typo

diff --git a/personal/_posts/2019-05-15-typeclasses-exponential-blowup.md b/personal/_posts/2019-05-15-typeclasses-exponential-blowup.md
index 47ce741a3d547a4ae984d26bfcdd700e5c2cde5d..9e682cb54109593d774e9b8de8c187bb33b894a0 100644 (file)
--- 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)`.
 {% 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]
 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]