Dear Vasili: The author doesn't refer to, nor even seem to know about, my book with J. Lambek, Introduction to Higher-Order Categorical Logic, J. Lambek and P. J. Scott, Cambridge Univ. Press, 1986, where all this was done in great detail. In fact, the three way correspondence between categories of deductive systems, of cartesian closed categories, and of typed lambda calculi (which the author wishes to explain) was first done there, with many applications. Best, Phil Scott On 2011-05-04, at 4:27 PM, Vasili I. Galchin wrote:
After thinking about my English, please let me add to my previous posting. I believe the author of the paper is proving an equivalence of an informal notion (Curry-Howard "Isomorphism) with a formal mathematical notion (the equivalence of categories).
Regards,
Vasili
On Tue, May 3, 2011 at 4:18 PM, Vasili I. Galchin <vigalchin@gmail.com> wrote:
Hello,
I started reading a paper www.math.uchicago.edu/~may/VIGRE/VIGRE2010/REUPapers/Berger.pdf entitled "A Categorical Approach to Proofs-As-Programs" by Carson Berger. He seems to be giving a formal equivalence of the various sides of this famous Correspondence using equivalence of categories. Have any members of this forum read this paper and if so, what significance do you give this paper?
Thank you,
Vasili
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