From a2d8557e3e8f58d9adfc028e66caf190d0911aca Mon Sep 17 00:00:00 2001 From: Marshall Lochbaum Date: Tue, 26 Apr 2022 21:25:24 -0400 Subject: Section on composing multiple hook modifiers --- docs/doc/hook.html | 29 +++++++++++++++++++++++++++++ 1 file changed, 29 insertions(+) (limited to 'docs/doc/hook.html') diff --git a/docs/doc/hook.html b/docs/doc/hook.html index 22054800..e300796a 100644 --- a/docs/doc/hook.html +++ b/docs/doc/hook.html @@ -159,3 +159,32 @@ ┘

In the more extreme case of wanting a modifier operand, you might try ⋈⟜({∘}˙)⊸⥊, or (⊣⋈{∘}˙)⊸⥊, or just cheat with ∾⟜⟨∘⟩⊸⥊.

+

Combinations

+

If you like to go tacit, you'll likely end up stringing together a few ⊸s and ⟜s at times. Of course the effects are entirely determined by the left-to-right precedence rule for modifiers, but it's interesting to examine what happens in more detail.

+

In the pattern F⊸G⟜H, the ordering doesn't matter at all! That is, it means (F⊸G)⟜H, but this is exactly the same function as F⊸(G⟜H). In both cases, F is applied to 𝕨, H is applied to 𝕩, and G acts on both the results.

+↗️
    4 -⊸⋈⟜⋆ 2
+⟨ ¯4 7.38905609893065 ⟩
+
+

I once named this pattern "split compose", but now I think it makes more sense to think of it as two pre-functions added separately to one central function (⋈ above). The whole is exactly the sum of its parts. When applied to just one argument, 𝕩 is reused on both sides, making the composition equivalent to a 3-train.

+↗️
    -⊸⋈⟜⋆ 2
+⟨ ¯2 7.38905609893065 ⟩
+
+    (-⋈⋆) 2  # Same thing
+⟨ ¯2 7.38905609893065 ⟩
+
+

More ⟜s can be added on the right, making 𝕩 flow through all the added functions. So for example F⟜G⟜H x is x F G H x, and could also be written F⟜(G H) x.

+

A sequence of ⊸s is more interesting. It doesn't just compose the functions (for that you need G∘F⊸H, but note the weird ordering—F applies before G!), but instead passes the current value and the initial function each time. Consider F⊸G⊸H⊸I, or ((F⊸G)⊸H)⊸I: every function but F is on the ring side, meaning it's dyadic!

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Here's a long example, that might show up if you want to sort an array but have an intolerance for the character ∧. In quicksort, you select a partition element from the array, then divide it into elements less than, and greater than or equal to, the pivot. You'd probably pick a random element for the pivot, but here I'll go with the middle element to avoid having a webpage that generates differently every time!

+↗️
    (⌊≠÷2˙)       "quicksort"  # Index of the pivot
+4
+
+    (⌊≠÷2˙)⊸⊑     "quicksort"  # Select pivot from 𝕩
+'k'
+
+    (⌊≠÷2˙)⊸⊑⊸≤   "quicksort"  # Compare with 𝕩
+⟨ 1 1 0 0 1 1 1 1 1 ⟩
+
+    (⌊≠÷2˙)⊸⊑⊸≤⊸⊔ "quicksort"  # Use to partition 𝕩
+⟨ "ic" "quksort" ⟩
+
+

Three is rare, but I use two ⊸s all the time, as well as ⟜ followed by ⊸, for example the <⟜'a'⊸/ filter on the front page. I think a combination like lots∘of○stuff⊸/ x reads very nicely when moving from left to right. When I see ⊸/ I know that I'm filtering x and can read the rest with that context. The reason ⊸ that has all this power, but not ⟜, has nothing to do with the modifiers themselves, as they're completely symmetrical. It's all in the way BQN defines modifier grammar, left to right.

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