Normalization and the Yoneda Embedding

@article{Cubric1998NormalizationAT,
  title={Normalization and the Yoneda Embedding},
  author={Djordje Cubric and Peter Dybjer and Philip J. Scott},
  journal={Math. Struct. Comput. Sci.},
  year={1998},
  volume={8},
  pages={153-192}
}
We show how to solve the word problem for simply typed λβη-calculus by using a few well-known facts about categories of presheaves and the Yoneda embedding. The formal setting for these results is P-category theory, a version of ordinary category theory where each hom-set is equipped with a partial equivalence relation. The part of P-category theory we develop here is constructive and thus permits extraction of programs from proofs. It is important to stress that in our method we make no use of… 
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