How does a compiler infer a value's type?

Question

From A Swift Tour — The Swift Programming Language (Swift 5):

var myVariable = 42
myVariable = 50
let myConstant = 42

A constant or variable must have the same type as the value you want to assign to it. However, you don’t always have to write the type explicitly. Providing a value when you create a constant or variable lets the compiler infer its type. In the example above, the compiler infers that myVariable is an integer because its initial value is an integer.

How does this work?

Answer 1

You did not provide an explicit type identifier in the left part of the variable declaration & initialization statement. However, by implicitly specifying an initialization value in the right part to have type int, which the compiler can infer from values of 42/50, these statements triggered the procedure of the compiler to handle S-Attributed Grammar.

Answer 2

When the compiler sees the var <identifier> = <expression>; construct it can parse the <expression> out of which a type will emerge.

That type is then used as the declared variable's type.

It is the same logic for type checking when you do declare the type explicitly or assign to a variable, only with the difference that when the type is already fixed and it doesn't match it emits an compiler error.