X-Git-Url: https://git.ralfj.de/web.git/blobdiff_plain/0cad4b0dbc24e0b57d9228de693c9885d6746cd5..46a9b461507c551a868eaf6c3d0038971ea68d70:/personal/_posts/2019-05-15-typeclasses-exponential-blowup.md

diff --git a/personal/_posts/2019-05-15-typeclasses-exponential-blowup.md b/personal/_posts/2019-05-15-typeclasses-exponential-blowup.md
index 47ce741..9e682cb 100644
--- a/personal/_posts/2019-05-15-typeclasses-exponential-blowup.md
+++ b/personal/_posts/2019-05-15-typeclasses-exponential-blowup.md
@@ -192,7 +192,7 @@ Class Monoid (A: Type) `{Op A, Unit A} := {
 {% endhighlight %}
 
 This limits the "index depth" to 2, and thus limits term complexity to `O(n^3)`.
-Still not great, but at least it doesn't grow further as we add more sublcasses.
+Still not great, but at least it doesn't grow further as we add more subclasses.
 However, this scheme does not support diamonds in the hierarchy as instances will be duplicated.
 Also, the instance we implicitly added by writing `:>`, namely that `Monoid A -> Semigroup A`, means we'll check all `Monoid` instances any time we just want a `Semigroup`.
 This leads to exponential complexity when performing backtracking typeclass search: a `Semigroup (A*A)` can be obtained either by searching for a `Monoid (A*A)` or via `prod_semigroup`, so in case of backtracking Coq will go through a combinatorial explosion when trying all possible ways to derive `Semigroup (A*A*A*...)`.[^2]