Hi Patrick.
What you are doing isn't possible in source code (Haskell doesn't prove
things at the value level like a dependently typed language does.)
Usually you document it just as you have, as a comment
-- inverse a ! a = e
You can also specify a QuickCheck property:
propInverse :: (Eq a, Group a) => a -> Bool
propInverse a = (inverse a ! a) == e
I've put up an example on hpaste at http://hpaste.org/47234/simple_monoid
-- ryan
On Sat, May 28, 2011 at 2:46 AM, Patrick Browne
Hi, I'm not sure if this is possible but I am trying to use Haskell’s type class to specify *model expansion*. Model expansion allows the specification of new symbols (known as enrichment) or the specification further properties that should hold on old symbols. I am trying to enrich simplified Monoids to Groups. The code below is not intended to do anything other than to specify simplified Groups as a subclass of Monoid. The main problem is that I cannot use ! on the LHS of equations in Group.
Is it possible to expand the specification of Monoid to Group using Haskell type classes?
Pat
data M = M deriving Show
-- Monoid with one operation (!) and identity e (no associativity) class Monoid a where (!) :: a -> a -> a e :: a a ! e = a
-- A Group is a Monoid with an inverse, every Group is a Monoid -- (a necessary condition in logic: Group implies Monoid) -- The inverse property could be expressed as: -- 1) forAll a thereExists b such that a ! b = e -- 2) (inv a) ! a = e class Monoid a => Group a where inverse :: a -> a -- Haskell does not like ! on the LHS of equation for inverse in Group. -- (inverse a) ! a = e
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