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<html><head><meta charset="UTF-8" /><title>Interpreting M-Expressions</title><link rel="icon" type="image/x-icon" href="../img/beowulf_logo_favicon.png" /><link rel="stylesheet" type="text/css" href="css/default.css" /><link rel="stylesheet" type="text/css" href="css/highlight.css" /><script type="text/javascript" src="js/highlight.min.js"></script><script type="text/javascript" src="js/jquery.min.js"></script><script type="text/javascript" src="js/page_effects.js"></script><script>hljs.initHighlightingOnLoad();</script></head><body><div id="header"><h2>Generated by <a href="https://github.com/weavejester/codox">Codox</a></h2><h1><a href="index.html"><span class="project-title"><span class="project-name">Beowulf</span> <span class="project-version">0.3.0</span></span></a></h1></div><div class="sidebar primary"><h3 class="no-link"><span class="inner">Project</span></h3><ul class="index-link"><li class="depth-1 "><a href="index.html"><div class="inner">Index</div></a></li></ul><h3 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name="interpreting-m-expressions"></a>Interpreting M-Expressions</h1>
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<p>M-Expressions (‘mexprs’) are the grammar which John McCarthy origininally used to write Lisp, and the grammar in which many of the function definitions in the <a href="https://www.softwarepreservation.org/projects/LISP/book/LISP%201.5%20Programmers%20Manual.pdf">Lisp 1.5 Programmer’s Manual</a> are stated. However, I have not seen anywhere a claim that Lisp 1.5 could <em>read</em> M-Expressions, and it is not clear to me whether it was even planned that it should do so, although the discussion on <a href="https://www.softwarepreservation.org/projects/LISP/book/LISP%201.5%20Programmers%20Manual.pdf#page=18">page 10</a> suggests that it was.</p>
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<p>Rather, it seems to me possible that M-Expressions were only ever a grammar intended to be written on paper, like <a href="https://en.wikipedia.org/wiki/Backus%E2%80%93Naur_form">Backus Naur Form</a>, to describe and to reason about algorithms. I think at the point at which the M-Expression grammar was written, the idea of the <a href="https://www.softwarepreservation.org/projects/LISP/book/LISP%201.5%20Programmers%20Manual.pdf#page=18">universal Lisp function</a></p>
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<p>I set out to make Beowulf read M-Expressions essentially out of curiousity, to see whether it could be done. I had this idea that if it could be done, I could implement most of Lisp 1.5 simply by copying in the M-Expression definitions out of the manual.</p>
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<p>Consequently, the Beowulf parser can parse the M-Expression grammar as stated in the manual, and generate S-Expressions from it according to the table specified on page 10 of the manual.</p>
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<p>There are two problems with this.</p>
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<h2><a href="#problems-with-interpreting-m-expressions" name="problems-with-interpreting-m-expressions"></a>Problems with interpreting M-Expressions</h2>
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<h3><a href="#generating-idiomatic-lisp" name="generating-idiomatic-lisp"></a>Generating idiomatic Lisp</h3>
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<p>In the M-Expression notation, a lower case character or sequence of characters represents a variable; an upper case character represents a constant. As the manual says,</p>
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<blockquote>
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<p>2 . The obvious translation of letting a constant translate into itself will not work. Since the translation of <code>x</code> is <code>X</code>, the translation of <code>X</code> must be something else to avoid ambiguity. The solution is to quote it. Thus <code>X</code> is translated into <code>(QUOTE X)</code>.</p>
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</blockquote>
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<p>Thus, necessarily, the translation of a constant must always be quoted. In practice, key constants in Lisp such as <code>T</code> are bound to themselves, so it is idiomatic in Lisp, certainly in the way we have learned to use it, to write, for example,</p>
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<pre><code>(SET (QUOTE NULL)
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(QUOTE (LAMBDA (X)
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(COND
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((EQUAL X NIL) T) (T F)))))
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</code></pre>
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<p>However, the literal translation of</p>
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<pre><code>null[x] = [x = NIL -> T; T -> F]
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</code></pre>
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<p>is</p>
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<pre><code>(SET (QUOTE NULL)
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(QUOTE (LAMBDA (X)
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(COND
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((EQUAL X (QUOTE NIL)) (QUOTE T))
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((QUOTE T) (QUOTE F))))))
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</code></pre>
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<p>This is certainly more prolix and more awkward.</p>
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<p>Is the value of <code>NIL</code> the atom <code>NIL</code>, or is it the empty list <code>()</code>? If the former, then the translation from the M-Expression above is correct. However, that means that recursive functions which recurse down a list seeking the end will fail. So the latter must be the case.</p>
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<p><code>NULL</code> is described thus (Ibid, p11):</p>
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<blockquote>
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<p>This is a predicate useful for deciding when a list is exhausted. It is true if and only if its argument is <code>NIL</code>.</p>
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</blockquote>
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<p><code>NIL</code> is used explicitly in an M-Expression for example in the definition of <code>intersection</code> (Ibid, p15).</p>
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<p>I think there is an ambiguity in referencing constants which are not bound to themselves in the M-Expression notation as given in the manual. This is particularly problematic with regards to <code>NIL</code> and <code>F</code>, but there may be others instances.</p>
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<p>However, so long as <code>F</code> is bound to <code>NIL</code>, and <code>NIL</code> is also bound to <code>NIL</code> (both of which are true by default, although changeable by the user), and <code>NIL</code> is the special marker used in the <code>CDR</code> of the last cons cell of a flat list, this is a difference which in practice does not make a difference. I still find it worrying, though, that rebinding variables could lead to disaster.</p>
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<h3><a href="#curly-braces" name="curly-braces"></a>Curly braces</h3>
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<p>The use of curly braces is not defined in the grammar as stated on page 10. They are not used in the initial definition of <code>APPLY</code> on page 13, but they are used in the more developed restatement on page 70. I believe they are to be read as indicating a section of assembly code to be assembled by the <a href="https://www.softwarepreservation.org/projects/LISP/book/LISP%201.5%20Programmers%20Manual.pdf#page=81">Lisp Assembly Program</a> – but I don’t find the exposition here particularly clear and I’m not sure of this.</p>
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<p>Consequently, the M-Expression interpreter in Beowulf does not interpret curly braces.</p></div></div></div></body></html> |