We describe a systematic method to build a logic from any programming language described as a Pure Type System (PTS). The formulas of this logic express properties about programs. We define a parametricity theory about programs and a realizability theory for the logic. The logic is expressive enough to internalize both theories. Thanks to the PTS setting, we abstract most idiosyncrasies specific to particular type theories. This confers generality to the results, and reveals parallels between parametricity and realizability.
International audienceConcurrent strategies are shown to support operations yielding an economic yet rich higher-order con-current process language, which shares features both with process calculi and nondeterministic dataflow. Its operational semantics and 'may and must' equivalence require that we take internal (neutral) moves seriously, leading to the introduction of 'partial strategies' which may contain neutral moves. Through partial strategies, we can present a transition semantics for a language of strategies and can formulate their 'may and must' behaviour. While partial strategies compose, in a way extending that of strategies, in general composition introduces extra neutral moves; in particular, copy-cat is no longer strictly an identity w.r.t. composition. However, a simple extension of concurrent strategies (with stopping configurations) maintains the fact that they form a bicategory while still capturing 'may and must' behaviour
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