I’m having trouble seeing the difference between a boolean formula and a boolean function, can you please highlight the difference?
A bit of philosophy: What is the difference between a dog, a “photo of a dog”, and the string of three letters “dog”?
These are the object, a depiction of the object, and a representation of the object using the English alphabet.
A function is an abstract definition.
A formula is a representation of a function.
Think of linear algebra. You have linear transformations and matrices.
A matrix is a representation of a linear transformation.