Realizability Interpretation and Normalization of Typed Call-by-Need λ-calculus With Control
Realizability Interpretation and Normalization of Typed Call-by-Need λ-calculus With Control
复制标题
带控制的类型化按需调用 λ 演算的可实现性解释和规范化
DOI：
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
Hugo Herbelin
中科院分区：
文献类型：
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作者：
Étienne Miquey;Hugo Herbelin
我们定义了一种可实现性的变体，其中实现者是一个术语和替代的对。这种变体使我们能够证明由于Ariola等人的控制而具有控制权的简单呼叫$$ lambda $ - $ cyculus的归一化。确实，在这种逐个呼叫的演算中，必须延迟替换，直到知道是否确实需要论点为止。在第二步中，我们将证明扩展到逐个呼叫的$$ lambda $$ - 装有类型系统等效的类型系统的微积分第二作者引入的需要经典的二阶算术，以提供对依赖选择的公理的验证解释。
We define a variant of realizability where realizers are pairs of a term and a substitution. This variant allows us to prove the normalization of a simply-typed call-by-need $$lambda$-$calculus with control due to Ariola et al. Indeed, in such call-by-need calculus, substitutions have to be delayed until knowing if an argument is really needed. In a second step, we extend the proof to a call-by-need $$lambda$$-calculus equipped with a type system equivalent to classical second-order predicate logic, representing one step towards proving the normalization of the call-by-need classical second-order arithmetic introduced by the second author to provide a proof-as-program interpretation of the axiom of dependent choice.