## Section: New Results

### Programming Languages

Participants : Walid Benghrabit, Ronan-Alexandre Cherrueau, Rémi Douence, Hervé Grall, Florent Marchand de Kerchove de Denterghem, Jacques Noyé, Jean-Claude Royer, Mario Südholt.

#### Formal Methods, logics and type theory

This year we have proposed “Gradual Certified Programming” as a bridge between type-based expressive proofs and programming languages, have extended previous type theories by new homotopy-based means, and have introduced “effect capabilities” to control monad-based effects in Haskell.

##### Gradual Certified Programming in Coq

Expressive static typing disciplines are a powerful way to achieve high-quality software. However, the adoption cost of such techniques should not be under-estimated. Just like gradual typing allows for a smooth transition from dynamically-typed to statically-typed programs, it seems desirable to support a gradual path to certified programming. We have explored gradual certified programming in Coq [33] , providing the possibility to postpone the proofs of selected properties, and to check “at runtime” whether the properties actually hold. Casts can be integrated with the implicit coercion mechanism of Coq to support implicit cast insertion à la gradual typing. Additionally, when extracting Coq functions to mainstream languages, our encoding of casts supports lifting assumed properties into runtime checks. Much to our surprise, it is not necessary to extend Coq in any way to support gradual certified programming. A simple mix of type classes and axioms makes it possible to bring gradual certified programming to Coq in a straightforward manner.

##### Homotopy Hypothesis in Type Theory

In classical homotopy theory, the homotopy hypothesis asserts that the fundamental omega-groupoid construction induces an equivalence between topological spaces and weak omega-groupoids. In the light of Voevodsky's univalent foundations program, which puts forward an interpretation of types as topological spaces, we have considered the question of transposing the homotopy hypothesis to type theory [16] . Indeed such a transposition could stand as a new approach to specifying higher inductive types. Since the formalization of general weak omega-groupoids in type theory is a difficult task, we have only taken a first step towards this goal, which consists in exploring a shortcut through strict omega-categories. The first outcome is a satisfactory type-theoretic notion of strict omega-category, which has hsets of cells in all dimensions. For this notion, defining the 'fundamental strict omega-category' of a type seems out of reach. The second outcome is an 'incoherently strict' notion of type-theoretic omega-category, which admits arbitrary types of cells in all dimensions. These are the 'wild' omega-categories of the title. They allow the definition of a 'fundamental wild omega-category' map, which leads to our (partial) homotopy hypothesis for type theory (stating an adjunction, not an equivalence). All of our results have been formalized in the Coq proof assistant. Our formalization makes systematic use of the machinery of coinductive types.

##### Effect Capabilities For Haskell

Computational effects complicate the tasks of reasoning about and maintaining software, due to the many kinds of interferences that can occur. While different proposals have been formulated to alleviate the fragility and burden of dealing with specific effects, such as state or exceptions, there is no prevalent robust mechanism that addresses the general interference issue. Building upon the idea of capability-based security, we have proposed effect capabilities [14] as an effective and flexible manner to control monadic effects and their interferences. Capabilities can be selectively shared between modules to establish secure effect-centric coordination. We have further refined capabilities with type-based permission lattices to allow fine-grained decomposition of authority. An implementation of effect capabilities in Haskell has been done, using type classes to establish a way to statically share capabilities between modules, as well as to check proper access permissions to effects at compile time.

##### Correct Refactoring Tools

Most integrated development environments provide refactoring tools. However, these tools are often unreliable. As a consequence, developers have to test their code after applying an automatic refactoring.

Refactoring tools for industrial languages are difficult to test and verify. We have developed a refactoring operation for C programs (renaming of global variables) for which we have proved that it preserves the set of possible behaviors of the transformed programs [39] . That proof of correctness relies on the operational semantics provided by CompCert C in Coq. We have also proved some properties of the transformation which are used to establish properties of a composed refactoring operations.

#### Language Mechanisms

This year we have contributed new results on domain-specific aspect languages, concurrent event-based programming, model transformations as well as the relationship between functional and constraint programming.

Furthermore, we have proposed language support for the definition and enforcement of security properties, in particular related to the accountability of service-based systems, see Sec. 7.3 .

##### Domain-Specific Aspect Languages

Domain-Specific Aspect Languages (DSALs) are Domain-Specific Languages (DSLs) designed to express crosscutting concerns. Compared to DSLs, their aspectual nature greatly amplifies the language design space. In the context of the Associate Team RAPIDS/REAL, we have structured this space in order to shed light on and compare the different domain-specific approaches to deal with crosscutting concerns [13] . We have reported on a corpus of 36 DSALs covering the space, discussed a set of design considerations and provided a taxonomy of DSAL implementation approaches. This work serves as a frame of reference to DSAL and DSL researchers, enabling further advances in the field, and to developers as a guide for DSAL implementations.

##### Concurrent Event-Based Programming

The advanced concurrency abstractions provided by the Join calculus overcome the drawbacks of low-level concurrent programming techniques. However, with current approaches, the coordination logic involved in complex coordination schemas is still fragmented. In [11] , Jurgen Van Ham presents JEScala, a language that captures coordination schemas in a more expressive and modular way by leveraging a seamless integration of an advanced event system with join abstractions. The implementation of joins-based state machines is discussed with alternative faster implementations made possible through a domain specific language. Event monitors are introduced as a way of synchronizing event handling and building concurrent event-based applications from sequential event-based parts.

##### Model Lazy Transformation

The Object Constraint Language (OCL) is a central component in modeling and transformation languages such as the Unified Modeling Language (UML), the Meta Object Facility (MOF), and Query View Transformation (QVT). OCL is standardized as a strict functional language. We have proposed a lazy evaluation strategy for OCL [36] . This lazy evaluation semantics is beneficial in some model-driven engineering scenarios for speeding up the evaluation times for very large models, simplifying expressions on models by using infinite data structures (e.g., infinite models) and increasing the reusability of OCL libraries. We have implemented the approach on the ATL virtual machine EMFTVM. This is a joint work with the Inria team Atlanmod.

##### Composition Mechanisms for Constraints Generalization

Structural time series (pattern for sequences of values) can be described with numerous automata-based constraints. In [12] , we describe a large family of constraints for structural time series by means of function composition. We formalize the patterns using finite transducers. Based on that description, we automatically synthesize automata with accumulators, as well as constraint checkers. The description scheme not only unifies the structure of the existing 30 time-series constraints, but also leads to over 600 new constraints, with more than 100,000 lines of synthesized code. This is a joint work with the Inria team Tasc.