Skip to content

Commit

Permalink
add comment that OFE expands to some nonsense
Browse files Browse the repository at this point in the history
  • Loading branch information
plt-amy committed Aug 10, 2023
1 parent 7141709 commit 9521097
Showing 1 changed file with 13 additions and 3 deletions.
16 changes: 13 additions & 3 deletions src/Cat/Instances/OFE.lagda.md
Original file line number Diff line number Diff line change
Expand Up @@ -14,10 +14,10 @@ open import Data.List hiding (map)
module Cat.Instances.OFE where
```

# Ordered families of equivalences
# Ordered families of equivalence relations

An **ordered family of equivalences** (OFE, for short) is a set $X$
equipped with a family of equivalence relations, indexed by natural
An **ordered family of equivalence relations** (OFE, for short) is a set
$X$ equipped with a family of equivalence relations, indexed by natural
numbers $n$ and written $x \within{n} y$, that _approximate_ the
equality on $X$. The family of equivalence relations can be thought of
as equipping $X$ with a notion of _fractional distance_: $x \within{n}
Expand All @@ -32,6 +32,16 @@ $d'$, for any $d' \le d$;

- Arbitrarily close points are the same.

::: warning
We remark that the term OFE generally stands for ordered family of
_equivalences_, rather than _equivalence relations_; However, this
terminology is mathematically incorrect: there is no meaningful sense in
which an OFE is a family $I \to (A \equiv B)$.

To preserve the connection with the literature, we shall maintain the
acronym "OFE"; Keep in mind that we do it with disapproval.
:::

Another perspective on OFEs, and indeed a large part for the
justification of their study, is in the semantics of programming
languages: in that case, the relation $x \within{n} y$ should be
Expand Down

0 comments on commit 9521097

Please sign in to comment.