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Pierre-Marie Pédrot
Iris
Commits
be549d5a
Commit
be549d5a
authored
Feb 16, 2016
by
Ralf Jung
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add a comment about the OFE vs COFE situation
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algebra/cofe.v
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be549d5a
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(** 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
.
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