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Full LOTOS Department of Computer Science University of Regina, Regina SK, Canada

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  1. Full LOTOSDepartment of Computer ScienceUniversity of Regina, ReginaSK, Canada November 18, 2002 Yashu Bither Amrudee Sukpan Tetyana Manuylenko Chakka Sreenivasulu

  2. Outline • Introduction. • Full LOTOS. • Difference from Basic LOTOS. • Spec(s) in Full LOTOS. • Facts of Full LOTOS. • Value Expression - Value and variable declaration. • Scope and binding of Variables. • Inter Process Communication. • Example.

  3. Introduction • Basic LOTOS only describes process synchronization. • Data exchange is an important feature in telecommunication and distributed systems.

  4. Full LOTOS • Full LOTOS enhances the expressive power of Basic • LOTOS by providing the finer structure to observable • actions and enrich process synchronization with value • passing thus providing inter process value communication. • Full LOTOS includes data description (ACT ONE) and • control components (enriched basic LOTOS). • Full LOTOS introduces value communication and data • types to the process algebraic concepts of Basic LOTOS.

  5. Difference from Basic LOTOS • An observable gate = a gate name + a list of values ( or value expression). event attributes Structured event Basic LOTOS For example: g<true> g<29, false> Contd...

  6. Difference from Basic LOTOS .. 2 • The representations of data values and value expressions • in full LOTOS are derived from the specification language • for abstract data types - ACT ONE. • As a major advantage, in full LOTOS we will be able to • enrich synchronization with value passing, thus providing • interprocess communication. • In basic LOTOS an observable action coincides with a gate • name, in full LOTOS it is formed by a gate name followed • by a list of zero or more values offered at that gate: • g <v 1 ... v n >. For example: g <TRUE, "tree", 3>

  7. Spec(s) in Full LOTOS Specification typical_spec [gate list] (parameter list) : functionality type definitions behavior behavior expression where type definitions process definitions end spec process typical_proc [gate list] (parameter list) : functionality := behavior expression where type definitions process definitions end proc

  8. Facts of Full LOTOS • Values can be offered at gates and exchanged between • processes (enrichment of the action prefix operator). • New Construct of guarding and selection predicates. • Values can be used to generalize choice operator. • Values can be used to instantiate parametric process • definitions; let construct. • InterProcess Communication (Sequential composition…).

  9. Value declarations • The general format for the value declaration is: • !E • where E is a LOTOS expression or (value expression) or ( an • expression describing a data value). • For example: !(3+5) !(x+1) !max(x,y) • In Basic LOTOS: g; B g B` • B is a process that offers g and then behaves like B`. • In Full LOTOS: g!E; B g<value(E)> B` • B is a process that offers g<value(E)> and then behaves like B`.

  10. Value declarations … contd For example: if x =3 and y =5 then g!max(x,y) = g!max(3,5) describes g<5>.

  11. Variable declarations • The general format for the variable declaration is: • g?x: t;B • where x is a variable name • and • t is a sort identifier.It indicates the domain of values over which x ranges. • For example: ?x:integer ?text:string ?x:nat • So g?x: t;B(x) is a process that offers all events g<v> where v • is any value in the domain of sort t and then behaves like B(v).

  12. Scope of ?y:nat Scope of ?x:nat Binding occurrence of x Binding occurrence of y Scope and binding of Variables For example: a?x:nat; b?y:nat; c!max(x,y); stop Usual rules for nested scopes apply.

  13. Inter Process Communication (IPC) • IPC may occur when two processes composed in parallel • are offering the same structure action i.e. same gate and • same values. • g1!sap1 ?x:cep_sort !”test”; g2!x; stop • || • g1!sap1 !cep_3 ?y:string; g3!y; stop • The processes if synchronize, are able to offer action • g1<sap1, cep-3, “test”> • Once the interaction has taken place, the exp. obtained is: • g2 !cep_3; stop • | | • g3 !”test”; stop • where the proper substitutions have been carried out.

  14. Forms of IPC • VALUE MATCHING: The synchronization actions are combined • with value declarations. If the provided values are equal, • the synchronization is possible. • VALUE PASSING: Combination of value declaration and variable • declaration results in value passing. The effect is that a value is • transmitted from one process to the other. • VALUE GENERATION: The only remaining case is the one where • actions are combined with the variable declarations of the same type • attached to them. Superposing another process in parallel that offers • a value of the required type yields a form of multicast communication.

  15. Forms of IPC … contd Process A Process B Synchron type effect condition of interaction Synchronization Value(E1) = value(E2) Value matching g!E1 g!E2 Value(E) is of sort t After Synchron. X = value(E) Value passing g!E g!x:t g!x:t g!y:u t = u Value generation After sync. x=y=v where v is in domain of t.

  16. Example in Full LOTOS Specification Max3 [in1, in2, in3, out]:noexit type natural is sorts nat opns zero:  nat succ: nat  nat largest: nat, nat  nat eqns ofsort nat forall x:nat largest(zero, x) = x largest(x, y) = largest(y, x) largest(succ(x), succ(y)) = succ(largest(x, y)) endtype (* natural *) behaviour hide mid in (Max2[in1, in2, mid] |[mid]| Max2[mid, in3, out]) where process Max2[a, b, c] : noexit := a ?x:nat; b ?y:nat; c !largest(x,y); stop [] b ?y:nat; a ?x:nat; c !largest(x,y); stop endproc (*Max2*) endspec (*Max3*)

  17. Conditional Constructs in Full LOTOS • Selection Predicate • Guarded Expression

  18. Selection Predicates Format: action denotation [equation]; Examples: [X=4] [X<0]

  19. Selection Predicate • A selection predicate can be associated with an action denotation • It imposes restrictions on the values that may be bound to these variables. • Selection predicate may contain variables that occur in the variable declarations (?x:t)

  20. Example:G1?x:nat [x<3] G1!0 G1!1 G1!2 G1?x:nat G1!0 G1!1 G1!2 G1!3 G1!4 G1!5 ... G1 G1 G1!0 [] G1!1[]G1!2

  21. g1<0> g1<2> g1<1> g2!1 g2!2 g2!0 Scope of variable declarations g1?x:nat[x<3];g2!x;stop • has the following three possible transitions • g1<0> -> g2!0;stop • g1<1> -> g2!1;stop • g1<2> -> g2!2;stop • be considered as part of the scope of the variable declarations in that action denotation.

  22. Selection Predicate • Synchronization • 2 processes negotiate the value of a parameter in an interaction which each one imposing its own condition P P

  23. Selection Predication Hide sap in sap?x:nat[x<max];B1(x) |[sap]| sap?y:nat[y>min];B2(y) Ex:max=10 and min=5 x=0,…,9 y=6,…,n possible values = 6,7,8,9 B1 B2 sap sap

  24. Selection Predicate Hide sap in B1(n) |[sap]|B2(n) * min<n<max Synchronization can occur with the environment on one of two actions.

  25. Conditional Constructs • Selection predicates • Guarded expressions

  26. Guarded expression • Any behaviour expression may be preceded by a predicate and an arrow if (expression) then Behaviour Format: [expression]->Behaviour

  27. Guarded Expression • if the predicate holds, then the behaviour described by the behaviour expression is possible, otherwise the whole expression is equivalent with stop

  28. Example [X>0]->sap!X;P[...](x,…) [] [X<=0]->sap!-X;P[...](x,…) * if x=1 then sap!1;P[...](1,…) * if x=-3 then sap!3;P[…](-3,…)

  29. Guarded expression [cond1]->process1 [] [cond2]->process2 [] ... [condn]->processn

  30. Guarded expression • The conditions in the guards need not be exclusive [x>0] -> process1 [] [x=5] -> process2 [] [x<9] -> process 3 *if X=10 then process1 *if X=5 then process1[]process2[]process3 *if X= 2 then process1[]process3

  31. g?x:Nat[x<=5];( [X=2 or X=3]-> g!X!0;stop [] [X<3] -> g!X!1;stop) Example g!0;g!0!1;stop [] g!1;g!1!1;stop [] g!2;(g!2!0;stop[]g!2!1;stop) [] g!3;g!3!0;stop [] g!4;stop [] g!5;stop

  32. Generalized Choice in Full LOTOS • Choice operator “[]” can only express a finite number of alternatives. • Generalized Choice specify the choice among all possible value expressions of a sort.

  33. Generalized Choice Choice X:S[]B(X) if t1,…,tn are all possible value expressions of sort S. The resulting behavior by substitution ti for X in B.

  34. Generalized Choice • Let B(x) be a behaviour expression, depends on a variable X of sort nat. • Specify the choice among the processes B(v) for all nat-values v • choice x:nat [] B(X) B(0) [] B(1) [] B(2) [] B(3) []…[] B(n)

  35. Generalized Choice • The generalized choice construct allows an alternative representation for the action prefix construct, when this include a variable declaration a?x:t;B(x) = choice x:t[]a!x;B(x)

  36. Example g!0;stop [] g!2;stop [] g!4;stop [] … ... Choice x:Nat[] [x mod 2=0]->g!x;stop

  37. Generalized Choice • choice x:t [] i;B(X) • choice x:t[] a;B(x) • more than one variables • choice x1:t1,…,xn:tn[] B(x1,…,xn) • sets of gate identifiers may be used for indexing • choice g in [a1,…,an] [] Process_X[g](…)

  38. Generalized Choice • sets of gate identifiers may be used for indexing • choice g in [a1,…,an] [] Process_X[g](…) • expressed among n instances of Process_X • formal gate g is actualized with a different element of the gatelist [a1,…,an]

  39. Full LOTOS • Interprocess communication • Conditional constructs • Selection Predicates • Guarded Expressions • Generalized Choice • Parametric processes

  40. Parametric Processes Full LOTOS offers the possibility to parameterize process definition in terms of a parameter list. process typical_proc[gate list](x1:t1, ..., xn:tn):functionality := … endproc Parameter list is a list of variable declarations.

  41. Specifications can be parametric as well as process definitions. process typical_proc[gate list](x1:t1, ..., xn:tn):functionality := … endproc Instantiation typical_proc[actual gate list] (E1, …, En) value expressions

  42. Example: process compare[inp, out] (min, max: int) : noexit := inp ?x:int; ( [min<x<max] -> out !x; compare[inp, out] (min, max) [] [x<=min] -> out !min; compare[inp, out] (x, max) [] [x>=max] -> out !max; compare[inp, out] (min, x) )endproc behaviour expression

  43. Instantiation: compare[one, two] (x, 2*x) one ?y:int; ( [x<y<2*x] ->two !y; compare [one, two] (x, 2*x) [] [y <=x] -> two !x; compare [one, two] (y, 2*x) [] [y>=2*x] -> two !2*x; compare [one, two] (x, y) ) actual parameters

  44. A more direct way to associate value expressions E1, …, En to the free variables x1, …, xn of a behaviour expressions B(x1, …xn) is offered by the ‘let’ construct: let x1:t1 = E1, …, xn:tn = Enin B(x1, …, xn) compare[one, two] (x, 2*x) one ?y:int;let z:int = x*2 in ( [x<y<z] ->two !y; compare [one, two] (x, z) [] [y <=x] -> two !x; compare [one, two] (y, z) [] [y>=z] -> two !z; compare [one, two] (x, y) )

  45. Sequential Composition with Value Passing • Connection-Phase[...] >> Data-Phase[...] • Data-Phase depends on parameters that are established in Connection-Phase. • Data-Phase is called Parametric Process. • Need a mechanism for passing these parameters. • Generalize the notion of Successful Termination. • Add some static constraints to the Full Lotos Language.

  46. Successful termination with value offers • In Full LOTOS, the exit process has a finite list of value expressions. The values expressed are those that are passed on to the subsequent process. For example, • a ?x:nat; b ?y:nat; exit(largest(x, y)) • tsap !cei ?quality-of-service : quality-parameter-sort ?expedited-data-option : bool; exit(quality-of-service, expedited-data-option) Functionality of the Termination

  47. Rules determining Functionality of Behaviour Expressions • The list of the sorts of the values offered at successful termination is called the functionality of that termination. • Functionality and Actual Termination are two different things. • The functionality is a sort of static typing mechanism, which is only meant to guarantee the predictability of the list of sorts offered at successful termination, in case, such termination occur.

  48. Rules determining Functionality of Behaviour Expressions (Cont…) • The actual occurrence of a successful termination, in general, cannot be decided statically, nor dynamically. “Halting Problem” for Turing Machines. • The functionality typing scheme helps in avoiding constructions however, of which the absence of successful terminations can be decided statically. • 'func(B)' to denote the functionality of expression B

  49. Stop • The functionality of processes that do not terminate successfully at all, like stop, is indicated with noexit.

  50. Exit • The Simple successful termination without value passing has a functionality that is indicated by the same name: func(exit) = exit.