Specification Patterns for Properties over Reachable States of Graph Grammars

Proof Tactics for Theorem Proving Graph Grammars through Rodin

“…Properties over states are properties over graphs, typically composed of different kinds of edges and vertices. In previous work [9], we have proposed patterns for the presentation, codification and reuse of property specifications and in [15] he have developed proof strategies for the demonstration of specific atomic properties belonging to such patterns. Here we extend the set of tactics describing proof strategies for discharging the properties presented in Figure 11.…”

“…. , ed k → t k })(mE(e p )) = t. In (I), after the instantiation, some rules (3,9,3,20,6, respectively) are automatically applied, reaching the H goal, which is automatically discharged by (2). In the same way, in (II), some rules are automatically applied (9, 3, 6, 3, 5, 7 and 2, respectively), generating three new sequents to be discharged:…”

“…In (II) (sub-tree b ), rules (9) and (3) are automatically applied. In order to complete the proof, we must add sourceLi(e p ) = targetLi(e p ) (30) as hypothesis, which generates three new sub-goals: (i) H e p ∈ dom(sourceLi) ∧ sourceLi ∈ edgeLi → vertLi; (ii) H sourceLi(e p ) = targetLi(e p ); and (iii) H sourceG(mE(e p )) = targetG(mE(e p )).…”

“…is automatically discharged after the automatic application of some rules (9,3,2). In order to demonstrate (II), we must instantiate the name of the deleted edge e i in grd_srctgt hypothesis, considering source.…”

“…Besides, in previous work [9], it was proposed patterns for the presentation, codification and reuse of property specifications over reachable states of graph grammars. Especially, in [15], it was presented the proof obligations generated by a GG specification in Rodin and proposed proof strategies to specific atomic properties defined in the previous patterns.…”