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Update type_classes.md #77

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@Erotemic Erotemic commented Oct 1, 2023

In https://lean-lang.org/theorem_proving_in_lean4/type_classes.html I noticed an error. In the 5th example part of it states:

#eval double (10 : Int)
-- 100

However, the actual evaluation returns 10 as-is. I'm not sure if this was meant to return 100 or 10 (the correct fix depends on the answer to that question), but assuming we really did want 100 there as a way to show how the resolution of Nat and Int are different, then this should be the correct patch.

Make code agree with results
@@ -92,7 +92,7 @@ We can now reimplement `double` using an instance implicit by:
# instance : Add Nat where
# add := Nat.add
# instance : Add Int where
# add := Int.add
# add := Int.mul
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These lines starting with # are hidden in the rendered book, and I assume they generally match code already shown earlier in the chapter. In the code block just above this one, this instance is defined to use Int.add, so readers would expect that definition here as well.

instance : Add Int where
add := Int.add

I think what actually happened here is a copy-paste error from

#eval double { add := Nat.add } 10
-- 20

#eval double { add := Nat.mul } 10
-- 100

#eval double { add := Int.add } 10
-- 20

and since I don't see an easy way to keep the Nat.mul example without confusing the reader, I would recommend just changing 100 to 20

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