Single-Sided Monitoring Sample Clauses

Single-Sided Monitoring. The following definition provides a characterization of the redundancy present on monitored ex- pressions when wrapped by several monitors. In what follows we say that an expression is a user expression if it does not contain runtime syntax.  ⟨(let x1 = [c+]c,q,p in    P → (νc)   let y1,x2 = receive x1 in let y2 = send 0 y1 in close x2; close y2)⟩p     ⟨(λx1.let y1 = connect b in  let x2 = send y1 x1 in close x2)[c-]c,p,q⟩q  →∗ (νc)  let y2 = send 0 y1 in close x2;  ⟨(let y1,x2 = receive [c+]c,q,p in   close y2)⟩p     ⟨(let y1 = connect b in  let x2 = send y1 [c-]c,p,q in close x2)⟩q ⟨(let y1,x2 = receive [c+]c,q,p in    let y2 = send 0 y1 in close x2;  close y2)⟩p + d,r,q  →∗ (νc)(νd)  ⟨(let y1 = [d ] in  let x2 = send y1 [c-]c,p,q in close x2)⟩q      ⟨(λy1.let z,y2 = receive y1 in  print z−1; close y2)[d-]d,q,r⟩r ⟨(let y1,x2 = receive [c+]c,q,p in      let y2 = send 0 y1 in close x2; →∗ (νc)(νd)  ⟨(let x2 = send [d+]d,r,q [c-]c,p,q in    close y2)⟩p  close x2)⟩q   ⟨(let z,y2 = receive [d-]d,q,r in    print z−1; close y2)⟩r Table 6: Reduction of the system described in Example 2.   ⟨(let y1,x2 = ([[[d+]d,r,q ]e,q,p]e,q,p,[c+]end_c,q,p) in    let y2 = send 0 y1 in close x2;  close y2)⟩p  →∗ (νc)(νd)  ⟨(let x2 = [c-]end_c,p,q in   close x2)⟩q     ⟨(let z,y2 = receive [d-]d,q,r in  print z−1; close y2)⟩r ⟨(let y2 = send 0 [[[d+]d,r,q]e,q,p]e,q,p in   close [c+] end_c,q,p;   close y2)⟩p   →∗ (νc)(νd) ⟨(close [c-]end_c,p,q)⟩q  ⟨(let z,y2 = receive [d-]d,q,r in    print z−1; close y2)⟩r ⟨(let y2 = [[[d+]end_c,r,q ]end_c,q,p]end_c,q,p in  close [c+]end_c,q,p;  close y2)⟩p   ⟨(let z,y2 = ([[[[0]any_c,p,q ]any_c,p,q ]f,q,r]f,q,r,[d-]end_c,q,r) in  →∗ (νc)(νd)  ⟨(close [c-]end_c,p,q)⟩q    print z−1; close y2)⟩r ⟨(close [c+]end_c,q,p;   close [[[d+]end_c,r,q ]end_c,q,p]end_c,q,p)⟩p  ∗  ⟨(close [c-]end_c,p,q)⟩q    → (νc)(νd)  ⟨(let z,y2 = ([[0]f,q,r]f,q,r,[d-]end_c,q,r) in  print z−1; close y2)⟩r ⟨(close [[[d+]end_c,r,q ]end_c,q,p]end_c,q,p)⟩p  →∗ (νd)  ⟨(let z,y2 = ([blame q]f,q,r,[d-]end_c,q,r) in   ⟨()⟩q    print z−1; close y2)⟩r Table 7: Reduction of the system described in Example 2 (cont.). Definition 15. A monitored expression is well-stacked if it has one of the following forms: • v is a user expression. • [blame p]_,_,_, • [v ap e]flat_c w,p,_ and v and w are user expressions and e ↓ v′ if and only if wv ↓ v′, • [aι]_,_,_, • [[e¯]c,p,q]c,p,q and e¯ is ...
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