The present work achieves a mathematical, in particular syntax-independent, formulation of dynamics and intensionality of computation in terms of games and strategies. Specifically, we give game semantics of a higher-order programming language that distinguishes programmes with the same value yet different algorithms (or intensionality) and the hiding operation on strategies that precisely corresponds to the (small-step) operational semantics (or dynamics) of the language. Categorically, our games and strategies give rise to a cartesian closed bicategory, and our game semantics forms an instance of a bicategorical generalisation of the standard interpretation of functional programming languages in cartesian closed categories. This work is intended to be a step towards a mathematical foundation of intensional and dynamic aspects of logic and computation; it should be applicable to a wide range of logics and computations.

中文翻译：

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动态游戏语义

目前的工作实现了数学，特别是与语法无关，公式为动力学和内涵性在计算方面游戏和策略. 具体来说，我们给游戏语义一种高阶编程语言，它区分具有相同值但不同算法（或内涵）的程序，以及隐藏操作关于与语言的（小步）操作语义（或动态）精确对应的策略。明确地说，我们的游戏和策略会导致笛卡尔封闭双范畴，并且我们的游戏语义形成了笛卡尔封闭类别中函数式编程语言的标准解释的双分类概括的实例。这项工作旨在为逻辑和计算的内涵和动态方面的数学基础迈出一步；它应该适用于广泛的逻辑和计算。