How to represent a map data structure mathematically

Question

Wondering how to represent a map object such as the following mathematically:

var foo = {
  a: 10,
  b: 'bar',
  c: true
}

You could say that it was a function like this:

foo(x, y, z)

where $x$ is an integer, $y$ is a string, and $z$ is a boolean. But the question then is how to say the names of the keys a, b, c. Something like:

foo(label(x, a), label(y, b), label(z, c))

But then wondering about how type theory deals with this, so I' a bit confused. Wondering how computer science would model this data structure using mathematical notation. Maybe:

$$ \begin{align*} foo = \left\{ \begin{array}{r@{}l} & a = x \\ & b = y \\ & c = z \end{array} \right\} \end{align*} $$