 # tcswiki

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git clone https://a3nm.net/git/tcswiki/
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commit c1ce717b345884cf5b2045e0fbc3ebe556d01aa9
parent 9da7c83bc2bae0d1b98d544f5c96b6054a424cfc
Author: a3nm <>
Date:   Sun, 17 Jun 2018 01:40:57 +0200

Diffstat:
Constraint languages.page | 22++++++++++++++++++++--

1 file changed, 20 insertions(+), 2 deletions(-)
diff --git a/Constraint languages.page b/Constraint languages.page
@@ -2,4 +2,22 @@ All constraint languages mentioned here are expressed in [first-order logic]().

# Tuple-generating dependencies

-A **Tuple-Generating Dependency** (TGD) is a logical constraint $\tau$ of the form $\forall \mathbf{x} ~ \phi(x) \rightarrow \exists \mathbf{y} ~ \psi(\mathbf{x}, \mathbf{y})$, where $\phi$ and $\psi$ are [conjunctive queries](Queries#conjunctive-queries-cqs). Given a [database instance](Basic database terminology#instance) $I$, a **trigger** for $\tau$ in $I$ is a [homomorphism](Queries#conjunctive-queries-cqs) $h$ from $\phi$ to $I$. We say that the trigger $h$ is **active** if there is no homomorphism $h'$ from $\psi$ to $I$ that extends $h$, i.e., the domain of $h'$ is a superset of that of $h$ and $h(x) = h'(x)$ for all $x$ in the domain of $h$. We say that $I$ **satisfies** the TGD $\tau$ if there are no active triggers of $\tau$ on $I$.-
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+A **Tuple-Generating Dependency** (TGD) is a logical constraint $\tau$ of the form $\forall \mathbf{x} ~ \phi(x) \rightarrow \exists \mathbf{y} ~ \psi(\mathbf{x}, \mathbf{y})$, where $\phi$ and $\psi$ are [conjunctive queries](Queries#conjunctive-queries-cqs). Given a [database instance](Basic database terminology#instance) $I$, a **trigger** for $\tau$ in $I$ is a [homomorphism](Queries#conjunctive-queries-cqs) $h$ from $\phi$ to $I$. We say that the trigger $h$ is **active** if there is no homomorphism $h'$ from $\psi$ to $I$ that extends $h$, i.e., the domain of $h'$ is a superset of that of $h$ and $h(x) = h'(x)$ for all $x$ in the domain of $h$. We say that $I$ **satisfies** the TGD $\tau$ if there are no active triggers of $\tau$ on $I$.
+
+## Inclusion dependencies
+
+TODO, arity, unary
+
+# Equality-generating dependencies
+
+## Functional dependencies
+
+TODO, arity, unary
+
+## Key dependencies
+
+TODO
+
+## Foreign keys
+
+TODO+
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