Add a sidenote about land and lor.
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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@ -263,8 +263,21 @@ ours, the analog to `min` is "greatest lower bound", or "the largest value
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that's smaller than both inputs". Such a function is denoted as \\(a\\sqcap b\\).
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that's smaller than both inputs". Such a function is denoted as \\(a\\sqcap b\\).
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As for what it means, where \\(s_1 \\sqcup s_2\\) means "combine two signs where
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As for what it means, where \\(s_1 \\sqcup s_2\\) means "combine two signs where
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you don't know which one will be used" (like in an `if`/`else`),
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you don't know which one will be used" (like in an `if`/`else`),
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\\(s_1 \\sqcap s_2\\) means "combine two signs where you know both of
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\\(s_1 \\sqcap s_2\\) means "combine two signs where you know
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them to be true". For example, \\((+\ \\sqcap\ ?)\ =\ +\\), because a variable
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{{< sidenote "right" "or-join-note" "both of them to be true" -7 >}}
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If you're familiar with <a href="https://en.wikipedia.org/wiki/Boolean_algebra">
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Boolean algebra</a>, this might look a little bit familiar to you. In fact,
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the symbol for "and" on booleans is \(\land\). Similarly, the symbol
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for "or" is \(\lor\). So, \(s_1 \sqcup s_2\) means "the sign is \(s_1\) or \(s_2\)",
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or "(the sign is \(s_1\)) \(\lor\) (the sign is \(s_2\))". Similarly,
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\(s_1 \sqcap s_2\) means "(the sign is \(s_1\)) \(\land\) (the sign is \(s_2\))".
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Don't these symbols look similar?<br>
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<br>
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In fact, booleans with \((\lor)\) and \((\land)\) satisfy the semilattice
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laws we've been discussing, and together form a lattice (to which I'm building
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to in the main body of the text). The same is true for the set union and
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intersection operations, \((\cup)\) and \((\cap)\).
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{{< /sidenote >}}". For example, \\((+\ \\sqcap\ ?)\ =\ +\\), because a variable
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that's both "any sign" and "positive" must be positive.
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that's both "any sign" and "positive" must be positive.
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There's just one hiccup: what's the greatest lower bound of `+` and `-`?
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There's just one hiccup: what's the greatest lower bound of `+` and `-`?
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