Maintainer | diagrams-discuss@googlegroups.com |
---|---|
Safe Haskell | Safe-Inferred |
A monoid transformer that allows deleting information from a concatenation of monoidal values.
Documentation
If m
is a Monoid
, then Deletable m
(intuitively speaking)
adds two distinguished new elements [
and ]
, such that an
occurrence of [ "deletes" everything from it to the next ]. For
example,
abc[def]gh == abcgh
This is all you really need to know to use Deletable m
values; to understand the actual implementation, read on.
To properly deal with nesting and associativity we need to be
able to assign meanings to things like [[
, ][
, and so on. (We
cannot just define, say, [[ == [
, since then ([[)] == [] ==
id
but [([]) == [id == [
.) Formally, elements of Deletable
m
are triples of the form (r, m, l) representing words ]^r m
[^l
. When combining two triples (r1, m1, l1) and (r2, m2, l2)
there are three cases:
- If l1 == r2 then the [s from the left and ]s from the right exactly cancel, and we are left with (r1, m1 <> m2, l2).
- If l1 < r2 then all of the [s cancel with some of the ]s, but m1 is still inside the remaining ]s and is deleted, yielding (r1 + r2 - l1, m2, l2)
- The remaining case is symmetric with the second.
toDeletable :: m -> Deletable mSource
Inject a value into a Deletable
wrapper. Satisfies the
property
unDelete . toDeletable === id