Substitution Model (CBV, CBN) with Classes

We are familiar with the substituion model, and how expressions with simple datatypes are evaluated using CBV/CBV.

Suppose we have a class definition as follows:

class C(x1, ..., xm){ ... def f(y1, ..., yn) = b ... }

Question: How is an instantiation of the class new C(e1, ..., em) evaluted?
Answer: The expression arguments e1, ..., em are evaluated like the arguments of a normal function. That’s it. The resulting expression, new C(v1, ..., vm), is already a value.

Question: How is an function call on an instantiation evaluated: new C(v1, ..., vm).f(w1, ..., wn)
Answer: The expression new C(v1, ..., vm).f(w1, ..., wn) is rewritten to:

[w1/y1, ..., wn/yn][v1/x1, ..., vm/xm][new C(v1, ..., vm)/this] b    // Here '/' indicates 'replaces'

There are three substitutions at work here:

• the substitution of the formal parameters y1, ..., yn of the function f by the arguments w1, ..., wn
• the substitution of the formal parameters x1, ..., xm of the class C by the class arguments v1, ..., vm
• the substitution of the self reference this by the value of the object new C(v1, ..., vn).

Example:

class Rational(x: Int, y: Int) {
    def numer = x
    def denom = y

    def less(that: Rational) =
        numer * that.denom < that.numer * denom

    def max(that: Rational) =
        if (this.less(that)) that else this
}

So the expression:

new Rational(1, 2).less(new Rational(2, 3))

is evaluated as:

-----> [1/x, 2/y] [newRational(2, 3)/that] [new Rational(1, 2)/this]
-----> new Rational(1, 2).numer * new Rational(2, 3).denom < new Rational(2, 3).numer * new Rational(1, 2).denom
-----> 1 * 3 < 2 * 2
-----> true