# add a new equation to Data.Type.Bool.If

Edward Kmett ekmett at gmail.com
Fri Dec 29 17:27:20 UTC 2017

```If you want a laundry list, there's an exhaustive set of normal forms in
'normalized' here:

which is used to shrink the size of my 'if-then-else' lookup tables for
BDDs.

You don't need the normal forms per se, (and getting them requires some
notion of ordering we can't offer), but you may find those and the base
cases at
to be useful at reducing the amount of stuff you need to compute.

-Edward

On Fri, Dec 29, 2017 at 10:34 AM, David Feuer <david.feuer at gmail.com> wrote:

> Heh. I already wrote the Phab differential weeks ago. But then I noticed
> there's room for more equations, and wasn't sure where to stop.
>
>     If x x False = x
>     If x True False = x
>     If x True x = x
>
> On Dec 29, 2017 10:27 AM, "Richard Eisenberg" <rae at cs.brynmawr.edu> wrote:
>
>> Currently, we have (in Data.Type.Bool):
>>
>> > -- | Type-level "If". @If True a b@ ==> @a@; @If False a b@ ==> @b@
>> > type family If cond tru fls where
>> >   If 'True  tru  fls = tru
>> >   If 'False tru  fls = fls
>>
>> I propose adding a new equation, thus:
>>
>> > -- | Type-level "If". @If True a b@ ==> @a@; @If False a b@ ==> @b@
>> > type family If cond tru fls where
>> >   If b same same = same
>> >   If 'True  tru  fls = tru
>> >   If 'False tru  fls = fls
>>
>> This new equation would allow If to reduce when we don't know the
>> condition but we do know that both branches are the same. All three
>> equations are *compatible* (a technical term defined in the closed type
>> families paper), meaning that GHC ignores the ordering between them and
>> will just choose whichever equation matches.
>>
>> Any objections?
>>
>> Thanks,
>> Richard
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