From be549d5ad9717111fcb5cb620eef3baf2547cd29 Mon Sep 17 00:00:00 2001 From: Ralf Jung Date: Tue, 16 Feb 2016 21:28:07 +0100 Subject: [PATCH] add a comment about the OFE vs COFE situation --- algebra/cofe.v | 19 +++++++++++++++++++ 1 file changed, 19 insertions(+) diff --git a/algebra/cofe.v b/algebra/cofe.v index baef7130..0e6e81a7 100644 --- a/algebra/cofe.v +++ b/algebra/cofe.v @@ -1,5 +1,24 @@ From algebra Require Export base. +(** This files defines (a shallow embedding of) the category of COFEs: + Complete ordered families of equivalences. This is a cartesian closed + category, and mathematically speaking, the entire development lives + in this category. However, we will generally prefer to work with raw + Coq functions plus some registered Proper instances for non-expansiveness. + This makes writing such functions much easier. It turns out that it many + cases, we do not even need non-expansiveness. + + In principle, it would be possible to perform a large part of the + development on OFEs, i.e., on bisected metric spaces that are not + necessary complete. This is because the function space A → B has a + completion if B has one - for A, the metric itself suffices. + That would result in a simplification of some constructions, becuase + no completion would have to be provided. However, on the other hand, + we would have to introduce the notion of OFEs into our alebraic + hierarchy, which we'd rather avoid. Furthermore, on paper, justifying + this mix of OFEs and COFEs is a little fuzzy. +*) + (** Unbundeled version *) Class Dist A := dist : nat → relation A. Instance: Params (@dist) 3. -- GitLab