Functional Kan Simplicial Sets: Non-Constructivity of Exponentiation
نویسنده
چکیده
Functional Kan simplicial sets are simplicial sets in which the horn-fillers required by the Kan extension condition are given explicitly by functions. We show the non-constructivity of the following basic result: if B and A are functional Kan simplicial sets, then A is a Kan simplicial set. This strengthens a similar result for the case of non-functional Kan simplicial sets shown by Bezem, Coquand and Parmann [TLCA 2015, v. 38 of LIPIcs]. Our result shows that – from a constructive point of view – functional Kan simplicial sets are, as it stands, unsatisfactory as a model of even simply typed lambda calculus. Our proof is based on a rather involved Kripke countermodel which has been encoded and verified in the Coq proof assistant. 1998 ACM Subject Classification F.4.1 Mathematical Logic and Formal Languages: Mathematical Logic
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