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Models as Values in a Model Expression Algebra: A Functional Approach to Model Driven Engineering

T0 review · 2 major / 7 minor · reviewed 2026-07-13 · grok-4.5

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Pith's one-line read Models, metamodels, templates, and transformations unify as terms and values in one model expression algebra with proven type safety.

desk verdict Solid formal unification of MDE construction/templates/transformations as a four-operator term algebra, with honest limits and a working TypeScript/JSX realization. read the letter →

arxiv 2604.05001 v1 submitted 2026-04-05 cs.SE

Sinisa Neskovic (IT University of Copenhagen , Copenhagen , Denmark) , Dejan Stojimirovic (University of Belgrade , Faculty of Organizational Sciences , Belgrade , Serbia) This is my paper · ORCID
classification cs.SE
keywords modeldrivenengineeringtransformationexpressionalgebratemplatesmetamodelingembeddeddomain-specificlanguagefunctionalprogramming
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper claims that model-driven engineering has been limited by treating models as fixed object graphs, which makes parameterization, reuse, and a single formal account of construction and transformation hard. It proposes a functional foundation: the model expression algebra, in which models are values, model expressions are terms built from four operators (create model, create element, reference, and embed computation), and evaluation is the map from terms to values. Metamodels become type schemas that constrain the algebra; templates are open terms with free variables; transformations are simply templates whose input is a source model. The authors prove type preservation under evaluation and type safety of transformation execution, and show that because models are themselves model elements, megamodels and weaving models need no extra machinery. Realized as an embedded language in a mainstream host, one type system can serve as metamodeling, construction, and transformation language. A sympathetic reader would care because that would collapse several separate MDE languages and reuse mechanisms into one compositional, checkable framework.

What carries the argument

The model expression algebra: terms built from four operators—μ (model creation), ε (element creation), ρ (reference), and κ (computation)—evaluated as the interpretation homomorphism from terms to model values under type schemas; templates are open terms, and transformations are templates over source models.

What would settle it

Build a non-trivial family of parameterized templates and transformations in the embedded language, then check whether the host type checker rejects every ill-typed expression and whether evaluation always yields models that conform to the declared type schemas for all parameter combinations the theorems cover.

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Extended reading notes

Core claim

Model construction, metamodels, templates, and transformations can be unified under a single model expression algebra in which models are values, expressions are terms composed from model-creation, element-creation, reference, and computation operators, and evaluation is the interpretation homomorphism from terms to values. Metamodels are type schemas; templates are open terms; transformations are templates over source models. Type preservation under evaluation and type safety of transformation execution are proved, and megamodels and weaving models arise without dedicated mechanisms because models are model elements.

Load-bearing premise

The type-safety proofs assume that every embedded computation always produces only well-typed sub-expressions for every allowed parameter value; if those computations can emit structure the host checker misses, the guarantees fail.

Editorial extensions

If this is right

  • Model templates become a native reuse mechanism that can vary cardinality, topology, and properties from one definition.
  • Transformations need no separate language: they are parameterized model expressions over source models, with dispatch and traces.
  • Megamodels and weaving models require no dedicated tooling once models are first-class elements in the algebra.
  • A mainstream host language can enforce most conformance conditions at compile time while serving as metamodeling, construction, and transformation language.
  • Type preservation and transformation type safety become theorems rather than informal properties of specialized tools.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the algebra maps cleanly onto host-language types, teams could adopt model-driven practice without learning specialized transformation languages.
  • Treating model-to-text as model-to-model against a fixed textual-content metamodel, as the paper sketches, would let the same type-safety results cover code and documentation generation.
  • Whether host type systems close enough of the κ loophole is an empirical question; large transformation suites would test if the formal guarantees hold in practice.
  • Extending the algebra to bidirectional and incremental settings would decide whether it can compete with graph-grammar approaches on synchronization tasks.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 7 minor

Summary. The paper proposes a functional foundation for model-driven engineering based on a model expression algebra with four operators (μ, ε, ρ, κ). Models are values, expressions are terms, and evaluation is the interpretation homomorphism. Metamodels are type schemas; templates are open terms with free variables; transformations are templates whose parameters are source elements. The authors prove type preservation under evaluation (Theorem 1) and type safety of transformation execution (Theorem 2), show that megamodels and weaving models arise without extra machinery, and realize the framework as Synthesis, an embedded TypeScript/JSX DSL in which the host type system is claimed to enforce the formal guarantees.

Significance. If the unification holds under its stated premises, the paper offers a coherent alternative to the fragmented OO foundations of MDA/EMF: a single algebra covering construction, metamodeling, templates, and transformations, with compositional semantics and reuse via parameterization and higher-order templates. The open-source Synthesis realization and the explicit mapping tables (Tables 1–2) are concrete strengths. The formal results are standard structural inductions once the well-typed-κ hypothesis is granted; they are not machine-checked, but they are stated clearly and match the definitions. The work is a solid definitional contribution to MDE foundations rather than an empirical or industrial validation study.

major comments (2)
  1. Theorem 1 (and Definition 15 / Theorem 2) rest on the standing hypothesis that every computation operator κ (and every transformation rule) produces only well-typed sub-expressions for all θ ∈ Θ. The paper never discharges this hypothesis inside the algebra; it is assumed and then mirrored by TypeScript’s type checker for the JSX surface (§4.3). If a κ can emit an ε node whose type is outside TE(Σ), or a non-terminating structure (cf. Proposition 2), type preservation and the claim that “a single mainstream language … enforces formal guarantees” fail. The manuscript should either (a) make the host-language discharge of the hypothesis precise (what is and is not checked at compile time vs. runtime), or (b) weaken the claim to “guarantees under well-typed κ” and state the residual runtime obligations (including ρ resolution, Definition 7(iii)) more prominently in the abstract and conclusio
  2. Empirical support for the practical claim is limited to illustrative examples (§4.4 Org2Workflow and the ConfigurableApproval/GenericApproval templates). Section 6.2 acknowledges the lack of large-scale case studies and controlled comparisons with ATL/QVT/EMF. For a journal contribution that advertises both formal foundations and a working eDSL, at least one non-toy end-to-end case (or a systematic comparison against Kusel et al.’s reuse scenarios) is needed to substantiate that the algebra improves reuse and adoption barriers in practice. Without that, the realization remains a proof-of-concept rather than evidence for the industrial path claimed in §6.4.
minor comments (7)
  1. Definition 8 uses C for the set of constructors, while Definition 11 writes K; unify the notation.
  2. Definition 12 and Proposition 1 have duplicated “(ii)” markers; clean numbering.
  3. References [10]/[11] are overloaded (Bézivin megamodels vs. AelasticS GitHub/website); renumber or disambiguate.
  4. Figure 1 and Figure 2 are described but not rendered in the text provided; ensure captions and call-outs match the architecture and evaluation-phase claims.
  5. Section 5.1 cites Aničić et al. as [14] while Höppner et al. is also [14]; fix the bibliography collision.
  6. The phrase “AI-genAnierated” in §6.3 is a typo.
  7. Proposition 1 is labeled “Operational Type Safety” but is closer to a preservation argument under construction primitives; a short remark distinguishing it from Theorem 1 would help readers.

Circularity Check

1 steps flagged · score 1.0 of 10

No significant circularity: formal algebra and Theorems 1–2 are self-contained under explicit hypotheses; only ordinary mild self-reference via the authors’ own Synthesis/AelasticS realization as demonstration.

  1. self citation load bearing [§4 (Realization), citations [10][11]; also Abstract contribution (4) and §6.1]
    "we have implemented a free, open-source embedded domain-specific language (eDSL) in TypeScript and JSX notation, named Synthesis. The source code is available on GitHub [10], and the project website [11] provides documentation... Synthesis builds on two supporting packages... aelastics-types... aelastics-store... The approach is realized through an embedded domain-specific language (DSL) that demonstrates how a single mainstream language can serve simultaneously as the metamodeling, model construction, and transformation language"

    The sole practical demonstration of the algebra (and the claim that formal guarantees are enforced by one mainstream language’s type system) is the authors’ own Synthesis stack on their prior AelasticS packages. This is ordinary self-reference for an eDSL paper and does not reduce Theorems 1–2 or the algebraic definitions, which stand independently; hence only a minor, non-load-bearing step (score contribution of 1).

full rationale

This is a definitional/formal-framework paper, not a fit-to-data or uniqueness-from-prior-self-work paper. The model expression algebra (μ, ε, ρ, κ), type schemas, templates as open terms, and transformations as templates over source models are introduced by definition in §3; evaluation is the interpretation homomorphism by construction (Def. 14); Theorems 1 and 2 are standard structural inductions that explicitly condition on the hypothesis that every κ (and every rule) produces only well-typed finite sub-expressions (and Prop. 2 on termination). That hypothesis is not discharged inside the algebra and is mirrored by the host TypeScript type system for the JSX surface, but the paper never claims an unconditional derivation or renames a fitted quantity as a prediction. Megamodels and weaving follow directly from Defs. 2 and 8 without extra mechanisms. The only mild self-reference is that the practical realization (contribution 4, §4, Tables 1–2) is the authors’ own open-source Synthesis eDSL built on their aelastics-types/store packages (citations [10],[11]), which is normal for an eDSL paper and does not load-bear the formal claims or reduce any theorem to an unverified self-citation. No self-definitional loop, no fitted-input-called-prediction, no uniqueness theorem imported from overlapping authors to forbid alternatives, and no ansatz smuggled via citation. Score 1 reflects only that ordinary self-referential demo; central unification holds independently under the stated premises. Empty of the six priority circular patterns.

Assumptions & free parameters 0 free parameters · 6 assumptions · 3 invented entities

The central claim is definitional and proof-theoretic: once models, type schemas, and the four operators are fixed, evaluation and transformation safety follow by induction under well-typedness hypotheses. There are no fitted numerical free parameters. Load-bearing background includes standard set/function/order mathematics, the MDA-style multi-level modeling picture, and the authors’ choice that host-language types plus a model store suffice for MDE. Invented entities are the algebra operators and the identification of metamodels with type schemas / templates with open terms—conceptual inventions with independent handle via the open-source implementation, not physical entities.

assumptions (6)
  • ad hoc to paper Axiom 1: a root model m₀ exists with empty element set and universal type schema Σ₀ admitting any element.
    Stated explicitly in §3.1; provides the outermost namespace for all constructions and megamodels.
  • standard math Standard set theory, functions, partial orders, and structural induction suffice for the semantics and proofs.
    Used throughout Definitions 1–22 and Theorems 1–2; no exotic foundations claimed.
  • domain assumption Metamodels can be adequately represented as finite type schemas over a small set of type constructors (entity, subtype, array, optional, ref, iref).
    §3.2–3.3; deliberately minimal M3; extensibility noted but completeness vs full MOF/UML not proven.
  • domain assumption Every κ computation and transformation rule produces well-typed, terminating, finitely nested sub-expressions for all θ of interest.
    Hypothesis of Theorem 1, Proposition 2, and Definition 15; not discharged by a general static analysis in the paper.
  • domain assumption Document-order (depth-first left-to-right) evaluation with parent-before-children creation is an adequate operational model for graph-structured models with cross-references.
    Definition 14 and Reference Safety remark; forward references that are not yet created fail at runtime.
  • domain assumption A mainstream host language type system (TypeScript) plus runtime store can enforce three of four conformance conditions statically and serve as metamodeling, construction, and transformation language simultaneously.
    Abstract and §4; practical claim of the realization contribution.
invented entities (3)
  • Model expression algebra with operators μ, ε, ρ, κ independent evidence
    purpose: Unify model construction, templates, and transformations as term evaluation to model values.
    Core formalism of §3.4; classical term-algebra pattern specialized to MDE with an explicit reference operator and computation operator.
  • Type schemas as metamodels (Σ = (TΣ, τmodel)) independent evidence
    purpose: Constrain which constructors and properties are valid; replace separate metamodeling languages in the formal core.
    Definition 11; maps M2 to a finite typed signature over the constructor system.
  • Synthesis eDSL (TypeScript/JSX) with decorator-based polymorphic dispatch independent evidence
    purpose: Demonstrate that the algebra is implementable and that one host language can host metamodels, models, and transforms.
    §4; open-source realization; independent of the pure math but load-bearing for the practical contribution.

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Pith. "Pith review of Models as Values in a Model Expression Algebra: A Functional Approach to Model Driven Engineering." pith.science (2026). https://pith.science/paper/2604.05001

@misc{pith2026260405001,
  author       = {Pith},
  title        = {Pith review of: Models as Values in a Model Expression Algebra: A Functional Approach to Model Driven Engineering},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2604.05001}},
  note         = {Machine review of arXiv:2604.05001}
}
read the original abstract

This paper proposes a functional foundation for model driven engineering that unifies model construction, metamodels, templates, and transformations under a single formalism: the model expression algebra. In this algebra, models are values, model expressions are terms, and evaluation is the interpretation homomorphism from terms to values. Model expressions are composed from four operators: model creation and element creation operators, reference operators for retrieving models and elements, and computation operators that embed functional computations. Metamodels are type schemas that constrain the algebra, and model templates, understood as parameterized model expressions, are formalized as open terms with free variables. Model transformations then arise naturally as model templates whose input parameter is a source model. We prove type preservation under evaluation and type safety of transformation execution. Since models are themselves model elements, the algebra also supports megamodels and weaving models without additional mechanisms. The approach is realized through an embedded domain-specific language (DSL) that demonstrates how a single mainstream language can serve simultaneously as the metamodeling, model construction, and transformation language, with formal guarantees enforced by the language's type system.

Figures

Figures reproduced from arXiv: 2604.05001 by the authors.

Figure 1
Figure 1. Synthesis architecture The rest of the section is structured as follows. Section 4.1 presents JSX as the concrete syntax for model expressions. Section 4.2 shows how metamodels are defined as type schemas. Section 4.3 demonstrates model templates through parameterized and higher-order examples. Section 4.4 illustrates a complete model transformation. 4.1. JSX as Concrete Syntax for Model Expressions JSX is an XML-li… view at source ↗
Figure 2
Figure 2. Evaluation phases of a model expression The following listings illustrate how model templates and higher-order templates are used in practice. Listing 6 defines ConfigurableApproval, a model template that generates approval workflows varying in document name, number of approvers, and structural arrangement. Listing 6. ConfigurableApproval. type IApprovalConfig = { document: string approvers: number mode?: "parallel"… view at source ↗

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. OpenAlex reports about 113 citations worldwide. Full citation record

  1. Supporting Design Decisions in Rule-Based Model Transformations

    cs.SE 2026-04 conditional novelty 5.5 of 10

    Design decisions in rule-based model transformations can be modeled as first-class artifacts (decision, binding, configuration, trace) with formal well-definedness guarantees and a working Synthesis implementation.

Reference graph

Works this paper leans on

32 extracted references · 16 canonical work pages · cited by 1 Pith paper

  1. [1]

    AcmeCorp to Approval

    Execution trace (representative entries). <TraceModel name="AcmeCorp to Approval" timestamp="2026-04-02T00:12:00.173Z" source={<Model $refByName="/AcmeCorp" />} targets={[<Model $refByName="/Approval" />]}> <TraceEntry source={<ModelElement $refByName="/AcmeCorp/Engineering" />} rule="OrgUnit2Approval" ruleType="RegularRule" targets={[<TraceEntry $refByNa...

    2026

  2. [2]

    Their central finding is that no single mechanism fully addresses reuse across all scenarios, and reuse across metamodel boundaries remains an unsolved problem

    provide the most comprehensive survey of reuse in model transformation languages, evaluating 13 reuse mechanisms across five transformation scenarios. Their central finding is that no single mechanism fully addresses reuse across all scenarios, and reuse across metamodel boundaries remains an unsolved problem. The survey won the 2025 MODELS ten-year most ...

    2025

  3. [3]

    MDA Distilled,

    S. J. Miller, K. Scott, A. Uhl, and D. Weise, “MDA Distilled,” AddisonWesley Professional, no. 520, p. 176, 2004, Accessed: Apr. 01,

    2004

  4. [4]

    Available: https://www.oreilly.com/library/view/mda-distilled-principles/0201788918/

    [Online]. Available: https://www.oreilly.com/library/view/mda-distilled-principles/0201788918/

    arXiv

  5. [5]

    Model-Driven Software Development: Technology, Engineering, Management (Wiley Software Patterns Series),

    T. Stahl and M. Voelter, “Model-Driven Software Development: Technology, Engineering, Management (Wiley Software Patterns Series),” p. 446, 2006, Accessed: Apr. 01,

    2006

  6. [6]

    Available: http://www.amazon.com/Model-Driven-Software-Development-Technology-Engineering/dp/0470025700

    [Online]. Available: http://www.amazon.com/Model-Driven-Software-Development-Technology-Engineering/dp/0470025700

    arXiv

  7. [7]

    The state of practice in model-driven engineering,

    J. Whittle, J. Hutchinson, and M. Rouncefield, “The state of practice in model-driven engineering,” IEEE Softw., vol. 31, no. 3, pp. 79–85, 2014, doi: 10.1109/MS.2013.65

    work page doi:10.1109/ms.2013.65 2014

  8. [8]

    The role of modularity in self-organisation dynamics in biological networks

    B. Selic, “The pragmatics of model-driven development,” IEEE Softw., vol. 20, no. 5, pp. 19–25, Sep. 2003, doi: 10.1109/MS.2003.1231146

    work page Pith review arXiv doi:10.1109/ms.2003.1231146 2003

Show all 32 references
  1. [9]

    ATL: A model transformation tool,

    F. Jouault, F. Allilaire, J. Bézivin, and I. Kurtev, “ATL: A model transformation tool,” Sci. Comput. Program., vol. 72, no. 1–2, pp. 31–39, Jun. 2008, doi: 10.1016/j.scico.2007.08.002

    2008 doi

  2. [10]

    Reuse in model-to-model transformation languages: are we there yet?,

    A. Kusel, J. Schönböck, M. Wimmer, G. Kappel, W. Retschitzegger, and W. Schwinger, “Reuse in model-to-model transformation languages: are we there yet?,” Softw. Syst. Model., vol. 14, no. 2, pp. 537–572, May 2015, doi: 10.1007/s10270-013-0343-7

    2015 doi

  3. [11]

    Contrasting dedicated model transformation languages versus general purpose languages: a historical perspective on ATL versus Java based on complexity and size,

    S. Höppner, T. Kehrer, and M. Tichy, “Contrasting dedicated model transformation languages versus general purpose languages: a historical perspective on ATL versus Java based on complexity and size,” Softw. Syst. Model., vol. 21, no. 2, pp. 805–837, Apr. 2022, doi: 10.1007/s10...

    2022 doi

  4. [12]

    Specification of graph translators with triple graph grammars,

    A. Schürr, “Specification of graph translators with triple graph grammars,” Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 903, pp. 151–163, 1995, doi: 10.1007/3-540-59071-4_45

    1995 doi

  5. [13]

    AGG: A Graph Transformation Environment for Modeling and Validation of Software,

    G. Taentzer, “AGG: A Graph Transformation Environment for Modeling and Validation of Software,” Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 3062, pp. 446–453, 2004, doi: 10.1007/978-...

    2004 doi

  6. [14]

    Henshin: Advanced Concepts and Tools for In-Place EMF Model Transformations,

    T. Arendt, E. Biermann, S. Jurack, C. Krause, and G. Taentzer, “Henshin: Advanced Concepts and Tools for In-Place EMF Model Transformations,” Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), v...

    2010 doi

  7. [15]

    doi: 10.1007/3-540-31188-2

    doi

  8. [16]

    Combinators for bidirectional tree transformations,

    J. N. Foster, M. B. Greenwald, J. T. Moore, B. C. Pierce, and A. Schmitt, “Combinators for bidirectional tree transformations,” ACM Transactions on Programming Languages and Systems, vol. 29, no. 3, p. 17, May 2007, doi: 10.1145/1232420.1232424

    2007 doi

  9. [17]

    Symmetric lenses,

    M. Hofmann, B. Pierce, and D. Wagner, “Symmetric lenses,” in Proceedings of the 38th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages, New York, NY, USA: ACM, Jan. 2011, pp. 371–384. doi: 10.1145/1926385.1926428

    2011 doi

  10. [18]

    Multiple model synchronization with multiary delta lenses,

    Z. Diskin, H. König, and M. Lawford, “Multiple model synchronization with multiary delta lenses,” Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 10802 LNCS, pp. 21–37, 2018, doi: 10.100...

    2018 doi

  11. [19]

    Representing first-order logic using graphs,

    A. Rensink, “Representing first-order logic using graphs,” Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 3256, pp. 319–335, 2004, doi: 10.1007/978-3-540-30203-2_23

    2004 doi

  12. [20]

    Stratego/XT 0.17. A language and toolset for program transformation,

    M. Bravenboer, K. T. Kalleberg, R. Vermaas, and E. Visser, “Stratego/XT 0.17. A language and toolset for program transformation,” Sci. Comput. Program., vol. 72, no. 1–2, pp. 52–70, Jun. 2008, doi: 10.1016/j.scico.2007.11.003

    2008 doi

  13. [21]

    The spoofax language workbench,

    L. C. L. Kats and E. Visser, “The spoofax language workbench,” in Proceedings of the ACM international conference on Object oriented programming systems languages and applications, New York, NY, USA: ACM, Oct. 2010, pp. 444–463. doi: 10.1145/1869459.1869497

    2010 doi

  14. [22]

    Model Synchronization: Mappings, Tiles, and Categories,

    Z. Diskin, “Model Synchronization: Mappings, Tiles, and Categories,” Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6491 LNCS, pp. 92–165, 2011, doi: 10.1007/978-3-642-18023-1_3

    2011 doi

  15. [23]

    A diagrammatic approach to model transformations,

    A. Rutle, U. Wolter, and Y. Lamo, “A diagrammatic approach to model transformations,” in Proceedings of the 2008 Euro American Conference on Telematics and Information Systems, New York, NY, USA: ACM, Sep. 2008, pp. 1–8. doi: 10.1145/1621087.1621105

    2008 doi

  16. [24]

    Initial Algebra Semantics and Continuous Algebras,

    J. A. Goguen, J. W. Thatcher, E. G. Wagner, and J. B. Wright, “Initial Algebra Semantics and Continuous Algebras,” Journal of the ACM (JACM), vol. 24, no. 1, pp. 68–95, Jan. 1977, doi: 10.1145/321992.321997

    1977 doi

  17. [25]

    Order-sorted algebra I: equational deduction for multiple inheritance, overloading, exceptions and partial operations,

    J. A. Goguen and J. Meseguer, “Order-sorted algebra I: equational deduction for multiple inheritance, overloading, exceptions and partial operations,” Theor. Comput. Sci., vol. 105, no. 2, pp. 217–273, Nov. 1992, doi: 10.1016/0304-3975(92)90302-V

    1992 doi

  18. [26]

    Building domain-specific embedded languages,

    HudakPaul, “Building domain-specific embedded languages,” ACM Computing Surveys (CSUR), vol. 28, no. 4es, p. 196, Dec. 1996, doi: 10.1145/242224.242477

    1996 doi

  19. [27]

    Finally tagless, partially evaluated: Tagless staged interpreters for simpler typed languages,

    J. Carette, O. Kiselyov, and C. C. Shan, “Finally tagless, partially evaluated: Tagless staged interpreters for simpler typed languages,” Journal of Functional Programming, vol. 19, no. 5, pp. 509–543, Sep. 2009, doi: 10.1017/S0956796809007205

    2009 doi

  20. [28]

    , Berlin, Heidelberg: Springer Berlin Heidelberg, 2010, pp. 1–20. doi: 10.1007/978-3-642-13953-6_1

    2010 doi

  21. [29]

    The Essence of Multilevel Metamodeling,

    C. Atkinson and T. Kühne, “The Essence of Multilevel Metamodeling,” Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2185, pp. 19–33, 2001, doi: 10.1007/3-540-45441-1_3

    2001 doi

  22. [30]

    On Model Subtyping,

    C. Guy, B. Combemale, S. Derrien, J. R. H. Steel, and J. M. Jézéquel, “On Model Subtyping,” Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 7349 LNCS, pp. 400–415, 2012, doi: 10.1007/978...

    2012 doi

  23. [31]

    On model typing,

    J. Steel and J. M. Jézéquel, “On model typing,” Software & Systems Modeling 2007 6:4, vol. 6, no. 4, pp. 401–413, Jan. 2007, doi: 10.1007/S10270-006-0036-6

    2007 doi

  24. [32]

    Exploring the Use of Package Templates for Flexible Re-use of Collections of Related Classes,

    S. Krogdahl, B. Møller-Pedersen, and F. Sørensen, “Exploring the Use of Package Templates for Flexible Re-use of Collections of Related Classes,” Journal of Object Technology, vol. 8, no. 7, pp. 59–85, 2009, doi: 10.5381/JOT.2009.8.7.A1

    2009 doi

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