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Let's say I have a type class with n type parameters and I want any of them to uniquely determine all the other ones. Is it enough to make the dependencies form a cycle like in
class Foo a b c | a -> b, b -> c, c -> a
(linear) where there is a path from every parameter to every other one, or do I need to expand all possible paths like in
class Bar a b c | a -> b, a -> c, b -> a, b -> c, c -> a, c -> b
(quadratic)? Is there any observable difference between the two? And how about
class Baz a b c | a -> b c, b -> a c, c -> a b
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There are four types of functional dependencies Trivial, Non-Trivial, Multivalued and Transitive functional dependency.
Trivial functional dependency. Non-Trivial functional dependency. Multivalued functional dependency.
Functional dependency in DBMS, as the name suggests is a relationship between attributes of a table dependent on each other. Introduced by E. F. Codd, it helps in preventing data redundancy and gets to know about bad designs.
A Ward will always have the same number and name making the functional dependency go both ways.
Operationally, all of the above are equivalent:
First of all, a -> b c is quite literally the same thing as a -> b, a -> c.
Next, assume we got Foo a b c => (a, b, c). Say, we realize that a ~ A. We find the a -> b fundep and scan through instances to find b ~ B. Again we find the b -> c fundep and realize c ~ C. Voila we got (A, B, C).
If instead we had Bar a b c => (a, b, c) with a ~ A, we would've found a -> b, and b ~ B, however before finding b -> c, we would have found a -> c.
The only difference is which fundep arrows are used to infer the types. a -> b, b -> c and a -> b, a -> c can't produce different results.
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