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@ -332,8 +332,10 @@ $R^n$, is defined inductively. |
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R^0 \defas \emptyset, \quad\qquad R^1 \defas R, \quad\qquad R^{1 + n} \defas R \circ R^n. |
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R^0 \defas \emptyset, \quad\qquad R^1 \defas R, \quad\qquad R^{1 + n} \defas R \circ R^n. |
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\] |
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\] |
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Reflexive and transitive relations and their closures feature |
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prominently in the dynamic semantics of programming languages. |
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Homogeneous relations play a prominent role in the design and |
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operational understanding of programming languages. There are two |
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particular properties and associated closure operations of homogeneous |
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relations that reoccur throughout this dissertation. |
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\begin{definition} |
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\begin{definition} |
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A homogeneous relation $R \subseteq A \times A$ is said to be |
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A homogeneous relation $R \subseteq A \times A$ is said to be |
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