Abstract
We compare formalizations of an example from elementary category theory in the systems HOL (an implementation of Church’s classical simple type theory) and ALF (an implementation of Martin-Löf’s intuitionistic type theory). The example is a proof of coherence for monoidal categories which was extracted from a proof of normalization for monoids. It makes essential use of the identification of proofs and programs which is fundamental to intuitionistic type theory. This aspect is naturally highlighted in the ALF formalization. However, it was possible to develop a similar formalization of the proof in HOL. An interesting aspect of the developments concerned the implementation of diagram chasing. The HOL development was greatly facilitated by an implementation of support for such equational reasoning in Standard ML.
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Agerholm, S., Beylin, I., Dybjer, P. (1996). A comparison of HOL and ALF formalizations of a categorical coherence theorem. In: Goos, G., Hartmanis, J., van Leeuwen, J., von Wright, J., Grundy, J., Harrison, J. (eds) Theorem Proving in Higher Order Logics. TPHOLs 1996. Lecture Notes in Computer Science, vol 1125. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0105394
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DOI: https://doi.org/10.1007/BFb0105394
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