reference request - Looking for a package for finite mappings

I am looking for a package for dealing with "mappings" $f\colon A\to B$ where $A$ and $B$ are finite subsets of the set of all possible (inert) expressions.

I need operations like:

• Computing $f(a)$ efficiently.


• Converting $f$ from and to a list of rules.


• Checking whether $f$ is injective (thus bijective).



• Computing the inverse function if possible.


• Listing the elements of $A$ and the set $f(A)$


• Ensuring or enforcing that the elements of $A$ and/or $B$ match a certain pattern, e.g. _Integer.


• Converting to and from a List for the case that $A$ is Range[1, n].


• Efficient handling of the case that $B$ is a list of MachineReals (PackedArray...).

I want this for the following purposes (not exhaustive):

• Abstract away different ways of representing variable-value assignments


• Abstract away differences between lists, matrices, tensors, SparseArrays, PackedArrays which can be understood as a mapping position $\to$ number.

Is there something out there that does this or could be extended easily or would you sit down the few hours it takes and program this from scratch? Am I missing some available functionality that provides a nice representation and implementation of such mappings?