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Abstract: What equations can we guarantee that simple functional programs must satisfy, irrespective of their obvious defining equations? Equivalently, what non-trivial identifications must hold between lambda terms, thought-of as encoding appropriate natural deduction proofs ? We show that the usual syntax guarantees that certain naturality equations from category theory are necessarily provable. At the same time, our categorical approach addresses an equational meaning of cut-elimination and... (Update)
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.... Reynolds and his student Ma, Rey83, MR91] The use of dinaturality has been proposed by Bainbridge, Freyd, Girard, Scedrov, and Scott, [BFSS90, GSS91]. On an abstract level, the idea behind the use of logical relations is that given an intepretation of the second order lambda...
.... in [12] where the strong eliminability of cut, rather than just the admissibility, is required; and, we anticipate, those in [5] and [15]) Herbelin called (following [6] his calculus LJT , a name we avoid in case of confusion with that in the first author s [9] we call...
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BibTeX entry: (Update)
Girard, J.-Y., A. Scedrov & P. Scott : "Normal forms and cut-free proofs as natural transformations", in "Logic from Computer Science", MSRI publications, Y. Moschovakis (editor), 21, Springer-Verlag, (1992), 217--241. http://citeseer.ist.psu.edu/girard92normal.html More
@incollection{ girard91normal,
author = "Jean-Yves Girard and Andre Scedrov and Philip J. Scott",
title = "Normal Forms and Cut-Free Proofs as Natural Transformations",
booktitle = "Proceedings Workshop Logic from Computer Science, Berkeley, {CA}, {USA}, 13--17 Nov 1989",
volume = "21",
publisher = "Springer-Verlag",
address = "New York",
editor = "Y. N. Moschovakis",
pages = "217--241",
year = "1991",
url = "citeseer.ist.psu.edu/girard92normal.html" }
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359 Introduction to Higher Order Categorical Logic (context) - Lambek, Scott - 1986 ACM
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