The article investigates behavioural equivalence between programs in a call-by-value functional language extended with a signature of (algebraic) effect-triggering operations. Two programs are considered as being behaviourally equivalent if they enjoy the same behavioural properties. To formulate this, we define a logic whose formulas specify behavioural properties. A crucial ingredient is a collection of modalities expressing effect-specific aspects of behaviour. We give a general theory of such modalities. If two conditions, openness and decomposability , are satisfied by the modalities, then the logically specified behavioural equivalence coincides with a modality-defined notion of applicative bisimilarity, which can be proven to be a congruence by a generalisation of Howe’s method. We show that the openness and decomposability conditions hold for several examples of algebraic effects: nondeterminism, probabilistic choice, global store, and input/output.

中文翻译：

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通过代数效应模态的行为等价

本文研究了在按值调用函数语言中扩展的程序之间的行为等效性，该语言扩展了（代数）效果触发操作的签名。如果两个程序具有相同的行为属性，则它们被认为是行为等效的。为了表述这一点，我们定义了一个逻辑，其公式指定了行为属性。一个关键的成分是一个集合方式表达行为的特定效果方面。我们给出了这种模式的一般理论。如果有两个条件，开放性和可分解性, 由模态满足，则逻辑上指定的行为等价与模态定义的应用双相似性概念相吻合，这可以通过 Howe 方法的推广证明是全等的。我们表明，开放性和可分解性条件适用于代数效应的几个示例：非确定性、概率选择、全局存储和输入/输出。