Rigorous modelling of natural and industrial systems still conveys various challenges related to abstractions, methods to proceed with and easy-to-use tools to build, compose and reason on models. Operads are mathematical structures that provide such abstractions to compose various objects and garanteeing well-formedness. Concrete implementations of operads will offer practical means to exploit operads and to use them for various technical applications. Going from the mathematical structures, we develop with Event-B a complete refinement chain that implements algebraic operads and their basic operations. The result of this work, can be used from the methodological point of view to handle similar implementations for symbolic computation questions, and also to reason on symbolic computation applications supported by operads structures.

翻译：自然与工业系统的严格建模仍面临诸多挑战，涉及抽象方法、建模流程以及用于构建、组合和推理模型的易用工具。操作数是提供此类抽象以组合各类对象并确保结构良好性的数学结构。操作数的具体实现将为实际应用操作数及将其用于多种技术场景提供实用手段。基于数学结构，我们利用Event-B开发了一套完整的精化链，实现了代数操作数及其基本运算。本工作的成果可从方法论角度用于处理符号计算问题的类似实现，并支持基于操作数结构的符号计算应用推理。