## 5 Assessment  
The CMGVC offers a significant departure from direct generation of views on models, and a more robust alternative to indirect generation of views based on DSML-specific representations. In Section 3.1 we have defined five propositions for this research:  
1. M\(\rightarrow\)G\(\rightarrow\)V (a GDS-mediated transformation from model to view) is superior to M\(\rightarrow\)V (a direct transformation from model to view)
2. M\(\rightarrow\)G\(\rightarrow\)V is superior to M\(\rightarrow\)R\(\rightarrow\)V (a transformation mediated by a language-bound representation, LBR)
3. M\(\rightarrow\)G is a feasible and valid transformation. 4. G\(\rightarrow\)V is a feasible and valid transformation. 5. G\(\rightarrow\)SIM is a feasible and valid transformation. We have presented a categorical framework for converting conceptual system models from one ML, OPM, into a GDS, and deriving SIM views from the GDS. We have thus managed to validate Propositions 3, 4, and 5 regarding the existence of the building blocks of a composed transform M\(\rightarrow\)G\(\rightarrow\)V based on \(GV\circ MG\), where \(MG:\,M\to G\), \(GV:\,G\to V\). To prove Propositions 1 and 2, we must compare the benefits and limitations of the CMGVC approach vis-a-vis the two alternative approaches:  
* MV: Direct generation of views from a model, that we denote V(M) or MV
* MRV: Indirect generation of views from a model via a common DSML-specific representation, that we would demote V(R\({}_{\text{DSML}}\)(M\({}_{\text{DSML}}\))) or MRV  
We define four lower-is-better (LIB) criteria for comparison, which reflect stakeholders needs for efficiency (C1), flexibility (C2), robustness (C3), and resilience (C4):  
* C1--Efficiency is measured by the number of required transformations of M models to V views. For MGV, MRV: sum of model-to-graph transformations (M) and graph-to-view transformations (V); for MV: product of models by views (\(M\cdot V\)). * C2--Flexibility is measured by the effort of creating new views for existing models. For MGV, MRV: one effort unit per view (graph-to-view or LBR-to-view); for M: M effort units (models-to-view). * C3--Robustness is measured by the effort of creating existing views for new models: For MGV: a single effort unit (model-to-graph); for MV: V effort units (model-to-views); for MRV: V+1 effort units (model-to- LBR and LBR-to-views). * C4--Resilience is measured by the dependency on DSML updates: for MGV, MRV: a single effort unit for updates (model-to-graph or model-to-LBR); for MV: V effort units (model-to-views). Since all criteria are LIB, the total score is also LIB. Table 6 defines metrics for each criterion. Total scores for MGV, MV, and MRV are defined in Equations (1)-(3). \[S_{MGV}=W_{1}(M+V)+W_{2}+W_{3}+W_{4} \tag{1}\]  
\[s_{MV}=W_{1}(MV)+W_{2}M+W_{3}V+W_{4}V \tag{2}\]  
\[S_{MRV}=W_{1}(M+V)+W_{2}M+W_{3}(V+1)+W_{4} \tag{3}\]\(MGV\) is superior to \(MRV\) (Proposition B) if \(S_{MGV}\leq S_{MRV}\):  
\[W_{1}(M+V)+W_{2}+W_{3}+W_{4}\leq\ W_{1}(M+V)+W_{2}M+W_{3}(V+1)+W_{4}.\]  
Cancelling equal terms, we obtain: \(W_{2}+W_{3}\leq W_{2}M+W_{3}(V+1)\). Homogenizing, we obtain: \(0\leq W_{2}(M-1)+W_{3}(V)\). This inequality always holds, and therefore \(S_{MGV}\leq S_{MRV}\), and MGV is superior to any MRV with a DSML-specific representation:  
\[S_{MGV}\leq S_{MRV}\Longleftrightarrow\mathbf{MGV}\succcurlyeq\mathbf{MRV} \tag{4}\]  
Conditions for \(MGV\) superiority to \(MV\):  
\[S_{MGV}\leq S_{MV}\Leftrightarrow W_{1}(M+V)+W_{2}+W_{3}+W_{4}\leq W_{1}(MV)+W _{2}M+W_{3}V+W_{4}V.\]  
Homogenizing, we obtain the following:  
\[S_{MGV}\leq S_{MV}\Longleftrightarrow\ W_{1}(MV-M-V)+W_{2}(M-1)+W_{3}(V-1)+W _{4}(V-1)\geq 0 \tag{5}\]  
We try Equation (5) with combinations of V = 1, V = 2, V > 2 with M = 1, M = 2, M > 2, as summarized in Table 7. For all practical purposes, multiple MLs \(M\geq 2\), and at least two views (we already have three),  
\[M\geq 2,\ V\geq 2\iff S_{MGV}\leq S_{MV}\iff\ MGV\succcurlyeq MV \tag{6}\]  
With this analysis, we have managed to corroborate Proposition 1 and Proposition 2.