P
( ; e)

Process (network) to read from both

and d and write on e: N et( ; d; e)
  • P
( ; e) j P (d; e)

UNIVERSITY OF TEXAS AT AUSTIN 30

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DEPARTMENT OF COMPUTER SCIENCES

Interaction

Run a dialog with a child. Forever: child inputs an integer on channel

p

Process outputs true on channel

q iff the number is prime.

Sites:

:g et and :put, for channel . P r ime?(x) returns true iff x is prime. D ial
  • g
(p; q )
  • p:g
et > x > P r ime?(x) > b > q :put(b)
  • D
ial
  • g
(p; q )

UNIVERSITY OF TEXAS AT AUSTIN 31

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DEPARTMENT OF COMPUTER SCIENCES

Laws of Kleene Algebra

(Zero and

j ) f j = f

(Commutativity of

j ) f j g = g j f

(Associativity of

j ) (f j g ) j h = f j (g j h)

(Idempotence of

j ) f j f = f

(Associativity of

) (f
  • g
)
  • h
= f
  • (g
  • h)

(Left zero of

)
  • f
=

(Right zero of

) f
  • =

(Left unit of

) S ig nal
  • f
= f

(Right unit of

) f > x > let (x) = f

(Left Distributivity of

  • ver
j ) f
  • (g
j h) = (f
  • g
) j (f
  • h)

(Right Distributivity of

  • ver
j ) (f j g )
  • h
= (f
  • h
j g
  • h)

UNIVERSITY OF TEXAS AT AUSTIN 32

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DEPARTMENT OF COMPUTER SCIENCES

Laws which do not hold

(Idempotence of

j ) f j f = f

(Right zero of

) f
  • =

(Left Distributivity of

  • ver
j ) f
  • (g
j h) = (f
  • g
) j (f
  • h)

UNIVERSITY OF TEXAS AT AUSTIN 33

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DEPARTMENT OF COMPUTER SCIENCES

Additional Laws

(Distributivity over

)

if

g is x-free (f
  • g
where x:2 h) = (f where x:2 h)
  • g

(Distributivity over

j )

if

g is x-free (f j g where x:2 h) = (f where x:2 h) j g

(Distributivity over where ) if

g is y-free ((f where x:2 g ) where y :2 h) = ((f where y :2 h) where x:2 g )

(Elimination of where) if

f is x-free, for site M (f where x:2 M ) = f j M
  • UNIVERSITY OF TEXAS AT AUSTIN

34

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DEPARTMENT OF COMPUTER SCIENCES

Rules for Site Call

k fresh M (v ) M k (v ) ! ?k

(SITECALL)

?k k ?v ! let (v )

(SITERET)

let (v ) !v !

(LET)

UNIVERSITY OF TEXAS AT AUSTIN 35

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DEPARTMENT OF COMPUTER SCIENCES

Symmetric Composition

f a ! f f j g a ! f j g

(SYM1)

g a ! g f j g a ! f j g

(SYM2)

UNIVERSITY OF TEXAS AT AUSTIN 36

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DEPARTMENT OF COMPUTER SCIENCES

Sequencing

f a ! f a 6= !v f > x > g a ! f > x > g

(SEQ1N)

f !v ! f f > x > g
  • !
(f > x > g ) j [v =x℄:g

(SEQ1V)

UNIVERSITY OF TEXAS AT AUSTIN 37

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DEPARTMENT OF COMPUTER SCIENCES

Asymmetric Composition

f a ! f f where x:2 g a ! f where x:2 g

(ASYM1N)

g !v ! g f where x:2 g
  • !
[v =x℄:f

(ASYM1V)

g a ! g a 6= !v f where x:2 g a ! f where x:2 g

(ASYM2)

UNIVERSITY OF TEXAS AT AUSTIN 38

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DEPARTMENT OF COMPUTER SCIENCES

Expression Call

[[ E (x)
  • f
℄℄ 2 D E (p)
  • !
[p=x℄:f

(DEF)

UNIVERSITY OF TEXAS AT AUSTIN 39

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SLIDE 41

DEPARTMENT OF COMPUTER SCIENCES

Rules

k fresh M (v ) M k (v ) ! ?k ?k k ?v ! let (v ) let (v ) !v ! f a ! f f j g a ! f j g g a ! g f j g a ! f j g [[ E (x)
  • f
℄℄ 2 D E (p)
  • !
[p=x℄:f f a ! f a 6= !v f > x > g a ! f > x > g f !v ! f f > x > g
  • !
(f > x > g ) j [v =x℄:g f a ! f f where x:2 g a ! f where x:2 g g !v ! g f where x:2 g
  • !
[v =x℄:f g a ! g a 6= !v f where x:2 g a ! f where x:2 g

UNIVERSITY OF TEXAS AT AUSTIN 40

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SLIDE 42

DEPARTMENT OF COMPUTER SCIENCES

Example

((M (x) j l et(x)) > y > R (y )) where x:2 (N j S ) S k ! fCall S : S S k ! ?k; N j S S k ! N j ?k g ((M (x) j l et(x)) > y > R (y )) where x:2 (N j ?k ) N l ! fCall N g ((M (x) j l et(x)) > y > R (y )) where x:2 (?l j ?k ) l ?5 ! f ?l l ?5 ! l et(5); ?l j ?k l ?5 ! l et(5) j ?k g ((M (x) j l et(x)) > y > R (y )) where x:2 (l et(5) j ?k )

UNIVERSITY OF TEXAS AT AUSTIN 41

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SLIDE 43

DEPARTMENT OF COMPUTER SCIENCES

Example; contd.

((M (x) j l et(x)) > y > R (y )) where x:2 (l et(5) j ?k )
  • !
f l et(5) !5 ! 0; l et(5) j ?k !5 ! j ?k g (M (5) j l et(5)) > y > R (y )
  • !
f l et(5) !5 ! 0; M (5) j l et(5) !5 ! M (5) j 0; f !v ! f 0 implies f > y > g
  • !
(f > y > g ) j [v =y ℄:g g ((M (5) j 0) > y > R (y )) j R (5) R n (5) ! fcall R with argument (5) g ((M (5) j 0) > y > R (y )) j ?n

UNIVERSITY OF TEXAS AT AUSTIN 42

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DEPARTMENT OF COMPUTER SCIENCES

Example; contd.

((M (5) j 0) > y > R (y )) j ?n n?7 ! f ?n n?7 ! l et(7) g ((M (5) j 0) > y > R (y )) j l et(7) !7 ! f f j l et(7) !7 ! f j g ((M (5) j 0) > y > R (y )) j

The sequence of events:

S k N l l ?5
  • R
n (5) n?7 !7

The sequence minus

events: S k N l l ?5 R n (5) n?7 !7

UNIVERSITY OF TEXAS AT AUSTIN 43

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DEPARTMENT OF COMPUTER SCIENCES

Executions and Traces

Define

f
  • )
f f a ! f 00 ; f 00 s ) f f as ) f Given f s ) f 0, s is an execution of f . A trace is an execution minus events. The set of executions of f (and traces) are prefix-closed.

UNIVERSITY OF TEXAS AT AUSTIN 44

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DEPARTMENT OF COMPUTER SCIENCES

Laws, using strong bisimulation

  • f
j
  • f
  • f
j g
  • g
j f
  • f
j (g j h)
  • (f
j g ) j h
  • f
> x > (g > y > h)
  • (f
> x > g ) > y > h,

if

h is x-free.
  • >
x > f
  • (f
j g ) > x > h
  • f
> x > h j g > x > h
  • (f
j g ) where x:2 h
  • (f
where x:2 h) j g,

if

g is x-free.
  • (f
> y > g ) where x:2 h
  • (f
where x:2 h) > y > g, if g is x-free.
  • (f
where x:2 g ) where y :2 h
  • (f
where y :2 h) where x:2 g,

if

g is y-free, h is x-free.

UNIVERSITY OF TEXAS AT AUSTIN 45

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DEPARTMENT OF COMPUTER SCIENCES

Relation

  • is an equality

Given

f
  • g, show

1.

f j h
  • g
j h h j f
  • h
j g

2.

f > x > h
  • g
> x > h h > x > f
  • h
> x > g

3.

f where x:2 h
  • g
where x:2 h h where x:2 f
  • h
where x:2 g

UNIVERSITY OF TEXAS AT AUSTIN 46

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DEPARTMENT OF COMPUTER SCIENCES

Treatment of Free Variables

Closed expression: No free variable. Open expression: Has free variable.

Law f
  • g holds only if both
f and g are closed.

Otherwise:

l et(x)
  • But
l et(1) > x > 6= l et(1) > x > l et(x) Then we can’t show l et(x) j l et(y )
  • l
et(y ) j l et(x)

UNIVERSITY OF TEXAS AT AUSTIN 47

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DEPARTMENT OF COMPUTER SCIENCES

Substitution Event

f [v =x℄ ! [v =x℄:f

(SUBST)

Now, l et(x) [1=x℄ ! l et(1).

So,

l et(x) 6= Earlier rules apply to base events only.

From

f [v =x℄ ! [v =x℄:f , we can not conclude: f j g [v =x℄ ! [v =x℄:f j g

UNIVERSITY OF TEXAS AT AUSTIN 48

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DEPARTMENT OF COMPUTER SCIENCES

Traces as Denotations

Define Orc combinators over trace sets,

S and T . Define: S j T , S > x > T , S where x:2 T .

Notation:

hf i is the set of traces of f .

Theorem

hf j g i = hf i j hg i hf > x > g i = hf i > x > hg i hf where x:2 g i = hf i where x:2 hg i

UNIVERSITY OF TEXAS AT AUSTIN 49

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DEPARTMENT OF COMPUTER SCIENCES

Expressions are equal if their trace sets are equal

Define:

f
  • =
g if hf i = hg i.

Theorem (Combinators preserve

  • = )

Given

f
  • =
g and any combinator : f
  • h
  • =
g
  • h,
h
  • f
  • =
h
  • g

Specifically, given

f
  • =
g

1.

f j h
  • =
g j h h j f
  • =
h j g

2.

f > x > h
  • =
g > x > h h > x > f
  • =
h > x > g

3.

f where x:2 h
  • =
g where x:2 h h where x:2 f
  • =
h where x:2 g

UNIVERSITY OF TEXAS AT AUSTIN 50

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DEPARTMENT OF COMPUTER SCIENCES

Monotonicity, Continuity

Define: f v g if hf i
  • hg
i.

Theorem (Monotonicity) Given

f v g and any combinator
  • f
  • h
v g
  • h,
h
  • f
v h
  • g
Chain f : f v f 1 ;
  • f
i v f i+1 ;
  • .

Theorem:

t(f i
  • h)
  • =
(tf )
  • h.

Theorem:

t(h
  • f
i )
  • =
h
  • (tf
).

UNIVERSITY OF TEXAS AT AUSTIN 51

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DEPARTMENT OF COMPUTER SCIENCES

Least Fixed Point

M
  • S
j R
  • M
M
  • =
M i+1
  • =
S j R
  • M
i, i
  • M is the least upper bound of the chain
M v M 1 v
  • UNIVERSITY OF TEXAS AT AUSTIN

52

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DEPARTMENT OF COMPUTER SCIENCES

Weak Bisimulation

sig nal
  • f
  • =
f f > x > l et(x)
  • =
f

UNIVERSITY OF TEXAS AT AUSTIN 53