The type-settheory package
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).
|Versions||0.1, 0.1.1, 0.1.2, 0.1.3, 0.1.3.1|
|Dependencies||base (==4.*), containers, syb, template-haskell, transformers, type-equality [details]|
|Category||Math, Language, Type System|
|Source repository||head: darcs get http://code.haskell.org/~daniels/type-settheory|
|Uploaded||Wed Nov 3 07:00:55 UTC 2010 by DanielSchuessler|
|Downloads||953 total (8 in the last 30 days)|
|Status||Docs uploaded by user
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