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<!--Weave of 'Quasinumeric Relations' generated by Inweb-->
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<div class="breadcrumbs">
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<ul class="crumbs"><li><a href="../index.html">Home</a></li><li><a href="../compiler.html">Inform7 Modules</a></li><li><a href="index.html">core</a></li><li><a href="index.html#12">Chapter 12: Use of Propositions</a></li><li><b>Quasinumeric Relations</b></li></ul></div>
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<p class="purpose">To define the binary predicates corresponding to numerical comparisons.</p>
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<ul class="toc"><li><a href="12-qr.html#SP2">§2. Initial stock</a></li><li><a href="12-qr.html#SP3">§3. Second stock</a></li><li><a href="12-qr.html#SP4">§4. Typechecking</a></li><li><a href="12-qr.html#SP5">§5. Assertion</a></li><li><a href="12-qr.html#SP6">§6. Compilation</a></li><li><a href="12-qr.html#SP7">§7. Problem message text</a></li></ul><hr class="tocbar">
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<p class="commentary firstcommentary"><a id="SP1" class="paragraph-anchor"></a><b>§1. </b>The inequality relations \(<\), \(>\), \(\leq\), and \(\geq\), which can be
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applied not only to numbers but also to units (height, length and so on).
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</p>
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<p class="commentary">It might seem redundant to define both <span class="extract"><span class="extract-syntax">R_numerically_greater_than</span></span> (which makes the
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numerical test \(a>b\)) and also <span class="extract"><span class="extract-syntax">R_numerically_less_than</span></span> (which tests \(a<b\)). Why
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not define only one, and get the other meaning free as its reversal? The
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answer is that is more convenient not to, because it allows us to give both
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of them names.
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</p>
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<p class="commentary">There is no numerical equality relation \(=\) as such: numbers use the same
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equality BP as everything else.
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</p>
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<pre class="displayed-code all-displayed-code code-font">
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<span class="identifier-syntax">binary_predicate</span><span class="plain-syntax"> *</span><span class="identifier-syntax">R_numerically_greater_than</span><span class="plain-syntax"> = </span><span class="identifier-syntax">NULL</span><span class="plain-syntax">;</span>
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<span class="identifier-syntax">binary_predicate</span><span class="plain-syntax"> *</span><span class="identifier-syntax">R_numerically_less_than</span><span class="plain-syntax"> = </span><span class="identifier-syntax">NULL</span><span class="plain-syntax">;</span>
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<span class="identifier-syntax">binary_predicate</span><span class="plain-syntax"> *</span><span class="identifier-syntax">R_numerically_greater_than_or_equal_to</span><span class="plain-syntax"> = </span><span class="identifier-syntax">NULL</span><span class="plain-syntax">;</span>
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<span class="identifier-syntax">binary_predicate</span><span class="plain-syntax"> *</span><span class="identifier-syntax">R_numerically_less_than_or_equal_to</span><span class="plain-syntax"> = </span><span class="identifier-syntax">NULL</span><span class="plain-syntax">;</span>
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</pre>
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<p class="commentary firstcommentary"><a id="SP2" class="paragraph-anchor"></a><b>§2. Initial stock. </b>These relations are all hard-wired in.
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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">void</span><span class="plain-syntax"> </span><span class="function-syntax">Calculus::QuasinumericRelations::REL_create_initial_stock</span><span class="plain-syntax">(</span><span class="reserved-syntax">void</span><span class="plain-syntax">) {</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">bp_term_details</span><span class="plain-syntax"> </span><span class="identifier-syntax">number_term</span><span class="plain-syntax"> = </span><span class="identifier-syntax">BinaryPredicates::new_term</span><span class="plain-syntax">(</span><a href="13-kak.html#SP1" class="function-link"><span class="function-syntax">Kinds::Knowledge::as_subject</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">K_number</span><span class="plain-syntax">));</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">R_numerically_greater_than</span><span class="plain-syntax"> =</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">BinaryPredicates::make_pair</span><span class="plain-syntax">(</span><span class="identifier-syntax">QUASINUMERIC_KBP</span><span class="plain-syntax">,</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">number_term</span><span class="plain-syntax">, </span><span class="identifier-syntax">number_term</span><span class="plain-syntax">,</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">I</span><span class="string-syntax">"greater-than"</span><span class="plain-syntax">, </span><span class="identifier-syntax">NULL</span><span class="plain-syntax">, </span><span class="identifier-syntax">NULL</span><span class="plain-syntax">, </span><span class="identifier-syntax">NULL</span><span class="plain-syntax">, </span><a href="12-is.html#SP3" class="function-link"><span class="function-syntax">Calculus::Schemas::new</span></a><span class="plain-syntax">(</span><span class="string-syntax">"*1 > *2"</span><span class="plain-syntax">),</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">PreformUtilities::wording</span><span class="plain-syntax">(</span><span class="function-syntax"><relation-names></span><span class="plain-syntax">, </span><span class="constant-syntax">GT_RELATION_NAME</span><span class="plain-syntax">));</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">R_numerically_less_than</span><span class="plain-syntax"> =</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">BinaryPredicates::make_pair</span><span class="plain-syntax">(</span><span class="identifier-syntax">QUASINUMERIC_KBP</span><span class="plain-syntax">,</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">number_term</span><span class="plain-syntax">, </span><span class="identifier-syntax">number_term</span><span class="plain-syntax">,</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">I</span><span class="string-syntax">"less-than"</span><span class="plain-syntax">, </span><span class="identifier-syntax">NULL</span><span class="plain-syntax">, </span><span class="identifier-syntax">NULL</span><span class="plain-syntax">, </span><span class="identifier-syntax">NULL</span><span class="plain-syntax">, </span><a href="12-is.html#SP3" class="function-link"><span class="function-syntax">Calculus::Schemas::new</span></a><span class="plain-syntax">(</span><span class="string-syntax">"*1 < *2"</span><span class="plain-syntax">),</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">PreformUtilities::wording</span><span class="plain-syntax">(</span><span class="function-syntax"><relation-names></span><span class="plain-syntax">, </span><span class="constant-syntax">LT_RELATION_NAME</span><span class="plain-syntax">));</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">R_numerically_greater_than_or_equal_to</span><span class="plain-syntax"> =</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">BinaryPredicates::make_pair</span><span class="plain-syntax">(</span><span class="identifier-syntax">QUASINUMERIC_KBP</span><span class="plain-syntax">,</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">number_term</span><span class="plain-syntax">, </span><span class="identifier-syntax">number_term</span><span class="plain-syntax">,</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">I</span><span class="string-syntax">"at-least"</span><span class="plain-syntax">, </span><span class="identifier-syntax">NULL</span><span class="plain-syntax">, </span><span class="identifier-syntax">NULL</span><span class="plain-syntax">, </span><span class="identifier-syntax">NULL</span><span class="plain-syntax">, </span><a href="12-is.html#SP3" class="function-link"><span class="function-syntax">Calculus::Schemas::new</span></a><span class="plain-syntax">(</span><span class="string-syntax">"*1 >= *2"</span><span class="plain-syntax">),</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">PreformUtilities::wording</span><span class="plain-syntax">(</span><span class="function-syntax"><relation-names></span><span class="plain-syntax">, </span><span class="constant-syntax">GE_RELATION_NAME</span><span class="plain-syntax">));</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">R_numerically_less_than_or_equal_to</span><span class="plain-syntax"> =</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">BinaryPredicates::make_pair</span><span class="plain-syntax">(</span><span class="identifier-syntax">QUASINUMERIC_KBP</span><span class="plain-syntax">,</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">number_term</span><span class="plain-syntax">, </span><span class="identifier-syntax">number_term</span><span class="plain-syntax">,</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">I</span><span class="string-syntax">"at-most"</span><span class="plain-syntax">, </span><span class="identifier-syntax">NULL</span><span class="plain-syntax">, </span><span class="identifier-syntax">NULL</span><span class="plain-syntax">, </span><span class="identifier-syntax">NULL</span><span class="plain-syntax">, </span><a href="12-is.html#SP3" class="function-link"><span class="function-syntax">Calculus::Schemas::new</span></a><span class="plain-syntax">(</span><span class="string-syntax">"*1 <= *2"</span><span class="plain-syntax">),</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">PreformUtilities::wording</span><span class="plain-syntax">(</span><span class="function-syntax"><relation-names></span><span class="plain-syntax">, </span><span class="constant-syntax">LE_RELATION_NAME</span><span class="plain-syntax">));</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">BinaryPredicates::set_index_details</span><span class="plain-syntax">(</span><span class="identifier-syntax">R_numerically_greater_than</span><span class="plain-syntax">,</span>
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<span class="plain-syntax"> </span><span class="string-syntax">"arithmetic value"</span><span class="plain-syntax">, </span><span class="string-syntax">"arithmetic value"</span><span class="plain-syntax">);</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">BinaryPredicates::set_index_details</span><span class="plain-syntax">(</span><span class="identifier-syntax">R_numerically_less_than</span><span class="plain-syntax">,</span>
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<span class="plain-syntax"> </span><span class="string-syntax">"arithmetic value"</span><span class="plain-syntax">, </span><span class="string-syntax">"arithmetic value"</span><span class="plain-syntax">);</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">BinaryPredicates::set_index_details</span><span class="plain-syntax">(</span><span class="identifier-syntax">R_numerically_greater_than_or_equal_to</span><span class="plain-syntax">,</span>
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<span class="plain-syntax"> </span><span class="string-syntax">"arithmetic value"</span><span class="plain-syntax">, </span><span class="string-syntax">"arithmetic value"</span><span class="plain-syntax">);</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">BinaryPredicates::set_index_details</span><span class="plain-syntax">(</span><span class="identifier-syntax">R_numerically_less_than_or_equal_to</span><span class="plain-syntax">,</span>
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<span class="plain-syntax"> </span><span class="string-syntax">"arithmetic value"</span><span class="plain-syntax">, </span><span class="string-syntax">"arithmetic value"</span><span class="plain-syntax">);</span>
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<span class="plain-syntax">}</span>
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</pre>
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<p class="commentary firstcommentary"><a id="SP3" class="paragraph-anchor"></a><b>§3. Second stock. </b>There is none — this is a family of relations which is all built in.
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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">void</span><span class="plain-syntax"> </span><span class="function-syntax">Calculus::QuasinumericRelations::REL_create_second_stock</span><span class="plain-syntax">(</span><span class="reserved-syntax">void</span><span class="plain-syntax">) {</span>
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<span class="plain-syntax">}</span>
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</pre>
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<p class="commentary firstcommentary"><a id="SP4" class="paragraph-anchor"></a><b>§4. Typechecking. </b></p>
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<pre class="displayed-code all-displayed-code code-font">
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<span class="reserved-syntax">int</span><span class="plain-syntax"> </span><span class="function-syntax">Calculus::QuasinumericRelations::REL_typecheck</span><span class="plain-syntax">(</span><span class="identifier-syntax">binary_predicate</span><span class="plain-syntax"> *</span><span class="identifier-syntax">bp</span><span class="plain-syntax">,</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">kind</span><span class="plain-syntax"> **</span><span class="identifier-syntax">kinds_of_terms</span><span class="plain-syntax">, </span><span class="identifier-syntax">kind</span><span class="plain-syntax"> **</span><span class="identifier-syntax">kinds_required</span><span class="plain-syntax">, </span><span class="reserved-syntax">tc_problem_kit</span><span class="plain-syntax"> *</span><span class="identifier-syntax">tck</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><span class="identifier-syntax">Kinds::compatible</span><span class="plain-syntax">(</span><span class="identifier-syntax">kinds_of_terms</span><span class="plain-syntax">[0], </span><span class="identifier-syntax">kinds_of_terms</span><span class="plain-syntax">[1]) == </span><span class="identifier-syntax">NEVER_MATCH</span><span class="plain-syntax">) &&</span>
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<span class="plain-syntax"> (</span><span class="identifier-syntax">Kinds::compatible</span><span class="plain-syntax">(</span><span class="identifier-syntax">kinds_of_terms</span><span class="plain-syntax">[1], </span><span class="identifier-syntax">kinds_of_terms</span><span class="plain-syntax">[0]) == </span><span class="identifier-syntax">NEVER_MATCH</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><span class="identifier-syntax">tck</span><span class="plain-syntax">-></span><span class="element-syntax">log_to_I6_text</span><span class="plain-syntax">)</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">LOG</span><span class="plain-syntax">(</span><span class="string-syntax">"Unable to apply inequality of %u and %u\n"</span><span class="plain-syntax">, </span><span class="identifier-syntax">kinds_of_terms</span><span class="plain-syntax">[0], </span><span class="identifier-syntax">kinds_of_terms</span><span class="plain-syntax">[1]);</span>
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<span class="plain-syntax"> </span><a href="2-sq.html#SP3" class="function-link"><span class="function-syntax">Problems::quote_kind</span></a><span class="plain-syntax">(4, </span><span class="identifier-syntax">kinds_of_terms</span><span class="plain-syntax">[0]);</span>
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<span class="plain-syntax"> </span><a href="2-sq.html#SP3" class="function-link"><span class="function-syntax">Problems::quote_kind</span></a><span class="plain-syntax">(5, </span><span class="identifier-syntax">kinds_of_terms</span><span class="plain-syntax">[1]);</span>
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<span class="plain-syntax"> </span><a href="2-si.html#SP6" class="function-link"><span class="function-syntax">StandardProblems::tcp_problem</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">_p_</span><span class="plain-syntax">(</span><span class="identifier-syntax">PM_InequalityFailed</span><span class="plain-syntax">), </span><span class="identifier-syntax">tck</span><span class="plain-syntax">,</span>
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<span class="plain-syntax"> </span><span class="string-syntax">"that would mean comparing two kinds of value which cannot mix - "</span>
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<span class="plain-syntax"> </span><span class="string-syntax">"%4 and %5 - so this must be incorrect."</span><span class="plain-syntax">);</span>
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<span class="plain-syntax"> </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="identifier-syntax">NEVER_MATCH</span><span class="plain-syntax">;</span>
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<span class="plain-syntax"> }</span>
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<span class="plain-syntax"> </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="identifier-syntax">ALWAYS_MATCH</span><span class="plain-syntax">;</span>
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<span class="plain-syntax">}</span>
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</pre>
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<p class="commentary firstcommentary"><a id="SP5" class="paragraph-anchor"></a><b>§5. Assertion. </b>These relations cannot be asserted.
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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">int</span><span class="plain-syntax"> </span><span class="function-syntax">Calculus::QuasinumericRelations::REL_assert</span><span class="plain-syntax">(</span><span class="identifier-syntax">binary_predicate</span><span class="plain-syntax"> *</span><span class="identifier-syntax">bp</span><span class="plain-syntax">,</span>
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<span class="plain-syntax"> </span><span class="reserved-syntax">inference_subject</span><span class="plain-syntax"> *</span><span class="identifier-syntax">infs0</span><span class="plain-syntax">, </span><span class="identifier-syntax">parse_node</span><span class="plain-syntax"> *</span><span class="identifier-syntax">spec0</span><span class="plain-syntax">,</span>
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<span class="plain-syntax"> </span><span class="reserved-syntax">inference_subject</span><span class="plain-syntax"> *</span><span class="identifier-syntax">infs1</span><span class="plain-syntax">, </span><span class="identifier-syntax">parse_node</span><span class="plain-syntax"> *</span><span class="identifier-syntax">spec1</span><span class="plain-syntax">) {</span>
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<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>
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<span class="plain-syntax">}</span>
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</pre>
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<p class="commentary firstcommentary"><a id="SP6" class="paragraph-anchor"></a><b>§6. Compilation. </b>For integer arithmetic, we need do nothing special: these relations can be
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compiled from their schemas. But real numbers have to be handled by a function
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call in I6.
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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">int</span><span class="plain-syntax"> </span><span class="function-syntax">Calculus::QuasinumericRelations::REL_compile</span><span class="plain-syntax">(</span><span class="reserved-syntax">int</span><span class="plain-syntax"> </span><span class="identifier-syntax">task</span><span class="plain-syntax">, </span><span class="identifier-syntax">binary_predicate</span><span class="plain-syntax"> *</span><span class="identifier-syntax">bp</span><span class="plain-syntax">, </span><span class="reserved-syntax">annotated_i6_schema</span><span class="plain-syntax"> *</span><span class="identifier-syntax">asch</span><span class="plain-syntax">) {</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">kind</span><span class="plain-syntax"> *</span><span class="identifier-syntax">st</span><span class="plain-syntax">[2];</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">st</span><span class="plain-syntax">[0] = </span><a href="12-cad.html#SP6" class="function-link"><span class="function-syntax">Calculus::Deferrals::Cinders::kind_of_value_of_term</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">asch</span><span class="plain-syntax">-></span><span class="element-syntax">pt0</span><span class="plain-syntax">);</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">st</span><span class="plain-syntax">[1] = </span><a href="12-cad.html#SP6" class="function-link"><span class="function-syntax">Calculus::Deferrals::Cinders::kind_of_value_of_term</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">asch</span><span class="plain-syntax">-></span><span class="element-syntax">pt1</span><span class="plain-syntax">);</span>
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<span class="plain-syntax"> </span><span class="reserved-syntax">switch</span><span class="plain-syntax"> (</span><span class="identifier-syntax">task</span><span class="plain-syntax">) {</span>
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<span class="plain-syntax"> </span><span class="reserved-syntax">case</span><span class="plain-syntax"> </span><span class="identifier-syntax">TEST_ATOM_TASK:</span>
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<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> ((</span><span class="identifier-syntax">st</span><span class="plain-syntax">[0]) && (</span><span class="identifier-syntax">st</span><span class="plain-syntax">[1])) {</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">text_stream</span><span class="plain-syntax"> *</span><span class="identifier-syntax">cr</span><span class="plain-syntax"> = </span><span class="identifier-syntax">NULL</span><span class="plain-syntax">;</span>
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<span class="plain-syntax"> </span><span class="reserved-syntax">int</span><span class="plain-syntax"> </span><span class="identifier-syntax">promote_left</span><span class="plain-syntax"> = </span><span class="identifier-syntax">FALSE</span><span class="plain-syntax">, </span><span class="identifier-syntax">promote_right</span><span class="plain-syntax"> = </span><span class="identifier-syntax">FALSE</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><span class="identifier-syntax">Kinds::FloatingPoint::uses_floating_point</span><span class="plain-syntax">(</span><span class="identifier-syntax">st</span><span class="plain-syntax">[0])) ||</span>
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<span class="plain-syntax"> (</span><span class="identifier-syntax">Kinds::FloatingPoint::uses_floating_point</span><span class="plain-syntax">(</span><span class="identifier-syntax">st</span><span class="plain-syntax">[1]))) {</span>
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<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><span class="identifier-syntax">Kinds::FloatingPoint::uses_floating_point</span><span class="plain-syntax">(</span><span class="identifier-syntax">st</span><span class="plain-syntax">[0]) == </span><span class="identifier-syntax">FALSE</span><span class="plain-syntax">)</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">promote_left</span><span class="plain-syntax"> = </span><span class="identifier-syntax">TRUE</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><span class="identifier-syntax">Kinds::FloatingPoint::uses_floating_point</span><span class="plain-syntax">(</span><span class="identifier-syntax">st</span><span class="plain-syntax">[1]) == </span><span class="identifier-syntax">FALSE</span><span class="plain-syntax">)</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">promote_right</span><span class="plain-syntax"> = </span><span class="identifier-syntax">TRUE</span><span class="plain-syntax">;</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">cr</span><span class="plain-syntax"> = </span><span class="identifier-syntax">Kinds::Behaviour::get_comparison_routine</span><span class="plain-syntax">(</span><span class="identifier-syntax">K_real_number</span><span class="plain-syntax">);</span>
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<span class="plain-syntax"> } </span><span class="reserved-syntax">else</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">cr</span><span class="plain-syntax"> = </span><span class="identifier-syntax">Kinds::Behaviour::get_comparison_routine</span><span class="plain-syntax">(</span><span class="identifier-syntax">st</span><span class="plain-syntax">[0]);</span>
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<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> ((</span><span class="identifier-syntax">Str::len</span><span class="plain-syntax">(</span><span class="identifier-syntax">cr</span><span class="plain-syntax">) == </span><span class="constant-syntax">0</span><span class="plain-syntax">) || (</span><span class="identifier-syntax">Str::eq_wide_string</span><span class="plain-syntax">(</span><span class="identifier-syntax">cr</span><span class="plain-syntax">, </span><span class="identifier-syntax">L</span><span class="string-syntax">"signed"</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>
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<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><span class="identifier-syntax">promote_left</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><span class="identifier-syntax">bp</span><span class="plain-syntax"> == </span><span class="identifier-syntax">R_numerically_greater_than</span><span class="plain-syntax">)</span>
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<span class="plain-syntax"> </span><a href="12-is.html#SP3_1" class="function-link"><span class="function-syntax">Calculus::Schemas::modify</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">asch</span><span class="plain-syntax">-></span><span class="element-syntax">schema</span><span class="plain-syntax">, </span><span class="string-syntax">"*_2(NUMBER_TY_to_REAL_NUMBER_TY(*1), *2) > 0"</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><span class="identifier-syntax">bp</span><span class="plain-syntax"> == </span><span class="identifier-syntax">R_numerically_less_than</span><span class="plain-syntax">)</span>
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<span class="plain-syntax"> </span><a href="12-is.html#SP3_1" class="function-link"><span class="function-syntax">Calculus::Schemas::modify</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">asch</span><span class="plain-syntax">-></span><span class="element-syntax">schema</span><span class="plain-syntax">, </span><span class="string-syntax">"*_2(NUMBER_TY_to_REAL_NUMBER_TY(*1), *2) < 0"</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><span class="identifier-syntax">bp</span><span class="plain-syntax"> == </span><span class="identifier-syntax">R_numerically_greater_than_or_equal_to</span><span class="plain-syntax">)</span>
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<span class="plain-syntax"> </span><a href="12-is.html#SP3_1" class="function-link"><span class="function-syntax">Calculus::Schemas::modify</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">asch</span><span class="plain-syntax">-></span><span class="element-syntax">schema</span><span class="plain-syntax">, </span><span class="string-syntax">"*_2(NUMBER_TY_to_REAL_NUMBER_TY(*1), *2) >= 0"</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><span class="identifier-syntax">bp</span><span class="plain-syntax"> == </span><span class="identifier-syntax">R_numerically_less_than_or_equal_to</span><span class="plain-syntax">)</span>
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<span class="plain-syntax"> </span><a href="12-is.html#SP3_1" class="function-link"><span class="function-syntax">Calculus::Schemas::modify</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">asch</span><span class="plain-syntax">-></span><span class="element-syntax">schema</span><span class="plain-syntax">, </span><span class="string-syntax">"*_2(NUMBER_TY_to_REAL_NUMBER_TY(*1), *2) <= 0"</span><span class="plain-syntax">);</span>
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|
<span class="plain-syntax"> } </span><span class="reserved-syntax">else</span><span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><span class="identifier-syntax">promote_right</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">bp</span><span class="plain-syntax"> == </span><span class="identifier-syntax">R_numerically_greater_than</span><span class="plain-syntax">)</span>
|
|
<span class="plain-syntax"> </span><a href="12-is.html#SP3_1" class="function-link"><span class="function-syntax">Calculus::Schemas::modify</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">asch</span><span class="plain-syntax">-></span><span class="element-syntax">schema</span><span class="plain-syntax">, </span><span class="string-syntax">"*_1(*1, NUMBER_TY_to_REAL_NUMBER_TY(*2)) > 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">bp</span><span class="plain-syntax"> == </span><span class="identifier-syntax">R_numerically_less_than</span><span class="plain-syntax">)</span>
|
|
<span class="plain-syntax"> </span><a href="12-is.html#SP3_1" class="function-link"><span class="function-syntax">Calculus::Schemas::modify</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">asch</span><span class="plain-syntax">-></span><span class="element-syntax">schema</span><span class="plain-syntax">, </span><span class="string-syntax">"*_1(*1, NUMBER_TY_to_REAL_NUMBER_TY(*2)) < 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">bp</span><span class="plain-syntax"> == </span><span class="identifier-syntax">R_numerically_greater_than_or_equal_to</span><span class="plain-syntax">)</span>
|
|
<span class="plain-syntax"> </span><a href="12-is.html#SP3_1" class="function-link"><span class="function-syntax">Calculus::Schemas::modify</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">asch</span><span class="plain-syntax">-></span><span class="element-syntax">schema</span><span class="plain-syntax">, </span><span class="string-syntax">"*_1(*1, NUMBER_TY_to_REAL_NUMBER_TY(*2)) >= 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">bp</span><span class="plain-syntax"> == </span><span class="identifier-syntax">R_numerically_less_than_or_equal_to</span><span class="plain-syntax">)</span>
|
|
<span class="plain-syntax"> </span><a href="12-is.html#SP3_1" class="function-link"><span class="function-syntax">Calculus::Schemas::modify</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">asch</span><span class="plain-syntax">-></span><span class="element-syntax">schema</span><span class="plain-syntax">, </span><span class="string-syntax">"*_1(*1, NUMBER_TY_to_REAL_NUMBER_TY(*2)) <= 0"</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">if</span><span class="plain-syntax"> (</span><span class="identifier-syntax">bp</span><span class="plain-syntax"> == </span><span class="identifier-syntax">R_numerically_greater_than</span><span class="plain-syntax">)</span>
|
|
<span class="plain-syntax"> </span><a href="12-is.html#SP3_1" class="function-link"><span class="function-syntax">Calculus::Schemas::modify</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">asch</span><span class="plain-syntax">-></span><span class="element-syntax">schema</span><span class="plain-syntax">, </span><span class="string-syntax">"*_1(*1, *2) > 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">bp</span><span class="plain-syntax"> == </span><span class="identifier-syntax">R_numerically_less_than</span><span class="plain-syntax">)</span>
|
|
<span class="plain-syntax"> </span><a href="12-is.html#SP3_1" class="function-link"><span class="function-syntax">Calculus::Schemas::modify</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">asch</span><span class="plain-syntax">-></span><span class="element-syntax">schema</span><span class="plain-syntax">, </span><span class="string-syntax">"*_1(*1, *2) < 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">bp</span><span class="plain-syntax"> == </span><span class="identifier-syntax">R_numerically_greater_than_or_equal_to</span><span class="plain-syntax">)</span>
|
|
<span class="plain-syntax"> </span><a href="12-is.html#SP3_1" class="function-link"><span class="function-syntax">Calculus::Schemas::modify</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">asch</span><span class="plain-syntax">-></span><span class="element-syntax">schema</span><span class="plain-syntax">, </span><span class="string-syntax">"*_1(*1, *2) >= 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">bp</span><span class="plain-syntax"> == </span><span class="identifier-syntax">R_numerically_less_than_or_equal_to</span><span class="plain-syntax">)</span>
|
|
<span class="plain-syntax"> </span><a href="12-is.html#SP3_1" class="function-link"><span class="function-syntax">Calculus::Schemas::modify</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">asch</span><span class="plain-syntax">-></span><span class="element-syntax">schema</span><span class="plain-syntax">, </span><span class="string-syntax">"*_1(*1, *2) <= 0"</span><span class="plain-syntax">);</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">if</span><span class="plain-syntax"> (</span><span class="identifier-syntax">problem_count</span><span class="plain-syntax"> == </span><span class="constant-syntax">0</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">"$0 and $0; %u and %u\n"</span><span class="plain-syntax">, &(</span><span class="identifier-syntax">asch</span><span class="plain-syntax">-></span><span class="element-syntax">pt0</span><span class="plain-syntax">), &(</span><span class="identifier-syntax">asch</span><span class="plain-syntax">-></span><span class="element-syntax">pt1</span><span class="plain-syntax">), </span><span class="identifier-syntax">st</span><span class="plain-syntax">[0], </span><span class="identifier-syntax">st</span><span class="plain-syntax">[1]);</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">internal_error</span><span class="plain-syntax">(</span><span class="string-syntax">"null kind in equality test"</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="identifier-syntax">TRUE</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="identifier-syntax">FALSE</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax">}</span>
|
|
</pre>
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<p class="commentary firstcommentary"><a id="SP7" class="paragraph-anchor"></a><b>§7. Problem message text. </b></p>
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<pre class="displayed-code all-displayed-code code-font">
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<span class="reserved-syntax">int</span><span class="plain-syntax"> </span><span class="function-syntax">Calculus::QuasinumericRelations::REL_describe_for_problems</span><span class="plain-syntax">(</span><span class="identifier-syntax">OUTPUT_STREAM</span><span class="plain-syntax">, </span><span class="identifier-syntax">binary_predicate</span><span class="plain-syntax"> *</span><span class="identifier-syntax">bp</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>
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</pre>
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