## Errata for gin and monotonic

Between packing and hacking on GHC, I didn’t have enough time to cough up the next post of the series or edit the pictures for the previous post, so all you get today is a small errata post.

- The full list diagram is missing some orderings: ★:⊥ ≤ ★:⊥:⊥ and so on.
- In usual denotational semantics, you can’t distinguish between ⊥ and
`λ_.⊥`. However, as Anders Kaseorg and the Haskell Report point out, with`seq`you can distinguish them. This is perhaps the true reason why seq is a kind of nasty function. I’ve been assuming the stronger guarantee (which is what zygoloid pointed out) when it’s not actually true for Haskell. - The “ought to exist” arrow in the halts diagram goes the wrong direction.
- In the same fashion of the full list diagram,
`head`is missing some orderings, so in fact they gray blob is entirely connected. There are situations when we can have disconnected blobs, but not for a domain with only one maximum. - Obvious typo for fst.
- The formal partial order on functions was not defined correctly: it originally stated that for f ≤ g, f(x) = g(x); actually, it’s weaker than that: f(x) ≤ g(x).
- A non-erratum: the right-side of the head diagram is omitted because... adding all the arrows makes it look pretty ugly. Here is the sketch I did before I decided it wasn’t a good picture.

Thanks Anders Kaseorg, zygoloid, polux, and whoever pointed out the mistake in the partial order on functions (can’t find that correspondence now) for corrections.

*Non sequitur.* Here is a *really* simple polyvariadic function. The same basic idea is how Text.Printf works. May it help you in your multivariadic travels.

{-# LANGUAGE FlexibleInstances #-} class PolyDisj t where disj :: Bool -> t instance PolyDisj Bool where disj x = x instance PolyDisj t => PolyDisj (Bool -> t) where disj x y = disj (x || y)