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pi calculus in kframework
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module PI-SYNTAX | |
imports ID | |
syntax Name ::= Id | |
syntax Process ::= NormalProcess | |
| Process "|" Process [klabel(Par), left] | |
| "!" Process [klabel(Replication)] | |
| "(" "nu" Name ")" Process [klabel(New)] | |
| "(" Process ")" [bracket] | |
syntax NormalProcess ::= Pi "." Process [klabel(Prefix)] | |
| "Nil" | |
| NormalProcess "+" NormalProcess [klabel(Or), left] | |
syntax Pi ::= Name "(" Name ")" | |
| Name "<" Name ">" | |
syntax priority Replication New Prefix > Or > Par | |
endmodule | |
module PI | |
imports PI-SYNTAX | |
configuration <T> | |
<par> | |
<proc multiplicity="*"> | |
<k> | |
$PGM:Process | |
</k> | |
<sum> | |
<summand multiplicity="*">.</summand> | |
</sum> | |
<bounds> | |
<bound multiplicity="*">.</bound> | |
</bounds> | |
</proc> | |
</par> | |
</T> | |
// STRUCTURAL EQUIVALENCES | |
// (P/\equiv, |, 0) is a symmetric monoid | |
// P | 0 \equiv P | |
// (P | Q) | R \equiv P | (Q | R) | |
rule | |
<proc>... <k> P:Process | Q:Process => P </k> <bounds> B </bounds> ...</proc> | |
(.Bag => <proc>... <k> Q </k> <bounds> B </bounds> ...</proc>) [structural] | |
rule | |
<proc>... <k> Nil </k> ...</proc> => .Bag [structural] | |
// (N/\equiv, +, 0) is a symmetric monoid | |
rule | |
<proc>... <k> N:NormalProcess => . </k> | |
<sum> .Bag => <summand> N </summand> </sum> ...</proc> [structural] | |
rule | |
<summand> N:NormalProcess + M:NormalProcess => N </summand> | |
(.Bag => <summand> M </summand>) [structural] | |
rule | |
<sum>... <summand> Nil </summand> => .Bag ...</sum> [structural] | |
rule | |
<proc>... <k> . </k> <sum> .Bag </sum> ...</proc> => .Bag [structural] | |
//(nu x) 0 \equiv 0 | |
//(nu x)(nu y)P \equiv (nu y)(nu x)P | |
rule | |
<k> ( nu X ) P => P </k> | |
<bounds>... (.Bag => <bound> X </bound>) ...</bounds> | |
// !(!P) \equiv !P | |
// !(Nil | Nil) \equiv !Nil | |
endmodule |
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