quox/lib/Quox/NatExtra.idr

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module Quox.NatExtra
import public Data.Nat
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import Data.Nat.Division
import Data.SnocList
import Data.Vect
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%default total
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public export
data LTE' : Nat -> Nat -> Type where
LTERefl : LTE' n n
LTESuccR : LTE' m n -> LTE' m (S n)
%builtin Natural LTE'
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public export %hint
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lteZero' : {n : Nat} -> LTE' 0 n
lteZero' {n = 0} = LTERefl
lteZero' {n = S n} = LTESuccR lteZero'
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public export %hint
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lteSucc' : LTE' m n -> LTE' (S m) (S n)
lteSucc' LTERefl = LTERefl
lteSucc' (LTESuccR p) = LTESuccR $ lteSucc' p
public export
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fromLte : {n : Nat} -> LTE m n -> LTE' m n
fromLte LTEZero = lteZero'
fromLte (LTESucc p) = lteSucc' $ fromLte p
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public export
toLte : {n : Nat} -> m `LTE'` n -> m `LTE` n
toLte LTERefl = reflexive
toLte (LTESuccR p) = lteSuccRight (toLte p)
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private
0 baseNZ : n `GTE` 2 => NonZero n
baseNZ @{LTESucc _} = SIsNonZero
parameters {base : Nat} {auto 0 _ : base `GTE` 2} (chars : Vect base Char)
private
showAtBase' : List Char -> Nat -> List Char
showAtBase' acc 0 = acc
showAtBase' acc k =
let dig = natToFinLT (modNatNZ k base baseNZ) @{boundModNatNZ {}} in
showAtBase' (index dig chars :: acc)
(assert_smaller k $ divNatNZ k base baseNZ)
export
showAtBase : Nat -> String
showAtBase = pack . showAtBase' []
export
showHex : Nat -> String
showHex = showAtBase $ fromList $ unpack "0123456789ABCDEF"