Model-driven engineering with domain-specific meta-modelling languages

Abstract

Domain-specific modelling languages are normally defined through general-purpose meta-modelling languages like the MOF. While this is satisfactory for many model-driven engineering (MDE) projects, several researchers have identified the need for domain-specific meta-modelling (DSMM) languages. These provide customised domain-specific meta-modelling primitives aimed at the definition of modelling languages for a specific domain, as well as the construction of meta-model families. Unfortunately, current approaches to DSMM rely on ad hoc methods which add unnecessary complexity to the realization of DSMM in practice. Hence, the goal of this paper is to simplify the definition and usage of DSMM languages. For this purpose, we apply multi-level meta-modelling for the systematic engineering of DSMM architectures. Our method integrates techniques to control the meta-modelling primitives offered to the users of the DSMM languages, provides a flexible approach to define textual concrete syntaxes for DSMM languages, and extends existing model management languages (for model-to-model transformation, in-place transformation and code generation) to work in a multi-level setting, thus enabling the practical use of DSMM in MDE. As a proof of concept, we report on a working implementation of these ideas in the MetaDepth tool.

Appendices

Appendix A

This appendix provides a formal definition of potency, linguistic ty**, and ontological ty**. For simplicity, we just consider clabjects and fields, which suffices to illustrate the main concepts of our framework.

Definition 1

(Model) A model $M=\langle CL, fields, FI \rangle$ is made of:

• a set $CL$ of clabjects,

• a set $FI$ of fields,

• a total function $fields :CL \rightarrow 2^{FI}$ assigning to each clabject $c$ a (perhaps empty) set $fields(c)$ of its owned fields, s.t. $\forall f \in FI~\exists _1 c \in CL$ with $f \in fields(c)$ (every field belongs to exactly one clabject).

Remark

We use $2^{FI}$ to denote the set of all subsets of $FI$ (its powerset). We sometimes use $cl(M)$ to denote $CL$, the set of clabjects of $M$, and $fi(M)$ to denote $FI$, the set of fields included in clabjects of $M$.

We write $U = \{ M_i=\langle CL_i, fields_i, FI_i \rangle \}_{i \in I}$ for the set of all possible models, which we sometimes call the universal set of models.

Next, we define the potency for models, clabjects, and fields as a family of functions to the natural numbers, including zero. The potency of clabjects should not be bigger than the potency of their enclosing model, and the potency of fields should not be bigger than the potency of their owner clabject. Having fields with potency bigger than their owning clabject may be useful in models with inheritance [15], but we omit inheritance in this formalization for simplicity.

Definition 2

(Potency) Given the universal set $U$, the potency $pot_U=\langle pot, \{ pot^i \}_{i\in I}\rangle$ is defined as:

• a total function $pot :U \rightarrow \mathbb N _0$ assigning each model $M_i$ a positive number, or zero;

• a family of total functions $\{pot^i :CL_i \cup FI_i \rightarrow \mathbb N _0\}_{i \in I}$ for each model $M_i \in U$, assigning each clabject and field a positive number or zero, s.t. $\forall c \in CL_i$, $pot^i(c) \le pot(M_i)$, and $\forall f \in fields_i(c)$, $pot^i(f) \le pot^i(c)$.

Remark

Potency for models is named level in [8].

In order to define the linguistic ty**, we assume a very simple linguistic meta-model $L_{MM}=\{MODEL, CLABJECT, FIELD\}$. Then, the linguistic type is a family of total functions with co-domain $L_{MM}$, as shown in the next definition.

Definition 3

(Linguistic ty**) Given the universal set $U$, the linguistic ty** $ltype_U=\langle ltype, \{ltype^i\}_{i\in I}\rangle$ is defined as:

• a total function $ltype :U \rightarrow L_{MM}$, s.t. $\forall M_i \in U, ltype(M_i) = MODEL$;

• a family of total functions $\{ltype^i :CL_i \cup FI_i \rightarrow L_{MM}\}_{i \!\in \! I}$ for each model $M_i \in U$, s.t. $\forall c\in CL_i~ltype^i(c)=CLABJECT$, and $\forall f\in FI_i~ltype^i(f)=FIELD$.

Remark

For the potency and the linguistic ty**, we sometimes use $pot$ and $ltype$ (without the superindex) for clabjects and fields when no confusion arises.

Next, we define the ontological ty** as a family of partial functions.

Definition 4

(Ontological ty**) Given the universal set $U = \{ M_i=\langle CL_i, fields_i, FI_i \rangle \}_{i \in I}$, with $CL=\uplus _{i \in I} CL_i$, $FI=\uplus _{i \in I} FI_i$, the ontological ty** $otype_U=\langle otype, \{ otype^i \}_{i\in I}\rangle$ is made of:

• a partial function $otype :U \rightarrow U$ assigning each model $M_i$ its ontological model type $otype(M_i)$;

• a family of partial functions $\{otype^i :CL \cup FI \rightarrow CL \cup FI\}_{i \in I}$,

s.t. $otype_U$ fulfils the following well-formedness rules, $\forall M_i \in U$:

• 1. $otype(M_i)=M^{\prime } \Rightarrow pot(M_i)+1=pot(M^{\prime })$,

• 2. $\forall c \in CL_i$, $otype^i(c)=c^{\prime } \Rightarrow$ $~~~~c^{\prime } \in CL$ (clabjects are typed by clabjects),

• 3. $\forall f \in FI_i$, $otype^i(f)=f^{\prime } \Rightarrow$ $~~~~f^{\prime } \in FI$ (fields are typed by fields),

• 4. $\forall c \in CL_i$, $otype^i(c) = c^{\prime } \Rightarrow$ $~~~~[ c^{\prime } \in cl(otype(M_i)) \wedge pot(c)+1 = pot(c^{\prime })~\wedge$ $~~~~~~\forall f^{\prime } \in fields(c^{\prime })~s.t.~pot(f^{\prime })>0$ $~~~~~~~~\exists _1 f\in fields(c)$ s.t. $~~~~~~~~~[otype^i(f)=f^{\prime }~\wedge ~pot(f)+1=pot(f^{\prime })]~]$

• 5. $\forall f \in FI_i$, $otype^i(f)=f^{\prime } \Rightarrow$ $~~~~[~\exists c, c^{\prime }~s.t.~otype(c)=c^{\prime }~\wedge ~$ $~~~~~~~f\in fields(c)~\wedge ~f^{\prime }\in fields(c^{\prime })$ $~~~~~~~~\wedge ~pot(f)+1=pot(f^{\prime })]$

• 6. $pot(M_i)=0 \Rightarrow \exists M^{\prime } \in U~s.t.~otype(M_i)=M^{\prime }$

• 7. $\forall c \in CL_i~[~pot^i(c)=0\Rightarrow$ $~~~~\exists c^{\prime } \in cl(otype(M_i))~s.t.~otype(c)=c^{\prime }~]$

• 8. $\forall f \in FI_i~[~pot^i(f)=0\Rightarrow$ $~~~~\exists f^{\prime } \in fi(otype(M_i))~s.t.~otype(f)=f^{\prime }~]$

Remark

We use $\uplus$ for disjoint union.

Remark

The first condition states that the potency of $M_i$ is one less than the potency of its ontological model type $M^{\prime }$. The second and third conditions state that clabjects and fields should be typed by clabjects and fields, respectively. The second condition is subsumed by the fourth, but we explicitly state it for clarity. The fourth condition states that if a clabject $c$ has $c^{\prime }$ as ontological type, then its potency is one less. As the codomain of the potency is $\mathbb N _0$, we have that elements with potency zero cannot be instantiated. The fourth condition also requires every field of $c^{\prime }$ with potency bigger than zero to be instantiated in $c$. The fifth condition is a compatibility condition specifying that if the ontological type of a field $f$ is $f^{\prime }$, then the ontological type of the owner of $f$ is the owner of $f^{\prime }$. The last three conditions state that elements with potency zero should have an ontological type.

The previous definition of ontological ty** reduces to the standard conformance relation in a two meta-levels setting, if we restrict the potency function to the set $\{0, 1\} \subset \mathbb N _0$, where models with potency 1 are the meta-models and those with potency 0 the models. However, model self-ty** (i.e. a model whose ontological type is itself, as suggested in the OMG’s MDA [39]) is not allowed in this formalization due to the requirement of the potency decrease in the model instances. Instead, we require top-level models to lack an ontological type and have a linguistic type only. Hence, the linguistic meta-model plays the role of the MOF in this architecture.

Next, we use the previous definitions to characterize linguistic extensions as elements with no ontological type.

Definition 5

(Linguistic extension) Given the universal set $U = \{ M_i=\langle CL_i, fields_i, FI_i \rangle \}_{i \in I}$, and an ontological ty** $otype_U=\langle otype, \{ otype^i \}_{i\in I}\rangle$, the linguistic extensions $LE_j$ of $M_j \in U$ are defined as the tuple $LE_j =\langle CL^{\prime }_j \subseteq CL_j, fields_j|_{CL^{\prime }_j}, FI^{\prime }_j \subseteq FI_j\rangle$ s.t.:

• $\forall c^{\prime } \in CL^{\prime }_j$ $otype(c^{\prime })$ is undefined,

• $\forall c \in CL_j {\setminus } CL^{\prime }_j$ $otype(c)$ is defined,

• $\forall f^{\prime } \in FI^{\prime }_j$ $otype(f^{\prime })$ is undefined,

• $\forall f \in FI_j {\setminus } FI^{\prime }_j$ $otype(f)$ is defined.

Remark

Function $otype^i$ partitions $CL_i$ and $FI_i$ into the set of ontologically typed clabjects and fields ($CL_i {\setminus } CL^{\prime }_i$ and $FI_i {\setminus } FI^{\prime }_i$) and the linguistic extensions ($CL^{\prime }_i$ and $FI^{\prime }_i$). Note that $LE_j$ may fail to be a model, according to Definition 1, because some field without ontological type (belonging to $FI^{\prime }_j$) may be owned by a clabject with ontological ty** (not belonging to $CL^{\prime }_j$). In any case, every element $M_i\in U$ is a correct model according to our framework.

Due to the fifth condition in Definition 4, we have that if a clabject has no ontological type, then no owned field can have an ontological type. Conversely, it is allowed to have fields with no ontological type, owned by clabjects with ontological type.

Appendix B

This appendix provides complete listings for the running example presented in Sect. 5.