derivable methods are contradictory

Applicative:

A value that implements the Applicative specification must also implement the Apply specification.

Apply:

A value that implements the Apply specification must also implement the Functor specification.

Functor:

A value which has a Functor must provide a map method.

So a value that implements the Applicative specification must provide a map method.

Here is the contradiction:

A value which satisfies the specification of an Applicative does not need to implement:

• Functor’s map; derivable as function(f) { return this.of(f).ap(this); }

Is there a semantic difference between “implements the Applicative specification” and “satisfies the specification of an Applicative”?

I’m wondering whether Ramda’s map function should operate on a value which provides of and ap but not map. The fact that derivations are mentioned in the spec suggests they are desirable, but as written it doesn’t seem correct to derive implementations.

[davidchambers]

@puffnfresh, could you state definitively how to resolve the contradiction? The rest of us are guessing.

[puffnfresh]

👍