# 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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## 53 Citations

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