# [Haskell-cafe] Current state of type-level natural number programming

Fri Jan 13 10:09:10 UTC 2023

```>> I'm a heavy user of ghc-typelits-natnormalise.
>>
>> I can feel your pain that it sometimes isn't able to solve seemingly "simple" constraints. But not all is lost in those cases. The `constraints` package allows one to solve `Nat` constraints out of thin air, provided you go through a function to do it.
>>
>> nLEZeroIsZeroRule :: (n <= 0) :- (n ~ 0)
>> nLEZeroIsZeroRule = Sub (unsafeCoerce (Dict :: Dict (a ~ a)))
>
> Good to know that there are ways to add missing transformations.
>
> Ideally there would be a way without unsafeCoerce, i.e. that I could prove a property manually using some proof steps expressed in functions.

I also developed [type-natural] package, which comes with the showcase of arithmetic lemma.
This builds on [equational-reasoning] package to make proof-writing easier.

-- Hiromi ISHII
konn.jinro at gmail.com

> 2023/01/13 19:02、Henning Thielemann <lemming at henning-thielemann.de>のメール:
>
>
> On Fri, 13 Jan 2023, rowan goemans wrote:
>
>> I'm a heavy user of ghc-typelits-natnormalise.
>>
>> I can feel your pain that it sometimes isn't able to solve seemingly "simple" constraints. But not all is lost in those cases. The `constraints` package allows one to solve `Nat` constraints out of thin air, provided you go through a function to do it.
>>
>> nLEZeroIsZeroRule :: (n <= 0) :- (n ~ 0)
>> nLEZeroIsZeroRule = Sub (unsafeCoerce (Dict :: Dict (a ~ a)))
>
> Good to know that there are ways to add missing transformations.
>
> Ideally there would be a way without unsafeCoerce, i.e. that I could prove a property manually using some proof steps expressed in functions.
>
>
> Alternatively, maybe I can write missing steps in a custom type checker plugin.
>
>
> Has someone already tried to connect SBV to a type checker plugin?
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