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@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@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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