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Coinduction All the Way Up

机译:一路走来

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摘要

We revisit coinductive proof principles from a lattice theoretic point of view. By associating to any monotone function a function which we call the companion, we give a new presentation of both Knaster-Tarski's seminal result, and of the more recent theory of enhancements of the coinductive proof method (up-to techniques).The resulting theory encompasses parameterized coinduction, as recently proposed by Hur et al., and second-order reasoning, i.e., the ability to reason coinductively about the enhancements themselves. It moreover resolves a historical peculiarity about up-to context techniques.Based on these results, we present an open-ended proof system allowing one to perform proofs on-the-fly and to neatly separate inductive and coinductive phases.
机译:我们从晶格理论的角度重新审视共归证明原理。通过将任何单调函数与我们称为伴随函数的函数相关联,我们给出了Knaster-Tarski的开创性结果以及最新的共归证明方法增强理论(最新技术)的新表述。如Hur等人最近所提出的,它包含参数化的共归,以及二阶推理,即,对增强本身进行共归推理的能力。此外,它还解决了有关上下文技术的历史特殊性。基于这些结果,我们提出了一种开放式的证明系统,该系统可以即时执行证明,并巧妙地将归纳和共归阶段分开。

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