Maps between finite sets

Question

With SageMath, one can do FiniteSetMaps(["a", "b"], [3, 4, 5]) to get all maps from {a,b} to {3,4,5}. Is something similar available in Mathematica?

Answer 1

alist = {3, 4, 5};
blist = {"a", "b"};
mapfs = Tuples@Outer[Rule, blist, alist]

$$\begin{array}{l} \{\text{a}\to 3,\text{b}\to 3\} \\ \{\text{a}\to 3,\text{b}\to 4\} \\ \{\text{a}\to 3,\text{b}\to 5\} \\ \{\text{a}\to 4,\text{b}\to 3\} \\ \{\text{a}\to 4,\text{b}\to 4\} \\ \{\text{a}\to 4,\text{b}\to 5\} \\ \{\text{a}\to 5,\text{b}\to 3\} \\ \{\text{a}\to 5,\text{b}\to 4\} \\ \{\text{a}\to 5,\text{b}\to 5\} \\ \end{array}$$

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EDIT

Following comment by @Alan (Thanks)

mapasc = Map[Association, mapfs]
mapasc[[2]]["b"]

4

Answer 2

There's no built-in function but the following constructs the mappings:

aa = {"a", "b"};
bb = {3, 4, 5};
Thread[aa -> #] & /@ Tuples[bb, Length@aa]

If you want "functional" expressions, then one way to get them is

funcs = ReplaceAll@Thread[aa -> #] & /@ Tuples[bb, Length@aa]

funcs[[2]]["b"]
(*  4  *)