Ah I was wrong! That's what I get for not coding in Haskell in a year and not checking my answer with GHC.

Function application always has higher precedence than infix operators so I can't emulate thread-first with functions in Haskell. If that wasn't the case, this would work (this was what I was thinking of)

    (|*>) :: b -> (a -> b -> c) -> (a -> c)
    (|*>) x f = (\y -> f y x)

    xs = 5
        |*> take [1, 2, 3]

Otherwise, I can come close with this.

    import Data.Function ((&))

    infix 9 *-
    (*-) :: (a -> b -> c) -> b -> (a -> c)
    (*-) f x = (\y -> f y x)

    xs :: [Int]
    xs = 5
        & take *- [1, 2, 3]
        & filter (/= 1)
        & head
        & take *- [1, 2, 3]

Using right-associativity of function types, and by sugaring the lambda into another function argument, we can rewrite this as

  (*-) :: (a -> b -> c) -> b -> a -> c
  (*-) f x y = f y x

This reveals that (*-) is simply flip, which is in the Prelude (re-exported from Data.Function). Alternatively, Hoogling the original type signature will reveal the same thing.

So the example doesn't require any new functions:

  import Data.Function ((&))

  xs :: [Int]
  xs =
    5
      & flip take [1, 2, 3]
      & filter (/= 1)
      & head
      & flip take [1, 2, 3]

In general, it's common in Haskell to use flip, curry/uncurry, and other higher-level functions to manipulate functions so they fit into the needed context.

If you don't like flip, you could also do

  xs :: [Int]
  xs =
    5
      & (`take` [1, 2, 3])
      & filter (/= 1)
      & head
      & (`take` [1, 2, 3])

But I'm not sure that's a better style than flip.

I really like `on` from Data.Function, too.

For maximum readability I'd be tempted to write the lambdas explicitly.

  xs =
    5
      & (\n -> take n [1, 2, 3])
      & filter (/= 1)
      & head
      & (\n -> take n [1, 2, 3])

That might be a wise choice.

It depends on what you are used to and your tolerance thresholds.

In a code base I worked on professionally, I came across the following idiom

    f a b `flip` d

which at first used to confuse me to no end. Later I figured out that you are supposed to read it as:

    f a b <place-holder> d

and thus

    \c -> f a b c d

In the same vein that Scala uses an underscore in somewhat implicit anonymous function syntax.

I still wasn't really happy with that usage, but at least I see why someone thought it would make sense.

(Mostly I wasn't so happy because it only works for the penultimate argument. If the syntax had worked out so that

    f a `flip` c d

would mean

    \b -> f a b c d

I would have been more amenable to the idiom. But you need the ugly

   f a `flip` c `flip` d

for that case. And that's clearly worse than the lambda syntax.

Oh good lord, that's horrible!

I think the Prelude answer would be to use `flip`[1], along with composition (`.`) or application (`$`) as usual.

    flip :: (a -> b -> c) -> b -> a -> c 

[1]: https://hackage.haskell.org/package/base-4.14.0.0/docs/Prelu...