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|
-- |
-- Module : Crypto.Number.Nat
-- License : BSD-style
-- Maintainer : Vincent Hanquez <vincent@snarc.org>
-- Stability : experimental
-- Portability : Good
--
-- Numbers at type level.
--
-- This module provides extensions to "GHC.TypeLits" and "GHC.TypeNats" useful
-- to work with cryptographic algorithms parameterized with a variable bit
-- length. Constraints like @'IsDivisibleBy8' n@ ensure that the type-level
-- parameter is applicable to the algorithm.
--
-- Functions are also provided to test whether constraints are satisfied from
-- values known at runtime. The following example shows how to discharge
-- 'IsDivisibleBy8' in a computation @fn@ requiring this constraint:
--
-- > withDivisibleBy8 :: Integer
-- > -> (forall proxy n . (KnownNat n, IsDivisibleBy8 n) => proxy n -> a)
-- > -> Maybe a
-- > withDivisibleBy8 len fn = do
-- > SomeNat p <- someNatVal len
-- > Refl <- isDivisibleBy8 p
-- > pure (fn p)
--
-- Function @withDivisibleBy8@ above returns 'Nothing' when the argument @len@
-- is negative or not divisible by 8.
{-# LANGUAGE DataKinds #-}
{-# LANGUAGE TypeOperators #-}
module Crypto.Number.Nat
( type IsDivisibleBy8
, type IsAtMost, type IsAtLeast
, isDivisibleBy8
, isAtMost
, isAtLeast
) where
import Data.Type.Equality
import GHC.TypeLits
import Unsafe.Coerce (unsafeCoerce)
import Crypto.Internal.Nat
-- | get a runtime proof that the constraint @'IsDivisibleBy8' n@ is satified
isDivisibleBy8 :: KnownNat n => proxy n -> Maybe (IsDiv8 n n :~: 'True)
isDivisibleBy8 n
| mod (natVal n) 8 == 0 = Just (unsafeCoerce Refl)
| otherwise = Nothing
-- | get a runtime proof that the constraint @'IsAtMost' value bound@ is
-- satified
isAtMost :: (KnownNat value, KnownNat bound)
=> proxy value -> proxy' bound -> Maybe ((value <=? bound) :~: 'True)
isAtMost x y
| natVal x <= natVal y = Just (unsafeCoerce Refl)
| otherwise = Nothing
-- | get a runtime proof that the constraint @'IsAtLeast' value bound@ is
-- satified
isAtLeast :: (KnownNat value, KnownNat bound)
=> proxy value -> proxy' bound -> Maybe ((bound <=? value) :~: 'True)
isAtLeast = flip isAtMost
|
