Proposal: Data.Bool.implies

[Andrew Butterfield]

HI Niklas,
> On 18 Jan 2016, at 02:17, Niklas Hambüchen <mail at nh2.me> wrote:
> 
> I propose to add to Data.Bool:
> 
>    -- | Boolean implication.
>    implies :: Bool -> Bool -> Bool
>    implies True  x = x
>    implies False _ = True

Fine by me (+1)
> 
>    infix 4 `implies` -- same as (==)
> 
> The request for this is quite old (see e.g.
> http://neilmitchell.blogspot.de/2007/02/logical-implication-in-haskell.html).
> 
> I believe that by not trying to use an operator for it, and keeping it
> in Data.Bool, we can avoid doing anything wrong.
> 
> A quick superficial search on Stackage Hoogle suggests that adding this
> function should create no breakage (4 packages define their own function
> called `implies`, none of them import Data.Bool).
> 
> `infix` instead of `infixl` or `infixr` to force you to bracket it; for
> the same reason it has the same precedence as `==`.

In equational logic, it makes more sense for implication to bind tighter than equivalence,
and it would usually be considered as infixr

a `implies` b `implies` c    same as  a `implies` (b `implies` c)  

But if this breaks something else then plain infix is fine....

That this is the same associativity rule as for function arrows is not a coincidence, by the way.

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Andrew Butterfield
School of Computer Science & Statistics
Trinity College
Dublin 2, Ireland