Some Lambda Calculus and Type Theory Formalized

@article{McKinna1999SomeLC,
  title={Some Lambda Calculus and Type Theory Formalized},
  author={James McKinna and Robert Pollack},
  journal={Journal of Automated Reasoning},
  year={1999},
  volume={23},
  pages={373-409}
}
We survey a substantial body of knowledge about lambda calculus and Pure Type Systems, formally developed in a constructive type theory using the LEGO proof system. On lambda calculus, we work up to an abstract, simplified proof of standardization for beta reduction that does not mention redex positions or residuals. Then we outline the meta theory of Pure Type Systems, leading to the strengthening lemma. One novelty is our use of named variables for the formalization. Along the way we point… CONTINUE READING
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