Opt-in flag for strictThisChecks

[EliSnow]

TypeScript Version: 2.3.4

Code
This is a repro of an actual bug that bit me which I was surprised the type checker did not catch.

class Foo {
    constructor(private name: string) { }
    public bar(s: string) {
        return this.name + s;
    }
}

const foo = new Foo("f");
["a", "b"].map(foo.bar);

Expected behavior:
The type checker should catch that bar will be called with a this of undefined (assuming strict mode). Methods should have an implicit this of the containing class (in this case this: Foo), or at least an interface with the properties accessed within the method (this: { name: string }).

Actual behavior:
No compile error is emitted and a runtime error is the result.

In #14936, @RyanCavanaugh mentions there being a performance cost to adding in implicit this types. At least in my case, since I was bit by this, I would be willing to pay the extra cost during compile to catch these kind of errors. Perhaps a compiler option would be worthwhile.

[RyanCavanaugh]

Closing due to lack of additional feedback