Consider that his Haskell program (ostensibly) relies on mathematical proofs, a chain of them. The compiler consumes and validates this chain of proofs and checks whether or not the program is "true." It's hard to imagine why you'd use the scientific method to verify that 1 + 1 + 1 == 3; basic math and logic--- something computers are good at--- are sufficient.
As he and others have pointed out, the author was pretty up-front about the scale (relatively small; looks like a few hundred LOC) and nature (implementing an extant, well-defined API) of the problem. It's not an application as you suggest, and the author doesn't suggest it's a good idea for applications, either.
The conclusion isn't "use Haskell & never test your code!". After all, he explicitly offers no conclusion. :) It's just an example of how, sometimes, you can be reasonably certain that your Haskell program is correct when it compiles.
Myself, I'd still run it, or at least QuickCheck it. I don't trust myself not to write logically sound, completely incorrect code.
Once you've figured out on paper that 1 + 1 = 2, you don't necessarily have to put one apple next to one apple and count two apples to “complete the exercise.”
As he and others have pointed out, the author was pretty up-front about the scale (relatively small; looks like a few hundred LOC) and nature (implementing an extant, well-defined API) of the problem. It's not an application as you suggest, and the author doesn't suggest it's a good idea for applications, either.
The conclusion isn't "use Haskell & never test your code!". After all, he explicitly offers no conclusion. :) It's just an example of how, sometimes, you can be reasonably certain that your Haskell program is correct when it compiles.
Myself, I'd still run it, or at least QuickCheck it. I don't trust myself not to write logically sound, completely incorrect code.