Bijections

This package provides a Bijection data type for Julia.

A Dict in Julia is not one-to-one. Two different keys might have the same value. This data structure behaves just like a Dict except it blocks assigning the same value to two different keys.

Getting Started

After using Bijections we create a new Bijection in one of the following ways:

• b = Bijection(): This gives a new Bijection in which the keys and values are of Any type.

• b = Bijection{S,T}(): This gives a new Bijection in which the keys are of type S and the values are of type T.

• b = Bijection(x,y): This gives a new Bijection in which the keys are type typeof(x), the values are type typeof(y) and the key-value pair (x,y) is inserted into the Bijection.

Adding and deleting pairs

Once a Bijection, b, is created, we add a new key-value pair in the same manner as with a Dict:

julia> b[1] = "hello"
"hello"

julia> b[2] = "bye"
"bye"

Notice, however, that if we add a new key with a value that already exists in the Bijection an error ensues:

julia> b[3] = "hello"
ERROR: One of x or y already in this Bijection

Likewise, if a key already has a value it cannot be changed by giving it a new value:

julia> b[1] = "ciao"
ERROR: One of x or y already in this Bijection

If we wish to change the value associated with a given key, the pair must first be deleted using delete!:

julia> delete!(b,1)
Bijection{Any,Any} (with 1 pairs)

julia> b[1] = "ciao"
"ciao"

Using a Bijection

To access a value associated with a given key, we use the same syntax as for a Dict:

julia> b[1]
"ciao"

julia> b[2]
"bye"

If the key is not in the Bijection an error is raised:

julia> b[3]
ERROR: KeyError: 3 not found

Since the values in a Bijection must be distinct, we can give a value as an input and retrieve its associate key. The function inverse(b,y) finds the value x such that b[x]==y. However, we provide the handy short cut b(y):

julia> b("bye")
2

julia> b("ciao")
1

Naturally, if the requested value is not in the Bijection an error is raised:

julia> b("hello")
ERROR: KeyError: hello not found

Inspection

Thinking of a Bijection as a mapping between finite sets, we provide the functions domain and image. These return, respectively, the set of keys and the set of values of the Bijection.

julia> domain(b)
Set(Any[2,1])

julia> image(b)
Set(Any["bye","ciao"])

The collect function returns the Bijection as an array of key-value pairs:

julia> collect(b)
2-element Array{Tuple{Any,Any},1}:
 (2,"bye") 
 (1,"ciao")

The length function returns the number of key-value pairs:

julia> length(b)
2

The isempty function returns true exactly when the Bijection contains no pairs:

julia> isempty(b)
false

To do list

These are features I may get around to adding:

• Create an inv(b) function which creates a new Bijection that reverses key-value pairs in b

• Create an active_inv(b) function that, like inv, creates an inverse but that is tied to b so that any modification of one affects the other.

• A Bijection ought to be iterable, but that's not implemented yet.