Translating Higher-Order Clauses to First-Order Clauses

@article{Meng2007TranslatingHC,
  title={Translating Higher-Order Clauses to First-Order Clauses},
  author={Jia Meng and Lawrence Charles Paulson},
  journal={Journal of Automated Reasoning},
  year={2007},
  volume={40},
  pages={35-60}
}
Interactive provers typically use higher-order logic, while automatic provers typically use first-order logic. To integrate interactive provers with automatic ones, one must translate higher-order formulas to first-order form. The translation should ideally be both sound and practical. We have investigated several methods of translating function applications, types, and λ-abstractions. Omitting some type information improves the success rate but can be unsound, so the interactive prover must… 
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