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| author | Marshall Lochbaum <mwlochbaum@gmail.com> | 2021-11-03 15:41:10 -0400 |
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| committer | Marshall Lochbaum <mwlochbaum@gmail.com> | 2021-11-03 15:41:10 -0400 |
| commit | 30b5188c23576d5e119bbc8d27cd08a3015a75c9 (patch) | |
| tree | ab3b0fa7ab2993cf81745dc01232000d23a10eaa /doc/pair.md | |
| parent | 946df11216a89db2d03ebf476c789462eeb92e2e (diff) | |
Enlist/Pair documentation
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| -rw-r--r-- | doc/pair.md | 53 |
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diff --git a/doc/pair.md b/doc/pair.md new file mode 100644 index 00000000..c36e3abd --- /dev/null +++ b/doc/pair.md @@ -0,0 +1,53 @@ +*View this file with results and syntax highlighting [here](https://mlochbaum.github.io/BQN/doc/pair.html).* + +# Pair + +The function `⋈` forms a list of all its arguments. When there's one argument, it's called "Enlist", and with two, it's called "Pair". + + ⋈ "enlist" # ⟨𝕩⟩ + + "pa" ⋈ "ir" # ⟨𝕨,𝕩⟩ + +It's usually preferable to use [list notation](arrayrepr.md#brackets) directly for such arrays, because it's easy to add or remove any number of elements. Pair is useful when a standalone function is needed, for example to be used as an operand. + + 2‿4‿1 ⋈⌜ "north"‿"south" # Cartesian product + + ⋈¨ "+-×÷" # Glyphs to strings + +Another common pattern is to use Pair in a [train](train.md), giving the results from applying each of two functions. + + 'c' (+⋈-) 1‿2 + +For longer lists, this pattern can be extended with the function `<⊸∾`, which prepends a single element to a list. + + "e0" <⊸∾ "e1" <⊸∾ "e2" ⋈ "e3" + +However, before making a long list of this sort, consider that your goal might be more easily accomplished with a list of functions. + + 6 (+ <⊸∾ - <⊸∾ × ⋈ ÷) 3 + + {6𝕏3}¨ +‿-‿×‿÷ + +## Pair versus Couple + +Enlist and Pair closely related to [Solo and Couple](couple.md), in that `⋈` is equivalent to `≍○<` and `≍` is equivalent to `>∘⋈`. However, the result of `⋈` is always a list (rank 1) while Solo or Couple return an array of rank at least 1. + + "abc" ≍ "def" + + "abc" ⋈ "def" + +And the arguments to Couple must have the same shape, while Enlist takes any two arguments. + + "abc" ≍ "defg" + + "abc" ⋈ "defg" + +The difference is that Couple treats the arguments as cells, and adds a dimension, while Pair treats them as elements, adding a layer of depth. Couple is a "flat" version of Pair, much like Cells (`˘`) is a flat version of Each (`¨`). Pair is more versatile, but—precisely because of its restrictions—Couple may allow more powerful array operations on the result. + +## Fill element + +Enlist and Pair set the result's [fill](fill.md) element, while list notation doesn't have to. So the following result is guaranteed: + + 4 ↑ "a"‿5 ⋈ "b"‿7 + +This means that `⋈` may always behave the same as the obvious implementation `{⟨𝕩⟩;⟨𝕨,𝕩⟩}`. However, `≍○<` and even `>∘{⟨𝕩⟩;⟨𝕨,𝕩⟩}○<` compute the result fill as `⋈` does and are identical implementations. |
