Tropical algebra overloading: Difference between revisions
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5 ⊗ 8 ⊕ 5 ⊗ 7 = 13
5 ⊗ (8 ⊕ 7) == 5 ⊗ 8 ⊕ 5 ⊗ 7 = true
</pre>
=={{header|Phix}}==
Phix does not support operator overloading. I trust max is self-evident, sq_add and sq_mul are existing wrappers to the + and * operators, admittedly with extra (sequence) functionality we don't really need here, but they'll do just fine.
<!--<lang Phix>(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #7060A8;">requires</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"1.0.1"</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- (minor/backportable bugfix rqd to handling of -inf in printf[1])</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">tropicalAdd</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">max</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">tropicalMul</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sq_add</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">tropicalExp</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sq_mul</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">inf</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1e300</span><span style="color: #0000FF;">*</span><span style="color: #000000;">1e300</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"tropicalMul(2,-2) = %g\n"</span><span style="color: #0000FF;">,</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">tropicalMul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)})</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"tropicalAdd(-0.001,-inf) = %g\n"</span><span style="color: #0000FF;">,</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">tropicalAdd</span><span style="color: #0000FF;">(-</span><span style="color: #000000;">0.001</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">inf</span><span style="color: #0000FF;">)})</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"tropicalMul(0,-inf) = %g\n"</span><span style="color: #0000FF;">,</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">tropicalMul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">inf</span><span style="color: #0000FF;">)})</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"tropicalAdd(1.5,-1) = %g\n"</span><span style="color: #0000FF;">,</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">tropicalAdd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1.5</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)})</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"tropicalMul(-0.5,0) = %g\n"</span><span style="color: #0000FF;">,</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">tropicalMul</span><span style="color: #0000FF;">(-</span><span style="color: #000000;">0.5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)})</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"tropicalExp(5,7) = %g\n"</span><span style="color: #0000FF;">,</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">tropicalExp</span><span style="color: #0000FF;">(</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">7</span><span style="color: #0000FF;">)})</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"tropicalMul(5,tropicalAdd(8,7)) = %g\n"</span><span style="color: #0000FF;">,</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">tropicalMul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">tropicalAdd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">8</span><span style="color: #0000FF;">,</span><span style="color: #000000;">7</span><span style="color: #0000FF;">))})</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"tropicalAdd(tropicalMul(5,8),tropicalMul(5,7)) = %g\n"</span><span style="color: #0000FF;">,</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">tropicalAdd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">tropicalMul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">8</span><span style="color: #0000FF;">),</span><span style="color: #000000;">tropicalMul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">7</span><span style="color: #0000FF;">))})</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"tropicalMul(5,tropicalAdd(8,7)) == tropicalAdd(tropicalMul(5,8),tropicalMul(5,7)) = %t\n"</span><span style="color: #0000FF;">,</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">tropicalMul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">tropicalAdd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">8</span><span style="color: #0000FF;">,</span><span style="color: #000000;">7</span><span style="color: #0000FF;">))</span> <span style="color: #0000FF;">==</span> <span style="color: #000000;">tropicalAdd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">tropicalMul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">8</span><span style="color: #0000FF;">),</span><span style="color: #000000;">tropicalMul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">7</span><span style="color: #0000FF;">))})</span>
<!--</lang>-->
<small>[1]This task exposed a couple of "and o!=inf" that needed to become "and o!=inf and o!=-inf" in builtins\VM\pprintfN.e - thanks!</small>
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<pre>
tropicalMul(2,-2) = 0
tropicalAdd(-0.001,-inf) = -0.001
tropicalMul(0,-inf) = -inf
tropicalAdd(1.5,-1) = 1.5
tropicalMul(-0.5,0) = -0.5
tropicalExp(5,7) = 35
tropicalMul(5,tropicalAdd(8,7)) = 13
tropicalAdd(tropicalMul(5,8),tropicalMul(5,7)) = 13
tropicalMul(5,tropicalAdd(8,7)) == tropicalAdd(tropicalMul(5,8),tropicalMul(5,7)) = true
</pre>
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