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Article summary:
1. The article discusses the type inference of linear lambda calculus with first-class continuations.
2. It introduces a modal variable in the types to substitute the linear modality and during type inference, modal variables are instantiated.
3. The article also explains how linear logic and first-class continuations are related to the Curry-Howard isomorphism and how it can be used to control erasability and replicability of formulas in a sequent.
Article analysis:
The article provides an overview of type inference of linear lambda calculus with first-class continuations, which is a relatively new concept in computer science. The article does a good job of explaining the concepts involved, such as linear logic, Curry-Howard isomorphism, and first-class continuations, in an easy to understand manner. However, there are some areas where more detail could have been provided. For example, while the article mentions that the cut-elimination step for classical logic involves computational inconsistency, it does not provide any further explanation or evidence for this claim. Additionally, while the article does mention possible risks associated with using this type of calculus, it does not provide any detailed analysis or discussion on these risks or potential solutions for mitigating them. Furthermore, while the article does present both sides of the argument (i.e., linear logic vs classical logic), it does not explore any counterarguments or alternative perspectives on this topic. Finally, there is no indication that any external sources were consulted when writing this article; thus, it may be biased towards one particular perspective or point of view without considering other perspectives or opinions on this topic.