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<!--Weave of 'The Lattice of Kinds' generated by Inweb-->
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<ul class="crumbs"><li><a href="../index.html">Home</a></li><li><a href="../services.html">Services</a></li><li><a href="index.html">kinds</a></li><li><a href="index.html#2">Chapter 2: Kinds</a></li><li><b>The Lattice of Kinds</b></li></ul></div>
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<p class="purpose">Placing a partial order on kinds according to whether one conforms to another.</p>
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<ul class="toc"><li><a href="2-tlok.html#SP1">§1. Conformance</a></li><li><a href="2-tlok.html#SP6">§6. Lattice operations</a></li><li><a href="2-tlok.html#SP8">§8. Compatibility</a></li><li><a href="2-tlok.html#SP13">§13. Common code</a></li></ul><hr class="tocbar">
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<p class="commentary firstcommentary"><a id="SP1" class="paragraph-anchor"></a><b>§1. Conformance. </b>If we write \(K\leq L\) to mean that \(K\) conforms to \(L\), then \(\leq\) provides
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an ordering on kinds. For any kinds \(K, L, M\) not making use of kind variables<sup id="fnref:1"><a href="#fn:1" rel="footnote">1</a></sup>
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it is true that:
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</p>
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<ul class="items"><li>● \(K \leq K\) — reflexivity.
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</li><li>● If \(K\leq L\) and \(L\leq M\) then \(K\leq M\) — transitivity.
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</li><li>● <span class="extract"><span class="extract-syntax">K_nil</span></span> \(\leq K \leq\) <span class="extract"><span class="extract-syntax">value</span></span> — there are top and bottom elements.<sup id="fnref:2"><a href="#fn:2" rel="footnote">2</a></sup>
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</li><li>● If \(K \leq L\) then a value of kind \(K\) can always be substituted for a
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value of kind \(L\) without modification — the Liskov substitution principle.<sup id="fnref:3"><a href="#fn:3" rel="footnote">3</a></sup>
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</li><li>● There is a join \(K\lor L\) and a meet \(K\land L\) such that
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\(K\land L\leq K, L\leq K\lor L\), where \(K\lor L\) is minimal and \(K\land L\)
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maximal with that property.
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</li></ul>
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<ul class="footnotetexts"><li class="footnote" id="fn:1"><p class="inwebfootnote"><sup id="fnref:1"><a href="#fn:1" rel="footnote">1</a></sup> Introducing kind variables complicates the picture, because whether or not
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<span class="extract"><span class="extract-syntax">list of K</span></span> conforms to <span class="extract"><span class="extract-syntax">list of arithmetic values</span></span> depends on the current
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value of <span class="extract"><span class="extract-syntax">K</span></span> and therefore on the current context.
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<a href="#fnref:1" title="return to text"> ↩</a></p></li><li class="footnote" id="fn:2"><p class="inwebfootnote"><sup id="fnref:2"><a href="#fn:2" rel="footnote">2</a></sup> <span class="extract"><span class="extract-syntax">K_nil</span></span> is a kind which exists only for kind-checking purposes, meaning
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"a member of the empty set". Clearly no value can ever have this. This
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differs from <span class="extract"><span class="extract-syntax">K_void</span></span>, which means "the absence of a value". Neither can ever
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be the kind of a variable, of course.
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<a href="#fnref:2" title="return to text"> ↩</a></p></li><li class="footnote" id="fn:3"><p class="inwebfootnote"><sup id="fnref:3"><a href="#fn:3" rel="footnote">3</a></sup> Also known as strong behavioural subtyping. This only applies to definite
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kinds, because no value ever has an indefinite kind.
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<a href="#fnref:3" title="return to text"> ↩</a></p></li></ul>
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<p class="commentary firstcommentary"><a id="SP2" class="paragraph-anchor"></a><b>§2. </b>In general there is no guarantee of antisymmetry, i.e., that \(K\leq L\)
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and \(L\leq K\) must mean \(K = L\), nor that \(K\lor L\) or \(K\land L\) are unique.
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We could imagine creating indefinite kinds <span class="extract"><span class="extract-syntax">rhyming with lumber value</span></span> and
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<span class="extract"><span class="extract-syntax">calculator value</span></span> such that <span class="extract"><span class="extract-syntax">number</span></span> and <span class="extract"><span class="extract-syntax">real number</span></span> would conform to both.
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If so, then either one of <span class="extract"><span class="extract-syntax">rhyming with lumber value</span></span> and <span class="extract"><span class="extract-syntax">calculator value</span></span>
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could equally well serve as \(K\lor L\). The set of kinds is therefore not
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formally a lattice.
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</p>
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<p class="commentary">As it happens, however, Inform's choice of indefinite kinds is made in
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such a way that this does not happen. The upshot is that although the set of
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kinds is not necessarily a lattice, it often will be in practice, and we use
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the language of lattices — hence, words like "join" and "meet" — as a guide.
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</p>
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<p class="commentary firstcommentary"><a id="SP3" class="paragraph-anchor"></a><b>§3. </b>Conformance is tested with the function <a href="2-knd.html#SP25" class="internal">Kinds::conforms_to</a>, and the
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following shows it in action.
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</p>
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<pre class="displayed-code all-displayed-code code-font">
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<span class="plain-syntax">'</span><span class="element-syntax">new kind thing of object</span><span class="plain-syntax">':</span><span class="string-syntax"> ok</span>
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<span class="plain-syntax">'</span><span class="element-syntax">new kind device of thing</span><span class="plain-syntax">':</span><span class="string-syntax"> ok</span>
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<span class="plain-syntax">'</span><span class="element-syntax">new kind vehicle of thing</span><span class="plain-syntax">':</span><span class="string-syntax"> ok</span>
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<span class="plain-syntax">'</span><span class="element-syntax">new unit length</span><span class="plain-syntax">':</span><span class="string-syntax"> ok</span>
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<span class="plain-syntax">'</span><span class="element-syntax">number <= number?</span><span class="plain-syntax">':</span><span class="string-syntax"> true</span>
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<span class="plain-syntax">'</span><span class="element-syntax">number <= real number?</span><span class="plain-syntax">':</span><span class="string-syntax"> false</span>
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<span class="plain-syntax">'</span><span class="element-syntax">value <= number?</span><span class="plain-syntax">':</span><span class="string-syntax"> false</span>
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<span class="plain-syntax">'</span><span class="element-syntax">object <= text?</span><span class="plain-syntax">':</span><span class="string-syntax"> false</span>
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<span class="plain-syntax">'</span><span class="element-syntax">object <= thing?</span><span class="plain-syntax">':</span><span class="string-syntax"> false</span>
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<span class="plain-syntax">'</span><span class="element-syntax">thing <= object?</span><span class="plain-syntax">':</span><span class="string-syntax"> true</span>
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<span class="plain-syntax">'</span><span class="element-syntax">device <= thing?</span><span class="plain-syntax">':</span><span class="string-syntax"> true</span>
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<span class="plain-syntax">'</span><span class="element-syntax">device <= object?</span><span class="plain-syntax">':</span><span class="string-syntax"> true</span>
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<span class="plain-syntax">'</span><span class="element-syntax">list of devices <= thing?</span><span class="plain-syntax">':</span><span class="string-syntax"> false</span>
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<span class="plain-syntax">'</span><span class="element-syntax">list of devices <= list of things?</span><span class="plain-syntax">':</span><span class="string-syntax"> true</span>
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</pre>
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<p class="commentary firstcommentary"><a id="SP4" class="paragraph-anchor"></a><b>§4. </b>The indefinite <span class="extract"><span class="extract-syntax">arithmetic kind</span></span> used by Inform is a good example of what
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in other languages would be called a protocol. Here we see conformance:
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</p>
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<pre class="displayed-code all-displayed-code code-font">
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<span class="plain-syntax">'</span><span class="element-syntax">new unit length</span><span class="plain-syntax">':</span><span class="string-syntax"> ok</span>
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<span class="plain-syntax">'</span><span class="element-syntax">number <= arithmetic value?</span><span class="plain-syntax">':</span><span class="string-syntax"> true</span>
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<span class="plain-syntax">'</span><span class="element-syntax">real number <= arithmetic value?</span><span class="plain-syntax">':</span><span class="string-syntax"> true</span>
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<span class="plain-syntax">'</span><span class="element-syntax">length <= arithmetic value?</span><span class="plain-syntax">':</span><span class="string-syntax"> true</span>
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<span class="plain-syntax">'</span><span class="element-syntax">text <= arithmetic value?</span><span class="plain-syntax">':</span><span class="string-syntax"> false</span>
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<span class="plain-syntax">'</span><span class="element-syntax">arithmetic value <= value?</span><span class="plain-syntax">':</span><span class="string-syntax"> true</span>
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<span class="plain-syntax">'</span><span class="element-syntax">value <= arithmetic value?</span><span class="plain-syntax">':</span><span class="string-syntax"> false</span>
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<span class="plain-syntax">'</span><span class="element-syntax">arithmetic value <= sayable value?</span><span class="plain-syntax">':</span><span class="string-syntax"> true</span>
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</pre>
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<p class="commentary firstcommentary"><a id="SP5" class="paragraph-anchor"></a><b>§5. </b>Here we see covariance versus contravariance:
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</p>
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<pre class="displayed-code all-displayed-code code-font">
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<span class="plain-syntax">'</span><span class="element-syntax">new kind larger of object</span><span class="plain-syntax">':</span><span class="string-syntax"> ok</span>
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<span class="plain-syntax">'</span><span class="element-syntax">new kind smaller of larger</span><span class="plain-syntax">':</span><span class="string-syntax"> ok</span>
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<span class="plain-syntax">'</span><span class="element-syntax">smaller <= larger?</span><span class="plain-syntax">':</span><span class="string-syntax"> true</span>
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<span class="plain-syntax">'</span><span class="element-syntax">larger <= smaller?</span><span class="plain-syntax">':</span><span class="string-syntax"> false</span>
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<span class="plain-syntax">'</span><span class="element-syntax">list of smaller <= list of larger?</span><span class="plain-syntax">':</span><span class="string-syntax"> true</span>
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<span class="plain-syntax">'</span><span class="element-syntax">list of larger <= list of smaller?</span><span class="plain-syntax">':</span><span class="string-syntax"> false</span>
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<span class="plain-syntax">'</span><span class="element-syntax">relation of larger to texts <= relation of smaller to texts?</span><span class="plain-syntax">':</span><span class="string-syntax"> false</span>
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<span class="plain-syntax">'</span><span class="element-syntax">relation of smaller to texts <= relation of larger to texts?</span><span class="plain-syntax">':</span><span class="string-syntax"> true</span>
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<span class="plain-syntax">'</span><span class="element-syntax">phrase larger -> text <= phrase smaller -> text?</span><span class="plain-syntax">':</span><span class="string-syntax"> true</span>
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<span class="plain-syntax">'</span><span class="element-syntax">phrase smaller -> text <= phrase larger -> text?</span><span class="plain-syntax">':</span><span class="string-syntax"> false</span>
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<span class="plain-syntax">'</span><span class="element-syntax">phrase text -> larger <= phrase text -> smaller?</span><span class="plain-syntax">':</span><span class="string-syntax"> false</span>
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<span class="plain-syntax">'</span><span class="element-syntax">phrase text -> smaller <= phrase text -> larger?</span><span class="plain-syntax">':</span><span class="string-syntax"> true</span>
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</pre>
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<ul class="items"><li>● A constructor \(\phi\) is "covariant" — meaning, goes the same way — if
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\(K\leq L\) means \(\phi(K)\leq\phi(L)\).
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</li><li>● It is "contravariant" — goes the opposite way — if \(K\leq L\) means
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\(\phi(L)\leq\phi(K)\).
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</li></ul>
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<p class="commentary">Note that "list of ..." is covariant; "phrase ... -> ..." is contravariant in
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the first term, but covariant in the second. To see why, consider a function
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\(f: K\to L\), and then considering expanding or contracting the sets \(K\) and \(L\).
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It's no problem if \(L\) grows larger — \(f\) can still be used — but if \(L\)
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shrinks then \(f\) might map outside it, which is unsafe. But the reverse is true
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for \(K\). If \(K\) shrinks we can still use \(f\), but if it grows then we may not
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be able to. If \(K_1\leq K\leq K_2\) and \(L_1\leq L\leq L_2\), then a function
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\(f:K\to L\) is also a function \(K_1\to L_2\), but not \(K_2\to L_1\).
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</p>
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<p class="commentary">See <a href="2-tlok.html#SP13" class="internal">Latticework::order_relation</a> for more.
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</p>
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<pre class="definitions code-font"><span class="definition-keyword">define</span> <span class="constant-syntax">COVARIANT</span><span class="plain-syntax"> </span><span class="constant-syntax">1</span>
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<span class="definition-keyword">define</span> <span class="constant-syntax">CONTRAVARIANT</span><span class="plain-syntax"> -1</span>
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</pre>
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<p class="commentary firstcommentary"><a id="SP6" class="paragraph-anchor"></a><b>§6. Lattice operations. </b>Every \(K\) other than <span class="extract"><span class="extract-syntax">value</span></span>, <span class="extract"><span class="extract-syntax">K_nil</span></span> and <span class="extract"><span class="extract-syntax">K_void</span></span> has a minimal element \(K^+\)
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such that \(K\leq K^+\) but \(K\neq K^+\): we call this the "superkind" of \(K\).
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Assuming kinds form a lattice, this will be unique. The following function
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returns the superkind, or <span class="extract"><span class="extract-syntax">NULL</span></span> for special cases which do not have one.
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</p>
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<p class="commentary">It is in this function that the basic conformance facts are expressed. We
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hard-code that for the built-in indefinite kinds, and give the client tool
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a chance to provide other conformances. For Inform, for example, the callback
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function is what tells us that the superkind of <span class="extract"><span class="extract-syntax">man</span></span> is <span class="extract"><span class="extract-syntax">person</span></span>.
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</p>
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<pre class="displayed-code all-displayed-code code-font">
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<span class="reserved-syntax">kind</span><span class="plain-syntax"> *</span><span class="function-syntax">Latticework::super</span><button class="popup" onclick="togglePopup('usagePopup1')"><span class="comment-syntax">?</span><span class="popuptext" id="usagePopup1">Usage of <span class="code-font"><span class="function-syntax">Latticework::super</span></span>:<br/><a href="2-tlok.html#SP7">§7</a>, <a href="2-tlok.html#SP13_6">§13.6</a><br/>Kinds - <a href="2-knd.html#SP21">§21</a></span></button><span class="plain-syntax">(</span><span class="reserved-syntax">kind</span><span class="plain-syntax"> *</span><span class="identifier-syntax">K</span><span class="plain-syntax">) {</span>
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<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><a href="2-knd.html#SP24" class="function-link"><span class="function-syntax">Kinds::eq</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">K</span><span class="plain-syntax">, </span><span class="identifier-syntax">K_real_arithmetic_value</span><span class="plain-syntax">)) </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="identifier-syntax">K_arithmetic_value</span><span class="plain-syntax">;</span>
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<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><a href="2-knd.html#SP24" class="function-link"><span class="function-syntax">Kinds::eq</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">K</span><span class="plain-syntax">, </span><span class="identifier-syntax">K_enumerated_value</span><span class="plain-syntax">)) </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="identifier-syntax">K_understandable_value</span><span class="plain-syntax">;</span>
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<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><a href="2-knd.html#SP24" class="function-link"><span class="function-syntax">Kinds::eq</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">K</span><span class="plain-syntax">, </span><span class="identifier-syntax">K_arithmetic_value</span><span class="plain-syntax">)) </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="identifier-syntax">K_understandable_value</span><span class="plain-syntax">;</span>
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<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><a href="2-knd.html#SP24" class="function-link"><span class="function-syntax">Kinds::eq</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">K</span><span class="plain-syntax">, </span><span class="identifier-syntax">K_understandable_value</span><span class="plain-syntax">)) </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="identifier-syntax">K_sayable_value</span><span class="plain-syntax">;</span>
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<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><a href="2-knd.html#SP24" class="function-link"><span class="function-syntax">Kinds::eq</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">K</span><span class="plain-syntax">, </span><span class="identifier-syntax">K_pointer_value</span><span class="plain-syntax">)) </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="identifier-syntax">K_sayable_value</span><span class="plain-syntax">;</span>
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<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><a href="2-knd.html#SP24" class="function-link"><span class="function-syntax">Kinds::eq</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">K</span><span class="plain-syntax">, </span><span class="identifier-syntax">K_sayable_value</span><span class="plain-syntax">)) </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="identifier-syntax">K_stored_value</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><a href="2-knd.html#SP24" class="function-link"><span class="function-syntax">Kinds::eq</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">K</span><span class="plain-syntax">, </span><span class="identifier-syntax">K_stored_value</span><span class="plain-syntax">)) </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="identifier-syntax">K_value</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><a href="2-knd.html#SP24" class="function-link"><span class="function-syntax">Kinds::eq</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">K</span><span class="plain-syntax">, </span><span class="identifier-syntax">K_value</span><span class="plain-syntax">)) </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="identifier-syntax">NULL</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><a href="2-knd.html#SP24" class="function-link"><span class="function-syntax">Kinds::eq</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">K</span><span class="plain-syntax">, </span><span class="identifier-syntax">K_nil</span><span class="plain-syntax">)) </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="identifier-syntax">NULL</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><a href="2-knd.html#SP24" class="function-link"><span class="function-syntax">Kinds::eq</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">K</span><span class="plain-syntax">, </span><span class="identifier-syntax">K_void</span><span class="plain-syntax">)) </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="identifier-syntax">NULL</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> #</span><span class="identifier-syntax">ifdef</span><span class="plain-syntax"> </span><span class="identifier-syntax">HIERARCHY_GET_SUPER_KINDS_CALLBACK</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">kind</span><span class="plain-syntax"> *</span><span class="identifier-syntax">S</span><span class="plain-syntax"> = </span><span class="identifier-syntax">HIERARCHY_GET_SUPER_KINDS_CALLBACK</span><span class="plain-syntax">(</span><span class="identifier-syntax">K</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><span class="identifier-syntax">S</span><span class="plain-syntax">) </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="identifier-syntax">S</span><span class="plain-syntax">;</span>
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|
<span class="plain-syntax"> #</span><span class="identifier-syntax">endif</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><a href="4-kc2.html#SP20" class="function-link"><span class="function-syntax">KindConstructors::compatible</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">K</span><span class="plain-syntax">-></span><span class="element-syntax">construct</span><span class="plain-syntax">, </span><span class="identifier-syntax">K_real_arithmetic_value</span><span class="plain-syntax">-></span><span class="element-syntax">construct</span><span class="plain-syntax">, </span><span class="identifier-syntax">FALSE</span><span class="plain-syntax">))</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="identifier-syntax">K_real_arithmetic_value</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><a href="4-kc2.html#SP20" class="function-link"><span class="function-syntax">KindConstructors::compatible</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">K</span><span class="plain-syntax">-></span><span class="element-syntax">construct</span><span class="plain-syntax">, </span><span class="identifier-syntax">K_enumerated_value</span><span class="plain-syntax">-></span><span class="element-syntax">construct</span><span class="plain-syntax">, </span><span class="identifier-syntax">FALSE</span><span class="plain-syntax">))</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="identifier-syntax">K_enumerated_value</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><a href="4-kc2.html#SP20" class="function-link"><span class="function-syntax">KindConstructors::compatible</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">K</span><span class="plain-syntax">-></span><span class="element-syntax">construct</span><span class="plain-syntax">, </span><span class="identifier-syntax">K_arithmetic_value</span><span class="plain-syntax">-></span><span class="element-syntax">construct</span><span class="plain-syntax">, </span><span class="identifier-syntax">FALSE</span><span class="plain-syntax">))</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="identifier-syntax">K_arithmetic_value</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><a href="4-kc2.html#SP20" class="function-link"><span class="function-syntax">KindConstructors::compatible</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">K</span><span class="plain-syntax">-></span><span class="element-syntax">construct</span><span class="plain-syntax">, </span><span class="identifier-syntax">K_pointer_value</span><span class="plain-syntax">-></span><span class="element-syntax">construct</span><span class="plain-syntax">, </span><span class="identifier-syntax">FALSE</span><span class="plain-syntax">))</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="identifier-syntax">K_pointer_value</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><a href="4-kc2.html#SP20" class="function-link"><span class="function-syntax">KindConstructors::compatible</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">K</span><span class="plain-syntax">-></span><span class="element-syntax">construct</span><span class="plain-syntax">, </span><span class="identifier-syntax">K_understandable_value</span><span class="plain-syntax">-></span><span class="element-syntax">construct</span><span class="plain-syntax">, </span><span class="identifier-syntax">FALSE</span><span class="plain-syntax">))</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="identifier-syntax">K_understandable_value</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><a href="4-kc2.html#SP20" class="function-link"><span class="function-syntax">KindConstructors::compatible</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">K</span><span class="plain-syntax">-></span><span class="element-syntax">construct</span><span class="plain-syntax">, </span><span class="identifier-syntax">K_sayable_value</span><span class="plain-syntax">-></span><span class="element-syntax">construct</span><span class="plain-syntax">, </span><span class="identifier-syntax">FALSE</span><span class="plain-syntax">))</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="identifier-syntax">K_sayable_value</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><a href="4-kc2.html#SP20" class="function-link"><span class="function-syntax">KindConstructors::compatible</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">K</span><span class="plain-syntax">-></span><span class="element-syntax">construct</span><span class="plain-syntax">, </span><span class="identifier-syntax">K_stored_value</span><span class="plain-syntax">-></span><span class="element-syntax">construct</span><span class="plain-syntax">, </span><span class="identifier-syntax">FALSE</span><span class="plain-syntax">))</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="identifier-syntax">K_stored_value</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="identifier-syntax">K_value</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax">}</span>
|
|
</pre>
|
|
<p class="commentary firstcommentary"><a id="SP7" class="paragraph-anchor"></a><b>§7. </b>Joins are defined above. So are meets, though in practice they are never useful
|
|
to us except as a way of calculating joins: the two are dual to each other as
|
|
they pass through contravariant constructors.
|
|
</p>
|
|
|
|
<p class="commentary">The main use of this for Inform is to handle literals such as:
|
|
</p>
|
|
|
|
<blockquote>
|
|
<p>{ 1, 2.1415, "frog" }</p>
|
|
</blockquote>
|
|
|
|
<p class="commentary">The kind of this is by definition the join of the kinds of the values in the
|
|
list, which as it happens is <span class="extract"><span class="extract-syntax">K_sayable_value</span></span> — an indefinite kind, so that
|
|
such a list can't be constructed as data.
|
|
</p>
|
|
|
|
<pre class="displayed-code all-displayed-code code-font">
|
|
<span class="reserved-syntax">kind</span><span class="plain-syntax"> *</span><span class="function-syntax">Latticework::join</span><span class="plain-syntax">(</span><span class="reserved-syntax">kind</span><span class="plain-syntax"> *</span><span class="identifier-syntax">K1</span><span class="plain-syntax">, </span><span class="reserved-syntax">kind</span><span class="plain-syntax"> *</span><span class="identifier-syntax">K2</span><span class="plain-syntax">) {</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><a href="2-tlok.html#SP7" class="function-link"><span class="function-syntax">Latticework::j_or_m</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">K1</span><span class="plain-syntax">, </span><span class="identifier-syntax">K2</span><span class="plain-syntax">, </span><span class="constant-syntax">1</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax">}</span>
|
|
|
|
<span class="reserved-syntax">kind</span><span class="plain-syntax"> *</span><span class="function-syntax">Latticework::meet</span><span class="plain-syntax">(</span><span class="reserved-syntax">kind</span><span class="plain-syntax"> *</span><span class="identifier-syntax">K1</span><span class="plain-syntax">, </span><span class="reserved-syntax">kind</span><span class="plain-syntax"> *</span><span class="identifier-syntax">K2</span><span class="plain-syntax">) {</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><a href="2-tlok.html#SP7" class="function-link"><span class="function-syntax">Latticework::j_or_m</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">K1</span><span class="plain-syntax">, </span><span class="identifier-syntax">K2</span><span class="plain-syntax">, -1);</span>
|
|
<span class="plain-syntax">}</span>
|
|
|
|
<span class="reserved-syntax">kind</span><span class="plain-syntax"> *</span><span class="function-syntax">Latticework::j_or_m</span><span class="plain-syntax">(</span><span class="reserved-syntax">kind</span><span class="plain-syntax"> *</span><span class="identifier-syntax">K1</span><span class="plain-syntax">, </span><span class="reserved-syntax">kind</span><span class="plain-syntax"> *</span><span class="identifier-syntax">K2</span><span class="plain-syntax">, </span><span class="reserved-syntax">int</span><span class="plain-syntax"> </span><span class="identifier-syntax">direction</span><span class="plain-syntax">) {</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><span class="identifier-syntax">K1</span><span class="plain-syntax"> == </span><span class="identifier-syntax">NULL</span><span class="plain-syntax">) </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="identifier-syntax">K2</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><span class="identifier-syntax">K2</span><span class="plain-syntax"> == </span><span class="identifier-syntax">NULL</span><span class="plain-syntax">) </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="identifier-syntax">K1</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">kind_constructor</span><span class="plain-syntax"> *</span><span class="identifier-syntax">con</span><span class="plain-syntax"> = </span><span class="identifier-syntax">K1</span><span class="plain-syntax">-></span><span class="element-syntax">construct</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">int</span><span class="plain-syntax"> </span><span class="identifier-syntax">a1</span><span class="plain-syntax"> = </span><a href="4-kc2.html#SP15" class="function-link"><span class="function-syntax">KindConstructors::arity</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">con</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">int</span><span class="plain-syntax"> </span><span class="identifier-syntax">a2</span><span class="plain-syntax"> = </span><a href="4-kc2.html#SP15" class="function-link"><span class="function-syntax">KindConstructors::arity</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">K2</span><span class="plain-syntax">-></span><span class="element-syntax">construct</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> ((</span><span class="identifier-syntax">a1</span><span class="plain-syntax"> > </span><span class="constant-syntax">0</span><span class="plain-syntax">) || (</span><span class="identifier-syntax">a2</span><span class="plain-syntax"> > </span><span class="constant-syntax">0</span><span class="plain-syntax">)) {</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><span class="identifier-syntax">K2</span><span class="plain-syntax">-></span><span class="element-syntax">construct</span><span class="plain-syntax"> != </span><span class="identifier-syntax">con</span><span class="plain-syntax">) </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="identifier-syntax">K_value</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">kind</span><span class="plain-syntax"> *</span><span class="identifier-syntax">ka</span><span class="plain-syntax">[</span><span class="constant-syntax">MAX_KIND_CONSTRUCTION_ARITY</span><span class="plain-syntax">] = { </span><span class="identifier-syntax">NULL</span><span class="plain-syntax">, };</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">for</span><span class="plain-syntax"> (</span><span class="reserved-syntax">int</span><span class="plain-syntax"> </span><span class="identifier-syntax">i</span><span class="plain-syntax">=0; </span><span class="identifier-syntax">i</span><span class="plain-syntax"><</span><span class="identifier-syntax">a1</span><span class="plain-syntax">; </span><span class="identifier-syntax">i</span><span class="plain-syntax">++)</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><span class="identifier-syntax">con</span><span class="plain-syntax">-></span><span class="element-syntax">variance</span><span class="plain-syntax">[</span><span class="identifier-syntax">i</span><span class="plain-syntax">] == </span><span class="constant-syntax">COVARIANT</span><span class="plain-syntax">)</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">ka</span><span class="plain-syntax">[</span><span class="identifier-syntax">i</span><span class="plain-syntax">] = </span><a href="2-tlok.html#SP7" class="function-link"><span class="function-syntax">Latticework::j_or_m</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">K1</span><span class="plain-syntax">-></span><span class="element-syntax">kc_args</span><span class="plain-syntax">[</span><span class="identifier-syntax">i</span><span class="plain-syntax">], </span><span class="identifier-syntax">K2</span><span class="plain-syntax">-></span><span class="element-syntax">kc_args</span><span class="plain-syntax">[</span><span class="identifier-syntax">i</span><span class="plain-syntax">], </span><span class="identifier-syntax">direction</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">else</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">ka</span><span class="plain-syntax">[</span><span class="identifier-syntax">i</span><span class="plain-syntax">] = </span><a href="2-tlok.html#SP7" class="function-link"><span class="function-syntax">Latticework::j_or_m</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">K1</span><span class="plain-syntax">-></span><span class="element-syntax">kc_args</span><span class="plain-syntax">[</span><span class="identifier-syntax">i</span><span class="plain-syntax">], </span><span class="identifier-syntax">K2</span><span class="plain-syntax">-></span><span class="element-syntax">kc_args</span><span class="plain-syntax">[</span><span class="identifier-syntax">i</span><span class="plain-syntax">], -</span><span class="identifier-syntax">direction</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><span class="identifier-syntax">a1</span><span class="plain-syntax"> == </span><span class="constant-syntax">1</span><span class="plain-syntax">) </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><a href="2-knd.html#SP6_3" class="function-link"><span class="function-syntax">Kinds::unary_con</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">con</span><span class="plain-syntax">, </span><span class="identifier-syntax">ka</span><span class="plain-syntax">[0]);</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">else</span><span class="plain-syntax"> </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><a href="2-knd.html#SP6_3" class="function-link"><span class="function-syntax">Kinds::binary_con</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">con</span><span class="plain-syntax">, </span><span class="identifier-syntax">ka</span><span class="plain-syntax">[0], </span><span class="identifier-syntax">ka</span><span class="plain-syntax">[1]);</span>
|
|
<span class="plain-syntax"> } </span><span class="reserved-syntax">else</span><span class="plain-syntax"> {</span>
|
|
<span class="plain-syntax"> </span><span class="named-paragraph-container code-font"><a href="2-tlok.html#SP7_1" class="named-paragraph-link"><span class="named-paragraph">Deal with nil</span><span class="named-paragraph-number">7.1</span></a></span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="named-paragraph-container code-font"><a href="2-tlok.html#SP7_2" class="named-paragraph-link"><span class="named-paragraph">Deal with floating-point promotions</span><span class="named-paragraph-number">7.2</span></a></span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><a href="2-knd.html#SP25" class="function-link"><span class="function-syntax">Kinds::conforms_to</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">K1</span><span class="plain-syntax">, </span><span class="identifier-syntax">K2</span><span class="plain-syntax">)) </span><span class="reserved-syntax">return</span><span class="plain-syntax"> (</span><span class="identifier-syntax">direction</span><span class="plain-syntax"> > </span><span class="constant-syntax">0</span><span class="plain-syntax">)?</span><span class="identifier-syntax">K2:K1</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><a href="2-knd.html#SP25" class="function-link"><span class="function-syntax">Kinds::conforms_to</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">K2</span><span class="plain-syntax">, </span><span class="identifier-syntax">K1</span><span class="plain-syntax">)) </span><span class="reserved-syntax">return</span><span class="plain-syntax"> (</span><span class="identifier-syntax">direction</span><span class="plain-syntax"> > </span><span class="constant-syntax">0</span><span class="plain-syntax">)?</span><span class="identifier-syntax">K1:K2</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><span class="identifier-syntax">direction</span><span class="plain-syntax"> > </span><span class="constant-syntax">0</span><span class="plain-syntax">) {</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">for</span><span class="plain-syntax"> (</span><span class="reserved-syntax">kind</span><span class="plain-syntax"> *</span><span class="identifier-syntax">K</span><span class="plain-syntax"> = </span><span class="identifier-syntax">K1</span><span class="plain-syntax">; </span><span class="identifier-syntax">K</span><span class="plain-syntax">; </span><span class="identifier-syntax">K</span><span class="plain-syntax"> = </span><a href="2-tlok.html#SP6" class="function-link"><span class="function-syntax">Latticework::super</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">K</span><span class="plain-syntax">))</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><a href="2-knd.html#SP25" class="function-link"><span class="function-syntax">Kinds::conforms_to</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">K2</span><span class="plain-syntax">, </span><span class="identifier-syntax">K</span><span class="plain-syntax">))</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="identifier-syntax">K</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="identifier-syntax">K_value</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> } </span><span class="reserved-syntax">else</span><span class="plain-syntax"> {</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="identifier-syntax">K_nil</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> }</span>
|
|
<span class="plain-syntax"> }</span>
|
|
<span class="plain-syntax">}</span>
|
|
</pre>
|
|
<p class="commentary firstcommentary"><a id="SP7_1" class="paragraph-anchor"></a><b>§7.1. </b>This ensures that \(K\land\) <span class="extract"><span class="extract-syntax">K_nil</span></span> \( = \) <span class="extract"><span class="extract-syntax">K_nil</span></span>, and that
|
|
\(K\lor\) <span class="extract"><span class="extract-syntax">K_nil</span></span> \( = K\).
|
|
</p>
|
|
|
|
<p class="commentary"><span class="named-paragraph-container code-font"><span class="named-paragraph-defn">Deal with nil</span><span class="named-paragraph-number">7.1</span></span><span class="comment-syntax"> =</span>
|
|
</p>
|
|
|
|
<pre class="displayed-code all-displayed-code code-font">
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> ((</span><a href="2-knd.html#SP24" class="function-link"><span class="function-syntax">Kinds::eq</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">K1</span><span class="plain-syntax">, </span><span class="identifier-syntax">K_nil</span><span class="plain-syntax">))) </span><span class="reserved-syntax">return</span><span class="plain-syntax"> (</span><span class="identifier-syntax">direction</span><span class="plain-syntax"> > </span><span class="constant-syntax">0</span><span class="plain-syntax">)?</span><span class="identifier-syntax">K2:K1</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> ((</span><a href="2-knd.html#SP24" class="function-link"><span class="function-syntax">Kinds::eq</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">K2</span><span class="plain-syntax">, </span><span class="identifier-syntax">K_nil</span><span class="plain-syntax">))) </span><span class="reserved-syntax">return</span><span class="plain-syntax"> (</span><span class="identifier-syntax">direction</span><span class="plain-syntax"> > </span><span class="constant-syntax">0</span><span class="plain-syntax">)?</span><span class="identifier-syntax">K1:K2</span><span class="plain-syntax">;</span>
|
|
</pre>
|
|
<ul class="endnotetexts"><li>This code is used in <a href="2-tlok.html#SP7">§7</a>.</li></ul>
|
|
<p class="commentary firstcommentary"><a id="SP7_2" class="paragraph-anchor"></a><b>§7.2. </b>If one of \(K_1\), \(K_2\) uses floating-point and the other doesn't, then
|
|
we promote the one which doesn't before taking the join. This is useful
|
|
when inferring the kind of a constant list or column which mixes floating-point
|
|
and integer literals; recall that <span class="extract"><span class="extract-syntax">number</span></span> \(\not\leq\) <span class="extract"><span class="extract-syntax">real number</span></span>, so
|
|
without this promotion there would be no way to join such kinds.
|
|
</p>
|
|
|
|
<p class="commentary"><span class="named-paragraph-container code-font"><span class="named-paragraph-defn">Deal with floating-point promotions</span><span class="named-paragraph-number">7.2</span></span><span class="comment-syntax"> =</span>
|
|
</p>
|
|
|
|
<pre class="displayed-code all-displayed-code code-font">
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> ((</span><a href="3-fv.html#SP2" class="function-link"><span class="function-syntax">Kinds::FloatingPoint::uses_floating_point</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">K1</span><span class="plain-syntax">) == </span><span class="identifier-syntax">FALSE</span><span class="plain-syntax">) &&</span>
|
|
<span class="plain-syntax"> (</span><a href="3-fv.html#SP2" class="function-link"><span class="function-syntax">Kinds::FloatingPoint::uses_floating_point</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">K2</span><span class="plain-syntax">)) &&</span>
|
|
<span class="plain-syntax"> (</span><a href="2-knd.html#SP24" class="function-link"><span class="function-syntax">Kinds::eq</span></a><span class="plain-syntax">(</span><a href="3-fv.html#SP1" class="function-link"><span class="function-syntax">Kinds::FloatingPoint::real_equivalent</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">K1</span><span class="plain-syntax">), </span><span class="identifier-syntax">K2</span><span class="plain-syntax">)))</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">return</span><span class="plain-syntax"> (</span><span class="identifier-syntax">direction</span><span class="plain-syntax"> > </span><span class="constant-syntax">0</span><span class="plain-syntax">)?</span><span class="identifier-syntax">K2:K1</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> ((</span><a href="3-fv.html#SP2" class="function-link"><span class="function-syntax">Kinds::FloatingPoint::uses_floating_point</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">K2</span><span class="plain-syntax">) == </span><span class="identifier-syntax">FALSE</span><span class="plain-syntax">) &&</span>
|
|
<span class="plain-syntax"> (</span><a href="3-fv.html#SP2" class="function-link"><span class="function-syntax">Kinds::FloatingPoint::uses_floating_point</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">K1</span><span class="plain-syntax">)) &&</span>
|
|
<span class="plain-syntax"> (</span><a href="2-knd.html#SP24" class="function-link"><span class="function-syntax">Kinds::eq</span></a><span class="plain-syntax">(</span><a href="3-fv.html#SP1" class="function-link"><span class="function-syntax">Kinds::FloatingPoint::real_equivalent</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">K2</span><span class="plain-syntax">), </span><span class="identifier-syntax">K1</span><span class="plain-syntax">)))</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">return</span><span class="plain-syntax"> (</span><span class="identifier-syntax">direction</span><span class="plain-syntax"> > </span><span class="constant-syntax">0</span><span class="plain-syntax">)?</span><span class="identifier-syntax">K1:K2</span><span class="plain-syntax">;</span>
|
|
</pre>
|
|
<ul class="endnotetexts"><li>This code is used in <a href="2-tlok.html#SP7">§7</a>.</li></ul>
|
|
<p class="commentary firstcommentary"><a id="SP8" class="paragraph-anchor"></a><b>§8. Compatibility. </b>A related but different question is "compatibility". This asks whether a
|
|
value of kind \(K\) can be used where \(L\) is expected, but:
|
|
</p>
|
|
|
|
<ul class="items"><li>(i) It is now okay if explicit code to perform a conversion would be needed; and
|
|
</li><li>(ii) There are now three possible answers — always, never and sometimes, where
|
|
"sometimes" means that code can be compiled which would test compatibility at
|
|
run time rather than compile time.
|
|
</li></ul>
|
|
<p class="commentary">Conformance implies compatibility but not vice versa. For example:
|
|
</p>
|
|
|
|
<pre class="displayed-code all-displayed-code code-font">
|
|
<span class="plain-syntax">'</span><span class="element-syntax">new kind thing of object</span><span class="plain-syntax">':</span><span class="string-syntax"> ok</span>
|
|
<span class="plain-syntax">'</span><span class="element-syntax">new kind device of thing</span><span class="plain-syntax">':</span><span class="string-syntax"> ok</span>
|
|
<span class="plain-syntax">'</span><span class="element-syntax">new kind vehicle of thing</span><span class="plain-syntax">':</span><span class="string-syntax"> ok</span>
|
|
<span class="plain-syntax">'</span><span class="element-syntax">new unit length</span><span class="plain-syntax">':</span><span class="string-syntax"> ok</span>
|
|
<span class="plain-syntax">'</span><span class="element-syntax">number compatible with number?</span><span class="plain-syntax">':</span><span class="string-syntax"> always</span>
|
|
<span class="plain-syntax">'</span><span class="element-syntax">number compatible with real number?</span><span class="plain-syntax">':</span><span class="string-syntax"> always</span>
|
|
<span class="plain-syntax">'</span><span class="element-syntax">value compatible with number?</span><span class="plain-syntax">':</span><span class="string-syntax"> never</span>
|
|
<span class="plain-syntax">'</span><span class="element-syntax">object compatible with text?</span><span class="plain-syntax">':</span><span class="string-syntax"> never</span>
|
|
<span class="plain-syntax">'</span><span class="element-syntax">object compatible with thing?</span><span class="plain-syntax">':</span><span class="string-syntax"> sometimes</span>
|
|
<span class="plain-syntax">'</span><span class="element-syntax">thing compatible with object?</span><span class="plain-syntax">':</span><span class="string-syntax"> always</span>
|
|
<span class="plain-syntax">'</span><span class="element-syntax">device compatible with thing?</span><span class="plain-syntax">':</span><span class="string-syntax"> always</span>
|
|
<span class="plain-syntax">'</span><span class="element-syntax">device compatible with object?</span><span class="plain-syntax">':</span><span class="string-syntax"> always</span>
|
|
<span class="plain-syntax">'</span><span class="element-syntax">list of devices compatible with thing?</span><span class="plain-syntax">':</span><span class="string-syntax"> never</span>
|
|
<span class="plain-syntax">'</span><span class="element-syntax">list of devices compatible with list of things?</span><span class="plain-syntax">':</span><span class="string-syntax"> always</span>
|
|
<span class="plain-syntax">'</span><span class="element-syntax">relation of things to texts compatible with relation of devices to texts?</span><span class="plain-syntax">':</span><span class="string-syntax"> never</span>
|
|
<span class="plain-syntax">'</span><span class="element-syntax">relation of devices to texts compatible with relation of things to texts?</span><span class="plain-syntax">':</span><span class="string-syntax"> always</span>
|
|
<span class="plain-syntax">'</span><span class="element-syntax">phrase thing -> text compatible with phrase device -> text?</span><span class="plain-syntax">':</span><span class="string-syntax"> always</span>
|
|
<span class="plain-syntax">'</span><span class="element-syntax">phrase device -> text compatible with phrase thing -> text?</span><span class="plain-syntax">':</span><span class="string-syntax"> never</span>
|
|
<span class="plain-syntax">'</span><span class="element-syntax">phrase text -> thing compatible with phrase text -> device?</span><span class="plain-syntax">':</span><span class="string-syntax"> never</span>
|
|
<span class="plain-syntax">'</span><span class="element-syntax">phrase text -> device compatible with phrase text -> thing?</span><span class="plain-syntax">':</span><span class="string-syntax"> always</span>
|
|
<span class="plain-syntax">'</span><span class="element-syntax">activity on numbers compatible with activity?</span><span class="plain-syntax">':</span><span class="string-syntax"> always</span>
|
|
<span class="plain-syntax">'</span><span class="element-syntax">first term of activity</span><span class="plain-syntax">':</span><span class="string-syntax"> nothing</span>
|
|
<span class="plain-syntax">'</span><span class="element-syntax">activity on numbers compatible with activity on values?</span><span class="plain-syntax">':</span><span class="string-syntax"> never</span>
|
|
</pre>
|
|
<p class="commentary">Note that <span class="extract"><span class="extract-syntax">number</span></span> is compatible with <span class="extract"><span class="extract-syntax">real number</span></span>. Run-time code will be
|
|
needed to convert the value, but the answer is "always". We also see that
|
|
<span class="extract"><span class="extract-syntax">device</span></span> is always compatible with <span class="extract"><span class="extract-syntax">thing</span></span> — every device is a thing —
|
|
but also that <span class="extract"><span class="extract-syntax">thing</span></span> is sometimes compatible with <span class="extract"><span class="extract-syntax">device</span></span>. If we pass a
|
|
thing to a function expecting to see a device, run-time code can check whether
|
|
the value passed is indeed a device, and reject the call with a run-time error
|
|
if not.
|
|
</p>
|
|
|
|
<p class="commentary firstcommentary"><a id="SP9" class="paragraph-anchor"></a><b>§9. </b>Kind checking can happen for many reasons, but the most difficult case
|
|
occurs when matching phrase prototypes. This is difficult because it involves
|
|
kind variables:
|
|
</p>
|
|
|
|
<blockquote>
|
|
<p>To add (new entry - K) to (L - list of values of kind K) ...</p>
|
|
</blockquote>
|
|
|
|
<p class="commentary">This matches "add 23 to L" if "L" is a list of numbers, but not if it
|
|
is a list of times.
|
|
</p>
|
|
|
|
<p class="commentary">Since kind variables can be changed only when matching phrase prototypes,
|
|
and this is not a recursive process, we can store the current definitions
|
|
of A to Z in a single array.
|
|
</p>
|
|
|
|
<pre class="definitions code-font"><span class="definition-keyword">define</span> <span class="constant-syntax">MAX_KIND_VARIABLES</span><span class="plain-syntax"> </span><span class="constant-syntax">27</span><span class="plain-syntax"> </span><span class="comment-syntax"> we number them from 1 (A) to 26 (Z)</span>
|
|
</pre>
|
|
<pre class="displayed-code all-displayed-code code-font">
|
|
<span class="reserved-syntax">kind</span><span class="plain-syntax"> *</span><span class="identifier-syntax">values_of_kind_variables</span><span class="plain-syntax">[</span><span class="constant-syntax">MAX_KIND_VARIABLES</span><span class="plain-syntax">];</span>
|
|
</pre>
|
|
<p class="commentary firstcommentary"><a id="SP10" class="paragraph-anchor"></a><b>§10. </b>In theory the kind-checker only needs to read the values of <span class="extract"><span class="extract-syntax">A</span></span> to <span class="extract"><span class="extract-syntax">Z</span></span>, not
|
|
to write them. If <span class="extract"><span class="extract-syntax">Q</span></span> is currently equal to <span class="extract"><span class="extract-syntax">number</span></span>, then it should check
|
|
kinds against <span class="extract"><span class="extract-syntax">Q</span></span> exactly as if it were checking against <span class="extract"><span class="extract-syntax">number</span></span>. It can
|
|
indeed do this — that's the <span class="extract"><span class="extract-syntax">MATCH_KIND_VARIABLES_AS_VALUES</span></span> mode. It can
|
|
also ignore the values of kind variables and treat them as names, so that
|
|
<span class="extract"><span class="extract-syntax">Q</span></span> matches only against <span class="extract"><span class="extract-syntax">Q</span></span>, regardless of its current value; that's the
|
|
<span class="extract"><span class="extract-syntax">MATCH_KIND_VARIABLES_AS_SYMBOLS</span></span> mode. Or it can match anything
|
|
against <span class="extract"><span class="extract-syntax">Q</span></span>, which is <span class="extract"><span class="extract-syntax">MATCH_KIND_VARIABLES_AS_UNIVERSAL</span></span> mode.
|
|
</p>
|
|
|
|
<p class="commentary">More interestingly, the kind-checker can also set the values of <span class="extract"><span class="extract-syntax">A</span></span> to <span class="extract"><span class="extract-syntax">Z</span></span>.
|
|
This is convenient since checking their correctness is more or less the same
|
|
thing as inferring what they seem to be in a given situation. So this is
|
|
<span class="extract"><span class="extract-syntax">MATCH_KIND_VARIABLES_INFERRING_VALUES</span></span> mode.
|
|
</p>
|
|
|
|
<pre class="definitions code-font"><span class="definition-keyword">define</span> <span class="constant-syntax">MATCH_KIND_VARIABLES_AS_SYMBOLS</span><span class="plain-syntax"> </span><span class="constant-syntax">0</span>
|
|
<span class="definition-keyword">define</span> <span class="constant-syntax">MATCH_KIND_VARIABLES_INFERRING_VALUES</span><span class="plain-syntax"> </span><span class="constant-syntax">1</span>
|
|
<span class="definition-keyword">define</span> <span class="constant-syntax">MATCH_KIND_VARIABLES_AS_VALUES</span><span class="plain-syntax"> </span><span class="constant-syntax">2</span>
|
|
<span class="definition-keyword">define</span> <span class="constant-syntax">MATCH_KIND_VARIABLES_AS_UNIVERSAL</span><span class="plain-syntax"> </span><span class="constant-syntax">3</span>
|
|
</pre>
|
|
<pre class="displayed-code all-displayed-code code-font">
|
|
<span class="reserved-syntax">int</span><span class="plain-syntax"> </span><span class="identifier-syntax">kind_checker_mode</span><span class="plain-syntax"> = </span><span class="constant-syntax">MATCH_KIND_VARIABLES_AS_SYMBOLS</span><span class="plain-syntax">;</span>
|
|
</pre>
|
|
<p class="commentary firstcommentary"><a id="SP11" class="paragraph-anchor"></a><b>§11. </b>When the kind-checker does choose a value for a variable, it not only
|
|
sets the relevant entry in the above array but also creates a note that
|
|
this has been done. (If a phrase is correctly matched by the specification
|
|
matcher, a linked list of these notes is attached to the results: thus
|
|
a match of "add 23 to L" in the example above would produce a successful
|
|
result plus a note that <span class="extract"><span class="extract-syntax">K</span></span> has to be <span class="extract"><span class="extract-syntax">list of numbers</span></span>.)
|
|
</p>
|
|
|
|
<pre class="displayed-code all-displayed-code code-font">
|
|
<span class="reserved-syntax">typedef</span><span class="plain-syntax"> </span><span class="reserved-syntax">struct</span><span class="plain-syntax"> </span><span class="reserved-syntax">kind_variable_declaration</span><span class="plain-syntax"> {</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">int</span><span class="plain-syntax"> </span><span class="identifier-syntax">kv_number</span><span class="plain-syntax">; </span><span class="comment-syntax"> must be from 1 to 26</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">struct</span><span class="plain-syntax"> </span><span class="reserved-syntax">kind</span><span class="plain-syntax"> *</span><span class="identifier-syntax">kv_value</span><span class="plain-syntax">; </span><span class="comment-syntax"> must be a definite non-</span><span class="extract"><span class="extract-syntax">NULL</span></span><span class="comment-syntax"> kind</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">struct</span><span class="plain-syntax"> </span><span class="reserved-syntax">kind_variable_declaration</span><span class="plain-syntax"> *</span><span class="identifier-syntax">next</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">CLASS_DEFINITION</span>
|
|
<span class="plain-syntax">} </span><span class="reserved-syntax">kind_variable_declaration</span><span class="plain-syntax">;</span>
|
|
</pre>
|
|
<ul class="endnotetexts"><li>The structure kind_variable_declaration is accessed in 3/dmn and here.</li></ul>
|
|
<p class="commentary firstcommentary"><a id="SP12" class="paragraph-anchor"></a><b>§12. </b>And this little function unpacks a list of KVDs into an array of values:
|
|
</p>
|
|
|
|
<pre class="displayed-code all-displayed-code code-font">
|
|
<span class="reserved-syntax">void</span><span class="plain-syntax"> </span><span class="function-syntax">Latticework::unpack_kvd</span><span class="plain-syntax">(</span><span class="reserved-syntax">kind</span><span class="plain-syntax"> **</span><span class="identifier-syntax">vals</span><span class="plain-syntax">, </span><span class="reserved-syntax">kind_variable_declaration</span><span class="plain-syntax"> *</span><span class="identifier-syntax">kvd</span><span class="plain-syntax">) {</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">for</span><span class="plain-syntax"> (</span><span class="reserved-syntax">int</span><span class="plain-syntax"> </span><span class="identifier-syntax">i</span><span class="plain-syntax">=0; </span><span class="identifier-syntax">i</span><span class="plain-syntax"><27; </span><span class="identifier-syntax">i</span><span class="plain-syntax">++) </span><span class="identifier-syntax">vals</span><span class="plain-syntax">[</span><span class="identifier-syntax">i</span><span class="plain-syntax">] = </span><span class="identifier-syntax">NULL</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">for</span><span class="plain-syntax"> (; </span><span class="identifier-syntax">kvd</span><span class="plain-syntax">; </span><span class="identifier-syntax">kvd</span><span class="plain-syntax">=</span><span class="identifier-syntax">kvd</span><span class="plain-syntax">-></span><span class="element-syntax">next</span><span class="plain-syntax">) </span><span class="identifier-syntax">vals</span><span class="plain-syntax">[</span><span class="identifier-syntax">kvd</span><span class="plain-syntax">-></span><span class="element-syntax">kv_number</span><span class="plain-syntax">] = </span><span class="identifier-syntax">kvd</span><span class="plain-syntax">-></span><span class="element-syntax">kv_value</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax">}</span>
|
|
</pre>
|
|
<p class="commentary firstcommentary"><a id="SP13" class="paragraph-anchor"></a><b>§13. Common code. </b>So the following routine tests conformance if <span class="extract"><span class="extract-syntax">comp</span></span> is <span class="extract"><span class="extract-syntax">FALSE</span></span>, returning
|
|
<span class="extract"><span class="extract-syntax">ALWAYS_MATCH</span></span> if and only if <span class="extract"><span class="extract-syntax">from</span></span> \(\leq\) <span class="extract"><span class="extract-syntax">to</span></span> holds; and otherwise it tests
|
|
compatibility, returning <span class="extract"><span class="extract-syntax">ALWAYS_MATCH</span></span>, <span class="extract"><span class="extract-syntax">SOMETIMES_MATCH</span></span> or <span class="extract"><span class="extract-syntax">NEVER_MATCH</span></span>
|
|
as appropriate.
|
|
</p>
|
|
|
|
<pre class="displayed-code all-displayed-code code-font">
|
|
<span class="reserved-syntax">int</span><span class="plain-syntax"> </span><span class="function-syntax">Latticework::order_relation</span><button class="popup" onclick="togglePopup('usagePopup2')"><span class="comment-syntax">?</span><span class="popuptext" id="usagePopup2">Usage of <span class="code-font"><span class="function-syntax">Latticework::order_relation</span></span>:<br/><a href="2-tlok.html#SP13_1">§13.1</a>, <a href="2-tlok.html#SP13_4">§13.4</a>, <a href="2-tlok.html#SP13_7_1">§13.7.1</a>, <a href="2-tlok.html#SP13_7_2">§13.7.2</a><br/>Kinds - <a href="2-knd.html#SP25">§25</a></span></button><span class="plain-syntax">(</span><span class="reserved-syntax">kind</span><span class="plain-syntax"> *</span><span class="identifier-syntax">from</span><span class="plain-syntax">, </span><span class="reserved-syntax">kind</span><span class="plain-syntax"> *</span><span class="identifier-syntax">to</span><span class="plain-syntax">, </span><span class="reserved-syntax">int</span><span class="plain-syntax"> </span><span class="identifier-syntax">allow_casts</span><span class="plain-syntax">) {</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><a href="2-knd.html#SP12" class="function-link"><span class="function-syntax">Kinds::get_variable_number</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">to</span><span class="plain-syntax">) > </span><span class="constant-syntax">0</span><span class="plain-syntax">) {</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">kind</span><span class="plain-syntax"> *</span><span class="identifier-syntax">var_k</span><span class="plain-syntax"> = </span><span class="identifier-syntax">to</span><span class="plain-syntax">, *</span><span class="identifier-syntax">other_k</span><span class="plain-syntax"> = </span><span class="identifier-syntax">from</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="named-paragraph-container code-font"><a href="2-tlok.html#SP13_7" class="named-paragraph-link"><span class="named-paragraph">Deal separately with matches against kind variables</span><span class="named-paragraph-number">13.7</span></a></span><span class="plain-syntax">;</span>
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|
<span class="plain-syntax"> }</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><a href="2-knd.html#SP12" class="function-link"><span class="function-syntax">Kinds::get_variable_number</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">from</span><span class="plain-syntax">) > </span><span class="constant-syntax">0</span><span class="plain-syntax">) {</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">kind</span><span class="plain-syntax"> *</span><span class="identifier-syntax">var_k</span><span class="plain-syntax"> = </span><span class="identifier-syntax">from</span><span class="plain-syntax">, *</span><span class="identifier-syntax">other_k</span><span class="plain-syntax"> = </span><span class="identifier-syntax">to</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="named-paragraph-container code-font"><a href="2-tlok.html#SP13_7" class="named-paragraph-link"><span class="named-paragraph">Deal separately with matches against kind variables</span><span class="named-paragraph-number">13.7</span></a></span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> }</span>
|
|
<span class="plain-syntax"> </span><span class="named-paragraph-container code-font"><a href="2-tlok.html#SP13_1" class="named-paragraph-link"><span class="named-paragraph">Deal separately with the sayability of lists</span><span class="named-paragraph-number">13.1</span></a></span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="named-paragraph-container code-font"><a href="2-tlok.html#SP13_2" class="named-paragraph-link"><span class="named-paragraph">Deal separately with the top and bottom of the lattice</span><span class="named-paragraph-number">13.2</span></a></span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="named-paragraph-container code-font"><a href="2-tlok.html#SP13_3" class="named-paragraph-link"><span class="named-paragraph">Deal separately with the special role of the unknown kind</span><span class="named-paragraph-number">13.3</span></a></span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="named-paragraph-container code-font"><a href="2-tlok.html#SP13_4" class="named-paragraph-link"><span class="named-paragraph">The general case of compatibility</span><span class="named-paragraph-number">13.4</span></a></span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax">}</span>
|
|
</pre>
|
|
<p class="commentary firstcommentary"><a id="SP13_1" class="paragraph-anchor"></a><b>§13.1. </b>A list is sayable if and only if it is empty, or its contents are sayable.
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|
</p>
|
|
|
|
<p class="commentary"><span class="named-paragraph-container code-font"><span class="named-paragraph-defn">Deal separately with the sayability of lists</span><span class="named-paragraph-number">13.1</span></span><span class="comment-syntax"> =</span>
|
|
</p>
|
|
|
|
<pre class="displayed-code all-displayed-code code-font">
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> ((</span><a href="2-knd.html#SP11" class="function-link"><span class="function-syntax">Kinds::get_construct</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">from</span><span class="plain-syntax">) == </span><span class="identifier-syntax">CON_list_of</span><span class="plain-syntax">) &&</span>
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|
<span class="plain-syntax"> (</span><a href="2-knd.html#SP24" class="function-link"><span class="function-syntax">Kinds::eq</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">to</span><span class="plain-syntax">, </span><span class="identifier-syntax">K_sayable_value</span><span class="plain-syntax">))) {</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">kind</span><span class="plain-syntax"> *</span><span class="identifier-syntax">CK</span><span class="plain-syntax"> = </span><a href="2-knd.html#SP14" class="function-link"><span class="function-syntax">Kinds::unary_construction_material</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">from</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><a href="2-knd.html#SP24" class="function-link"><span class="function-syntax">Kinds::eq</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">CK</span><span class="plain-syntax">, </span><span class="identifier-syntax">K_nil</span><span class="plain-syntax">)) </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="constant-syntax">ALWAYS_MATCH</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><span class="identifier-syntax">CK</span><span class="plain-syntax"> == </span><span class="identifier-syntax">NULL</span><span class="plain-syntax">) </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="constant-syntax">ALWAYS_MATCH</span><span class="plain-syntax">; </span><span class="comment-syntax"> for an internal test case making dodgy lists</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><a href="2-tlok.html#SP13" class="function-link"><span class="function-syntax">Latticework::order_relation</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">CK</span><span class="plain-syntax">, </span><span class="identifier-syntax">K_sayable_value</span><span class="plain-syntax">, </span><span class="identifier-syntax">allow_casts</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> }</span>
|
|
</pre>
|
|
<ul class="endnotetexts"><li>This code is used in <a href="2-tlok.html#SP13">§13</a>.</li></ul>
|
|
<p class="commentary firstcommentary"><a id="SP13_2" class="paragraph-anchor"></a><b>§13.2. </b><span class="named-paragraph-container code-font"><span class="named-paragraph-defn">Deal separately with the top and bottom of the lattice</span><span class="named-paragraph-number">13.2</span></span><span class="comment-syntax"> =</span>
|
|
</p>
|
|
|
|
<pre class="displayed-code all-displayed-code code-font">
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><a href="2-knd.html#SP24" class="function-link"><span class="function-syntax">Kinds::eq</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">to</span><span class="plain-syntax">, </span><span class="identifier-syntax">K_value</span><span class="plain-syntax">)) </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="constant-syntax">ALWAYS_MATCH</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><a href="2-knd.html#SP24" class="function-link"><span class="function-syntax">Kinds::eq</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">from</span><span class="plain-syntax">, </span><span class="identifier-syntax">K_nil</span><span class="plain-syntax">)) </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="constant-syntax">ALWAYS_MATCH</span><span class="plain-syntax">;</span>
|
|
</pre>
|
|
<ul class="endnotetexts"><li>This code is used in <a href="2-tlok.html#SP13">§13</a>.</li></ul>
|
|
<p class="commentary firstcommentary"><a id="SP13_3" class="paragraph-anchor"></a><b>§13.3. </b><span class="extract"><span class="extract-syntax">NULL</span></span> as a kind means "unknown". It's compatible only with itself
|
|
and, of course, "value".
|
|
</p>
|
|
|
|
<p class="commentary"><span class="named-paragraph-container code-font"><span class="named-paragraph-defn">Deal separately with the special role of the unknown kind</span><span class="named-paragraph-number">13.3</span></span><span class="comment-syntax"> =</span>
|
|
</p>
|
|
|
|
<pre class="displayed-code all-displayed-code code-font">
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> ((</span><span class="identifier-syntax">to</span><span class="plain-syntax"> == </span><span class="identifier-syntax">NULL</span><span class="plain-syntax">) && (</span><span class="identifier-syntax">from</span><span class="plain-syntax"> == </span><span class="identifier-syntax">NULL</span><span class="plain-syntax">)) </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="constant-syntax">ALWAYS_MATCH</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> ((</span><span class="identifier-syntax">to</span><span class="plain-syntax"> == </span><span class="identifier-syntax">NULL</span><span class="plain-syntax">) || (</span><span class="identifier-syntax">from</span><span class="plain-syntax"> == </span><span class="identifier-syntax">NULL</span><span class="plain-syntax">)) </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="constant-syntax">NEVER_MATCH</span><span class="plain-syntax">;</span>
|
|
</pre>
|
|
<ul class="endnotetexts"><li>This code is used in <a href="2-tlok.html#SP13">§13</a>.</li></ul>
|
|
<p class="commentary firstcommentary"><a id="SP13_4" class="paragraph-anchor"></a><b>§13.4. </b><span class="named-paragraph-container code-font"><span class="named-paragraph-defn">The general case of compatibility</span><span class="named-paragraph-number">13.4</span></span><span class="comment-syntax"> =</span>
|
|
</p>
|
|
|
|
<pre class="displayed-code all-displayed-code code-font">
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">int</span><span class="plain-syntax"> </span><span class="identifier-syntax">f_a</span><span class="plain-syntax"> = </span><a href="4-kc2.html#SP15" class="function-link"><span class="function-syntax">KindConstructors::arity</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">from</span><span class="plain-syntax">-></span><span class="element-syntax">construct</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">int</span><span class="plain-syntax"> </span><span class="identifier-syntax">t_a</span><span class="plain-syntax"> = </span><a href="4-kc2.html#SP15" class="function-link"><span class="function-syntax">KindConstructors::arity</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">to</span><span class="plain-syntax">-></span><span class="element-syntax">construct</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">int</span><span class="plain-syntax"> </span><span class="identifier-syntax">arity</span><span class="plain-syntax"> = (</span><span class="identifier-syntax">f_a</span><span class="plain-syntax"> < </span><span class="identifier-syntax">t_a</span><span class="plain-syntax">)?</span><span class="identifier-syntax">f_a:t_a</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">int</span><span class="plain-syntax"> </span><span class="identifier-syntax">o</span><span class="plain-syntax"> = </span><span class="constant-syntax">ALWAYS_MATCH</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><span class="identifier-syntax">from</span><span class="plain-syntax">-></span><span class="element-syntax">construct</span><span class="plain-syntax"> != </span><span class="identifier-syntax">to</span><span class="plain-syntax">-></span><span class="element-syntax">construct</span><span class="plain-syntax">)</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">o</span><span class="plain-syntax"> = </span><a href="2-tlok.html#SP13_6" class="function-link"><span class="function-syntax">Latticework::construct_compatible</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">from</span><span class="plain-syntax">, </span><span class="identifier-syntax">to</span><span class="plain-syntax">, </span><span class="identifier-syntax">allow_casts</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">int</span><span class="plain-syntax"> </span><span class="identifier-syntax">i</span><span class="plain-syntax">, </span><span class="identifier-syntax">this_o</span><span class="plain-syntax"> = </span><span class="constant-syntax">NEVER_MATCH</span><span class="plain-syntax">, </span><span class="identifier-syntax">fallen</span><span class="plain-syntax"> = </span><span class="identifier-syntax">FALSE</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">for</span><span class="plain-syntax"> (</span><span class="identifier-syntax">i</span><span class="plain-syntax">=0; </span><span class="identifier-syntax">i</span><span class="plain-syntax"><</span><span class="identifier-syntax">arity</span><span class="plain-syntax">; </span><span class="identifier-syntax">i</span><span class="plain-syntax">++) {</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> ((</span><a href="2-tlok.html#SP13_5" class="function-link"><span class="function-syntax">Latticework::vacuous</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">from</span><span class="plain-syntax">-></span><span class="element-syntax">kc_args</span><span class="plain-syntax">[</span><span class="identifier-syntax">i</span><span class="plain-syntax">])) && (</span><a href="2-tlok.html#SP13_5" class="function-link"><span class="function-syntax">Latticework::vacuous</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">to</span><span class="plain-syntax">-></span><span class="element-syntax">kc_args</span><span class="plain-syntax">[</span><span class="identifier-syntax">i</span><span class="plain-syntax">])))</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">continue</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><a href="4-kc2.html#SP15" class="function-link"><span class="function-syntax">KindConstructors::variance</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">from</span><span class="plain-syntax">-></span><span class="element-syntax">construct</span><span class="plain-syntax">, </span><span class="identifier-syntax">i</span><span class="plain-syntax">) == </span><span class="constant-syntax">COVARIANT</span><span class="plain-syntax">)</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">this_o</span><span class="plain-syntax"> = </span><a href="2-tlok.html#SP13" class="function-link"><span class="function-syntax">Latticework::order_relation</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">from</span><span class="plain-syntax">-></span><span class="element-syntax">kc_args</span><span class="plain-syntax">[</span><span class="identifier-syntax">i</span><span class="plain-syntax">], </span><span class="identifier-syntax">to</span><span class="plain-syntax">-></span><span class="element-syntax">kc_args</span><span class="plain-syntax">[</span><span class="identifier-syntax">i</span><span class="plain-syntax">], </span><span class="identifier-syntax">allow_casts</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">else</span><span class="plain-syntax"> {</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">this_o</span><span class="plain-syntax"> = </span><a href="2-tlok.html#SP13" class="function-link"><span class="function-syntax">Latticework::order_relation</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">to</span><span class="plain-syntax">-></span><span class="element-syntax">kc_args</span><span class="plain-syntax">[</span><span class="identifier-syntax">i</span><span class="plain-syntax">], </span><span class="identifier-syntax">from</span><span class="plain-syntax">-></span><span class="element-syntax">kc_args</span><span class="plain-syntax">[</span><span class="identifier-syntax">i</span><span class="plain-syntax">], </span><span class="identifier-syntax">allow_casts</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> }</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">switch</span><span class="plain-syntax"> (</span><span class="identifier-syntax">this_o</span><span class="plain-syntax">) {</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">case</span><span class="plain-syntax"> </span><span class="identifier-syntax">NEVER_MATCH:</span><span class="plain-syntax"> </span><span class="identifier-syntax">o</span><span class="plain-syntax"> = </span><span class="identifier-syntax">this_o</span><span class="plain-syntax">; </span><span class="reserved-syntax">break</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">case</span><span class="plain-syntax"> </span><span class="identifier-syntax">SOMETIMES_MATCH:</span><span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><span class="identifier-syntax">o</span><span class="plain-syntax"> != </span><span class="constant-syntax">NEVER_MATCH</span><span class="plain-syntax">) { </span><span class="identifier-syntax">o</span><span class="plain-syntax"> = </span><span class="identifier-syntax">this_o</span><span class="plain-syntax">; </span><span class="identifier-syntax">fallen</span><span class="plain-syntax"> = </span><span class="identifier-syntax">TRUE</span><span class="plain-syntax">; } </span><span class="reserved-syntax">break</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> }</span>
|
|
<span class="plain-syntax"> }</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> ((</span><span class="identifier-syntax">fallen</span><span class="plain-syntax">) && (</span><span class="identifier-syntax">to</span><span class="plain-syntax">-></span><span class="element-syntax">construct</span><span class="plain-syntax"> != </span><span class="identifier-syntax">CON_list_of</span><span class="plain-syntax">)) </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="constant-syntax">NEVER_MATCH</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="identifier-syntax">o</span><span class="plain-syntax">;</span>
|
|
</pre>
|
|
<ul class="endnotetexts"><li>This code is used in <a href="2-tlok.html#SP13">§13</a>.</li></ul>
|
|
<p class="commentary firstcommentary"><a id="SP13_5" class="paragraph-anchor"></a><b>§13.5. </b></p>
|
|
|
|
<pre class="displayed-code all-displayed-code code-font">
|
|
<span class="reserved-syntax">int</span><span class="plain-syntax"> </span><span class="function-syntax">Latticework::vacuous</span><button class="popup" onclick="togglePopup('usagePopup3')"><span class="comment-syntax">?</span><span class="popuptext" id="usagePopup3">Usage of <span class="code-font"><span class="function-syntax">Latticework::vacuous</span></span>:<br/><a href="2-tlok.html#SP13_4">§13.4</a></span></button><span class="plain-syntax">(</span><span class="reserved-syntax">kind</span><span class="plain-syntax"> *</span><span class="identifier-syntax">K</span><span class="plain-syntax">) {</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> ((</span><a href="2-knd.html#SP24" class="function-link"><span class="function-syntax">Kinds::eq</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">K</span><span class="plain-syntax">, </span><span class="identifier-syntax">K_nil</span><span class="plain-syntax">)) || (</span><a href="2-knd.html#SP24" class="function-link"><span class="function-syntax">Kinds::eq</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">K</span><span class="plain-syntax">, </span><span class="identifier-syntax">K_void</span><span class="plain-syntax">))) </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="identifier-syntax">TRUE</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="identifier-syntax">FALSE</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax">}</span>
|
|
</pre>
|
|
<p class="commentary firstcommentary"><a id="SP13_6" class="paragraph-anchor"></a><b>§13.6. </b></p>
|
|
|
|
<pre class="displayed-code all-displayed-code code-font">
|
|
<span class="reserved-syntax">int</span><span class="plain-syntax"> </span><span class="function-syntax">Latticework::construct_compatible</span><button class="popup" onclick="togglePopup('usagePopup4')"><span class="comment-syntax">?</span><span class="popuptext" id="usagePopup4">Usage of <span class="code-font"><span class="function-syntax">Latticework::construct_compatible</span></span>:<br/><a href="2-tlok.html#SP13_4">§13.4</a></span></button><span class="plain-syntax">(</span><span class="reserved-syntax">kind</span><span class="plain-syntax"> *</span><span class="identifier-syntax">from</span><span class="plain-syntax">, </span><span class="reserved-syntax">kind</span><span class="plain-syntax"> *</span><span class="identifier-syntax">to</span><span class="plain-syntax">, </span><span class="reserved-syntax">int</span><span class="plain-syntax"> </span><span class="identifier-syntax">allow_casts</span><span class="plain-syntax">) {</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">kind</span><span class="plain-syntax"> *</span><span class="identifier-syntax">K</span><span class="plain-syntax"> = </span><span class="identifier-syntax">from</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">while</span><span class="plain-syntax"> (</span><span class="identifier-syntax">K</span><span class="plain-syntax">) {</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><a href="2-knd.html#SP24" class="function-link"><span class="function-syntax">Kinds::eq</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">K</span><span class="plain-syntax">, </span><span class="identifier-syntax">to</span><span class="plain-syntax">)) </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="constant-syntax">ALWAYS_MATCH</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">K</span><span class="plain-syntax"> = </span><a href="2-tlok.html#SP6" class="function-link"><span class="function-syntax">Latticework::super</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">K</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> }</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> ((</span><span class="identifier-syntax">allow_casts</span><span class="plain-syntax">) && (</span><a href="4-kc2.html#SP18" class="function-link"><span class="function-syntax">KindConstructors::find_cast</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">from</span><span class="plain-syntax">-></span><span class="element-syntax">construct</span><span class="plain-syntax">, </span><span class="identifier-syntax">to</span><span class="plain-syntax">-></span><span class="element-syntax">construct</span><span class="plain-syntax">)))</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="constant-syntax">ALWAYS_MATCH</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">K</span><span class="plain-syntax"> = </span><span class="identifier-syntax">to</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">while</span><span class="plain-syntax"> (</span><span class="identifier-syntax">K</span><span class="plain-syntax">) {</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><a href="2-knd.html#SP24" class="function-link"><span class="function-syntax">Kinds::eq</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">K</span><span class="plain-syntax">, </span><span class="identifier-syntax">from</span><span class="plain-syntax">)) {</span>
|
|
<span class="plain-syntax"> #</span><span class="identifier-syntax">ifdef</span><span class="plain-syntax"> </span><span class="identifier-syntax">HIERARCHY_ALLOWS_SOMETIMES_MATCH_KINDS_CALLBACK</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><span class="identifier-syntax">HIERARCHY_ALLOWS_SOMETIMES_MATCH_KINDS_CALLBACK</span><span class="plain-syntax">(</span><span class="identifier-syntax">from</span><span class="plain-syntax">))</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="constant-syntax">SOMETIMES_MATCH</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> #</span><span class="identifier-syntax">endif</span>
|
|
<span class="plain-syntax"> #</span><span class="identifier-syntax">ifndef</span><span class="plain-syntax"> </span><span class="identifier-syntax">HIERARCHY_ALLOWS_SOMETIMES_MATCH_KINDS_CALLBACK</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="constant-syntax">SOMETIMES_MATCH</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> #</span><span class="identifier-syntax">endif</span>
|
|
<span class="plain-syntax"> }</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">K</span><span class="plain-syntax"> = </span><a href="2-tlok.html#SP6" class="function-link"><span class="function-syntax">Latticework::super</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">K</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> }</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="constant-syntax">NEVER_MATCH</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax">}</span>
|
|
</pre>
|
|
<p class="commentary firstcommentary"><a id="SP13_7" class="paragraph-anchor"></a><b>§13.7. </b>Recall that kind variables are identified by a number in the range 1 ("A")
|
|
to 26 ("Z"), and that it is also possible to assign them a domain, or a
|
|
"declaration". This marks that they are free to take on a value, within
|
|
that domain. For example, in
|
|
</p>
|
|
|
|
<blockquote>
|
|
<p>To add (new entry - K) to (L - list of values of kind K) ...</p>
|
|
</blockquote>
|
|
|
|
<p class="commentary">the first appearance of <span class="extract"><span class="extract-syntax">K</span></span> will be an ordinary use of a kind variable,
|
|
whereas the second has the declaration <span class="extract"><span class="extract-syntax">value</span></span> — meaning that it can
|
|
become any kind matching <span class="extract"><span class="extract-syntax">value</span></span>. (It could alternatively have had a
|
|
more restrictive declaration like <span class="extract"><span class="extract-syntax">arithmetic value</span></span>.)
|
|
</p>
|
|
|
|
<p class="commentary"><span class="named-paragraph-container code-font"><span class="named-paragraph-defn">Deal separately with matches against kind variables</span><span class="named-paragraph-number">13.7</span></span><span class="comment-syntax"> =</span>
|
|
</p>
|
|
|
|
<pre class="displayed-code all-displayed-code code-font">
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">switch</span><span class="plain-syntax">(</span><span class="identifier-syntax">kind_checker_mode</span><span class="plain-syntax">) {</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">case</span><span class="plain-syntax"> </span><span class="identifier-syntax">MATCH_KIND_VARIABLES_AS_SYMBOLS:</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><a href="2-knd.html#SP12" class="function-link"><span class="function-syntax">Kinds::get_variable_number</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">other_k</span><span class="plain-syntax">) ==</span>
|
|
<span class="plain-syntax"> </span><a href="2-knd.html#SP12" class="function-link"><span class="function-syntax">Kinds::get_variable_number</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">var_k</span><span class="plain-syntax">)) </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="constant-syntax">ALWAYS_MATCH</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="constant-syntax">NEVER_MATCH</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">case</span><span class="plain-syntax"> </span><span class="identifier-syntax">MATCH_KIND_VARIABLES_AS_UNIVERSAL:</span><span class="plain-syntax"> </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="constant-syntax">ALWAYS_MATCH</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">default:</span><span class="plain-syntax"> {</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">int</span><span class="plain-syntax"> </span><span class="identifier-syntax">vn</span><span class="plain-syntax"> = </span><a href="2-knd.html#SP12" class="function-link"><span class="function-syntax">Kinds::get_variable_number</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">var_k</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><a href="2-knd.html#SP12" class="function-link"><span class="function-syntax">Kinds::get_variable_stipulation</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">var_k</span><span class="plain-syntax">))</span>
|
|
<span class="plain-syntax"> </span><span class="named-paragraph-container code-font"><a href="2-tlok.html#SP13_7_1" class="named-paragraph-link"><span class="named-paragraph">Act on a declaration usage, where inference is allowed</span><span class="named-paragraph-number">13.7.1</span></a></span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">else</span>
|
|
<span class="plain-syntax"> </span><span class="named-paragraph-container code-font"><a href="2-tlok.html#SP13_7_2" class="named-paragraph-link"><span class="named-paragraph">Act on an ordinary usage, where inference is not allowed</span><span class="named-paragraph-number">13.7.2</span></a></span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> }</span>
|
|
<span class="plain-syntax"> }</span>
|
|
</pre>
|
|
<ul class="endnotetexts"><li>This code is used in <a href="2-tlok.html#SP13">§13</a> (twice).</li></ul>
|
|
<p class="commentary firstcommentary"><a id="SP13_7_1" class="paragraph-anchor"></a><b>§13.7.1. </b>When the specification matcher works on matching text such as
|
|
</p>
|
|
|
|
<blockquote>
|
|
<p>add 23 to the scores list;</p>
|
|
</blockquote>
|
|
|
|
<p class="commentary">it works through the prototype:
|
|
</p>
|
|
|
|
<blockquote>
|
|
<p>To add (new entry - K) to (L - list of values of kind K) ...</p>
|
|
</blockquote>
|
|
|
|
<p class="commentary">in two passes. On the first pass, it tries to match the tokens "23" and
|
|
"scores list" against <span class="extract"><span class="extract-syntax">K</span></span> and <span class="extract"><span class="extract-syntax">list of values of kind K</span></span> respectively
|
|
in <span class="extract"><span class="extract-syntax">MATCH_KIND_VARIABLES_INFERRING_VALUES</span></span> mode; on the second pass, it
|
|
does the same in <span class="extract"><span class="extract-syntax">MATCH_KIND_VARIABLES_AS_VALUES</span></span> mode. In this example,
|
|
on the first pass we infer (from the kind of "scores list", which is
|
|
indeed a list of numbers) that <span class="extract"><span class="extract-syntax">K</span></span> must be <span class="extract"><span class="extract-syntax">number</span></span>; on the second pass
|
|
we verify that "23" is a <span class="extract"><span class="extract-syntax">K</span></span>.
|
|
</p>
|
|
|
|
<p class="commentary">The following shows what happens matching <span class="extract"><span class="extract-syntax">values of kind K</span></span>, which is
|
|
a declaration usage of the variable <span class="extract"><span class="extract-syntax">K</span></span>.
|
|
</p>
|
|
|
|
<p class="commentary"><span class="named-paragraph-container code-font"><span class="named-paragraph-defn">Act on a declaration usage, where inference is allowed</span><span class="named-paragraph-number">13.7.1</span></span><span class="comment-syntax"> =</span>
|
|
</p>
|
|
|
|
<pre class="displayed-code all-displayed-code code-font">
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">switch</span><span class="plain-syntax">(</span><span class="identifier-syntax">kind_checker_mode</span><span class="plain-syntax">) {</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">case</span><span class="plain-syntax"> </span><span class="identifier-syntax">MATCH_KIND_VARIABLES_INFERRING_VALUES:</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><a href="2-tlok.html#SP13" class="function-link"><span class="function-syntax">Latticework::order_relation</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">other_k</span><span class="plain-syntax">,</span>
|
|
<span class="plain-syntax"> </span><a href="2-knd.html#SP12" class="function-link"><span class="function-syntax">Kinds::get_variable_stipulation</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">var_k</span><span class="plain-syntax">), </span><span class="identifier-syntax">allow_casts</span><span class="plain-syntax">) != </span><span class="constant-syntax">ALWAYS_MATCH</span><span class="plain-syntax">)</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="constant-syntax">NEVER_MATCH</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">LOGIF</span><span class="plain-syntax">(</span><span class="identifier-syntax">KIND_CHECKING</span><span class="plain-syntax">, </span><span class="string-syntax">"Inferring kind variable %d from %u (declaration %u)\n"</span><span class="plain-syntax">,</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">vn</span><span class="plain-syntax">, </span><span class="identifier-syntax">other_k</span><span class="plain-syntax">, </span><a href="2-knd.html#SP12" class="function-link"><span class="function-syntax">Kinds::get_variable_stipulation</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">var_k</span><span class="plain-syntax">));</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">values_of_kind_variables</span><span class="plain-syntax">[</span><span class="identifier-syntax">vn</span><span class="plain-syntax">] = </span><span class="identifier-syntax">other_k</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">kind_variable_declaration</span><span class="plain-syntax"> *</span><span class="identifier-syntax">kvd</span><span class="plain-syntax"> = </span><span class="identifier-syntax">CREATE</span><span class="plain-syntax">(</span><span class="reserved-syntax">kind_variable_declaration</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">kvd</span><span class="plain-syntax">-></span><span class="element-syntax">kv_number</span><span class="plain-syntax"> = </span><span class="identifier-syntax">vn</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">kvd</span><span class="plain-syntax">-></span><span class="element-syntax">kv_value</span><span class="plain-syntax"> = </span><span class="identifier-syntax">other_k</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">kvd</span><span class="plain-syntax">-></span><span class="element-syntax">next</span><span class="plain-syntax"> = </span><span class="identifier-syntax">NULL</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="constant-syntax">ALWAYS_MATCH</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">case</span><span class="plain-syntax"> </span><span class="identifier-syntax">MATCH_KIND_VARIABLES_AS_VALUES:</span><span class="plain-syntax"> </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="constant-syntax">ALWAYS_MATCH</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> }</span>
|
|
</pre>
|
|
<ul class="endnotetexts"><li>This code is used in <a href="2-tlok.html#SP13_7">§13.7</a>.</li></ul>
|
|
<p class="commentary firstcommentary"><a id="SP13_7_2" class="paragraph-anchor"></a><b>§13.7.2. </b>Whereas this is what happens when matching just <span class="extract"><span class="extract-syntax">K</span></span>. On the inference pass,
|
|
we always make a match, which is legitimate because we know we are going to
|
|
make a value-checking pass later.
|
|
</p>
|
|
|
|
<p class="commentary"><span class="named-paragraph-container code-font"><span class="named-paragraph-defn">Act on an ordinary usage, where inference is not allowed</span><span class="named-paragraph-number">13.7.2</span></span><span class="comment-syntax"> =</span>
|
|
</p>
|
|
|
|
<pre class="displayed-code all-displayed-code code-font">
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">switch</span><span class="plain-syntax">(</span><span class="identifier-syntax">kind_checker_mode</span><span class="plain-syntax">) {</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">case</span><span class="plain-syntax"> </span><span class="identifier-syntax">MATCH_KIND_VARIABLES_INFERRING_VALUES:</span><span class="plain-syntax"> </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="constant-syntax">ALWAYS_MATCH</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">case</span><span class="plain-syntax"> </span><span class="identifier-syntax">MATCH_KIND_VARIABLES_AS_VALUES:</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">LOGIF</span><span class="plain-syntax">(</span><span class="identifier-syntax">KIND_CHECKING</span><span class="plain-syntax">, </span><span class="string-syntax">"Checking %u against kind variable %d (=%u)\n"</span><span class="plain-syntax">,</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">other_k</span><span class="plain-syntax">, </span><span class="identifier-syntax">vn</span><span class="plain-syntax">, </span><span class="identifier-syntax">values_of_kind_variables</span><span class="plain-syntax">[</span><span class="identifier-syntax">vn</span><span class="plain-syntax">]);</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><a href="2-tlok.html#SP13" class="function-link"><span class="function-syntax">Latticework::order_relation</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">other_k</span><span class="plain-syntax">,</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">values_of_kind_variables</span><span class="plain-syntax">[</span><span class="identifier-syntax">vn</span><span class="plain-syntax">], </span><span class="identifier-syntax">allow_casts</span><span class="plain-syntax">) == </span><span class="constant-syntax">NEVER_MATCH</span><span class="plain-syntax">)</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="constant-syntax">NEVER_MATCH</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">else</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="constant-syntax">ALWAYS_MATCH</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> }</span>
|
|
</pre>
|
|
<ul class="endnotetexts"><li>This code is used in <a href="2-tlok.html#SP13_7">§13.7</a>.</li></ul>
|
|
<p class="commentary firstcommentary"><a id="SP14" class="paragraph-anchor"></a><b>§14. </b>It's easy to confused when writing a type checker, especially with variables
|
|
getting in the way, so these logging functions can be helpful:
|
|
</p>
|
|
|
|
<pre class="displayed-code all-displayed-code code-font">
|
|
<span class="reserved-syntax">void</span><span class="plain-syntax"> </span><span class="function-syntax">Latticework::show_variables</span><span class="plain-syntax">(</span><span class="reserved-syntax">void</span><span class="plain-syntax">) {</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">LOG</span><span class="plain-syntax">(</span><span class="string-syntax">"Variables: "</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">for</span><span class="plain-syntax"> (</span><span class="reserved-syntax">int</span><span class="plain-syntax"> </span><span class="identifier-syntax">i</span><span class="plain-syntax">=1; </span><span class="identifier-syntax">i</span><span class="plain-syntax"><=26; </span><span class="identifier-syntax">i</span><span class="plain-syntax">++) {</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">kind</span><span class="plain-syntax"> *</span><span class="identifier-syntax">K</span><span class="plain-syntax"> = </span><span class="identifier-syntax">values_of_kind_variables</span><span class="plain-syntax">[</span><span class="identifier-syntax">i</span><span class="plain-syntax">];</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><span class="identifier-syntax">K</span><span class="plain-syntax"> == </span><span class="identifier-syntax">NULL</span><span class="plain-syntax">) </span><span class="reserved-syntax">continue</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">LOG</span><span class="plain-syntax">(</span><span class="string-syntax">"%c=%u "</span><span class="plain-syntax">, </span><span class="character-syntax">'A'</span><span class="plain-syntax">+</span><span class="identifier-syntax">i</span><span class="plain-syntax">-1, </span><span class="identifier-syntax">K</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> }</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">LOG</span><span class="plain-syntax">(</span><span class="string-syntax">"\n"</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax">}</span>
|
|
|
|
<span class="reserved-syntax">void</span><span class="plain-syntax"> </span><span class="function-syntax">Latticework::show_frame_variables</span><span class="plain-syntax">(</span><span class="reserved-syntax">void</span><span class="plain-syntax">) {</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">int</span><span class="plain-syntax"> </span><span class="identifier-syntax">shown</span><span class="plain-syntax"> = </span><span class="constant-syntax">0</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">for</span><span class="plain-syntax"> (</span><span class="reserved-syntax">int</span><span class="plain-syntax"> </span><span class="identifier-syntax">i</span><span class="plain-syntax">=1; </span><span class="identifier-syntax">i</span><span class="plain-syntax"><=26; </span><span class="identifier-syntax">i</span><span class="plain-syntax">++) {</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">kind</span><span class="plain-syntax"> *</span><span class="identifier-syntax">K</span><span class="plain-syntax"> = </span><a href="2-knd.html#SP23" class="function-link"><span class="function-syntax">Kinds::variable_from_context</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">i</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><span class="identifier-syntax">K</span><span class="plain-syntax">) {</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><span class="identifier-syntax">shown</span><span class="plain-syntax">++ == </span><span class="constant-syntax">0</span><span class="plain-syntax">) </span><span class="identifier-syntax">LOGIF</span><span class="plain-syntax">(</span><span class="identifier-syntax">MATCHING</span><span class="plain-syntax">, </span><span class="string-syntax">"Stack frame uses kind variables: "</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">LOGIF</span><span class="plain-syntax">(</span><span class="identifier-syntax">MATCHING</span><span class="plain-syntax">, </span><span class="string-syntax">"%c=%u "</span><span class="plain-syntax">, </span><span class="character-syntax">'A'</span><span class="plain-syntax">+</span><span class="identifier-syntax">i</span><span class="plain-syntax">-1, </span><span class="identifier-syntax">K</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> }</span>
|
|
<span class="plain-syntax"> }</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><span class="identifier-syntax">shown</span><span class="plain-syntax"> == </span><span class="constant-syntax">0</span><span class="plain-syntax">) </span><span class="identifier-syntax">LOGIF</span><span class="plain-syntax">(</span><span class="identifier-syntax">MATCHING</span><span class="plain-syntax">, </span><span class="string-syntax">"Stack frame sets no kind variables"</span><span class="plain-syntax">);</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">LOGIF</span><span class="plain-syntax">(</span><span class="identifier-syntax">MATCHING</span><span class="plain-syntax">, </span><span class="string-syntax">"\n"</span><span class="plain-syntax">);</span>
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<span class="plain-syntax">}</span>
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</pre>
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