Functional dependency vectors

Creates a set of functional dependencies with length-one dependants.

Usage

functional_dependency(FDs, attrs_order, unique = TRUE)

Arguments

FDs

a list of functional dependencies, in the form of two-elements lists: the first element contains a character vector of all attributes in the determinant set, and the second element contains the single dependent attribute (dependant).

attrs_order

a character vector, giving the names of all attributes. These need not be present in FDs, but all attributes in FDs must be present in attrs.

unique

a logical, TRUE by default, for whether to remove duplicate dependencies.

Value

A functional_dependency object, containing the list given in FDs, with attrs_order an attribute of the same name. Functional dependencies are returned with their determinant sets sorted according to the attribute order in attrs. Any duplicates found after sorting are removed.

Details

When several sets of functional dependencies are concatenated, their attrs_order attributes are merged, so as to preserve all of the original attribute orders, if possible. If this is not possible, because the orderings disagree, then the returned value of the attrs_order attribute is their union instead.

See also

detset, dependant, and attrs_order for extracting parts of the information in a functional_dependency; rename_attrs for renaming the attributes in attrs_order.

Examples

fds <- functional_dependency(
  list(list(c("a", "b"), "c"), list(character(), "d")),
  attrs_order = c("a", "b", "c", "d")
)
print(fds)
#> 2 functional dependencies
#> 4 attributes: a, b, c, d
#> a, b -> c
#>      -> d
detset(fds)
#> [[1]]
#> [1] "a" "b"
#> 
#> [[2]]
#> character(0)
#> 
dependant(fds)
#> [1] "c" "d"
attrs_order(fds)
#> [1] "a" "b" "c" "d"

# vector operations
fds2 <- functional_dependency(list(list("e", "a")), c("a", "e"))
c(fds, fds2) # attrs_order attributes are merged
#> 3 functional dependencies
#> 5 attributes: a, b, c, d, e
#> a, b -> c
#>      -> d
#>    e -> a
unique(c(fds, fds))
#> 2 functional dependencies
#> 4 attributes: a, b, c, d
#> a, b -> c
#>      -> d

# subsetting
fds[1]
#> 1 functional dependency
#> 4 attributes: a, b, c, d
#> a, b -> c
fds[c(1, 2, 1)]
#> 3 functional dependencies
#> 4 attributes: a, b, c, d
#> a, b -> c
#>      -> d
#> a, b -> c
stopifnot(identical(fds[[2]], fds[2]))

# reassignment
fds3 <- fds
fds3[2] <- functional_dependency(list(list("a", "c")), attrs_order(fds3))
print(fds3)
#> 2 functional dependencies
#> 4 attributes: a, b, c, d
#> a, b -> c
#>    a -> c
detset(fds3)[[2]] <- character()
dependant(fds3)[[2]] <- "d"
stopifnot(identical(fds3, fds))
# changing appearance priority for attributes
attrs_order(fds3) <- rev(attrs_order(fds3))
fds3
#> 2 functional dependencies
#> 4 attributes: d, c, b, a
#> b, a -> c
#>      -> d

# reconstructing from components
fds_recon <- functional_dependency(
 Map(list, detset(fds), dependant(fds)),
 attrs_order(fds)
)
stopifnot(identical(fds_recon, fds))

# can be a data frame column
data.frame(id = 1:2, fd = fds)
#>   id        fd
#> 1  1 a, b -> c
#> 2  2      -> d

# (in)equality ignores header
stopifnot(all(fds3 == fds))
stopifnot(!any(fds != fds))