On the Symmetry of Sequentiality

We offer a symmetric account of sequentiality, by means of symmetric algorithms, which are pairs of sequential functions, mapping input data to output data, and output exploration trees to input exploration trees, respectively. We use the framework of sequential data structures, a reformulation of a class of Kahn-Plotkin's concrete data structures. In sequential data structures, data are constructed by alternating questions and answers. Sequential data structures and symmetric algorithms are the objects and morphisms of a symmetric monoidal closed category, which is also cartesian, and is such that the unit is terminal. Our category is a full subcategory of categories of games considered by Lamarche, and by Abramsky-Jagadeesan, respectively.

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