From 5df53ddd256ce99123a874a3fece3408638d9400 Mon Sep 17 00:00:00 2001 From: Marshall Lochbaum Date: Mon, 3 Jan 2022 13:29:53 -0500 Subject: Clarify introduction of modifiers a little --- docs/tutorial/expression.html | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) (limited to 'docs/tutorial/expression.html') diff --git a/docs/tutorial/expression.html b/docs/tutorial/expression.html index bfcdc6f7..98b4530d 100644 --- a/docs/tutorial/expression.html +++ b/docs/tutorial/expression.html @@ -280,7 +280,7 @@

It's a convenient way to write non-printing characters without having to include them in your source code: for example @+10 is the newline character.

Addition and subtraction with affine characters have all the same algebraic properties that they do with numbers. One way to see this is to think of values as a combination of "characterness" (0 for numbers and 1 for characters) and either numeric value or code point. Addition and subtraction are done element-wise on these pairs of numbers, and are allowed if the result is a valid value, that is, its characterness is 0 or 1 and its value is a valid code point if the characterness is 1. However, because the space of values is no longer closed under addition and subtraction, certain rearrangements of valid computations might not work, if one of the values produced in the middle isn't legal.

Modifiers

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Functions are nice and all, but to really bring us into the space age BQN has a second level of function called modifiers (the space age in this case is when operators were introduced to APL in the early 60s—hey, did you know the second APL conference was held at Goddard Space Flight Center?). While functions apply to subjects, modifiers can apply to functions or subjects, and return functions. For example, the 1-modifier ˜ modifies one function by swapping the arguments before calling it (Swap), or copying the right argument to the left if there's only one (Self).

+

Functions are nice and all, but to really bring us into the space age BQN has a second level of function called modifiers (the space age in this case is when operators were introduced to APL in the early 60s—hey, did you know the second APL conference was held at Goddard Space Flight Center?). While functions apply to subjects, modifiers can apply to functions or subjects, and return functions. For example, the 1-modifier ˜ modifies one function—that's where the 1 comes from—by swapping the arguments before calling it (Swap), or copying the right argument to the left if there's only one (Self).

↗️
    2 -˜ 'd'  # Subtract from
 'b'
     +˜ 3      # Add to itself
@@ -333,7 +333,7 @@
 
Well, I guess it's not pedagogically useless, as it does demonstrate that a modifier can be applied to subjects as well as functions. Even though 3 is a subject, 3˙ is a function, and can be applied to and ignore the two arguments 2 and 4.

 
With three examples you may have noticed that 1-modifiers tend to cluster at the top of the screen. In fact, every primitive 1-modifer is a superscript character: we've covered ˜⁼˙, and the remaining array-based modifiers ˘¨⌜´˝` will show up later.

 
2-modifiers

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Made it to the last role, the 2-modifier (if you think something's been skipped, you're free to call subjects 0-modifiers. They don't modify anything. Just not when other people can hear you). To introduce them we'll use Atop ∘, which works a lot like mathematical composition, except that it's extended to use one or two arguments. These arguments are passed to the function on the right, and the result is passed to the function on the left. So the function on the left is only ever called with one argument.

+
Made it to the last role, the 2-modifier (if you think something's been skipped, you're free to call subjects 0-modifiers. They don't modify anything. Just not when other people can hear you). To introduce them we'll use Atop ∘, which composes two functions as in mathematics. The resulting function allows one or two arguments like any BQN function: these are all passed to the function on the right, and the result of that application is passed to the function on the left. So the function on the left is only ever called with one argument.

 ↗️
    3 ט∘+ 4  # Square of 3 plus 4
 49
     -∘(ט) 5  # Negative square of 5
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