MPRI course 2-4-2 “Functional programming languages” Answers to the exercises

class Closure { abstract Object apply(Object arg); Object apply2(Object arg1, Object arg2) { return ((Closure)(apply(arg1))).apply(arg2); } } abstract class Closure2 extends Closure { Object apply(Object arg) { return new PartialApplication(this, arg); } abstract Object apply2(Object arg1, Object arg2); } class PartialApplication extends Closure { Closure2 fn; Object arg1; PartialApplication(Closure2 fn, Object arg1) { this.fn = fn; this.arg1 = arg1; } Object apply(Object arg2) { return fn.apply2(arg1, arg2); } } Now, the class generated for a two-argument function λx.λy.a of free variables x1, . . . , xn is class Cλx.λy.a extends Closure2 { Object x1; ...; Object xn; Cλx.λy.a(Object x1, ..., Object xn) { this.x1 = x1; ...; this.xn = xn; } Object apply2(Object x, Object y) { return [[a]]; } } The class generated for a one-argument function λx.a of free variables x1, . . . , xn is class Cλx.λy.a extends Closure { Object x1; ...; Object xn; Cλx.a(Object x1, ..., Object xn) { this.x1 = x1; ...; this.xn = xn; } Object apply(Object x) { return [[a]]; } }