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CoqTL: a Coq DSL for rule-based model transformation

Zheng Cheng, Massimo Tisi, Rémi Douence

2019
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Journal of Software and Systems Modeling
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In model-driven engineering, model transformation (MT) verification is essential for reliably producing software artifacts. While recent advancements have enabled automatic Hoare-style verification for non-trivial MTs, there are certain verification tasks (e.g. induction) that are intrinsically difficult to automate. Existing tools that aim at simplifying the interactive verification of MTs typically translate the MT specification (e.g. in ATL) and properties to prove (e.g. in OCL) into an
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... active theorem prover. However, since the MT specification and proof phases happen in separate languages, the proof developer needs a detailed knowledge of the translation logic. Naturally, any error in the MT translation could cause unsound verification, i.e. the MT executed in the original environment may have different semantics from the verified MT. We propose an alternative solution by designing and implementing an internal domain specific language, namely CoqTL, for the specification of declarative MTs directly in the Coq interactive theorem prover. Expressions in CoqTL are written in Gallina (the specification language of Coq), increasing the possibilities of reusing native Coq libraries in the transformation definition and proof. CoqTL specifications can be directly executed by our transformation engine encoded in Coq, or a certified implementation of the transformation can be generated by the native Coq extraction mechanism. We ensure that CoqTL has the same expressive power of Gallina (i.e. if a MT can be computed in Gallina, then it can also be represented in CoqTL). In this article, we introduce CoqTL, evaluate its practical applicability on a use case, and identify its current limitations. 2 Zheng Cheng et al. Keywords Model-Driven Engineering · Model Transformation · Domain-specific Language · Interactive Theorem Proving · Coq Introduction Model-driven engineering (MDE), i.e. software engineering centered on software models and MTs, is widely recognized as an effective way to manage the complexity of software development. With the increasing complexity of MTs (e.g., in automotive industry [31] , medical data processing [38] , aviation [4]), it is urgent to develop techniques and tools that prevent incorrect MTs from generating faulty models. The effects of such faulty models could be unpredictably propagated into subsequent MDE steps, e.g. code generation. Deductive verification is a promising approach for quality assurance in MT: correctness is specified by MT developers using contracts (i.e. pre/postconditions), then the semantics of the MT language together with contracts and metamodels are encoded into a deductive theorem prover. Thanks especially to recent advancements in SMT solvers, automatic deductive verification is giving good results in several scenarios [7, 6, 10, 27] . However, because of the general undecidability, interactive deductive verification is inevitable for complex tasks (for instance, automatic deductive theorem provers usually lack support for induction, or finding witnesses for existential quantifiers). Coq is an interactive theorem prover. The user can use Coq to write mathematical definitions, executable algorithms and theorems together with an environment for semi-interactive development of proofs (in the sense that routine proofs can be automatically performed while difficult proofs require human guidance). It has been used to prove non-trivial mathematical theorems, or as an environment for developing formally certified software and hardware (e.g. [25, 16] ). Moreover, a certified executable program (e.g., in OCaml, Haskell) can be generated from a Coq function by the native Coq extraction mechanism. While not strictly needed for understanding this paper, we refer the reader to [29] for an introduction to the Coq system. Previous work aiming at simplifying the interactive verification of MTs, has already proposed translations from MT specifications (e.g. in MT languages like ATL) and properties to prove (e.g. in OCL) into Coq. However, the practical applicability of this translational approach is hampered by the fact that the two phases of MT specification and correctness proof require developments in languages (e.g. ATL+OCL and Coq, respectively) at two different levels of abstraction. The proof developer needs a deep knowledge of the translation logic to be able to write meaningful proofs. Any change in the MT code propagates through the translator, and it is difficult to predict the proof steps that will be invalidated. Naturally, any error in the MT translation could cause unsound verification, i.e. the MT executed in the original environment may have different semantics from the verified MT. Certifying that the semantics of the MT language has being correctly axiomatized in the back-end theorem prover is a hard task, and very few attempts exist [10, 1]. Coq includes Gallina, a functional programming language with pattern matching and a rich type system, well suited as a platform for embedding domain-specific programming languages (DSLs) (e.g. [12] ). In this work, we draw on this aspect of Coq and propose a DSL, namely CoqTL, to turn Coq into a tool for developing

doi:10.1007/s10270-019-00765-6
fatcat:4tgvy3nxfnaqzal6xzu6yl5zfu