numtype-dk 0.5.0.1 → 0.5.0.2

raw patch · 8 files changed

+1047/−1033 lines, 8 filesdep ~basesetup-changednew-uploaderPVP: major bump suggested

API removals or changes: PVP suggests a major version bump

Dependency ranges changed: base

API changes (from Hackage documentation)

Files

• LICENSE +31/−31
• Numeric/NumType/DK/Integers.hs +462/−458
• Numeric/NumType/DK/Naturals.hs +57/−52
• Numeric/NumType/DKTests.hs +427/−427
• README.md +19/−18
• Setup.lhs +2/−2
• changelog.md +11/−7
• numtype-dk.cabal +38/−38

@@ -1,31 +1,31 @@-Copyright (c) 2008-2014, Bjorn Buckwalter.
-All rights reserved.
-
-Redistribution and use in source and binary forms, with or without
-modification, are permitted provided that the following conditions
-are met:
-
-  * Redistributions of source code must retain the above copyright
-    notice, this list of conditions and the following disclaimer.
-
-  * Redistributions in binary form must reproduce the above
-    copyright notice, this list of conditions and the following
-    disclaimer in the documentation and/or other materials provided
-    with the distribution.
-
-  * Neither the name of the copyright holder(s) nor the names of
-    contributors may be used to endorse or promote products derived
-    from this software without specific prior written permission.
-
-THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
-"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
-LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
-FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
-COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
-INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
-BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
-LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
-CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
-LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
-ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
-POSSIBILITY OF SUCH DAMAGE.
+Copyright (c) 2008-2014, Bjorn Buckwalter.+All rights reserved.++Redistribution and use in source and binary forms, with or without+modification, are permitted provided that the following conditions+are met:++  * Redistributions of source code must retain the above copyright+    notice, this list of conditions and the following disclaimer.++  * Redistributions in binary form must reproduce the above+    copyright notice, this list of conditions and the following+    disclaimer in the documentation and/or other materials provided+    with the distribution.++  * Neither the name of the copyright holder(s) nor the names of+    contributors may be used to endorse or promote products derived+    from this software without specific prior written permission.++THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS+"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT+LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS+FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE+COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,+INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,+BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;+LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER+CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT+LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN+ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE+POSSIBILITY OF SUCH DAMAGE.

@@ -1,458 +1,462 @@-{-# OPTIONS_HADDOCK show-extensions #-}
-
-{-# LANGUAGE AutoDeriveTypeable #-}
-{-# LANGUAGE CPP #-}
-{-# LANGUAGE DataKinds #-}
-{-# LANGUAGE FlexibleInstances #-}
-{-# LANGUAGE TypeFamilies #-}
-{-# LANGUAGE TypeOperators #-}
-{-# LANGUAGE UndecidableInstances #-}
-
-{- |
-   Copyright  : Copyright (C) 2006-2015 Bjorn Buckwalter
-   License    : BSD3
-
-   Maintainer : bjorn.buckwalter@gmail.com
-   Stability  : Stable
-   Portability: GHC only
-
-= Summary
-
-Type-level integers for GHC 7.8+.
-
-We provide type level arithmetic operations. We also provide term-level arithmetic operations on proxys, 
-and conversion from the type level to the term level.
-
-= Planned Obsolesence
-
-We commit this package to hackage in sure and certain hope of the coming of glorious GHC integer type literals,
-when the sea shall give up her dead, and this package shall be rendered unto obsolescence.
-
--}
-module Numeric.NumType.DK.Integers
-(
-  -- * Type-Level Integers
-  type TypeInt(..),
-  -- * Type-level Arithmetic
-  Pred, Succ, Negate, Abs, Signum,
-  type (+), type (-), type (*), type (/), type (^),
-  -- * Arithmetic on Proxies
-  pred, succ, negate, abs, signum,
-  (+), (-), (*), (/), (^),
-  -- * Convenience Synonyms for Proxies
-  zero,
-  pos1, pos2, pos3, pos4, pos5, pos6, pos7, pos8, pos9,
-  neg1, neg2, neg3, neg4, neg5, neg6, neg7, neg8, neg9,
-  -- * Conversion from Types to Terms
-  KnownTypeInt(..)
-)
-where
-
-import Data.Proxy
-import Prelude hiding ((+), (-), (*), (/), (^), pred, succ, negate, abs, signum)
-import qualified Prelude
-
-#if MIN_VERSION_base(4, 8, 0)
--- Use @Nat@s from @GHC.TypeLits@.
-import qualified GHC.TypeLits as TN
-
-type Z  = 0  -- GHC.TypeLits
-type N1 = 1  -- GHC.TypeLits
-#else
--- Use custom @Typeable@ @Nat@s.
-import qualified Numeric.NumType.DK.Naturals as TN
-
-type Z = 'TN.Z
-type N1 = 'TN.S 'TN.Z  -- TypeInt.DK.Nats
-#endif
-
--- Use the same fixity for operators as the Prelude.
-infixr 8  ^
-infixl 7  *, /
-infixl 6  +, -
-
-
--- Natural numbers
--- ===============
-
-type family NatPred (n::TN.Nat) :: TN.Nat where NatPred n = n TN.- N1
-type family NatSucc (n::TN.Nat) :: TN.Nat where NatSucc n = n TN.+ N1
-
-
--- Integers
--- ========
-
-data TypeInt = Neg10Minus TN.Nat  -- 10, 11, 12, 13, ...
-             | Neg9
-             | Neg8
-             | Neg7
-             | Neg6
-             | Neg5
-             | Neg4
-             | Neg3
-             | Neg2
-             | Neg1
-             | Zero -- 0
-             | Pos1
-             | Pos2
-             | Pos3
-             | Pos4
-             | Pos5
-             | Pos6
-             | Pos7
-             | Pos8
-             | Pos9
-             | Pos10Plus TN.Nat  -- -10, -11, -12, -13, ...
-
-
--- Unary operations
--- ----------------
-
-type family Pred (i::TypeInt) :: TypeInt where
-  Pred ('Neg10Minus n) = 'Neg10Minus (NatSucc n)
-  Pred 'Neg9 = 'Neg10Minus Z
-  Pred 'Neg8 = 'Neg9
-  Pred 'Neg7 = 'Neg8
-  Pred 'Neg6 = 'Neg7
-  Pred 'Neg5 = 'Neg6
-  Pred 'Neg4 = 'Neg5
-  Pred 'Neg3 = 'Neg4
-  Pred 'Neg2 = 'Neg3
-  Pred 'Neg1 = 'Neg2
-  Pred 'Zero = 'Neg1
-  Pred 'Pos1 = 'Zero
-  Pred 'Pos2 = 'Pos1
-  Pred 'Pos3 = 'Pos2
-  Pred 'Pos4 = 'Pos3
-  Pred 'Pos5 = 'Pos4
-  Pred 'Pos6 = 'Pos5
-  Pred 'Pos7 = 'Pos6
-  Pred 'Pos8 = 'Pos7
-  Pred 'Pos9 = 'Pos8
-  Pred ('Pos10Plus Z) = 'Pos9
-  Pred ('Pos10Plus n) = 'Pos10Plus (NatPred n)
-
-type family Succ (i::TypeInt) :: TypeInt where
-  Succ ('Neg10Minus Z) = 'Neg9
-  Succ ('Neg10Minus n) = 'Neg10Minus (NatPred n)
-  Succ 'Neg9 = 'Neg8
-  Succ 'Neg8 = 'Neg7
-  Succ 'Neg7 = 'Neg6
-  Succ 'Neg6 = 'Neg5
-  Succ 'Neg5 = 'Neg4
-  Succ 'Neg4 = 'Neg3
-  Succ 'Neg3 = 'Neg2
-  Succ 'Neg2 = 'Neg1
-  Succ 'Neg1 = 'Zero
-  Succ 'Zero = 'Pos1
-  Succ 'Pos1 = 'Pos2
-  Succ 'Pos2 = 'Pos3
-  Succ 'Pos3 = 'Pos4
-  Succ 'Pos4 = 'Pos5
-  Succ 'Pos5 = 'Pos6
-  Succ 'Pos6 = 'Pos7
-  Succ 'Pos7 = 'Pos8
-  Succ 'Pos8 = 'Pos9
-  Succ 'Pos9 = 'Pos10Plus Z
-  Succ ('Pos10Plus n) = 'Pos10Plus (NatSucc n)
-
--- | TypeInt negation.
-type family Negate (i::TypeInt) :: TypeInt where
-  Negate ('Neg10Minus n) = 'Pos10Plus  n
-  Negate 'Neg9 = 'Pos9
-  Negate 'Neg8 = 'Pos8
-  Negate 'Neg7 = 'Pos7
-  Negate 'Neg6 = 'Pos6
-  Negate 'Neg5 = 'Pos5
-  Negate 'Neg4 = 'Pos4
-  Negate 'Neg3 = 'Pos3
-  Negate 'Neg2 = 'Pos2
-  Negate 'Neg1 = 'Pos1
-  Negate 'Zero = 'Zero
-  Negate 'Pos1 = 'Neg1
-  Negate 'Pos2 = 'Neg2
-  Negate 'Pos3 = 'Neg3
-  Negate 'Pos4 = 'Neg4
-  Negate 'Pos5 = 'Neg5
-  Negate 'Pos6 = 'Neg6
-  Negate 'Pos7 = 'Neg7
-  Negate 'Pos8 = 'Neg8
-  Negate 'Pos9 = 'Neg9
-  Negate ('Pos10Plus  n) = 'Neg10Minus n
-
--- | Absolute value.
-type family Abs (i::TypeInt) :: TypeInt where
-  Abs ('Neg10Minus n) = 'Pos10Plus  n
-  Abs 'Neg9 = 'Pos9
-  Abs 'Neg8 = 'Pos8
-  Abs 'Neg7 = 'Pos7
-  Abs 'Neg6 = 'Pos6
-  Abs 'Neg5 = 'Pos5
-  Abs 'Neg4 = 'Pos4
-  Abs 'Neg3 = 'Pos3
-  Abs 'Neg2 = 'Pos2
-  Abs 'Neg1 = 'Pos1
-  Abs i = i
-
--- | Signum.
-type family Signum (i::TypeInt) :: TypeInt where
-  Signum ('Neg10Minus n) = 'Neg1
-  Signum 'Neg9 = 'Neg1
-  Signum 'Neg8 = 'Neg1
-  Signum 'Neg7 = 'Neg1
-  Signum 'Neg6 = 'Neg1
-  Signum 'Neg5 = 'Neg1
-  Signum 'Neg4 = 'Neg1
-  Signum 'Neg3 = 'Neg1
-  Signum 'Neg2 = 'Neg1
-  Signum 'Neg1 = 'Neg1
-  Signum 'Zero = 'Zero
-  Signum i = 'Pos1
-
-
--- Binary operations
--- -----------------
-
--- | TypeInt addition.
-type family (i::TypeInt) + (i'::TypeInt) :: TypeInt where
-  'Zero + i = i
-  i + 'Neg10Minus n = Pred i + Succ ('Neg10Minus n)
-  i + 'Neg9 = Pred i + 'Neg8
-  i + 'Neg8 = Pred i + 'Neg7
-  i + 'Neg7 = Pred i + 'Neg6
-  i + 'Neg6 = Pred i + 'Neg5
-  i + 'Neg5 = Pred i + 'Neg4
-  i + 'Neg4 = Pred i + 'Neg3
-  i + 'Neg3 = Pred i + 'Neg2
-  i + 'Neg2 = Pred i + 'Neg1
-  i + 'Neg1 = Pred i
-  i + 'Zero = i
-  i + i' = Succ i + Pred i'  -- i + Pos
-
--- | TypeInt subtraction.
-type family (i::TypeInt) - (i'::TypeInt) :: TypeInt where
-  i - i' = i + Negate i'
-
--- | TypeInt multiplication.
-type family (i::TypeInt) * (i'::TypeInt) :: TypeInt
-  where
-    'Zero * i = 'Zero
-    i * 'Zero = 'Zero
-    i * 'Pos1 = i
-    i * 'Pos2 = i + i
-    i * 'Pos3 = i + i + i
-    i * 'Pos4 = i + i + i + i
-    i * 'Pos5 = i + i + i + i + i
-    i * 'Pos6 = i + i + i + i + i + i
-    i * 'Pos7 = i + i + i + i + i + i + i
-    i * 'Pos8 = i + i + i + i + i + i + i + i
-    i * 'Pos9 = i + i + i + i + i + i + i + i + i
-    i * 'Pos10Plus n = i + i * Pred ('Pos10Plus n)
-    i * i' = Negate (i * Negate i')
-
--- | TypeInt exponentiation.
-type family (i::TypeInt) ^ (i'::TypeInt) :: TypeInt
-  where
-    i ^ 'Zero = 'Pos1
-    i ^ 'Pos1 = i
-    i ^ 'Pos2 = i * i
-    i ^ 'Pos3 = i * i * i
-    i ^ 'Pos4 = i * i * i * i
-    i ^ 'Pos5 = i * i * i * i * i
-    i ^ 'Pos6 = i * i * i * i * i * i
-    i ^ 'Pos7 = i * i * i * i * i * i * i
-    i ^ 'Pos8 = i * i * i * i * i * i * i * i
-    i ^ 'Pos9 = i * i * i * i * i * i * i * i * i
-    i ^ 'Pos10Plus n = i * i ^ Pred ('Pos10Plus n)
-
--- | TypeInt division.
-type family (i::TypeInt) / (i'::TypeInt) :: TypeInt
-  where
- 
-    i / 'Pos1 = i
-    i / 'Neg1 = Negate i
-    -- @Zero / n = Zero@ would allow division by zero.
-    -- @i / i = Pos1@ would allow division by zero.
-    'Zero / ('Neg10Minus n) = 'Zero
-    'Zero / 'Neg9 = 'Zero
-    'Zero / 'Neg8 = 'Zero
-    'Zero / 'Neg7 = 'Zero
-    'Zero / 'Neg6 = 'Zero
-    'Zero / 'Neg5 = 'Zero
-    'Zero / 'Neg4 = 'Zero
-    'Zero / 'Neg3 = 'Zero
-    'Zero / 'Neg2 = 'Zero
-    'Zero / 'Pos2 = 'Zero
-    'Zero / 'Pos3 = 'Zero
-    'Zero / 'Pos4 = 'Zero
-    'Zero / 'Pos5 = 'Zero
-    'Zero / 'Pos6 = 'Zero
-    'Zero / 'Pos7 = 'Zero
-    'Zero / 'Pos8 = 'Zero
-    'Zero / 'Pos9 = 'Zero
-    'Zero / ('Pos10Plus n) = 'Zero
-
-    'Neg2 / 'Neg2 = 'Pos1
-    'Neg3 / 'Neg3 = 'Pos1
-    'Neg4 / 'Neg4 = 'Pos1
-    'Neg5 / 'Neg5 = 'Pos1
-    'Neg6 / 'Neg6 = 'Pos1
-    'Neg7 / 'Neg7 = 'Pos1
-    'Neg8 / 'Neg8 = 'Pos1
-    'Neg9 / 'Neg9 = 'Pos1
-    'Neg10Minus n / 'Neg10Minus n = 'Pos1
-
-    'Neg2 / 'Pos2 = 'Neg1
-    'Neg3 / 'Pos3 = 'Neg1
-    'Neg4 / 'Pos4 = 'Neg1
-    'Neg5 / 'Pos5 = 'Neg1
-    'Neg6 / 'Pos6 = 'Neg1
-    'Neg7 / 'Pos7 = 'Neg1
-    'Neg8 / 'Pos8 = 'Neg1
-    'Neg9 / 'Pos9 = 'Neg1
-    'Neg10Minus n / 'Pos10Plus n = 'Neg1
-
-    'Pos2 / 'Neg2 = 'Neg1
-    'Pos3 / 'Neg3 = 'Neg1
-    'Pos4 / 'Neg4 = 'Neg1
-    'Pos5 / 'Neg5 = 'Neg1
-    'Pos6 / 'Neg6 = 'Neg1
-    'Pos7 / 'Neg7 = 'Neg1
-    'Pos8 / 'Neg8 = 'Neg1
-    'Pos9 / 'Neg9 = 'Neg1
-    'Pos10Plus n / 'Neg10Minus n = 'Neg1
-
-    'Pos2 / 'Pos2 = 'Pos1
-    'Pos3 / 'Pos3 = 'Pos1
-    'Pos4 / 'Pos4 = 'Pos1
-    'Pos5 / 'Pos5 = 'Pos1
-    'Pos6 / 'Pos6 = 'Pos1
-    'Pos7 / 'Pos7 = 'Pos1
-    'Pos8 / 'Pos8 = 'Pos1
-    'Pos9 / 'Pos9 = 'Pos1
-    'Pos10Plus n / 'Pos10Plus n = 'Pos1
-
-    'Neg4 / 'Neg2 = 'Pos2
-    'Neg6 / 'Neg2 = 'Pos3
-    'Neg8 / 'Neg2 = 'Pos4
-    'Neg6 / 'Neg3 = 'Pos2
-    'Neg9 / 'Neg3 = 'Pos3
-    'Neg8 / 'Neg4 = 'Pos2
-    'Neg10Minus n / i = ('Neg10Minus n + Abs i) / i - Signum i
-
-    'Neg4 / 'Pos2 = 'Neg2
-    'Neg6 / 'Pos2 = 'Neg3
-    'Neg8 / 'Pos2 = 'Neg4
-    'Neg6 / 'Pos3 = 'Neg2
-    'Neg9 / 'Pos3 = 'Neg3
-    'Neg8 / 'Pos4 = 'Neg2
-
-    'Pos4 / 'Neg2 = 'Neg2
-    'Pos6 / 'Neg2 = 'Neg3
-    'Pos8 / 'Neg2 = 'Neg4
-    'Pos6 / 'Neg3 = 'Neg2
-    'Pos9 / 'Neg3 = 'Neg3
-    'Pos8 / 'Neg4 = 'Neg2
-
-    'Pos4 / 'Pos2 = 'Pos2
-    'Pos6 / 'Pos2 = 'Pos3
-    'Pos8 / 'Pos2 = 'Pos4
-    'Pos6 / 'Pos3 = 'Pos2
-    'Pos9 / 'Pos3 = 'Pos3
-    'Pos8 / 'Pos4 = 'Pos2
-    'Pos10Plus n / i = ('Pos10Plus n - Abs i) / i + Signum i
-
-
--- Term level
--- ==========
-
--- Term level operators
--- --------------------
-
-pred   :: Proxy i -> Proxy (Pred   i); pred   _ = Proxy
-succ   :: Proxy i -> Proxy (Succ   i); succ   _ = Proxy
-negate :: Proxy i -> Proxy (Negate i); negate _ = Proxy
-abs    :: Proxy i -> Proxy (Abs    i); abs    _ = Proxy
-signum :: Proxy i -> Proxy (Signum i); signum _ = Proxy
-
-(+) :: Proxy i -> Proxy i' -> Proxy (i + i'); _ + _ = Proxy
-(-) :: Proxy i -> Proxy i' -> Proxy (i - i'); _ - _ = Proxy
-(*) :: Proxy i -> Proxy i' -> Proxy (i * i'); _ * _ = Proxy
-(/) :: Proxy i -> Proxy i' -> Proxy (i / i'); _ / _ = Proxy
-(^) :: Proxy i -> Proxy i' -> Proxy (i ^ i'); _ ^ _ = Proxy
-
-
--- Term level TypeNats for convenience
--- -----------------------------------
-
-neg9 :: Proxy 'Neg9
-neg9 = Proxy :: Proxy 'Neg9
-neg8 :: Proxy 'Neg8
-neg8 = Proxy :: Proxy 'Neg8
-neg7 :: Proxy 'Neg7
-neg7 = Proxy :: Proxy 'Neg7
-neg6 :: Proxy 'Neg6
-neg6 = Proxy :: Proxy 'Neg6
-neg5 :: Proxy 'Neg5
-neg5 = Proxy :: Proxy 'Neg5
-neg4 :: Proxy 'Neg4
-neg4 = Proxy :: Proxy 'Neg4
-neg3 :: Proxy 'Neg3
-neg3 = Proxy :: Proxy 'Neg3
-neg2 :: Proxy 'Neg2
-neg2 = Proxy :: Proxy 'Neg2
-neg1 :: Proxy 'Neg1
-neg1 = Proxy :: Proxy 'Neg1
-zero :: Proxy 'Zero
-zero = Proxy :: Proxy 'Zero
-pos1 :: Proxy 'Pos1
-pos1 = Proxy :: Proxy 'Pos1
-pos2 :: Proxy 'Pos2
-pos2 = Proxy :: Proxy 'Pos2
-pos3 :: Proxy 'Pos3
-pos3 = Proxy :: Proxy 'Pos3
-pos4 :: Proxy 'Pos4
-pos4 = Proxy :: Proxy 'Pos4
-pos5 :: Proxy 'Pos5
-pos5 = Proxy :: Proxy 'Pos5
-pos6 :: Proxy 'Pos6
-pos6 = Proxy :: Proxy 'Pos6
-pos7 :: Proxy 'Pos7
-pos7 = Proxy :: Proxy 'Pos7
-pos8 :: Proxy 'Pos8
-pos8 = Proxy :: Proxy 'Pos8
-pos9 :: Proxy 'Pos9
-pos9 = Proxy :: Proxy 'Pos9
-
-
--- Reification
--- -----------
-
--- | Conversion to a @Num@.
-class KnownTypeInt (i::TypeInt) where toNum :: Num a => Proxy i -> a
-
-instance KnownTypeInt (Succ ('Neg10Minus n)) => KnownTypeInt ('Neg10Minus n)
-  where toNum = (Prelude.- 1) . toNum . succ
-
-instance KnownTypeInt 'Neg9 where toNum _ = -9
-instance KnownTypeInt 'Neg8 where toNum _ = -8
-instance KnownTypeInt 'Neg7 where toNum _ = -7
-instance KnownTypeInt 'Neg6 where toNum _ = -6
-instance KnownTypeInt 'Neg5 where toNum _ = -5
-instance KnownTypeInt 'Neg4 where toNum _ = -4
-instance KnownTypeInt 'Neg3 where toNum _ = -3
-instance KnownTypeInt 'Neg2 where toNum _ = -2
-instance KnownTypeInt 'Neg1 where toNum _ = -1
-instance KnownTypeInt 'Zero where toNum _ = 0
-instance KnownTypeInt 'Pos1 where toNum _ = 1
-instance KnownTypeInt 'Pos2 where toNum _ = 2
-instance KnownTypeInt 'Pos3 where toNum _ = 3
-instance KnownTypeInt 'Pos4 where toNum _ = 4
-instance KnownTypeInt 'Pos5 where toNum _ = 5
-instance KnownTypeInt 'Pos6 where toNum _ = 6
-instance KnownTypeInt 'Pos7 where toNum _ = 7
-instance KnownTypeInt 'Pos8 where toNum _ = 8
-instance KnownTypeInt 'Pos9 where toNum _ = 9
-
-instance KnownTypeInt (Pred ('Pos10Plus n)) => KnownTypeInt ('Pos10Plus n)
-  where toNum = (Prelude.+ 1) . toNum . pred
+{-# OPTIONS_HADDOCK show-extensions #-}++{-# LANGUAGE AutoDeriveTypeable #-}+{-# LANGUAGE CPP #-}+{-# LANGUAGE DataKinds #-}+{-# LANGUAGE FlexibleInstances #-}+{-# LANGUAGE TypeFamilies #-}+{-# LANGUAGE TypeOperators #-}+{-# LANGUAGE UndecidableInstances #-}++#if __GLASGOW_HASKELL__ > 805+{-# LANGUAGE NoStarIsType #-}+#endif++{- |+   Copyright  : Copyright (C) 2006-2015 Bjorn Buckwalter+   License    : BSD3++   Maintainer : bjorn.buckwalter@gmail.com+   Stability  : Stable+   Portability: GHC only++= Summary++Type-level integers for GHC 7.8+.++We provide type level arithmetic operations. We also provide term-level arithmetic operations on proxys,+and conversion from the type level to the term level.++= Planned Obsolesence++We commit this package to hackage in sure and certain hope of the coming of glorious GHC integer type literals,+when the sea shall give up her dead, and this package shall be rendered unto obsolescence.++-}+module Numeric.NumType.DK.Integers+(+  -- * Type-Level Integers+  type TypeInt(..),+  -- * Type-level Arithmetic+  Pred, Succ, Negate, Abs, Signum,+  type (+), type (-), type (*), type (/), type (^),+  -- * Arithmetic on Proxies+  pred, succ, negate, abs, signum,+  (+), (-), (*), (/), (^),+  -- * Convenience Synonyms for Proxies+  zero,+  pos1, pos2, pos3, pos4, pos5, pos6, pos7, pos8, pos9,+  neg1, neg2, neg3, neg4, neg5, neg6, neg7, neg8, neg9,+  -- * Conversion from Types to Terms+  KnownTypeInt(..)+)+where++import Data.Proxy+import Prelude hiding ((+), (-), (*), (/), (^), pred, succ, negate, abs, signum)+import qualified Prelude++#if MIN_VERSION_base(4, 8, 0)+-- Use @Nat@s from @GHC.TypeLits@.+import qualified GHC.TypeLits as TN++type Z  = 0  -- GHC.TypeLits+type N1 = 1  -- GHC.TypeLits+#else+-- Use custom @Typeable@ @Nat@s.+import qualified Numeric.NumType.DK.Naturals as TN++type Z = 'TN.Z+type N1 = 'TN.S 'TN.Z  -- TypeInt.DK.Nats+#endif++-- Use the same fixity for operators as the Prelude.+infixr 8  ^+infixl 7  *, /+infixl 6  +, -+++-- Natural numbers+-- ===============++type family NatPred (n::TN.Nat) :: TN.Nat where NatPred n = n TN.- N1+type family NatSucc (n::TN.Nat) :: TN.Nat where NatSucc n = n TN.+ N1+++-- Integers+-- ========++data TypeInt = Neg10Minus TN.Nat  -- 10, 11, 12, 13, ...+             | Neg9+             | Neg8+             | Neg7+             | Neg6+             | Neg5+             | Neg4+             | Neg3+             | Neg2+             | Neg1+             | Zero -- 0+             | Pos1+             | Pos2+             | Pos3+             | Pos4+             | Pos5+             | Pos6+             | Pos7+             | Pos8+             | Pos9+             | Pos10Plus TN.Nat  -- -10, -11, -12, -13, ...+++-- Unary operations+-- ----------------++type family Pred (i::TypeInt) :: TypeInt where+  Pred ('Neg10Minus n) = 'Neg10Minus (NatSucc n)+  Pred 'Neg9 = 'Neg10Minus Z+  Pred 'Neg8 = 'Neg9+  Pred 'Neg7 = 'Neg8+  Pred 'Neg6 = 'Neg7+  Pred 'Neg5 = 'Neg6+  Pred 'Neg4 = 'Neg5+  Pred 'Neg3 = 'Neg4+  Pred 'Neg2 = 'Neg3+  Pred 'Neg1 = 'Neg2+  Pred 'Zero = 'Neg1+  Pred 'Pos1 = 'Zero+  Pred 'Pos2 = 'Pos1+  Pred 'Pos3 = 'Pos2+  Pred 'Pos4 = 'Pos3+  Pred 'Pos5 = 'Pos4+  Pred 'Pos6 = 'Pos5+  Pred 'Pos7 = 'Pos6+  Pred 'Pos8 = 'Pos7+  Pred 'Pos9 = 'Pos8+  Pred ('Pos10Plus Z) = 'Pos9+  Pred ('Pos10Plus n) = 'Pos10Plus (NatPred n)++type family Succ (i::TypeInt) :: TypeInt where+  Succ ('Neg10Minus Z) = 'Neg9+  Succ ('Neg10Minus n) = 'Neg10Minus (NatPred n)+  Succ 'Neg9 = 'Neg8+  Succ 'Neg8 = 'Neg7+  Succ 'Neg7 = 'Neg6+  Succ 'Neg6 = 'Neg5+  Succ 'Neg5 = 'Neg4+  Succ 'Neg4 = 'Neg3+  Succ 'Neg3 = 'Neg2+  Succ 'Neg2 = 'Neg1+  Succ 'Neg1 = 'Zero+  Succ 'Zero = 'Pos1+  Succ 'Pos1 = 'Pos2+  Succ 'Pos2 = 'Pos3+  Succ 'Pos3 = 'Pos4+  Succ 'Pos4 = 'Pos5+  Succ 'Pos5 = 'Pos6+  Succ 'Pos6 = 'Pos7+  Succ 'Pos7 = 'Pos8+  Succ 'Pos8 = 'Pos9+  Succ 'Pos9 = 'Pos10Plus Z+  Succ ('Pos10Plus n) = 'Pos10Plus (NatSucc n)++-- | TypeInt negation.+type family Negate (i::TypeInt) :: TypeInt where+  Negate ('Neg10Minus n) = 'Pos10Plus  n+  Negate 'Neg9 = 'Pos9+  Negate 'Neg8 = 'Pos8+  Negate 'Neg7 = 'Pos7+  Negate 'Neg6 = 'Pos6+  Negate 'Neg5 = 'Pos5+  Negate 'Neg4 = 'Pos4+  Negate 'Neg3 = 'Pos3+  Negate 'Neg2 = 'Pos2+  Negate 'Neg1 = 'Pos1+  Negate 'Zero = 'Zero+  Negate 'Pos1 = 'Neg1+  Negate 'Pos2 = 'Neg2+  Negate 'Pos3 = 'Neg3+  Negate 'Pos4 = 'Neg4+  Negate 'Pos5 = 'Neg5+  Negate 'Pos6 = 'Neg6+  Negate 'Pos7 = 'Neg7+  Negate 'Pos8 = 'Neg8+  Negate 'Pos9 = 'Neg9+  Negate ('Pos10Plus  n) = 'Neg10Minus n++-- | Absolute value.+type family Abs (i::TypeInt) :: TypeInt where+  Abs ('Neg10Minus n) = 'Pos10Plus  n+  Abs 'Neg9 = 'Pos9+  Abs 'Neg8 = 'Pos8+  Abs 'Neg7 = 'Pos7+  Abs 'Neg6 = 'Pos6+  Abs 'Neg5 = 'Pos5+  Abs 'Neg4 = 'Pos4+  Abs 'Neg3 = 'Pos3+  Abs 'Neg2 = 'Pos2+  Abs 'Neg1 = 'Pos1+  Abs i = i++-- | Signum.+type family Signum (i::TypeInt) :: TypeInt where+  Signum ('Neg10Minus n) = 'Neg1+  Signum 'Neg9 = 'Neg1+  Signum 'Neg8 = 'Neg1+  Signum 'Neg7 = 'Neg1+  Signum 'Neg6 = 'Neg1+  Signum 'Neg5 = 'Neg1+  Signum 'Neg4 = 'Neg1+  Signum 'Neg3 = 'Neg1+  Signum 'Neg2 = 'Neg1+  Signum 'Neg1 = 'Neg1+  Signum 'Zero = 'Zero+  Signum i = 'Pos1+++-- Binary operations+-- -----------------++-- | TypeInt addition.+type family (i::TypeInt) + (i'::TypeInt) :: TypeInt where+  'Zero + i = i+  i + 'Neg10Minus n = Pred i + Succ ('Neg10Minus n)+  i + 'Neg9 = Pred i + 'Neg8+  i + 'Neg8 = Pred i + 'Neg7+  i + 'Neg7 = Pred i + 'Neg6+  i + 'Neg6 = Pred i + 'Neg5+  i + 'Neg5 = Pred i + 'Neg4+  i + 'Neg4 = Pred i + 'Neg3+  i + 'Neg3 = Pred i + 'Neg2+  i + 'Neg2 = Pred i + 'Neg1+  i + 'Neg1 = Pred i+  i + 'Zero = i+  i + i' = Succ i + Pred i'  -- i + Pos++-- | TypeInt subtraction.+type family (i::TypeInt) - (i'::TypeInt) :: TypeInt where+  i - i' = i + Negate i'++-- | TypeInt multiplication.+type family (i::TypeInt) * (i'::TypeInt) :: TypeInt+  where+    'Zero * i = 'Zero+    i * 'Zero = 'Zero+    i * 'Pos1 = i+    i * 'Pos2 = i + i+    i * 'Pos3 = i + i + i+    i * 'Pos4 = i + i + i + i+    i * 'Pos5 = i + i + i + i + i+    i * 'Pos6 = i + i + i + i + i + i+    i * 'Pos7 = i + i + i + i + i + i + i+    i * 'Pos8 = i + i + i + i + i + i + i + i+    i * 'Pos9 = i + i + i + i + i + i + i + i + i+    i * 'Pos10Plus n = i + i * Pred ('Pos10Plus n)+    i * i' = Negate (i * Negate i')++-- | TypeInt exponentiation.+type family (i::TypeInt) ^ (i'::TypeInt) :: TypeInt+  where+    i ^ 'Zero = 'Pos1+    i ^ 'Pos1 = i+    i ^ 'Pos2 = i * i+    i ^ 'Pos3 = i * i * i+    i ^ 'Pos4 = i * i * i * i+    i ^ 'Pos5 = i * i * i * i * i+    i ^ 'Pos6 = i * i * i * i * i * i+    i ^ 'Pos7 = i * i * i * i * i * i * i+    i ^ 'Pos8 = i * i * i * i * i * i * i * i+    i ^ 'Pos9 = i * i * i * i * i * i * i * i * i+    i ^ 'Pos10Plus n = i * i ^ Pred ('Pos10Plus n)++-- | TypeInt division.+type family (i::TypeInt) / (i'::TypeInt) :: TypeInt+  where++    i / 'Pos1 = i+    i / 'Neg1 = Negate i+    -- @Zero / n = Zero@ would allow division by zero.+    -- @i / i = Pos1@ would allow division by zero.+    'Zero / ('Neg10Minus n) = 'Zero+    'Zero / 'Neg9 = 'Zero+    'Zero / 'Neg8 = 'Zero+    'Zero / 'Neg7 = 'Zero+    'Zero / 'Neg6 = 'Zero+    'Zero / 'Neg5 = 'Zero+    'Zero / 'Neg4 = 'Zero+    'Zero / 'Neg3 = 'Zero+    'Zero / 'Neg2 = 'Zero+    'Zero / 'Pos2 = 'Zero+    'Zero / 'Pos3 = 'Zero+    'Zero / 'Pos4 = 'Zero+    'Zero / 'Pos5 = 'Zero+    'Zero / 'Pos6 = 'Zero+    'Zero / 'Pos7 = 'Zero+    'Zero / 'Pos8 = 'Zero+    'Zero / 'Pos9 = 'Zero+    'Zero / ('Pos10Plus n) = 'Zero++    'Neg2 / 'Neg2 = 'Pos1+    'Neg3 / 'Neg3 = 'Pos1+    'Neg4 / 'Neg4 = 'Pos1+    'Neg5 / 'Neg5 = 'Pos1+    'Neg6 / 'Neg6 = 'Pos1+    'Neg7 / 'Neg7 = 'Pos1+    'Neg8 / 'Neg8 = 'Pos1+    'Neg9 / 'Neg9 = 'Pos1+    'Neg10Minus n / 'Neg10Minus n = 'Pos1++    'Neg2 / 'Pos2 = 'Neg1+    'Neg3 / 'Pos3 = 'Neg1+    'Neg4 / 'Pos4 = 'Neg1+    'Neg5 / 'Pos5 = 'Neg1+    'Neg6 / 'Pos6 = 'Neg1+    'Neg7 / 'Pos7 = 'Neg1+    'Neg8 / 'Pos8 = 'Neg1+    'Neg9 / 'Pos9 = 'Neg1+    'Neg10Minus n / 'Pos10Plus n = 'Neg1++    'Pos2 / 'Neg2 = 'Neg1+    'Pos3 / 'Neg3 = 'Neg1+    'Pos4 / 'Neg4 = 'Neg1+    'Pos5 / 'Neg5 = 'Neg1+    'Pos6 / 'Neg6 = 'Neg1+    'Pos7 / 'Neg7 = 'Neg1+    'Pos8 / 'Neg8 = 'Neg1+    'Pos9 / 'Neg9 = 'Neg1+    'Pos10Plus n / 'Neg10Minus n = 'Neg1++    'Pos2 / 'Pos2 = 'Pos1+    'Pos3 / 'Pos3 = 'Pos1+    'Pos4 / 'Pos4 = 'Pos1+    'Pos5 / 'Pos5 = 'Pos1+    'Pos6 / 'Pos6 = 'Pos1+    'Pos7 / 'Pos7 = 'Pos1+    'Pos8 / 'Pos8 = 'Pos1+    'Pos9 / 'Pos9 = 'Pos1+    'Pos10Plus n / 'Pos10Plus n = 'Pos1++    'Neg4 / 'Neg2 = 'Pos2+    'Neg6 / 'Neg2 = 'Pos3+    'Neg8 / 'Neg2 = 'Pos4+    'Neg6 / 'Neg3 = 'Pos2+    'Neg9 / 'Neg3 = 'Pos3+    'Neg8 / 'Neg4 = 'Pos2+    'Neg10Minus n / i = ('Neg10Minus n + Abs i) / i - Signum i++    'Neg4 / 'Pos2 = 'Neg2+    'Neg6 / 'Pos2 = 'Neg3+    'Neg8 / 'Pos2 = 'Neg4+    'Neg6 / 'Pos3 = 'Neg2+    'Neg9 / 'Pos3 = 'Neg3+    'Neg8 / 'Pos4 = 'Neg2++    'Pos4 / 'Neg2 = 'Neg2+    'Pos6 / 'Neg2 = 'Neg3+    'Pos8 / 'Neg2 = 'Neg4+    'Pos6 / 'Neg3 = 'Neg2+    'Pos9 / 'Neg3 = 'Neg3+    'Pos8 / 'Neg4 = 'Neg2++    'Pos4 / 'Pos2 = 'Pos2+    'Pos6 / 'Pos2 = 'Pos3+    'Pos8 / 'Pos2 = 'Pos4+    'Pos6 / 'Pos3 = 'Pos2+    'Pos9 / 'Pos3 = 'Pos3+    'Pos8 / 'Pos4 = 'Pos2+    'Pos10Plus n / i = ('Pos10Plus n - Abs i) / i + Signum i+++-- Term level+-- ==========++-- Term level operators+-- --------------------++pred   :: Proxy i -> Proxy (Pred   i); pred   _ = Proxy+succ   :: Proxy i -> Proxy (Succ   i); succ   _ = Proxy+negate :: Proxy i -> Proxy (Negate i); negate _ = Proxy+abs    :: Proxy i -> Proxy (Abs    i); abs    _ = Proxy+signum :: Proxy i -> Proxy (Signum i); signum _ = Proxy++(+) :: Proxy i -> Proxy i' -> Proxy (i + i'); _ + _ = Proxy+(-) :: Proxy i -> Proxy i' -> Proxy (i - i'); _ - _ = Proxy+(*) :: Proxy i -> Proxy i' -> Proxy (i * i'); _ * _ = Proxy+(/) :: Proxy i -> Proxy i' -> Proxy (i / i'); _ / _ = Proxy+(^) :: Proxy i -> Proxy i' -> Proxy (i ^ i'); _ ^ _ = Proxy+++-- Term level TypeNats for convenience+-- -----------------------------------++neg9 :: Proxy 'Neg9+neg9 = Proxy :: Proxy 'Neg9+neg8 :: Proxy 'Neg8+neg8 = Proxy :: Proxy 'Neg8+neg7 :: Proxy 'Neg7+neg7 = Proxy :: Proxy 'Neg7+neg6 :: Proxy 'Neg6+neg6 = Proxy :: Proxy 'Neg6+neg5 :: Proxy 'Neg5+neg5 = Proxy :: Proxy 'Neg5+neg4 :: Proxy 'Neg4+neg4 = Proxy :: Proxy 'Neg4+neg3 :: Proxy 'Neg3+neg3 = Proxy :: Proxy 'Neg3+neg2 :: Proxy 'Neg2+neg2 = Proxy :: Proxy 'Neg2+neg1 :: Proxy 'Neg1+neg1 = Proxy :: Proxy 'Neg1+zero :: Proxy 'Zero+zero = Proxy :: Proxy 'Zero+pos1 :: Proxy 'Pos1+pos1 = Proxy :: Proxy 'Pos1+pos2 :: Proxy 'Pos2+pos2 = Proxy :: Proxy 'Pos2+pos3 :: Proxy 'Pos3+pos3 = Proxy :: Proxy 'Pos3+pos4 :: Proxy 'Pos4+pos4 = Proxy :: Proxy 'Pos4+pos5 :: Proxy 'Pos5+pos5 = Proxy :: Proxy 'Pos5+pos6 :: Proxy 'Pos6+pos6 = Proxy :: Proxy 'Pos6+pos7 :: Proxy 'Pos7+pos7 = Proxy :: Proxy 'Pos7+pos8 :: Proxy 'Pos8+pos8 = Proxy :: Proxy 'Pos8+pos9 :: Proxy 'Pos9+pos9 = Proxy :: Proxy 'Pos9+++-- Reification+-- -----------++-- | Conversion to a @Num@.+class KnownTypeInt (i::TypeInt) where toNum :: Num a => Proxy i -> a++instance KnownTypeInt (Succ ('Neg10Minus n)) => KnownTypeInt ('Neg10Minus n)+  where toNum = (Prelude.- 1) . toNum . succ++instance KnownTypeInt 'Neg9 where toNum _ = -9+instance KnownTypeInt 'Neg8 where toNum _ = -8+instance KnownTypeInt 'Neg7 where toNum _ = -7+instance KnownTypeInt 'Neg6 where toNum _ = -6+instance KnownTypeInt 'Neg5 where toNum _ = -5+instance KnownTypeInt 'Neg4 where toNum _ = -4+instance KnownTypeInt 'Neg3 where toNum _ = -3+instance KnownTypeInt 'Neg2 where toNum _ = -2+instance KnownTypeInt 'Neg1 where toNum _ = -1+instance KnownTypeInt 'Zero where toNum _ = 0+instance KnownTypeInt 'Pos1 where toNum _ = 1+instance KnownTypeInt 'Pos2 where toNum _ = 2+instance KnownTypeInt 'Pos3 where toNum _ = 3+instance KnownTypeInt 'Pos4 where toNum _ = 4+instance KnownTypeInt 'Pos5 where toNum _ = 5+instance KnownTypeInt 'Pos6 where toNum _ = 6+instance KnownTypeInt 'Pos7 where toNum _ = 7+instance KnownTypeInt 'Pos8 where toNum _ = 8+instance KnownTypeInt 'Pos9 where toNum _ = 9++instance KnownTypeInt (Pred ('Pos10Plus n)) => KnownTypeInt ('Pos10Plus n)+  where toNum = (Prelude.+ 1) . toNum . pred

@@ -1,52 +1,57 @@-{-# LANGUAGE AutoDeriveTypeable #-}
-{-# LANGUAGE DataKinds #-}
-{-# LANGUAGE FlexibleInstances #-}
-{-# LANGUAGE TypeFamilies #-}
-{-# LANGUAGE TypeOperators #-}
-{-# LANGUAGE UndecidableInstances #-}
-
-module Numeric.NumType.DK.Naturals where
-
-import Prelude hiding (pred)
-
--- Use the same fixity for operators as the Prelude.
-infixr 8  ^
-infixl 7  *
-infixl 6  +
-
-data Nat = Z | S Nat  -- Natural numbers starting at 0.
-
--- | Nat addition.
-type family (n::Nat) + (n'::Nat) :: Nat where
-  -- Z + n = n  -- Redundant.
-  n + 'Z = n
-  n + 'S n' = 'S n + n'
-
--- | Nat subtraction.
-type family (n::Nat) - (n'::Nat) :: Nat where
-  n - 'Z = n
-  'S n - 'S n' = n - n'
-
--- | Nat multiplication.
-type family (n::Nat) * (n'::Nat) :: Nat
-  where
-    --Z * n = Z  -- Redundant
-    n * 'Z = 'Z
-    n * ('S n') = n + n * n'  -- i * Pos n
-
--- | Nat exponentiation.
-type family (n::Nat) ^ (n'::Nat) :: Nat
-  where
-    --Zero ^ Pos n = Zero  -- Redundant.
-    n ^ 'Z = 'S 'Z
-    n ^ 'S n' = n * n ^ n'
-
-
-class KnownNat (n::Nat) where natVal :: proxy n -> Integer
-
-instance KnownNat 'Z where natVal _ = 0
-instance KnownNat n => KnownNat ('S n) where
-  natVal = (1 +) . natVal . pred
-    where
-      pred :: proxy ('S n) -> proxy n
-      pred = undefined
+{-# LANGUAGE AutoDeriveTypeable #-}+{-# LANGUAGE CPP #-}+{-# LANGUAGE DataKinds #-}+{-# LANGUAGE FlexibleInstances #-}+{-# LANGUAGE TypeFamilies #-}+{-# LANGUAGE TypeOperators #-}+{-# LANGUAGE UndecidableInstances #-}++#if __GLASGOW_HASKELL__ > 805+{-# LANGUAGE NoStarIsType #-}+#endif++module Numeric.NumType.DK.Naturals where++import Prelude hiding (pred)++-- Use the same fixity for operators as the Prelude.+infixr 8  ^+infixl 7  *+infixl 6  +++data Nat = Z | S Nat  -- Natural numbers starting at 0.++-- | Nat addition.+type family (n::Nat) + (n'::Nat) :: Nat where+  -- Z + n = n  -- Redundant.+  n + 'Z = n+  n + 'S n' = 'S n + n'++-- | Nat subtraction.+type family (n::Nat) - (n'::Nat) :: Nat where+  n - 'Z = n+  'S n - 'S n' = n - n'++-- | Nat multiplication.+type family (n::Nat) * (n'::Nat) :: Nat+  where+    --Z * n = Z  -- Redundant+    n * 'Z = 'Z+    n * ('S n') = n + n * n'  -- i * Pos n++-- | Nat exponentiation.+type family (n::Nat) ^ (n'::Nat) :: Nat+  where+    --Zero ^ Pos n = Zero  -- Redundant.+    n ^ 'Z = 'S 'Z+    n ^ 'S n' = n * n ^ n'+++class KnownNat (n::Nat) where natVal :: proxy n -> Integer++instance KnownNat 'Z where natVal _ = 0+instance KnownNat n => KnownNat ('S n) where+  natVal = (1 +) . natVal . pred+    where+      pred :: proxy ('S n) -> proxy n+      pred = undefined

@@ -1,427 +1,427 @@-{-# LANGUAGE RankNTypes #-}
-{-# LANGUAGE DataKinds #-}
-{-# LANGUAGE KindSignatures #-}
-
-module Numeric.NumType.DKTests where
-
-import Numeric.NumType.DK.Integers
-import Prelude hiding ((*), (/), (+), (-), (^), pred, succ, negate, abs, signum)
-import qualified Prelude as P ((*), (/), (+), (-), (^), pred, succ, negate, abs, signum)
-import Data.Proxy
-import Test.HUnit
-
--- Some “large” NumTypes.
-neg12 = pred neg11
-neg11 = pred neg10
-neg10 = pred neg9
-
-pos10 = succ pos9
-pos11 = succ pos10
-pos12 = succ pos11
-
--- | Compares a type level unary function with a value level unary function
-  -- by converting 'NumType' to a @Num@. This assumes that the 'toNum'
-  -- function is solid.
-unaryTest :: (KnownNumType i, KnownNumType i', Num a, Eq a, Show a)
-          => (Proxy i -> Proxy i') -> (a -> a) -> Proxy i -> Test
-unaryTest f f' x = TestCase $ assertEqual
-    "Unary function Num equivalence"
-    (f' (toNum x)) (toNum (f x))
-
--- | 'unaryTest' with @Num a@ fixed to @Integer@. This is needed by
-  -- 'testIncrDecr'.
-unaryTest' :: (KnownNumType i, KnownNumType i')
-          => (Proxy i -> Proxy i') -> (Integer -> Integer) -> Proxy i -> Test
-unaryTest' = unaryTest
-
--- | Compares a type level binary function with a value level binary function
-  -- by converting 'NumType' to 'Num'. This assumes that the 'toNum'
-  -- function is solid.
-binaryTest :: (KnownNumType i, KnownNumType i', KnownNumType i'', Num a, Eq a, Show a)
-           => (Proxy i -> Proxy i' -> Proxy i'')
-           -> (a -> a -> a)
-           -> Proxy i -> Proxy i' -> Test
-binaryTest f f' x y = TestCase $ assertEqual
-    "Binary function Num equivalence"
-    (f' (toNum x) (toNum y)) (toNum (f x y))
-
-binaryTest' :: (KnownNumType i, KnownNumType i', KnownNumType i'', Num a, Eq a, Show a)
-           => (Proxy i -> Proxy i' -> Proxy i'')
-           -> (Integer -> Integer -> Integer)
-           -> Proxy i -> Proxy i' -> Test
-binaryTest' = binaryTest
-
-
--- | Test that conversion to 'Num a' works as expected. This is sort of a
-  -- prerequisite for the other tests.
-testAsIntegral = TestLabel "Num equivalence tests" $ TestList
-    [ TestCase $ -12 @=? toNum neg12
-    , TestCase $ -11 @=? toNum neg11
-    , TestCase $ -10 @=? toNum neg10
-    , TestCase $  -9 @=? toNum neg9
-    , TestCase $  -8 @=? toNum neg8
-    , TestCase $  -7 @=? toNum neg7
-    , TestCase $  -6 @=? toNum neg6
-    , TestCase $  -5 @=? toNum neg5
-    , TestCase $  -4 @=? toNum neg4
-    , TestCase $  -3 @=? toNum neg3
-    , TestCase $  -2 @=? toNum neg2
-    , TestCase $  -1 @=? toNum neg1
-    , TestCase $   0 @=? toNum zero
-    , TestCase $   1 @=? toNum pos1
-    , TestCase $   2 @=? toNum pos2
-    , TestCase $   3 @=? toNum pos3
-    , TestCase $   4 @=? toNum pos4
-    , TestCase $   5 @=? toNum pos5
-    , TestCase $   6 @=? toNum pos6
-    , TestCase $   7 @=? toNum pos7
-    , TestCase $   8 @=? toNum pos8
-    , TestCase $   9 @=? toNum pos9
-    , TestCase $  10 @=? toNum pos10
-    , TestCase $  11 @=? toNum pos11
-    , TestCase $  12 @=? toNum pos12
-    ] -- By induction all other NumTypes should be good if these are.
-
--- | Test incrementing and decrementing.
-testIncrDecr = TestLabel "Increment and decrement tests" $ TestList
-    [ t neg12
-    , t neg11
-    , t neg10
-    , t neg9
-    , t neg8
-    , t neg7
-    , t neg6
-    , t neg5
-    , t neg4
-    , t neg3
-    , t neg2
-    , t neg1
-    , t zero
-    , t pos1
-    , t pos2
-    , t pos3
-    , t pos4
-    , t pos5
-    , t pos6
-    , t pos7
-    , t pos8
-    , t pos9
-    , t pos10
-    , t pos11
-    , t pos12
-    ] where
-        t x = TestList [ unaryTest' (+ pos1) (P.+ 1) x
-                       , unaryTest' (+ neg1) (P.- 1) x
-                       , unaryTest' (\x -> x - neg1) (P.+ 1) x
-                       , unaryTest' (\x -> x - pos1) (P.- 1) x
-                       , unaryTest' pred P.pred x
-                       , unaryTest' succ P.succ x
-                       ]
-
--- | Test negation.
-testNegate = TestLabel "Negation tests" $ TestList
-    [ unaryTest negate P.negate neg12
-    , unaryTest negate P.negate neg11
-    , unaryTest negate P.negate neg10
-    , unaryTest negate P.negate neg9
-    , unaryTest negate P.negate neg8
-    , unaryTest negate P.negate neg7
-    , unaryTest negate P.negate neg6
-    , unaryTest negate P.negate neg5
-    , unaryTest negate P.negate neg4
-    , unaryTest negate P.negate neg3
-    , unaryTest negate P.negate neg2
-    , unaryTest negate P.negate neg1
-    , unaryTest negate P.negate zero
-    , unaryTest negate P.negate pos1
-    , unaryTest negate P.negate pos2
-    , unaryTest negate P.negate pos3
-    , unaryTest negate P.negate pos4
-    , unaryTest negate P.negate pos5
-    , unaryTest negate P.negate pos6
-    , unaryTest negate P.negate pos7
-    , unaryTest negate P.negate pos8
-    , unaryTest negate P.negate pos9
-    , unaryTest negate P.negate pos10
-    , unaryTest negate P.negate pos11
-    , unaryTest negate P.negate pos12
-    ]
-
--- | Test absolute value.
-testAbs = TestLabel "Absolute value tests" $ TestList
-    [ unaryTest abs P.abs neg12
-    , unaryTest abs P.abs neg11
-    , unaryTest abs P.abs neg10
-    , unaryTest abs P.abs neg9
-    , unaryTest abs P.abs neg8
-    , unaryTest abs P.abs neg7
-    , unaryTest abs P.abs neg6
-    , unaryTest abs P.abs neg5
-    , unaryTest abs P.abs neg4
-    , unaryTest abs P.abs neg3
-    , unaryTest abs P.abs neg2
-    , unaryTest abs P.abs neg1
-    , unaryTest abs P.abs zero
-    , unaryTest abs P.abs pos1
-    , unaryTest abs P.abs pos2
-    , unaryTest abs P.abs pos3
-    , unaryTest abs P.abs pos4
-    , unaryTest abs P.abs pos5
-    , unaryTest abs P.abs pos6
-    , unaryTest abs P.abs pos7
-    , unaryTest abs P.abs pos8
-    , unaryTest abs P.abs pos9
-    , unaryTest abs P.abs pos10
-    , unaryTest abs P.abs pos11
-    , unaryTest abs P.abs pos12
-    ]
-
--- | Test signum.
-testSignum = TestLabel "Signum tests" $ TestList
-    [ unaryTest signum P.signum neg12
-    , unaryTest signum P.signum neg11
-    , unaryTest signum P.signum neg10
-    , unaryTest signum P.signum neg9
-    , unaryTest signum P.signum neg8
-    , unaryTest signum P.signum neg7
-    , unaryTest signum P.signum neg6
-    , unaryTest signum P.signum neg5
-    , unaryTest signum P.signum neg4
-    , unaryTest signum P.signum neg3
-    , unaryTest signum P.signum neg2
-    , unaryTest signum P.signum neg1
-    , unaryTest signum P.signum zero
-    , unaryTest signum P.signum pos1
-    , unaryTest signum P.signum pos2
-    , unaryTest signum P.signum pos3
-    , unaryTest signum P.signum pos4
-    , unaryTest signum P.signum pos5
-    , unaryTest signum P.signum pos6
-    , unaryTest signum P.signum pos7
-    , unaryTest signum P.signum pos8
-    , unaryTest signum P.signum pos9
-    , unaryTest signum P.signum pos10
-    , unaryTest signum P.signum pos11
-    , unaryTest signum P.signum pos12
-    ]
-
--- | Test absolute value.
-testAbs = TestLabel "Absolute value tests" $ TestList
-    [ unaryTest abs P.abs neg2
-    , unaryTest abs P.abs neg1
-    , unaryTest abs P.abs zero
-    , unaryTest abs P.abs pos1
-    , unaryTest abs P.abs pos1
-    ]
-
--- | Test signum.
-testSignum = TestLabel "Signum tests" $ TestList
-    [ unaryTest signum P.signum neg2
-    , unaryTest signum P.signum neg1
-    , unaryTest signum P.signum zero
-    , unaryTest signum P.signum pos1
-    , unaryTest signum P.signum pos1
-    ]
-
--- | Test addition.
-testAddition = TestLabel "Addition tests" $ TestList
-    [ binaryTest (+) (P.+) pos2 pos5
-    , binaryTest (+) (P.+) pos12 pos2
-    , binaryTest (+) (P.+) pos11 pos2
-    , binaryTest (+) (P.+) pos10 pos2
-    , binaryTest (+) (P.+) pos2 pos12
-    , binaryTest (+) (P.+) pos2 pos11
-    , binaryTest (+) (P.+) pos2 pos10
-    , binaryTest (+) (P.+) neg2 pos5
-    , binaryTest (+) (P.+) pos2 neg5
-    , binaryTest (+) (P.+) neg2 neg5
-    , binaryTest (+) (P.+) neg2 neg12
-    , binaryTest (+) (P.+) neg2 neg11
-    , binaryTest (+) (P.+) neg2 neg10
-    , binaryTest (+) (P.+) neg12 neg2
-    , binaryTest (+) (P.+) neg11 neg2
-    , binaryTest (+) (P.+) neg10 neg2
-    , binaryTest (+) (P.+) zero zero
-    , binaryTest (+) (P.+) pos2 zero
-    , binaryTest (+) (P.+) neg2 zero
-    , binaryTest (+) (P.+) zero pos5
-    , binaryTest (+) (P.+) zero neg5
-    ]
-
--- | Test subtraction.
-testSubtraction = TestLabel "Subtraction tests" $ TestList
-    [ binaryTest (-) (P.-) pos2 pos5
-    , binaryTest (-) (P.-) pos12 pos2
-    , binaryTest (-) (P.-) pos11 pos2
-    , binaryTest (-) (P.-) pos10 pos2
-    , binaryTest (-) (P.-) pos2 pos12
-    , binaryTest (-) (P.-) pos2 pos11
-    , binaryTest (-) (P.-) pos2 pos10
-    , binaryTest (-) (P.-) neg2 pos5
-    , binaryTest (-) (P.-) pos2 neg5
-    , binaryTest (-) (P.-) neg2 neg5
-    , binaryTest (-) (P.-) neg2 neg12
-    , binaryTest (-) (P.-) neg2 neg11
-    , binaryTest (-) (P.-) neg2 neg10
-    , binaryTest (-) (P.-) neg12 neg2
-    , binaryTest (-) (P.-) neg11 neg2
-    , binaryTest (-) (P.-) neg10 neg2
-    , binaryTest (-) (P.-) zero zero
-    , binaryTest (-) (P.-) pos2 zero
-    , binaryTest (-) (P.-) neg2 zero
-    , binaryTest (-) (P.-) zero pos5
-    , binaryTest (-) (P.-) zero neg5
-    ]
-
--- | Test multiplication.
-testMultiplication = TestLabel "Multiplication tests" $ TestList
-    [ binaryTest (*) (P.*) pos2 pos5
-    , binaryTest (*) (P.*) pos12 pos2
-    , binaryTest (*) (P.*) pos11 pos2
-    , binaryTest (*) (P.*) pos10 pos2
-    , binaryTest (*) (P.*) pos2 pos12
-    , binaryTest (*) (P.*) pos2 pos11
-    , binaryTest (*) (P.*) pos2 pos10
-    , binaryTest (*) (P.*) neg2 pos5
-    , binaryTest (*) (P.*) pos2 neg5
-    , binaryTest (*) (P.*) neg2 neg5
-    , binaryTest (*) (P.*) neg2 neg12
-    , binaryTest (*) (P.*) neg2 neg11
-    , binaryTest (*) (P.*) neg2 neg10
-    , binaryTest (*) (P.*) neg12 neg2
-    , binaryTest (*) (P.*) neg11 neg2
-    , binaryTest (*) (P.*) neg10 neg2
-    , binaryTest (*) (P.*) zero zero
-    , binaryTest (*) (P.*) pos2 zero
-    , binaryTest (*) (P.*) neg2 zero
-    , binaryTest (*) (P.*) zero pos5
-    , binaryTest (*) (P.*) zero neg5
-    -- Probably some duplicates in the below.
-    , binaryTest (*) (P.*) pos10 pos2
-    , binaryTest (*) (P.*) pos9 pos3
-    , binaryTest (*) (P.*) pos8 pos4
-    , binaryTest (*) (P.*) pos8 pos2
-    , binaryTest (*) (P.*) pos6 pos3
-    , binaryTest (*) (P.*) pos6 pos2
-    , binaryTest (*) (P.*) pos4 pos2
-    , binaryTest (*) (P.*) pos9 neg3
-    , binaryTest (*) (P.*) pos8 neg4
-    , binaryTest (*) (P.*) pos8 neg2
-    , binaryTest (*) (P.*) pos6 neg3
-    , binaryTest (*) (P.*) pos6 neg2
-    , binaryTest (*) (P.*) pos4 neg2
-    , binaryTest (*) (P.*) zero pos5
-    , binaryTest (*) (P.*) zero neg3
-    , binaryTest (*) (P.*) neg4 pos2
-    , binaryTest (*) (P.*) neg6 pos2
-    , binaryTest (*) (P.*) neg6 pos3
-    , binaryTest (*) (P.*) neg8 pos2
-    , binaryTest (*) (P.*) neg8 pos4
-    , binaryTest (*) (P.*) neg9 pos3
-    , binaryTest (*) (P.*) neg4 neg2
-    , binaryTest (*) (P.*) neg6 neg2
-    , binaryTest (*) (P.*) neg6 neg3
-    , binaryTest (*) (P.*) neg8 neg2
-    , binaryTest (*) (P.*) neg8 neg4
-    , binaryTest (*) (P.*) neg9 neg3
-    , binaryTest (*) (P.*) neg12 pos4
-    ]
-
--- | Test division.
-testDivision = TestLabel "Division tests" $ TestList
-    [ binaryTest (/) (P./) pos12 pos4
-    , binaryTest (/) (P./) pos12 neg4
-    , binaryTest (/) (P./) pos10 pos5
-    , binaryTest (/) (P./) pos10 pos2
-    , binaryTest (/) (P./) pos9 pos3
-    , binaryTest (/) (P./) pos8 pos4
-    , binaryTest (/) (P./) pos8 pos2
-    , binaryTest (/) (P./) pos6 pos3
-    , binaryTest (/) (P./) pos6 pos2
-    , binaryTest (/) (P./) pos4 pos2
-    , binaryTest (/) (P./) pos9 neg3
-    , binaryTest (/) (P./) pos8 neg4
-    , binaryTest (/) (P./) pos8 neg2
-    , binaryTest (/) (P./) pos6 neg3
-    , binaryTest (/) (P./) pos6 neg2
-    , binaryTest (/) (P./) pos4 neg2
-    , binaryTest (/) (P./) zero pos5
-    , binaryTest (/) (P./) zero neg3
-    , binaryTest (/) (P./) neg4 pos2
-    , binaryTest (/) (P./) neg6 pos2
-    , binaryTest (/) (P./) neg6 pos3
-    , binaryTest (/) (P./) neg8 pos2
-    , binaryTest (/) (P./) neg8 pos4
-    , binaryTest (/) (P./) neg9 pos3
-    , binaryTest (/) (P./) neg4 neg2
-    , binaryTest (/) (P./) neg6 neg2
-    , binaryTest (/) (P./) neg6 neg3
-    , binaryTest (/) (P./) neg8 neg2
-    , binaryTest (/) (P./) neg8 neg4
-    , binaryTest (/) (P./) neg9 neg3
-    , binaryTest (/) (P./) neg12 pos4
-    , binaryTest (/) (P./) neg12 neg4
-    , binaryTest (/) (P./) neg10 neg5
-    , binaryTest (/) (P./) neg10 neg2
-
-    , binaryTest (/) (P./) pos5 pos5
-    , binaryTest (/) (P./) neg5 pos5
-    , binaryTest (/) (P./) pos5 neg5
-    , binaryTest (/) (P./) zero neg5
-    , binaryTest (/) (P./) zero pos5
-    , binaryTest (/) (P./) pos5 pos1
-    , binaryTest (/) (P./) pos5 neg1
-
-    , binaryTest (/) (P./) pos12 pos12
-    , binaryTest (/) (P./) neg12 pos12
-    , binaryTest (/) (P./) pos12 neg12
-    , binaryTest (/) (P./) zero neg12
-    , binaryTest (/) (P./) zero pos12
-    , binaryTest (/) (P./) pos12 pos1
-    , binaryTest (/) (P./) pos12 neg1
-    ]
-
--- | Test exponentiation.
-testExponentiation = TestLabel "Exponentiation tests" $ TestList
-    [ binaryTest (^) (P.^) pos2 pos3
-    , binaryTest (^) (P.^) zero pos5
-    , binaryTest (^) (P.^) neg2 pos3
-
-    , binaryTest (^) (P.^) pos3 pos3
-    , binaryTest (^) (P.^) pos3 pos2
-    , binaryTest (^) (P.^) pos3 pos1
-    , binaryTest (^) (P.^) pos2 pos4
-    , binaryTest (^) (P.^) pos2 pos3
-    , binaryTest (^) (P.^) pos2 pos2
-    , binaryTest (^) (P.^) pos2 pos1
-    , binaryTest (^) (P.^) pos1 pos12
-    , binaryTest (^) (P.^) pos1 pos9
-    , binaryTest (^) (P.^) pos1 zero
-
-    , binaryTest (^) (P.^) neg3 pos3
-    , binaryTest (^) (P.^) neg3 pos2
-    , binaryTest (^) (P.^) neg3 pos1
-    , binaryTest (^) (P.^) neg2 pos4
-    , binaryTest (^) (P.^) neg2 pos3
-    , binaryTest (^) (P.^) neg2 pos2
-    , binaryTest (^) (P.^) neg2 pos1
-    , binaryTest (^) (P.^) neg1 pos12
-    , binaryTest (^) (P.^) neg1 pos9
-    , binaryTest (^) (P.^) neg1 zero
-    ]
-
--- | Collect the test cases.
-tests = TestList
-    [ testAsIntegral
-    , testIncrDecr
-    , testNegate
-    , testAbs
-    , testSignum
-    , testAddition
-    , testSubtraction
-    , testMultiplication
-    , testDivision
-    , testExponentiation
-    ]
-
-main = runTestTT tests
+{-# LANGUAGE RankNTypes #-}+{-# LANGUAGE DataKinds #-}+{-# LANGUAGE KindSignatures #-}++module Numeric.NumType.DKTests where++import Numeric.NumType.DK.Integers+import Prelude hiding ((*), (/), (+), (-), (^), pred, succ, negate, abs, signum)+import qualified Prelude as P ((*), (/), (+), (-), (^), pred, succ, negate, abs, signum)+import Data.Proxy+import Test.HUnit++-- Some “large” NumTypes.+neg12 = pred neg11+neg11 = pred neg10+neg10 = pred neg9++pos10 = succ pos9+pos11 = succ pos10+pos12 = succ pos11++-- | Compares a type level unary function with a value level unary function+  -- by converting 'NumType' to a @Num@. This assumes that the 'toNum'+  -- function is solid.+unaryTest :: (KnownNumType i, KnownNumType i', Num a, Eq a, Show a)+          => (Proxy i -> Proxy i') -> (a -> a) -> Proxy i -> Test+unaryTest f f' x = TestCase $ assertEqual+    "Unary function Num equivalence"+    (f' (toNum x)) (toNum (f x))++-- | 'unaryTest' with @Num a@ fixed to @Integer@. This is needed by+  -- 'testIncrDecr'.+unaryTest' :: (KnownNumType i, KnownNumType i')+          => (Proxy i -> Proxy i') -> (Integer -> Integer) -> Proxy i -> Test+unaryTest' = unaryTest++-- | Compares a type level binary function with a value level binary function+  -- by converting 'NumType' to 'Num'. This assumes that the 'toNum'+  -- function is solid.+binaryTest :: (KnownNumType i, KnownNumType i', KnownNumType i'', Num a, Eq a, Show a)+           => (Proxy i -> Proxy i' -> Proxy i'')+           -> (a -> a -> a)+           -> Proxy i -> Proxy i' -> Test+binaryTest f f' x y = TestCase $ assertEqual+    "Binary function Num equivalence"+    (f' (toNum x) (toNum y)) (toNum (f x y))++binaryTest' :: (KnownNumType i, KnownNumType i', KnownNumType i'', Num a, Eq a, Show a)+           => (Proxy i -> Proxy i' -> Proxy i'')+           -> (Integer -> Integer -> Integer)+           -> Proxy i -> Proxy i' -> Test+binaryTest' = binaryTest+++-- | Test that conversion to 'Num a' works as expected. This is sort of a+  -- prerequisite for the other tests.+testAsIntegral = TestLabel "Num equivalence tests" $ TestList+    [ TestCase $ -12 @=? toNum neg12+    , TestCase $ -11 @=? toNum neg11+    , TestCase $ -10 @=? toNum neg10+    , TestCase $  -9 @=? toNum neg9+    , TestCase $  -8 @=? toNum neg8+    , TestCase $  -7 @=? toNum neg7+    , TestCase $  -6 @=? toNum neg6+    , TestCase $  -5 @=? toNum neg5+    , TestCase $  -4 @=? toNum neg4+    , TestCase $  -3 @=? toNum neg3+    , TestCase $  -2 @=? toNum neg2+    , TestCase $  -1 @=? toNum neg1+    , TestCase $   0 @=? toNum zero+    , TestCase $   1 @=? toNum pos1+    , TestCase $   2 @=? toNum pos2+    , TestCase $   3 @=? toNum pos3+    , TestCase $   4 @=? toNum pos4+    , TestCase $   5 @=? toNum pos5+    , TestCase $   6 @=? toNum pos6+    , TestCase $   7 @=? toNum pos7+    , TestCase $   8 @=? toNum pos8+    , TestCase $   9 @=? toNum pos9+    , TestCase $  10 @=? toNum pos10+    , TestCase $  11 @=? toNum pos11+    , TestCase $  12 @=? toNum pos12+    ] -- By induction all other NumTypes should be good if these are.++-- | Test incrementing and decrementing.+testIncrDecr = TestLabel "Increment and decrement tests" $ TestList+    [ t neg12+    , t neg11+    , t neg10+    , t neg9+    , t neg8+    , t neg7+    , t neg6+    , t neg5+    , t neg4+    , t neg3+    , t neg2+    , t neg1+    , t zero+    , t pos1+    , t pos2+    , t pos3+    , t pos4+    , t pos5+    , t pos6+    , t pos7+    , t pos8+    , t pos9+    , t pos10+    , t pos11+    , t pos12+    ] where+        t x = TestList [ unaryTest' (+ pos1) (P.+ 1) x+                       , unaryTest' (+ neg1) (P.- 1) x+                       , unaryTest' (\x -> x - neg1) (P.+ 1) x+                       , unaryTest' (\x -> x - pos1) (P.- 1) x+                       , unaryTest' pred P.pred x+                       , unaryTest' succ P.succ x+                       ]++-- | Test negation.+testNegate = TestLabel "Negation tests" $ TestList+    [ unaryTest negate P.negate neg12+    , unaryTest negate P.negate neg11+    , unaryTest negate P.negate neg10+    , unaryTest negate P.negate neg9+    , unaryTest negate P.negate neg8+    , unaryTest negate P.negate neg7+    , unaryTest negate P.negate neg6+    , unaryTest negate P.negate neg5+    , unaryTest negate P.negate neg4+    , unaryTest negate P.negate neg3+    , unaryTest negate P.negate neg2+    , unaryTest negate P.negate neg1+    , unaryTest negate P.negate zero+    , unaryTest negate P.negate pos1+    , unaryTest negate P.negate pos2+    , unaryTest negate P.negate pos3+    , unaryTest negate P.negate pos4+    , unaryTest negate P.negate pos5+    , unaryTest negate P.negate pos6+    , unaryTest negate P.negate pos7+    , unaryTest negate P.negate pos8+    , unaryTest negate P.negate pos9+    , unaryTest negate P.negate pos10+    , unaryTest negate P.negate pos11+    , unaryTest negate P.negate pos12+    ]++-- | Test absolute value.+testAbs = TestLabel "Absolute value tests" $ TestList+    [ unaryTest abs P.abs neg12+    , unaryTest abs P.abs neg11+    , unaryTest abs P.abs neg10+    , unaryTest abs P.abs neg9+    , unaryTest abs P.abs neg8+    , unaryTest abs P.abs neg7+    , unaryTest abs P.abs neg6+    , unaryTest abs P.abs neg5+    , unaryTest abs P.abs neg4+    , unaryTest abs P.abs neg3+    , unaryTest abs P.abs neg2+    , unaryTest abs P.abs neg1+    , unaryTest abs P.abs zero+    , unaryTest abs P.abs pos1+    , unaryTest abs P.abs pos2+    , unaryTest abs P.abs pos3+    , unaryTest abs P.abs pos4+    , unaryTest abs P.abs pos5+    , unaryTest abs P.abs pos6+    , unaryTest abs P.abs pos7+    , unaryTest abs P.abs pos8+    , unaryTest abs P.abs pos9+    , unaryTest abs P.abs pos10+    , unaryTest abs P.abs pos11+    , unaryTest abs P.abs pos12+    ]++-- | Test signum.+testSignum = TestLabel "Signum tests" $ TestList+    [ unaryTest signum P.signum neg12+    , unaryTest signum P.signum neg11+    , unaryTest signum P.signum neg10+    , unaryTest signum P.signum neg9+    , unaryTest signum P.signum neg8+    , unaryTest signum P.signum neg7+    , unaryTest signum P.signum neg6+    , unaryTest signum P.signum neg5+    , unaryTest signum P.signum neg4+    , unaryTest signum P.signum neg3+    , unaryTest signum P.signum neg2+    , unaryTest signum P.signum neg1+    , unaryTest signum P.signum zero+    , unaryTest signum P.signum pos1+    , unaryTest signum P.signum pos2+    , unaryTest signum P.signum pos3+    , unaryTest signum P.signum pos4+    , unaryTest signum P.signum pos5+    , unaryTest signum P.signum pos6+    , unaryTest signum P.signum pos7+    , unaryTest signum P.signum pos8+    , unaryTest signum P.signum pos9+    , unaryTest signum P.signum pos10+    , unaryTest signum P.signum pos11+    , unaryTest signum P.signum pos12+    ]++-- | Test absolute value.+testAbs = TestLabel "Absolute value tests" $ TestList+    [ unaryTest abs P.abs neg2+    , unaryTest abs P.abs neg1+    , unaryTest abs P.abs zero+    , unaryTest abs P.abs pos1+    , unaryTest abs P.abs pos1+    ]++-- | Test signum.+testSignum = TestLabel "Signum tests" $ TestList+    [ unaryTest signum P.signum neg2+    , unaryTest signum P.signum neg1+    , unaryTest signum P.signum zero+    , unaryTest signum P.signum pos1+    , unaryTest signum P.signum pos1+    ]++-- | Test addition.+testAddition = TestLabel "Addition tests" $ TestList+    [ binaryTest (+) (P.+) pos2 pos5+    , binaryTest (+) (P.+) pos12 pos2+    , binaryTest (+) (P.+) pos11 pos2+    , binaryTest (+) (P.+) pos10 pos2+    , binaryTest (+) (P.+) pos2 pos12+    , binaryTest (+) (P.+) pos2 pos11+    , binaryTest (+) (P.+) pos2 pos10+    , binaryTest (+) (P.+) neg2 pos5+    , binaryTest (+) (P.+) pos2 neg5+    , binaryTest (+) (P.+) neg2 neg5+    , binaryTest (+) (P.+) neg2 neg12+    , binaryTest (+) (P.+) neg2 neg11+    , binaryTest (+) (P.+) neg2 neg10+    , binaryTest (+) (P.+) neg12 neg2+    , binaryTest (+) (P.+) neg11 neg2+    , binaryTest (+) (P.+) neg10 neg2+    , binaryTest (+) (P.+) zero zero+    , binaryTest (+) (P.+) pos2 zero+    , binaryTest (+) (P.+) neg2 zero+    , binaryTest (+) (P.+) zero pos5+    , binaryTest (+) (P.+) zero neg5+    ]++-- | Test subtraction.+testSubtraction = TestLabel "Subtraction tests" $ TestList+    [ binaryTest (-) (P.-) pos2 pos5+    , binaryTest (-) (P.-) pos12 pos2+    , binaryTest (-) (P.-) pos11 pos2+    , binaryTest (-) (P.-) pos10 pos2+    , binaryTest (-) (P.-) pos2 pos12+    , binaryTest (-) (P.-) pos2 pos11+    , binaryTest (-) (P.-) pos2 pos10+    , binaryTest (-) (P.-) neg2 pos5+    , binaryTest (-) (P.-) pos2 neg5+    , binaryTest (-) (P.-) neg2 neg5+    , binaryTest (-) (P.-) neg2 neg12+    , binaryTest (-) (P.-) neg2 neg11+    , binaryTest (-) (P.-) neg2 neg10+    , binaryTest (-) (P.-) neg12 neg2+    , binaryTest (-) (P.-) neg11 neg2+    , binaryTest (-) (P.-) neg10 neg2+    , binaryTest (-) (P.-) zero zero+    , binaryTest (-) (P.-) pos2 zero+    , binaryTest (-) (P.-) neg2 zero+    , binaryTest (-) (P.-) zero pos5+    , binaryTest (-) (P.-) zero neg5+    ]++-- | Test multiplication.+testMultiplication = TestLabel "Multiplication tests" $ TestList+    [ binaryTest (*) (P.*) pos2 pos5+    , binaryTest (*) (P.*) pos12 pos2+    , binaryTest (*) (P.*) pos11 pos2+    , binaryTest (*) (P.*) pos10 pos2+    , binaryTest (*) (P.*) pos2 pos12+    , binaryTest (*) (P.*) pos2 pos11+    , binaryTest (*) (P.*) pos2 pos10+    , binaryTest (*) (P.*) neg2 pos5+    , binaryTest (*) (P.*) pos2 neg5+    , binaryTest (*) (P.*) neg2 neg5+    , binaryTest (*) (P.*) neg2 neg12+    , binaryTest (*) (P.*) neg2 neg11+    , binaryTest (*) (P.*) neg2 neg10+    , binaryTest (*) (P.*) neg12 neg2+    , binaryTest (*) (P.*) neg11 neg2+    , binaryTest (*) (P.*) neg10 neg2+    , binaryTest (*) (P.*) zero zero+    , binaryTest (*) (P.*) pos2 zero+    , binaryTest (*) (P.*) neg2 zero+    , binaryTest (*) (P.*) zero pos5+    , binaryTest (*) (P.*) zero neg5+    -- Probably some duplicates in the below.+    , binaryTest (*) (P.*) pos10 pos2+    , binaryTest (*) (P.*) pos9 pos3+    , binaryTest (*) (P.*) pos8 pos4+    , binaryTest (*) (P.*) pos8 pos2+    , binaryTest (*) (P.*) pos6 pos3+    , binaryTest (*) (P.*) pos6 pos2+    , binaryTest (*) (P.*) pos4 pos2+    , binaryTest (*) (P.*) pos9 neg3+    , binaryTest (*) (P.*) pos8 neg4+    , binaryTest (*) (P.*) pos8 neg2+    , binaryTest (*) (P.*) pos6 neg3+    , binaryTest (*) (P.*) pos6 neg2+    , binaryTest (*) (P.*) pos4 neg2+    , binaryTest (*) (P.*) zero pos5+    , binaryTest (*) (P.*) zero neg3+    , binaryTest (*) (P.*) neg4 pos2+    , binaryTest (*) (P.*) neg6 pos2+    , binaryTest (*) (P.*) neg6 pos3+    , binaryTest (*) (P.*) neg8 pos2+    , binaryTest (*) (P.*) neg8 pos4+    , binaryTest (*) (P.*) neg9 pos3+    , binaryTest (*) (P.*) neg4 neg2+    , binaryTest (*) (P.*) neg6 neg2+    , binaryTest (*) (P.*) neg6 neg3+    , binaryTest (*) (P.*) neg8 neg2+    , binaryTest (*) (P.*) neg8 neg4+    , binaryTest (*) (P.*) neg9 neg3+    , binaryTest (*) (P.*) neg12 pos4+    ]++-- | Test division.+testDivision = TestLabel "Division tests" $ TestList+    [ binaryTest (/) (P./) pos12 pos4+    , binaryTest (/) (P./) pos12 neg4+    , binaryTest (/) (P./) pos10 pos5+    , binaryTest (/) (P./) pos10 pos2+    , binaryTest (/) (P./) pos9 pos3+    , binaryTest (/) (P./) pos8 pos4+    , binaryTest (/) (P./) pos8 pos2+    , binaryTest (/) (P./) pos6 pos3+    , binaryTest (/) (P./) pos6 pos2+    , binaryTest (/) (P./) pos4 pos2+    , binaryTest (/) (P./) pos9 neg3+    , binaryTest (/) (P./) pos8 neg4+    , binaryTest (/) (P./) pos8 neg2+    , binaryTest (/) (P./) pos6 neg3+    , binaryTest (/) (P./) pos6 neg2+    , binaryTest (/) (P./) pos4 neg2+    , binaryTest (/) (P./) zero pos5+    , binaryTest (/) (P./) zero neg3+    , binaryTest (/) (P./) neg4 pos2+    , binaryTest (/) (P./) neg6 pos2+    , binaryTest (/) (P./) neg6 pos3+    , binaryTest (/) (P./) neg8 pos2+    , binaryTest (/) (P./) neg8 pos4+    , binaryTest (/) (P./) neg9 pos3+    , binaryTest (/) (P./) neg4 neg2+    , binaryTest (/) (P./) neg6 neg2+    , binaryTest (/) (P./) neg6 neg3+    , binaryTest (/) (P./) neg8 neg2+    , binaryTest (/) (P./) neg8 neg4+    , binaryTest (/) (P./) neg9 neg3+    , binaryTest (/) (P./) neg12 pos4+    , binaryTest (/) (P./) neg12 neg4+    , binaryTest (/) (P./) neg10 neg5+    , binaryTest (/) (P./) neg10 neg2++    , binaryTest (/) (P./) pos5 pos5+    , binaryTest (/) (P./) neg5 pos5+    , binaryTest (/) (P./) pos5 neg5+    , binaryTest (/) (P./) zero neg5+    , binaryTest (/) (P./) zero pos5+    , binaryTest (/) (P./) pos5 pos1+    , binaryTest (/) (P./) pos5 neg1++    , binaryTest (/) (P./) pos12 pos12+    , binaryTest (/) (P./) neg12 pos12+    , binaryTest (/) (P./) pos12 neg12+    , binaryTest (/) (P./) zero neg12+    , binaryTest (/) (P./) zero pos12+    , binaryTest (/) (P./) pos12 pos1+    , binaryTest (/) (P./) pos12 neg1+    ]++-- | Test exponentiation.+testExponentiation = TestLabel "Exponentiation tests" $ TestList+    [ binaryTest (^) (P.^) pos2 pos3+    , binaryTest (^) (P.^) zero pos5+    , binaryTest (^) (P.^) neg2 pos3++    , binaryTest (^) (P.^) pos3 pos3+    , binaryTest (^) (P.^) pos3 pos2+    , binaryTest (^) (P.^) pos3 pos1+    , binaryTest (^) (P.^) pos2 pos4+    , binaryTest (^) (P.^) pos2 pos3+    , binaryTest (^) (P.^) pos2 pos2+    , binaryTest (^) (P.^) pos2 pos1+    , binaryTest (^) (P.^) pos1 pos12+    , binaryTest (^) (P.^) pos1 pos9+    , binaryTest (^) (P.^) pos1 zero++    , binaryTest (^) (P.^) neg3 pos3+    , binaryTest (^) (P.^) neg3 pos2+    , binaryTest (^) (P.^) neg3 pos1+    , binaryTest (^) (P.^) neg2 pos4+    , binaryTest (^) (P.^) neg2 pos3+    , binaryTest (^) (P.^) neg2 pos2+    , binaryTest (^) (P.^) neg2 pos1+    , binaryTest (^) (P.^) neg1 pos12+    , binaryTest (^) (P.^) neg1 pos9+    , binaryTest (^) (P.^) neg1 zero+    ]++-- | Collect the test cases.+tests = TestList+    [ testAsIntegral+    , testIncrDecr+    , testNegate+    , testAbs+    , testSignum+    , testAddition+    , testSubtraction+    , testMultiplication+    , testDivision+    , testExponentiation+    ]++main = runTestTT tests

@@ -1,18 +1,19 @@-numtype-dk
-==========
-
-This package provides type level representations of the integers
-(`TypeInt`s) and basic operations (addition, subtraction, multiplication,
-division, exponentiation) on these.
-
-Requires GHC 7.8 or later.
-
-
-[![Build Status](https://travis-ci.org/bjornbm/numtype-dk.svg?branch=master)](https://travis-ci.org/bjornbm/numtype-dk)
-[![Hackage Version](https://img.shields.io/hackage/v/numtype-dk.svg)](http://hackage.haskell.org/package/numtype-dk)
-
-Contributing
-------------
-
-For project information (code, issues) see:
-  http://github.com/bjornbm/numtype-dk
+numtype-dk+==========++This package provides type level representations of the integers+(`TypeInt`s) and basic operations (addition, subtraction, multiplication,+division, exponentiation) on these.++Requires GHC 7.8 or later.+++[![Build Status](https://travis-ci.org/bjornbm/numtype-dk.svg?branch=master)](https://travis-ci.org/bjornbm/numtype-dk)+[![Hackage Version](https://img.shields.io/hackage/v/numtype-dk.svg)](http://hackage.haskell.org/package/numtype-dk)+[![Stackage version](https://www.stackage.org/package/numtype-dk/badge/lts?label=Stackage)](https://www.stackage.org/package/numtype-dk)++Contributing+------------++For project information (code, issues) see:+  http://github.com/bjornbm/numtype-dk

@@ -1,3 +1,3 @@-#!/usr/bin/env runhaskell
-> import Distribution.Simple
+#!/usr/bin/env runhaskell+> import Distribution.Simple > main = defaultMain

@@ -1,7 +1,11 @@-0.5.0.1 (2016-05)
------------------
-Internal changes to support compilation on GHC 8.0.1 release candidate.
-
-0.5 (2015-05)
--------------
-First public (Hackage) release.
+0.5.0.2 (2018-07)+-----------------+Internal changes to support compilation on GHC 8.6.1 release candidate.++0.5.0.1 (2016-05)+-----------------+Internal changes to support compilation on GHC 8.0.1 release candidate.++0.5 (2015-05)+-------------+First public (Hackage) release.

@@ -1,38 +1,38 @@-name:                numtype-dk
-version:             0.5.0.1
-license:             BSD3
-license-File:        LICENSE
-copyright:           Bjorn Buckwalter 2012-2015
-author:              Bjorn Buckwalter
-maintainer:          bjorn@buckwalter.se
-category:            Math
-stability:           provisional
-cabal-version:       >= 1.6
-build-type:          Simple
-homepage:            https://github.com/bjornbm/numtype-dk
-synopsis:            Type-level integers, using TypeNats, Data
-                     Kinds, and Closed Type Families.
-description:
-
-    This package provides type level representations of the
-    (positive and negative) integers and basic operations (addition,
-    subtraction, multiplication, division, exponentiation) on these.
-
-    The numtype-dk package differs from the numtype package in that
-    the NumTypes are implemented using Data Kinds, TypeNats, and
-    Closed Type Families rather than Functional Dependencies.
-
-    Requires GHC 7.8 or later.
-
-extra-source-files:  README.md,
-                     changelog.md
-                     Numeric/NumType/DKTests.hs
-
-source-repository head
-  type:     git
-  location: https://github.com/bjornbm/numtype-dk/
-
-library
-  build-depends:       base < 5
-  exposed-modules:     Numeric.NumType.DK.Integers
-  other-modules:       Numeric.NumType.DK.Naturals
+name:                numtype-dk+version:             0.5.0.2+license:             BSD3+license-File:        LICENSE+copyright:           Bjorn Buckwalter 2012-2015+author:              Bjorn Buckwalter+maintainer:          bjorn@buckwalter.se+category:            Math+stability:           provisional+cabal-version:       >= 1.6+build-type:          Simple+homepage:            https://github.com/bjornbm/numtype-dk+synopsis:            Type-level integers, using TypeNats, Data+                     Kinds, and Closed Type Families.+description:++    This package provides type level representations of the+    (positive and negative) integers and basic operations (addition,+    subtraction, multiplication, division, exponentiation) on these.++    The numtype-dk package differs from the numtype package in that+    the NumTypes are implemented using Data Kinds, TypeNats, and+    Closed Type Families rather than Functional Dependencies.++    Requires GHC 7.8 or later.++extra-source-files:  README.md,+                     changelog.md+                     Numeric/NumType/DKTests.hs++source-repository head+  type:     git+  location: https://github.com/bjornbm/numtype-dk/++library+  build-depends:       base < 5+  exposed-modules:     Numeric.NumType.DK.Integers+  other-modules:       Numeric.NumType.DK.Naturals