From 0d6c26b9aa607ff14e14e6488bace207e324022a Mon Sep 17 00:00:00 2001 From: Marshall Lochbaum Date: Mon, 13 Jun 2022 13:20:34 -0400 Subject: =?UTF-8?q?Highlight=20[]=20as=20list=20brackets,=20like=20?= =?UTF-8?q?=E2=9F=A8=E2=9F=A9?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- docs/doc/array.html | 2 +- docs/doc/arrayrepr.html | 2 +- docs/doc/based.html | 4 ++-- docs/doc/embed.html | 10 +++++----- docs/doc/fromDyalog.html | 4 ++-- docs/doc/fromJ.html | 12 ++++++------ 6 files changed, 17 insertions(+), 17 deletions(-) (limited to 'docs/doc') diff --git a/docs/doc/array.html b/docs/doc/array.html index ec4eab33..827f05c0 100644 --- a/docs/doc/array.html +++ b/docs/doc/array.html @@ -6,7 +6,7 @@
(github) / BQN / doc

The array

As BQN is an array language, it's often helpful to understand what an array is when writing BQN programs. Fully describing the concept is sometimes held to be tricky; here we'll see definitions, examples, and metaphors.

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In BQN, as in APL, arrays are multidimensional, instead of strictly linear. Languages like Python, Javascript, or Haskell offer only one-dimensional arrays with [] syntax, and typically represent multidimensional data with nested arrays. Multidimensional arrays have fundamental differences relative to this model.

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In BQN, as in APL, arrays are multidimensional, instead of strictly linear. Languages like Python, Javascript, or Haskell offer only one-dimensional arrays with [] syntax, and typically represent multidimensional data with nested arrays. Multidimensional arrays have fundamental differences relative to this model.

BQN's arrays are immutable, meaning that an array is entirely defined by its attributes, and there is no way to modify an existing array, only to produce another array that has changes relative to it. As a result, an array can never contain itself, and arrays form an inductive type. BQN's mutable types are operations and namespaces.

An array might also have a fill element that captures some structural information about its elements and is used by a few operations. The fill, as an inferred property, isn't considered to truly be part of the array but is instead some information about the array that the interpreter keeps track of. So it's out of scope here.

diff --git a/docs/doc/arrayrepr.html b/docs/doc/arrayrepr.html index 0e59315a..ce74c543 100644 --- a/docs/doc/arrayrepr.html +++ b/docs/doc/arrayrepr.html @@ -229,4 +229,4 @@ 0 5 ┘ -

The characters [] are reserved to potentially combine list notation with merging, allowing the above to be written [2‿3, 4‿1, 0‿5]. This would allow non-empty arrays with rank one or more to be written without a primitive, but not rank 0 or empty arrays. Since creating arrays in general would still require primitives like < or ⥊, it's not clear whether this notation is worth it. General array notation is a surprisingly complicated topic; see the article about it on the APL Wiki.

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The characters [] are reserved to potentially combine list notation with merging, allowing the above to be written [2‿3, 4‿1, 0‿5]. This would allow non-empty arrays with rank one or more to be written without a primitive, but not rank 0 or empty arrays. Since creating arrays in general would still require primitives like < or ⥊, it's not clear whether this notation is worth it. General array notation is a surprisingly complicated topic; see the article about it on the APL Wiki.

diff --git a/docs/doc/based.html b/docs/doc/based.html index 7974f1d5..f03adf29 100644 --- a/docs/doc/based.html +++ b/docs/doc/based.html @@ -43,10 +43,10 @@

Arrays in BQN, like nearly all data structures in modern programming languages, are an inductive type. That means that an array can be constructed from existing values, but can't contain itself (including recursively: an array always has finite depth). To construct the type of all BQN values inductively, we would say that atoms form the base case, and arrays are an inductive case: an array is a shaped collection of existing BQN values. For an array programmer, this is of course the easy part.

Versus the nested array model

The nested array model of NARS, APL2, Dyalog, and GNU APL can be constructed from the based model by adding a rule: a unit (or "scalar" in APL) array containing an atom is equivalent to that atom. The equivalents of atoms in nested array theory are thus called "simple scalars", and they are considered arrays but share the characteristics of BQN atoms. Nested arrays don't form an inductive type, because simple scalars contain themselves.

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Nested array theory can seem simpler to use, because the programmer never has to worry about simple scalars being enclosed the wrong number of times: all these encloses have been identified with each other. For example, 'abcd'[2] returns a character while BQN's 2⊏"abcd" returns an array containing a character. However, these issues usually still appear with more complex arrays: 'ab' 1 'ef'[2] (here spaces are used for stranding) is not a string but an enclosed string!

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Nested array theory can seem simpler to use, because the programmer never has to worry about simple scalars being enclosed the wrong number of times: all these encloses have been identified with each other. For example, 'abcd'[2] returns a character while BQN's 2⊏"abcd" returns an array containing a character. However, these issues usually still appear with more complex arrays: 'ab' 1 'ef'[2] (here spaces are used for stranding) is not a string but an enclosed string!

A property that might warn about dangerous issues like this is that nested array theory tends to create inversions where the depth of a particular array depends on its rank (reversing the normal hierarchy of depth→rank→shape). A 1-character string has depth 1, but when its rank is reduced to 0, its depth is reduced as well.

In some cases nested array theory can remove a depth issue entirely, and not just partially. Most notable is the search function result depth issue, in which it's impossible for a search function in BQN to return an atomic number because it always returns an array. Nested array theory doesn't have this issue since a scalar number is "just a number", and more complicated arrays can't cause problems because a search function's result is always a numeric array. The other half of the problem, about the non-principal argument depth, is only partly hidden, and causes problems for example when searching for a single string out of a list of strings.

Versus the boxed array model

The boxed array model of SHARP APL, A+, and J is an inductive system like BQN's. But this model uses arrays as the base case: numeric and character arrays are the simplest kind of data allowed, and "a number" means a rank-0 numeric array. The inductive step is the array of boxes; as with numbers "a box" is simply a rank-0 array of boxes.

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Numeric and character arrays in this system have depth 0. In general these correspond to arrays of depth 1 in BQN, but because there's no lower depth they are also used where BQN atoms would appear. For example, both Shape ($) and Length (#) return depth-0 results in J. For an array a with rank at least 1, the length #a is exactly [/ $ a, while the identical BQN code ⊣˝ ≢ a returns not ≠ a but < ≠ a. Like the nested model, the boxed model can hide depth issues that occur at lower depths but generally reveals them at higher depths.

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Numeric and character arrays in this system have depth 0. In general these correspond to arrays of depth 1 in BQN, but because there's no lower depth they are also used where BQN atoms would appear. For example, both Shape ($) and Length (#) return depth-0 results in J. For an array a with rank at least 1, the length #a is exactly [/ $ a, while the identical BQN code ⊣˝ ≢ a returns not ≠ a but < ≠ a. Like the nested model, the boxed model can hide depth issues that occur at lower depths but generally reveals them at higher depths.

The boundary at depth 0 will tend to cause inconsistencies and confusion in any array language, and boxed array languages push this boundary up a level. This leads to the programmer spending more effort managing boxes: for example, to reverse each list in a list of lists, the programmer can use reverse under open, |. &. >. But to find the lengths of each of these lists, # &. > would yield a boxed list, which is usually not wanted, so # @ > is needed instead. BQN shows that a system that doesn't require these distinctions is possible, as a BQN programmer would use ⌽¨ and ≠¨.

diff --git a/docs/doc/embed.html b/docs/doc/embed.html index b02342cc..b911046d 100644 --- a/docs/doc/embed.html +++ b/docs/doc/embed.html @@ -16,13 +16,13 @@ i←4⥊0 {i+↩𝕩»i} `); -push(3); // [3,0,0,0] -push(-2); // [1,3,0,0] -push(4); // [5,4,3,0] +push(3); // [3,0,0,0] +push(-2); // [1,3,0,0] +push(4); // [5,4,3,0]

Note that this program doesn't have any outer braces. It's only run once, and it initializes i and returns a function. Just putting braces around it wouldn't have any effect—it just changes it from a program that does something to a program that runs a block that does the same thing—but adding braces and using 𝕨 or 𝕩 inside them would turn it into a function that could be run multiple times to create different closures. For example, pushGen = bqn("{i←4⥊𝕩⋄{i+↩𝕩»i}}") causes pushGen(n) to create a new closure with i initialized to 4⥊n.

The program also returns only one function, which can be limiting. But it's possible to get multiple closures out of the same program by returning a list of functions. For example, the following program defines three functions that manipulate a shared array in different ways.

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let [rotx, roty, flip] = bqn(`
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let [rotx, roty, flip] = bqn(`
     a ← 3‿2⥊↕6
     RotX ← {a↩𝕩⌽˘a}
     RotY ← {a↩𝕩⌽a}
@@ -35,7 +35,7 @@
 
JS encodings

 
In the programs above we've used numbers and functions of one argument, which mean the same thing in BQN and JS. This isn't the case for all types: although every BQN value is stored as some JS value, the way it's represented may not be obvious and there are many JS values that don't represent any BQN value and could cause errors. BQN operations don't verify that their inputs are valid BQN values (this would have a large performance cost), so it's up to the JS programmer to make sure that values passed in are valid. To do this, you need to know the encodings for each of the seven BQN types you're going to use.

 
The two atomic data values are simple: numbers are just JS numbers, and characters are strings containing a single code point. Arrays are JS arrays, but with some extra information. Since JS arrays are 1-dimensional, a BQN array a is stored as the element list ⥊a. Its shape ≢a, a list of numbers, is a.sh in JS (the shape isn't necessarily a BQN array so it doesn't have to have a sh property). Optionally, its fill element is a.fill. Note that a BQN string is not a JS string, but instead an array of BQN characters, or JS strings. To convert it to a JS string you can use str.join("").

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There are two utilities for converting from JS to BQN data: list([…]) converts a JS array to a BQN list, and str("JS string") converts a string.

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There are two utilities for converting from JS to BQN data: list([…]) converts a JS array to a BQN list, and str("JS string") converts a string.

 
Operations are all stored as JS functions, with one or two arguments for the inputs. The type is determined by the .m property, which is 1 for a 1-modifier and 2 for a 2-modifier, and undefined or falsy for a function. Functions might be called with one or two arguments. In either case, 𝕩 is the first argument; 𝕨, if present, is the second. Note that F(x,w) in JS corresponds to w F x in BQN, reversing the visual ordering of the arguments! For modifiers there's no such reversal, as 𝕗 is always the first argument, and for 2-modifiers 𝕘 is the second argument. As in BQN, a modifier may or may not return a function.

 
Operations may have some extra properties set that aren't terribly important for the JS programmer: for each primitive p, p.glyph gives its glyph, and for a compound operation o such as a train, or a modifier with bound operands, o.repr() decomposes it into its parts. It wouldn't make sense to define either of these properties for a function created in JS.

 
Other functionality

diff --git a/docs/doc/fromDyalog.html b/docs/doc/fromDyalog.html
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@@ -133,8 +133,8 @@
 Monad
 *
 *∘(÷2)
-[⍋]
-[⍒]
+[⍋]
+[⍒]
 ~
 ≢⍤⍴
 ≢
diff --git a/docs/doc/fromJ.html b/docs/doc/fromJ.html
index 524ec8d3..338a17d5 100644
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-[:
+[:
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 Cap
 
@@ -138,8 +138,8 @@
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 <:
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 Dyad
 {.
 }.
-]\
+]\
 #@]{.,
 -@#@]{.,~
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 %:
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