94 lines
2.2 KiB
Idris
94 lines
2.2 KiB
Idris
module Quox.NatExtra
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import public Data.Nat
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import Data.Nat.Division
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import Data.SnocList
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import Data.Vect
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import Data.String
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%default total
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public export
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data LTE' : Nat -> Nat -> Type where
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LTERefl : LTE' n n
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LTESuccR : LTE' m n -> LTE' m (S n)
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%builtin Natural LTE'
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public export %hint
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lteZero' : {n : Nat} -> LTE' 0 n
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lteZero' {n = 0} = LTERefl
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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)
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lteSucc' LTERefl = LTERefl
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lteSucc' (LTESuccR p) = LTESuccR $ lteSucc' p
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public export
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fromLte : {n : Nat} -> LTE m n -> LTE' m n
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fromLte LTEZero = lteZero'
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fromLte (LTESucc p) = lteSucc' $ fromLte p
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public export
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toLte : {n : Nat} -> m `LTE'` n -> m `LTE` n
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toLte LTERefl = reflexive
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toLte (LTESuccR p) = lteSuccRight (toLte p)
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private
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0 baseNZ : n `GTE` 2 => NonZero n
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baseNZ @{LTESucc _} = SIsNonZero
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parameters {base : Nat} {auto 0 _ : base `GTE` 2} (chars : Vect base Char)
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private
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showAtBase' : List Char -> Nat -> List Char
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showAtBase' acc 0 = acc
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showAtBase' acc k =
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let dig = natToFinLT (modNatNZ k base baseNZ) @{boundModNatNZ {}} in
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showAtBase' (index dig chars :: acc)
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(assert_smaller k $ divNatNZ k base baseNZ)
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export
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showAtBase : Nat -> String
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showAtBase = pack . showAtBase' []
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namespace Nat
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export
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showHex : Nat -> String
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showHex = showAtBase $ fromList $ unpack "0123456789abcdef"
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namespace Int
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export
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showHex : Int -> String
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showHex x =
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if x < 0 then "-" ++ Nat.showHex (cast (-x)) else Nat.showHex (cast x)
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namespace Int
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export
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fromHexit : Char -> Maybe Int
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fromHexit c =
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if c >= '0' && c <= '9' then Just $ ord c - ord '0'
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else if c >= 'a' && c <= 'f' then Just $ ord c - ord 'a' + 10
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else if c >= 'A' && c <= 'F' then Just $ ord c - ord 'A' + 10
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else Nothing
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private
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fromHex' : Int -> String -> Maybe Int
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fromHex' acc str = case strM str of
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StrNil => Just acc
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StrCons c cs => fromHex' (16 * acc + !(fromHexit c)) (assert_smaller str cs)
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export %inline
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fromHex : String -> Maybe Int
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fromHex = fromHex' 0
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namespace Nat
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export
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fromHexit : Char -> Maybe Nat
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fromHexit = map cast . Int.fromHexit
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export %inline
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fromHex : String -> Maybe Nat
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fromHex = map cast . Int.fromHex
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