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cartesianproducts [2015/04/21 17:43] wikiadmin |
cartesianproducts [2015/04/21 17:44] wikiadmin |
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The constraints on the patterns are: | The constraints on the patterns are: | ||
- | \[p_1 = ENode \] | + | \begin{equation*}p_1 = ENode \end{equation*} |
- | \[p_2 = ELeaf \] | + | \begin{equation*}p_2 = ELeaf \end{equation*} |
Completeness is expressed as $p_1 \cup p_2 \supseteq Tree$ and disjointness as $p_1 \cap p_2 = \emptyset$. Both are trivial with our axioms. | Completeness is expressed as $p_1 \cup p_2 \supseteq Tree$ and disjointness as $p_1 \cap p_2 = \emptyset$. Both are trivial with our axioms. | ||
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Here we have two positions ("annoted" [a] and [b]). The types A and B are both Tree. We hence have $s = Tree \times Tree$. | Here we have two positions ("annoted" [a] and [b]). The types A and B are both Tree. We hence have $s = Tree \times Tree$. | ||
The constraints on the patterns are: | The constraints on the patterns are: | ||
- | \[p_1 = EvenNode \times OddNode \] | + | \begin{equation*}p_1 = EvenNode \times OddNode \end{equation*} |
- | \[p_2 = EvenNode \times EvenNode \] | + | \begin{equation*}_2 = EvenNode \times EvenNode \end{equation*} |
- | \[p_3 = OddNode \times Tree \] | + | \begin{equation*}p_3 = OddNode \times Tree \end{equation*} |
- | \[p_4 = ELeaf \times Tree \] | + | \begin{equation*}p_4 = ELeaf \times Tree \end{equation*} |
(recall that when a position is not present in a pattern we use its general type) | (recall that when a position is not present in a pattern we use its general type) | ||