This package is not currently in any snapshots. If you're interested in using it, we recommend adding it to Stackage Nightly. Doing so will make builds more reliable, and allow stackage.org to host generated Haddocks.
Type classes can express sets and functions on the type level, but they are not first-class. This package expresses type-level sets and functions as types instead.
Instances are replaced by value-level proofs which can be directly manipulated; this makes quite a bit of (constructive) set theory expressible; for example, we have:
Subsets and extensional set equality
Unions (binary or of sets of sets), intersections, cartesian products, powersets, and a sort of dependent sum and product
Functions and their composition, images, preimages, injectivity
The proposition-types (derived from the :=: equality type) aren't meaningful purely by convention; they relate to the rest of Haskell as follows: A proof of A :=: B gives us a safe coercion operator A -> B (while the logic is inevitably inconsistent at compile-time since undefined proves anything, I think that we still have the property that if the Refl value is successfully pattern-matched, then the two parameters in its type are actually equal).
