Remove special treatment of non-compliant values in lte and equals

[Avaq]

This PR competes with and so closes #154

Instead of arbitrarily returning false, these functions now throw when
given invalid (without the proper type class) input.

[davidchambers]

We should update the type signatures of equals, lt, lte, gt, and gte. :)

[Avaq]

In which way?

[Avaq]

Oh! I see. Yes.

[Avaq]

I can't figure out the signature. Hindley Milner is not versatile enough to cleanly separate garbage inputs from desired inputs. The best I can come up with is this overloaded function.

equals :: Setoid a => (a, a) -> Boolean
equals :: (a, AnythingBut a) -> Boolean

[Avaq]

We could say that the function wants (Setoid a, Setoid b) => (a, b) -> Boolean, but that precludes non-setoid values of differing types.

[davidchambers]

I suggest using equals :: Setoid a => (a, a) -> Boolean. A clear, imprecise type signature has more pedagogical value than an unclear, precise one. We can document in other ways how the function behaves when given values of different types.

[Avaq]

@davidchambers Updated.

[davidchambers]

I don't think this change is necessary, as we already include the clause if its arguments are of the same type.

[Avaq]

But false otherwise is too broad: When a user provides two values of the same type that don't have Setoid, the function throws.

[davidchambers]

We do not typically document the behaviour of a function when applied to an argument outside its domain. The description of S.trim, for example, does not consider the possibility of application to a non-string value.

[Avaq]

So you'd prefer to remove the false otherwise part altogether, and treat the special treatment of inputs of differing types as an undocumented "feature", or simply garbage?

[Avaq]

when applied to an argument outside its domain

Supplying two values of differing types is within the domain of the function. So is supplying two Setoids of the same type. Anything else isn't.

[davidchambers]

I do not see how Setoid a => (a, a) -> Boolean permits inputs of differing types. 🤔

[Avaq]

But the real signature is:

equals :: Setoid a => (a, a) -> Boolean
equals :: (a, AnythingBut a) -> Boolean

Remember..? But you said that is not pedagogical.

[Avaq]

The function has a special code path to facilitate the latter overload.

[Avaq]

That makes these inputs part of the domain in my book.

[Avaq]

You yourself said:

We can document in other ways how the function behaves when given values of different types. -- #147 (comment)

That's what I'm trying to do here.