J function-boxing bug has been fixed

Author: mlochbaum

doc/functional.md

@@ -86,7 +86,7 @@ Another topic we're interested in is *lexical scoping* and *closures*. [Lexical
 
 ## Functions in APL
 
-This seems like a good place for a brief and entirely optional discussion of how APL handles functions and why it does it this way. As mentioned above, APL's functions are second class rather than first class. But the barriers to making functions first-class objects have been entirely syntactic and conceptual, not technical. In fact, the J language has for a long time had [a bug](http://www.jsoftware.com/pipermail/programming/2013-January/031260.html) that allows an array containing a function to be created: by selecting from the array, the function itself can even be passed through tacit functions as an argument!
+This seems like a good place for a brief and entirely optional discussion of how APL handles functions and why it does it this way. As mentioned above, APL's functions are second class rather than first class. But the barriers to making functions first-class objects have been entirely syntactic and conceptual, not technical. In fact, the J language for a long time had [a bug](http://www.jsoftware.com/pipermail/programming/2013-January/031260.html) allowing an array containing a function to be created: by selecting from the array, the function itself could even be passed through tacit functions as an argument!
 
 The primary reason why APL doesn't allow functions to be passed as arguments is probably syntax: in particular, there's no way to say that a function should be used as the left argument to another function, as an expression like `F G x` with functions `F` and `G` and an array `x` will simply be evaluated as two monadic function applications. However, there's no syntactic rule that prevents a function from returning a function, and Dyalog APL for example allows this (so `⍎'+'` returns the function `+`). Dyalog's `⎕OR` is another interesting phenomenon in this context: it creates an array from a function or operator, which can then be used as an element or argument like any array. The mechanism is essentially the same as BQN's first class functions, and in fact `⎕OR`s even share a form of BQN's [syntactic type erasure](../commentary/problems.md#syntactic-type-erasure), as a `⎕OR` of a function passed as an operand magically becomes a function again. But outside of this property, it's cumbersome and slow to convert functions to and from `⎕OR`s, so they don't work very well as a first-class function mechanism.
 

docs/doc/functional.html

@@ -63,7 +63,7 @@ <h1 id="functional-programming"><a class="header" href="#functional-programming"
 <p>The term <em>functional programming</em> is more contentious, and has many meanings some of which can be vague. Here I use it for what might be called <em>first-class functional programming</em>, programming that makes significant use of first-class functions; in this usage, Scheme is probably the archetypal functional programming language. However, other definitions are also worth mentioning. APL is often called a functional programming language on the grounds that functions can be assigned and manipulated, and called recursively, all characteristics it shares with Lisp. I prefer the term <em>function-level programming</em> for this usage. A newer usage, which I call <em>pure functional programming</em>, restricts the term &quot;function&quot; to mathematical functions, which have no side effects, so that functional programming is programming with no side effects, often using monads to accumulate effects as part of arguments and results instead. Finally, <em>typed functional programming</em> is closely associated with pure functional programming and refers to languages influenced by type theory such as <a href="https://www.haskell.org/">Haskell</a>, <a href="https://fsharp.org/">F#</a>, and <a href="https://www.idris-lang.org/">Idris</a> (the last of which even supports <em><a href="https://en.wikipedia.org/wiki/Dependent_type">dependently-typed</a> functional programming</em>, but I already said &quot;finally&quot; so we'll stop there). Of these, BQN supports first-class functional and function-level programming, allows but doesn't encourage pure functional programming, and doesn't support typed functional programming, as it's dynamically and not statically typed.</p>
 <p>Another topic we're interested in is <em>lexical scoping</em> and <em>closures</em>. <a href="lexical.html">Lexical scoping</a> means that the realm in which a variable exists is determined by its containing context (in BQN, the surrounding set of curly braces <code><span class='Brace'>{}</span></code>, if any) within the source code. A closure is really an implementation mechanism, but it's often used to refer to a property of lexical scoping that appears when functions defined in a particular block can be accessed after the block finishes execution. For example, they might be returned from a function or assigned to a variable outside of that function's scope. In this case the functions can still access variables in the original scope. I consider this property to be a requirement for a correct lexical scoping implementation, but it's traditionally not a part of APL: implementation might not have lexical scoping (for example, J and K use static scoping where functions can't access variables in containing scopes) or might cut off the scope once execution ends, leading to value errors that one wouldn't predict from the rules of lexical scoping.</p>
 <h2 id="functions-in-apl"><a class="header" href="#functions-in-apl">Functions in APL</a></h2>
-<p>This seems like a good place for a brief and entirely optional discussion of how APL handles functions and why it does it this way. As mentioned above, APL's functions are second class rather than first class. But the barriers to making functions first-class objects have been entirely syntactic and conceptual, not technical. In fact, the J language has for a long time had <a href="http://www.jsoftware.com/pipermail/programming/2013-January/031260.html">a bug</a> that allows an array containing a function to be created: by selecting from the array, the function itself can even be passed through tacit functions as an argument!</p>
+<p>This seems like a good place for a brief and entirely optional discussion of how APL handles functions and why it does it this way. As mentioned above, APL's functions are second class rather than first class. But the barriers to making functions first-class objects have been entirely syntactic and conceptual, not technical. In fact, the J language for a long time had <a href="http://www.jsoftware.com/pipermail/programming/2013-January/031260.html">a bug</a> allowing an array containing a function to be created: by selecting from the array, the function itself could even be passed through tacit functions as an argument!</p>
 <p>The primary reason why APL doesn't allow functions to be passed as arguments is probably syntax: in particular, there's no way to say that a function should be used as the left argument to another function, as an expression like <code><span class='Function'>F</span> <span class='Function'>G</span> <span class='Value'>x</span></code> with functions <code><span class='Function'>F</span></code> and <code><span class='Function'>G</span></code> and an array <code><span class='Value'>x</span></code> will simply be evaluated as two monadic function applications. However, there's no syntactic rule that prevents a function from returning a function, and Dyalog APL for example allows this (so <code><span class='Value'>⍎</span><span class='String'>'+'</span></code> returns the function <code><span class='Function'>+</span></code>). Dyalog's <code><span class='Value'>⎕</span><span class='Function'>OR</span></code> is another interesting phenomenon in this context: it creates an array from a function or operator, which can then be used as an element or argument like any array. The mechanism is essentially the same as BQN's first class functions, and in fact <code><span class='Value'>⎕</span><span class='Function'>OR</span></code>s even share a form of BQN's <a href="../commentary/problems.html#syntactic-type-erasure">syntactic type erasure</a>, as a <code><span class='Value'>⎕</span><span class='Function'>OR</span></code> of a function passed as an operand magically becomes a function again. But outside of this property, it's cumbersome and slow to convert functions to and from <code><span class='Value'>⎕</span><span class='Function'>OR</span></code>s, so they don't work very well as a first-class function mechanism.</p>
 <p>Another reason for APL's reluctance to adopt first-class functions is that Iverson and others seemed to believe that functions fundamentally are not a kind of data, because it's impossible to uniquely represent, compare, and order them. One effect of this viewpoint is J's gerund mechanism, which converts a function to an array representation, primarily so that lists of gerunds can be created. Gerunds are nested arrays containing character vectors at the leaves, so they are arrays as Iverson thought of them. However, I consider this conversion of functions to arrays, intended to avoid arrays that contain &quot;black box&quot; functions, to be a mistake: while it doesn't compromise the purity of arrays, it gives the illusion that a function corresponds to a particular array, which is not true from the mathematical perspective of functions as mappings from an arbitrary input to an output. I also think the experience of countless languages with first-class functions shows that there is no practical issue with arrays that contain functions. While having all arrays be concrete entities with a unique canonical representation seems desirable, I don't find the existence of arrays without this property to be detract from working with arrays that do have it.</p>
 <h2 id="functional-programming-in-bqn"><a class="header" href="#functional-programming-in-bqn">Functional programming in BQN</a></h2>