[Haskell-cafe] Is there a name for this property: x + x - x == x

[Omari Norman]

Is there a more general name for it?  Here's what I'm thinking of.  I would
think there's a name for it rather than "inversion", which I made up.

module Builders where

import Test.QuickCheck

-- | Takes a single value, x.  Applies a function to that value,
-- and then applies a second function to the result of the
-- application of the first function.  Passes if the result of the
-- second function equals the original value.

inversion
  :: (Eq a, Show a)
  => (a -> b)
  -- ^ Apply this function to the original value
  -> (b -> a)
  -- ^ Apply this function to the result of the first function
  -> a
  -> Property
inversion f1 f2 a = f2 (f1 a) === a



On Wed, Jun 4, 2014 at 10:42 AM, David Thomas <davidleothomas at gmail.com>
wrote:

> If you have associativity, this seems roughly the same as saying there
> is an additive inverse for every x, because x + x - x = x => x + (x -
> x) = x => x + 0 = x.
>
> On Wed, Jun 4, 2014 at 7:34 AM, Omari Norman <omari at smileystation.com>
> wrote:
> > It's not quite idempotence, because more than one function is involved.
> >
> > It's a common property and I figure I can write a higher order function
> to
> > build QuickCheck tests for it.  I was just wondering if it has a name.
> >
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> >
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