Constraints that any type, resp. no type fulfills

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GPL-3.0-only licensed by Justus Sagemüller
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Since GHC 7.4, constraints are first-class: we have the constraint kind, and thus type-classes have a kind of form k -> Constraint, or k -> l -> m -> ... -> Constraint for a multi-param type class. Such type-level functions can be used as arguments to data types, or as instances for other type classes.

For any given arity, the constraint-valued functions form a semigroup with respect to “constraint intersection”, which Haskell supports with tuple syntax, e.g.

type NewCstrt¹ a = (Cstrt¹₀ a, Cstrt¹₁ a)

means that NewCstrt¹ :: * -> Constraint requires that for any given parameter both Cstrt¹₀ and Cstrt¹₁ be fulfilled. It is intuitive enough that this type-level semigroup can be extended to a monoid, but out of the box this is only possible for arity 0, i.e. for Cstrt⁰ :: Constraint

(Cstrt⁰, ()) ~ ((), Cstrt⁰) ~ Cstrt⁰

For higher arity, this would require type-level lambdas, like for Cstrt² :: * -> * -> Constraint

(Cstrt², \a b -> ()) ~ (\a b -> (), Cstrt²) ~ Cstrt²

which is not valid Haskell syntax. It is easy enough to define the lambdas in an ad-hoc manner as

type Unconstrained² a b = ()

and then

(Cstrt², Unconstrained²) ~ (Unconstrained², Cstrt²) ~ Cstrt²

This library provides those trivial constraints in a single, documented place, and it uses classes instead of type-synonyms (which would be problematic when it comes to partial application). Arities 0-9 are provided.

They can be useful in any construction that is parameterised over a constrainer-class, when you do not wish to actually constrain the domain with it.

The other thing this library provides are the opposite classes, i.e. \a b ... -> Impossible, constraints which can never be fulfilled. They are essentially dual to the Unconstrained ones, and can likewise be useful as parameters that should completely “disable” a conditional feature.