diff options
Diffstat (limited to 'docs/doc/based.html')
| -rw-r--r-- | docs/doc/based.html | 4 |
1 files changed, 2 insertions, 2 deletions
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 @@ <p>Arrays in BQN, like nearly all data structures in modern programming languages, are an <a href="https://en.wikipedia.org/wiki/Inductive_type">inductive type</a>. 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.</p> <h2 id="versus-the-nested-array-model"><a class="header" href="#versus-the-nested-array-model">Versus the nested array model</a></h2> <p>The <a href="https://aplwiki.com/wiki/Array_model#Nested_array_theory">nested array model</a> 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.</p> -<p>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, <code><span class='String'>'</span><span class='Value'>abcd</span><span class='String'>'</span><span class='Value'>[</span><span class='Number'>2</span><span class='Value'>]</span></code> returns a character while BQN's <code><span class='Number'>2</span><span class='Function'>⊏</span><span class='String'>"abcd"</span></code> returns an array containing a character. However, these issues usually still appear with more complex arrays: <code><span class='String'>'</span><span class='Value'>ab</span><span class='String'>'</span> <span class='Number'>1</span> <span class='String'>'</span><span class='Value'>ef</span><span class='String'>'</span><span class='Value'>[</span><span class='Number'>2</span><span class='Value'>]</span></code> (here spaces are used for stranding) is not a string but an enclosed string!</p> +<p>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, <code><span class='String'>'</span><span class='Value'>abcd</span><span class='String'>'</span><span class='Bracket'>[</span><span class='Number'>2</span><span class='Bracket'>]</span></code> returns a character while BQN's <code><span class='Number'>2</span><span class='Function'>⊏</span><span class='String'>"abcd"</span></code> returns an array containing a character. However, these issues usually still appear with more complex arrays: <code><span class='String'>'</span><span class='Value'>ab</span><span class='String'>'</span> <span class='Number'>1</span> <span class='String'>'</span><span class='Value'>ef</span><span class='String'>'</span><span class='Bracket'>[</span><span class='Number'>2</span><span class='Bracket'>]</span></code> (here spaces are used for stranding) is not a string but an enclosed string!</p> <p>A property that might warn about dangerous issues like this is that nested array theory tends to create <em>inversions</em> 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.</p> <p>In some cases nested array theory can remove a depth issue entirely, and not just partially. Most notable is the <a href="../commentary/problems.html#search-function-depth">search function result depth</a> 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.</p> <h2 id="versus-the-boxed-array-model"><a class="header" href="#versus-the-boxed-array-model">Versus the boxed array model</a></h2> <p>The <a href="https://aplwiki.com/wiki/Array_model#Boxes">boxed array model</a> 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.</p> -<p>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 (<code><span class='Value'>$</span></code>) and Length (<code><span class='Comment'>#</span></code>) return depth-0 results in J. For an array <code><span class='Value'>a</span></code> with rank at least 1, the length <code><span class='Comment'>#a</span></code> is exactly <code><span class='Value'>[</span><span class='Function'>/</span> <span class='Value'>$</span> <span class='Value'>a</span></code>, while the identical BQN code <code><span class='Function'>⊣</span><span class='Modifier'>˝</span> <span class='Function'>≢</span> <span class='Value'>a</span></code> returns not <code><span class='Function'>≠</span> <span class='Value'>a</span></code> but <code><span class='Function'><</span> <span class='Function'>≠</span> <span class='Value'>a</span></code>. Like the nested model, the boxed model can hide depth issues that occur at lower depths but generally reveals them at higher depths.</p> +<p>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 (<code><span class='Value'>$</span></code>) and Length (<code><span class='Comment'>#</span></code>) return depth-0 results in J. For an array <code><span class='Value'>a</span></code> with rank at least 1, the length <code><span class='Comment'>#a</span></code> is exactly <code><span class='Bracket'>[</span><span class='Function'>/</span> <span class='Value'>$</span> <span class='Value'>a</span></code>, while the identical BQN code <code><span class='Function'>⊣</span><span class='Modifier'>˝</span> <span class='Function'>≢</span> <span class='Value'>a</span></code> returns not <code><span class='Function'>≠</span> <span class='Value'>a</span></code> but <code><span class='Function'><</span> <span class='Function'>≠</span> <span class='Value'>a</span></code>. Like the nested model, the boxed model can hide depth issues that occur at lower depths but generally reveals them at higher depths.</p> <p>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, <code><span class='Function'>|</span><span class='Value'>.</span> <span class='Value'>&.</span> <span class='Function'>></span></code>. But to find the lengths of each of these lists, <code><span class='Comment'># &. ></span></code> would yield a boxed list, which is usually not wanted, so <code><span class='Comment'># @ ></span></code> is needed instead. BQN shows that a system that doesn't require these distinctions is possible, as a BQN programmer would use <code><span class='Function'>⌽</span><span class='Modifier'>¨</span></code> and <code><span class='Function'>≠</span><span class='Modifier'>¨</span></code>.</p> |