Derive KnownNat constraints from other KnownNat constraints

Version on this page:0.3.1
LTS Haskell 11.1:0.4.1
Stackage Nightly 2018-03-19:0.4.1
Latest on Hackage:0.4.1

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BSD2 licensed by Christiaan Baaij
Maintained by

Module documentation for 0.3.1


Build Status Hackage Hackage Dependencies

A type checker plugin for GHC that can derive "complex" KnownNat constraints from other simple/variable KnownNat constraints. i.e. without this plugin, you must have both a KnownNat n and a KnownNat (n+2) constraint in the type signature of the following function:

f :: forall n . (KnownNat n, KnownNat (n+2)) => Proxy n -> Integer
f _ = natVal (Proxy :: Proxy n) + natVal (Proxy :: Proxy (n+2))

Using the plugin you can omit the KnownNat (n+2) constraint:

f :: forall n . KnownNat n => Proxy n -> Integer
f _ = natVal (Proxy :: Proxy n) + natVal (Proxy :: Proxy (n+2))

The plugin can derive KnownNat constraints for types consisting of:

  • Type variables, when there is a corresponding KnownNat constraint
  • Type-level naturals
  • Applications of the arithmetic expression: {+,-,*,^}
  • Type functions, when there is either: a matching given KnownNat constraint; or a corresponding KnownNat<N> instance for the type function

To elaborate the latter points, given the type family Min:

type family Min (a :: Nat) (b :: Nat) :: Nat where
  Min 0 b = 0
  Min a b = If (a <=? b) a b

the plugin can derive a KnownNat (Min x y + 1) constraint given only a KnownNat (Min x y) constraint:

g :: forall x y . (KnownNat (Min x y)) => Proxy x -> Proxy y -> Integer
g _ _ = natVal (Proxy :: Proxy (Min x y + 1))

And, given the type family Max:

type family Max (a :: Nat) (b :: Nat) :: Nat where
  Max 0 b = b
  Max a b = If (a <=? b) b a

and corresponding KnownNat2 instance:

instance (KnownNat a, KnownNat b) => KnownNat2 "TestFunctions.Max" a b where
  natSing2 = let x = natVal (Proxy @ a)
                 y = natVal (Proxy @ b)
                 z = max x y
             in  SNatKn z
  {-# INLINE natSing2 #-}

the plugin can derive a KnownNat (Max x y + 1) constraint given only a KnownNat x and KnownNat y constraint:

h :: forall x y . (KnownNat x, KnownNat y) => Proxy x -> Proxy y -> Integer
h _ _ = natVal (Proxy :: Proxy (Max x y + 1))

To use the plugin, add the

OPTIONS_GHC -fplugin GHC.TypeLits.KnownNat.Solver

Pragma to the header of your file.


Changelog for the ghc-typelits-knownnat package

0.4.1 March 17th, 2018

  • Add support for GHC 8.4.1

0.4 January 4th, 2018

  • Add partial GHC 8.4.1-alpha1 support
  • Drop singletons dependency #15 * KnownNatN classes no longer have the KnownNatFN associated type family

0.3.1 August 17th 2017

  • Fix testsuite for GHC 8.2.1

0.3 May 15th 2017

  • GHC 8.2.1 support: Underlying representation for KnownNat in GHC 8.2 is Natural, meaning users of this plugin will need to update their code to use Natural for GHC 8.2 as well.

0.2.4 April 10th 2017

  • New features: Derive constraints for unary functions via a KnownNat1 instance; thanks to @nshepperd #11 Use type-substituted [G]iven KnownNats (partial solve for #13)

0.2.3 January 15th 2017

  • Solve normalised literal constraints, i.e.: * KnownNat (((addrSize + 1) - (addrSize - 1))) ~ KnownNat 2

0.2.2 September 29th 2016

  • New features: * Derive smaller constraints from larger constraints when they differ by a single variable, i.e. KnownNat (a + b), KnownNat b implies KnownNat a.

0.2.1 August 19th 2016

  • Fixes bugs: * Source location of derived wanted constraints is, erroneously, always set to line 1, column 1

0.2 August 17th 2016

  • New features: Handle GHC.TypeLits.- Handle custom, user-defined, type-level operations * Thanks to Gabor Greif (@ggreif): derive smaller from larger constraints, i.e. KnownNat (n+1) implies KnownNat n


  • New features: Solve "complex" KnownNat constraints involving arbitrary type-functions, as long as there is a given KnownNat constraint for this type functions.

0.1.1 August 11th 2016

  • Fixes bug: panic on a non-given KnownNat constraint variable

0.1 August 10th 2016

  • Initial release
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