typos

diff --git a/personal/_posts/2019-05-15-typeclasses-exponential-blowup.md b/personal/_posts/2019-05-15-typeclasses-exponential-blowup.md
index e59917b87ed92336f88e3925decffd72432179e5..2eda6134d0bb1005adb1fa7ee95175ac133e5829 100644 (file)
--- a/personal/_posts/2019-05-15-typeclasses-exponential-blowup.md
+++ b/personal/_posts/2019-05-15-typeclasses-exponential-blowup.md
@@ -4,10 +4,10 @@ categories: research coq
 forum: https://coq.discourse.group/t/blog-post-exponential-blowup-when-using-unbundled-typeclasses-to-model-algebraic-hierarchies/289
 ---
 
 forum: https://coq.discourse.group/t/blog-post-exponential-blowup-when-using-unbundled-typeclasses-to-model-algebraic-hierarchies/289
 ---
 

-When formalizing a proof in an interactive theorem prover like [Coq](https://coq.inria.fr/), one reoccuring issue is the handling of algebraic hierarchies.
+When formalizing a proof in an interactive theorem prover like [Coq](https://coq.inria.fr/), one reoccurring issue is the handling of algebraic hierarchies.

 Such hierarchies are everywhere:  some operations are associative, while others commute; some types have an equivalence relation, while others also have a (pre-)order or maybe even a well-ordering; and so on.
 So the question arises:  What is the best way to actually encode these hierarchies in Coq?
 Such hierarchies are everywhere:  some operations are associative, while others commute; some types have an equivalence relation, while others also have a (pre-)order or maybe even a well-ordering; and so on.
 So the question arises:  What is the best way to actually encode these hierarchies in Coq?

-Coq offers two mechanism that are suited to solve this task: typeclasses and canonical structures.
+Coq offers two mechanisms that are suited to solve this task: typeclasses and canonical structures.

 Both can be instrumented in different ways to obtain a (more or less) convenient-to-use algebraic hierarchy.
 A common approach using typeclasses is the ["unbundled" approach by Bas Spitters and Eelis van der Weegen](http://www.eelis.net/research/math-classes/mscs.pdf).
 However as we learned the hard way in the Coq formalization of the [original Iris paper](https://iris-project.org/pdfs/2015-popl-iris1-final.pdf), this approach quickly leads to terms that seem to be exponential in size.
 Both can be instrumented in different ways to obtain a (more or less) convenient-to-use algebraic hierarchy.
 A common approach using typeclasses is the ["unbundled" approach by Bas Spitters and Eelis van der Weegen](http://www.eelis.net/research/math-classes/mscs.pdf).
 However as we learned the hard way in the Coq formalization of the [original Iris paper](https://iris-project.org/pdfs/2015-popl-iris1-final.pdf), this approach quickly leads to terms that seem to be exponential in size.