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Diffstat (limited to 'doc/compose.md')
| -rw-r--r-- | doc/compose.md | 6 |
1 files changed, 3 insertions, 3 deletions
diff --git a/doc/compose.md b/doc/compose.md index 9c8c2106..84c3987c 100644 --- a/doc/compose.md +++ b/doc/compose.md @@ -6,7 +6,7 @@ DrawComp ≍"∘○" --> -Atop and Over are 2-modifiers that extend the idea of "apply this, then that" in two different ways. They're modelled after the mathematical notation f∘g to compose two functions, and both do the same thing when there's one argument: `F∘G x` or `F○G x` is `F G x`. +Atop and Over are 2-modifiers that extend the idea of "apply this, then that" in two different ways. They're modelled after the mathematical notation f∘g to compose two functions, and both do the same thing when there's one argument: either `F∘G x` or `F○G x` is `F G x`. | `Cmp` | `Cmp 𝕩` | `𝕨 Cmp 𝕩` | Unified | On list |-------|---------|:--------------:|:-----------:|:-------: @@ -17,7 +17,7 @@ When there are two arguments, we might say Atop treats the right operand `𝔾` ## Atop -Of the two modifiers on this page, Atop is more common but less impactful. The composition `F∘G` is equivalent to the 2-[train](train.md) `F G` (the trains page has hints on when you'd choose one or the other). Its definition `{F𝕨G𝕩}` means that `G` is applied to one or two arguments and `F` is applied monadically to the result. It could be considered a "default way" to compose two functions. Keeps [tacit](tacit.md) programming syntax running smoothly, without making noise about it. Not like that busybody `⊸`. Some examples: +Of the two modifiers on this page, Atop is more common but less impactful. The composition `F∘G` is equivalent to the 2-[train](train.md) `F G` (the trains page has hints on when you'd choose one or the other). Its definition `{F𝕨G𝕩}` means that `G` is applied to one or two arguments and `F` is applied monadically to the result. It's sort of a "default way" to compose two functions. Keeps [tacit](tacit.md) programming syntax running smoothly, without making noise about it. Not like that busybody `⊸`. Some examples: `↕∘≠` is useful with one argument: `↕≠l` is a list of indices for `l`. @@ -35,7 +35,7 @@ Once you get used to Over, it's painful to go without it. I'd use it all the tim Usually Over is used just for the dyadic meaning. If you have a composition that only works with one argument it's typical to write it with Atop (`∘`). And cases that work with one or two arguments do come up from time to time, but they're fairly rare, so the examples below are just for two arguments. -A classic is the function `≡○∧`, which tests whether `𝕨` is a reordering of `𝕩`. The idea is to sort both arrays with `∧` to remove the ordering information +A classic is the function `≡○∧`, which tests whether `𝕨` is a reordering of `𝕩`. The idea is to sort both arrays with `∧` to remove the ordering information, then see if they match. "BQN" ≡○∧ "QNB" "BQN" ≡○∧ "BBQ" |