Update/Change Condition and Inference Rule Sample Clauses

Update/Change Condition and Inference Rule. Given a change contract (ϕ, ψ, θ ; ϕr,ψr,θ r) and two versions of a program that satisfy c1 c2, (σ1, h1, σ2, h2) c (σ1r , hr1, σ2r , h2r ), we check whether the given change contract is satisfied using the inference rule shown in Figure 5(d). We write c1 c2, (σ1, h1, σ2, h2) (ϕ, ψ, θ ; ϕr,ψr,θ r) in the conclusion part of the inference rule to mean that change contract (ϕ, ψ, θ ; ϕr,ψr,θ r) is satisfied in the context of configuration c1 c2, (σ1, h1, σ2, h2) .

Update/Change Condition and Inference Rule. Given a change contract (ϕ, ψ, θ ; ϕr,ψr,θ r) and two versions of a program that satisfy c1 c2, (σ1, h1, σ2, h2) c (σ1r , hr1, σ2r , hr2), we check whether the given change contract is satisfied using the inference rule shown in Figure 5(d). We write c1 c2, (σ1, h1, σ2, h2) (ϕ, ψ, θ ; ϕr,ψr,θ r) in the conclusion part of the inference rule to mean that change contract (ϕ, ψ, θ ; ϕr,ψr,θ r) is satisfied in the context of configuration c1 c2, (σ1, h1, σ2, h2) . ▶ ▶ In order for a change contract to be satisfied, the precondition of the previous version must be satisfied beforehand at the pre-state of the previous version. Such a condition is expressed in the premise part of the rule as (σ1, h1) ϕ; we write (σ1, h1) ϕ if predicate ϕ is satisfied at state (σ1, h1). ▶ v ▶ In addition, one of postconditions of the previous version (recall that there are two kinds of postconditions, depending on whether the target method terminates normally) must also be satisfied at the post-state of the previous version. Such a condition is denoted in the inference rule as (σ1r , hr1) ψ (σ1r , hr1) θ . We say that the update condition is satisfied if the preceding two conditions hold true, as described in the second line of the inference rule. If the update condition holds, it means that a given input state (σ1, h1) triggers in the previous version an execution whose behavior is intended to be changed in the updated version. Once the update condition holds, we next check another condition we call the change condition to see whether the behavior of the execution of interest changes as intended. The change condition is described in the third line of the inference rule. To see whether the change condition is satisfied, we check the following two conditions. First, we ACM Transactions on Software Engineering and Methodology, Vol. 24, No. 3, Article 18, Pub. date: May 2015. 18:12 X. Xx et al. Table I. Rules to Fill in Omitted Clauses with Default Predicates Omitted clause Context Default predicate when ensured / Ewhen signaled false Ewhen signaled true when signaled / Ewhen ensured false Ewhen ensured true / E when required Erequires ϕr ϕr requires requires true always true ensures always true signals always true For explanation, refer to Section 3.2.4. ▶ ( || ⟩ ↓ ▶ check whether the precondition of the updated version is satisfied at the pre-state of the updated version (i.e., (σ2, h2) ϕr of the rule). Note we can assume that (σ2, h2) is isomorphic to (σ1, h1) because this is impli...