diff --git a/CHANGELOG.md b/CHANGELOG.md new file mode 100644 --- /dev/null +++ b/CHANGELOG.md @@ -0,0 +1,5 @@ +# Revision history for finitary + +## 0.1.0.0 -- 2019-09-10 + +* First version. Released on an unsuspecting world. diff --git a/LICENSE.md b/LICENSE.md new file mode 100644 --- /dev/null +++ b/LICENSE.md @@ -0,0 +1,675 @@ +### GNU GENERAL PUBLIC LICENSE + +Version 3, 29 June 2007 + +Copyright (C) 2007 Free Software Foundation, Inc. + + +Everyone is permitted to copy and distribute verbatim copies of this +license document, but changing it is not allowed. + +### Preamble + +The GNU General Public License is a free, copyleft license for +software and other kinds of works. + +The licenses for most software and other practical works are designed +to take away your freedom to share and change the works. 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If the Program +specifies that a certain numbered version of the GNU General Public +License "or any later version" applies to it, you have the option of +following the terms and conditions either of that numbered version or +of any later version published by the Free Software Foundation. If the +Program does not specify a version number of the GNU General Public +License, you may choose any version ever published by the Free +Software Foundation. + +If the Program specifies that a proxy can decide which future versions +of the GNU General Public License can be used, that proxy's public +statement of acceptance of a version permanently authorizes you to +choose that version for the Program. + +Later license versions may give you additional or different +permissions. However, no additional obligations are imposed on any +author or copyright holder as a result of your choosing to follow a +later version. + +#### 15. Disclaimer of Warranty. + +THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY +APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT +HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT +WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT +LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR +A PARTICULAR PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND +PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE PROGRAM PROVE +DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING, REPAIR OR +CORRECTION. + +#### 16. Limitation of Liability. + +IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING +WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR +CONVEYS THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, +INCLUDING ANY GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES +ARISING OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT +NOT LIMITED TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR +LOSSES SUSTAINED BY YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM +TO OPERATE WITH ANY OTHER PROGRAMS), EVEN IF SUCH HOLDER OR OTHER +PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES. + +#### 17. Interpretation of Sections 15 and 16. + +If the disclaimer of warranty and limitation of liability provided +above cannot be given local legal effect according to their terms, +reviewing courts shall apply local law that most closely approximates +an absolute waiver of all civil liability in connection with the +Program, unless a warranty or assumption of liability accompanies a +copy of the Program in return for a fee. + +END OF TERMS AND CONDITIONS + +### How to Apply These Terms to Your New Programs + +If you develop a new program, and you want it to be of the greatest +possible use to the public, the best way to achieve this is to make it +free software which everyone can redistribute and change under these +terms. + +To do so, attach the following notices to the program. It is safest to +attach them to the start of each source file to most effectively state +the exclusion of warranty; and each file should have at least the +"copyright" line and a pointer to where the full notice is found. + + + Copyright (C) + + This program is free software: you can redistribute it and/or modify + it under the terms of the GNU General Public License as published by + the Free Software Foundation, either version 3 of the License, or + (at your option) any later version. + + This program is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + GNU General Public License for more details. + + You should have received a copy of the GNU General Public License + along with this program. If not, see . + +Also add information on how to contact you by electronic and paper +mail. + +If the program does terminal interaction, make it output a short +notice like this when it starts in an interactive mode: + + Copyright (C) + This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. + This is free software, and you are welcome to redistribute it + under certain conditions; type `show c' for details. + +The hypothetical commands \`show w' and \`show c' should show the +appropriate parts of the General Public License. Of course, your +program's commands might be different; for a GUI interface, you would +use an "about box". + +You should also get your employer (if you work as a programmer) or +school, if any, to sign a "copyright disclaimer" for the program, if +necessary. For more information on this, and how to apply and follow +the GNU GPL, see . + +The GNU General Public License does not permit incorporating your +program into proprietary programs. If your program is a subroutine +library, you may consider it more useful to permit linking proprietary +applications with the library. If this is what you want to do, use the +GNU Lesser General Public License instead of this License. But first, +please read . diff --git a/README.md b/README.md new file mode 100644 --- /dev/null +++ b/README.md @@ -0,0 +1,146 @@ +# ``finitary`` + +## What's all this about? + +``finitary`` allows us to specify that a type is _finite_ (that is, contains +finitely many inhabitants which are not ``_|_``), and have confirmation of this +fact by GHC. Additionally, it offers a ``Generics``-based auto-derivation +interface for this, as well as multiple helper functions that are enabled by all +this machinery. + +### Why is this a big deal? + +Consider ``Enum``. It's not difficult to see that ``Enum`` has issues: + +#### It's partial all over the place + +What will this code do? + +```haskell +toEnum 3 :: Bool +``` + +The answer is 'a runtime error'. How about this? + +```haskell +succ True +``` + +The answer, again, is 'a runtime error'. Many of the methods provided by ``Enum`` +are partial like this, because many types that happen to be ``Enum`` instances +have cardinalities (much) smaller than ``Int``, which necessitates leaving some +``Int`` values 'out'. + +The converse is not much better: on some platforms, ``Int`` has _smaller_ +cardinality than some types with ``Enum`` instances in ``base``. For example, on +a platform where ``Int`` is 32 bits wide, the ``Word64`` instance will definitely +cause problems, as it's 'too big'. + +#### It gives us almost no information + +An ``Enum`` instance says that a type can be munged to and from an ``Int``... +somehow. While ``base`` and the Haskell Report certainly provide some limits +on its behaviour, a lot of questions remain unanswered, including: + +* What is the cardinality of this type? +* What are the 'safe' values of ``Int`` I can feed to ``toEnum``? +* For any ``x``, is ``toEnum . (+ 1) . fromEnum $ x`` safe (in that it'll give + us a value instead of blowing up)? + +#### We don't have a (default) way to auto-derive it + +Quoting ``base``: + +> Instances of ``Enum`` may be derived for any enumeration type (types whose +> constructors have no fields). + +But what if your type has fields, especially when they're instances of ``Enum``? +Unfortunately, no auto-derivation for you. While this stance makes some sense, +it's still rather inconvenient. + +## OK, so what are you offering instead? + +The core of ``finitary`` is the ``Finitary`` type class. If we have an instance +of ``Finitary`` for some type ``a``, we have a witness to an isomorphism between +``a`` and some ``(KnownNat n) => Finite n``. More precisely, we (together with GHC) +know: + +* That ``a`` has finitely-many non-``_|_`` inhabitants +* The value of ``n``, which is the _cardinality_ of ``a`` (how many inhabitants we have exactly) +* Two functions to 'witness' the isomorphism, namely ``fromFinite :: Finite n -> + a`` and ``toFinite :: a -> Finite n`` + +### How does ``Finitary`` solve the issues behind ``Enum``? + +#### Everything is total, forever + +There is no way to call ``fromFinite`` or ``toFinite`` with an 'inappropriate' +argument. We always know - if you give me a ``Finite n``, I will give you back a +(unique) ``a``, guaranteed. + +#### We learn a lot from a type having a ``Finitary`` instance + +Aside from cardinality, we also inherently get the ability to: + +* Have a 'starting' and 'ending' value +* Get the 'next' or 'previous' value, or report that it doesn't exist +* Enumerate ranges of these values + +All of this is safe, total and can be relied upon. Check out the documentation +for more details - all of this functionality is provided. + +#### But what about auto-derivation? + +We have you covered. If you want to auto-derive an instance of +``Finitary`` for your type, you absolutely can, using the power of +``GHC.Generics``: + +```haskell +{-# LANGUAGE DeriveAnyClass #-} +{-# LANGUAGE DeriveGeneric #-} +{-# LANGUAGE TypeInType #-} + +import GHC.Generics +import GHC.TypeNats +import Data.Word + +import qualified Data.Vector.Sized as VS + +data Foo = Bar | Baz (Word8, Word8) | Quux (VS.Vector 4 Bool) + deriving (Generic, Finitary) +``` + +Furthermore, GHC will even calculate the cardinality for you. To assist in this, +we have provided as many instances of ``Finitary`` for 'base' types as possible - +see the documentation for full details. + +### That all seems rather cool - what else can I do with this? + +Knowing that a type has finite cardinality is usable for many things - all of +which we plan to provide. Some examples (with links once we have working, tested +code) include: + +* Automatic derivation of ``Unbox`` instances +* Efficient sets, allowing operations like complements and a ``Monoid`` under + intersection +* Efficient maps +* Various clever ``lens`` tricks + +If there's something else interesting you think can be done with this, let us +know: it might make it onto this list, and into code. + +## What will this work on? + +Currently, we have tested ``finitary`` (meaning 'run tests, not just compiled') +on GHC 8.4.4 and GHC 8.6.5. GHC 8.8.1 is still in the pipeline, as some of our +dependencies don't support it yet, but as soon as they do, we plan to test with +it also. If you would like any additional versions supported, please let us +know. + +So far, the tests have all been on x86_64 GNU/Linux. If you have results on +other platforms or architectures, please let us know too! + +## License + +This library is under the GNU General Public License, version 3 or later (SPDX +code ``GPL-3.0-or-later``). For more details, see the ``LICENSE.md`` file. diff --git a/Setup.hs b/Setup.hs new file mode 100644 --- /dev/null +++ b/Setup.hs @@ -0,0 +1,3 @@ +import Distribution.Simple + +main = defaultMain diff --git a/finitary.cabal b/finitary.cabal new file mode 100644 --- /dev/null +++ b/finitary.cabal @@ -0,0 +1,59 @@ +cabal-version: 2.2 +name: finitary +-- PVP summary: +-+------- breaking API changes +-- | | +----- non-breaking API additions +-- | | | +--- code changes with no API change +version: 0.1.0.0 +synopsis: A better, more type-safe Enum. +description: Provides a type class witnessing that a type has + finitely-many inhabitants, as well as its cardinality. + Also provides an auto-deriving framework using GHC + Generics, together with a range of instances for existing + types. +homepage: https://notabug.org/koz.ross/finitary +bug-reports: https://notabug.org/koz/ross/finitary/issues +license: GPL-3.0-or-later +license-file: LICENSE.md +author: Koz Ross +maintainer: koz.ross@retro-freedom.nz +copyright: (C) Koz Ross 2019 +category: Data +build-type: Simple +tested-with: GHC == 8.6.5, + GHC == 8.4.4 +extra-source-files: CHANGELOG.md, + README.md, + LICENSE.md + +source-repository head + type: git + location: git://notabug.org/koz.ross/finitary.git + +library + exposed-modules: Data.Finitary + other-modules: Data.Finitary.TH + build-depends: base >= 4.11 && < 4.13, + finite-typelits >= 0.1.4.2 && < 1.0.0.0, + coercible-utils >= 0.0.0 && < 1.0.0, + ghc-typelits-knownnat >= 0.7 && < 1.0, + ghc-typelits-natnormalise >= 0.7 && < 1.0, + vector-sized >= 1.2.0.1 && < 2.0.0.0, + mtl >= 2.2.2 && < 3.0.0, + template-haskell >= 2.13.0.0 && < 3.0.0.0, + bitvec >= 1.0.0.1 && < 2.0.0.0 + hs-source-dirs: src + default-language: Haskell2010 + +test-suite tests + type: exitcode-stdio-1.0 + main-is: Main.hs + hs-source-dirs: test + ghc-options: -threaded -rtsopts -with-rtsopts=-N + build-depends: base, + hedgehog >= 1.0 && < 2.0, + finitary, + finite-typelits, + vector-sized, + monad-loops >= 0.4.3 && < 1.0.0, + bitvec + default-language: Haskell2010 diff --git a/src/Data/Finitary.hs b/src/Data/Finitary.hs new file mode 100644 --- /dev/null +++ b/src/Data/Finitary.hs @@ -0,0 +1,729 @@ +{- + - Copyright (C) 2019 Koz Ross + - + - This program is free software: you can redistribute it and/or modify + - it under the terms of the GNU General Public License as published by + - the Free Software Foundation, either version 3 of the License, or + - (at your option) any later version. + - + - This program is distributed in the hope that it will be useful, + - but WITHOUT ANY WARRANTY; without even the implied warranty of + - MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + - GNU General Public License for more details. + - + - You should have received a copy of the GNU General Public License + - along with this program. If not, see . + -} + +{-# OPTIONS_GHC -fplugin GHC.TypeLits.Normalise #-} +{-# OPTIONS_GHC -fplugin GHC.TypeLits.KnownNat.Solver #-} + +{-# LANGUAGE ConstrainedClassMethods #-} +{-# LANGUAGE TypeInType #-} +{-# LANGUAGE FlexibleContexts #-} +{-# LANGUAGE TypeFamilies #-} +{-# LANGUAGE TypeOperators #-} +{-# LANGUAGE TypeApplications #-} +{-# LANGUAGE ScopedTypeVariables #-} +{-# LANGUAGE DefaultSignatures #-} +{-# LANGUAGE UndecidableInstances #-} +{-# LANGUAGE TemplateHaskell #-} +{-# LANGUAGE FlexibleInstances #-} +{-# LANGUAGE CPP #-} + +#if MIN_VERSION_base(4,12,0) +{-# LANGUAGE NoStarIsType #-} +#endif + +-- | +-- Module: Data.Finitary +-- Description: A type class witnessing that a type has finite cardinality. +-- Copyright: (C) Koz Ross, 2019 +-- License: GPL version 3.0 or later +-- Maintainer: koz.ross@retro-freedom.nz +-- Stability: Experimental +-- Portability: GHC only +-- +-- This package provides the 'Finitary' type class, as well as a range of useful +-- \'base\' instances for commonly-used finitary types. +-- +-- For your own types, there are three possible ways to define an instance of +-- 'Finitary': +-- +-- __Via 'Generic'__ +-- +-- If your data type implements 'Generic' (and is finitary), you can +-- automatically derive your instance: +-- +-- > {-# LANGUAGE DeriveAnyClass #-} +-- > {-# LANGUAGE DeriveGeneric #-} +-- > +-- > import GHC.Generics +-- > import Data.Word +-- > +-- > data Foo = Bar | Baz (Word8, Word8) | Quux Word16 +-- > deriving (Generic, Finitary) +-- +-- This is the easiest method, and also the safest, as GHC will automatically +-- determine the cardinality of @Foo@, as well as defining law-abiding methods. +-- It may be somewhat slower than a \'hand-rolled\' method in some cases. +-- +-- __By defining only 'Cardinality', 'fromFinite' and 'toFinite'__ +-- +-- If you want a manually-defined instance, but don't wish to define every +-- method, only 'fromFinite' and 'toFinite' are needed, along with +-- 'Cardinality'. 'Cardinality' in particular must be defined with care, as +-- otherwise, you may end up with inconstructable values or values of @Finite +-- (Cardinality YourType)@ that don't correspond to anything. +-- +-- __By defining everything__ +-- +-- For maximum control, you can define all the methods. Ensure you follow all +-- the laws! +-- +module Data.Finitary ( +Finitary(..) +) where + +import Data.Semigroup (Max, Min, Sum, Product, Dual, Last, First, Any, All) +import Data.Functor.Identity (Identity) +#if MIN_VERSION_base(4,12,0) +import Data.Ord (Down) +#else +import Data.Ord (Down(..)) +#endif +import Foreign.Storable (Storable) +import Data.Maybe (fromJust) +import Control.Monad.State.Strict (MonadState(..), modify, evalState) +import Data.Int (Int8, Int16, Int32, Int64) +import Data.Word (Word8, Word16, Word32, Word64) +import Data.Proxy (Proxy(..)) +import Data.Void (Void) +import Data.Bool (bool) +import CoercibleUtils (op) +import GHC.Generics (Generic, Rep, U1(..), K1(..), V1, (:+:)(..), (:*:)(..), M1(..), from, to) +import Control.Applicative (Alternative(..), Const) +import Data.Kind (Type) +import GHC.TypeNats +import Data.Finite (Finite, separateSum, separateProduct, combineProduct, weakenN, shiftN, strengthenN, finite) + +import qualified Data.Bit as B +import qualified Data.Bit.ThreadSafe as BTS +import qualified Data.Vector.Sized as VS +import qualified Data.Vector.Unboxed.Sized as VUS +import qualified Data.Vector.Storable.Sized as VSS + +import Data.Finitary.TH + +-- | Witnesses an isomorphism between @a@ and @(KnownNat n) => Finite n@. +-- Effectively, a lawful instance of this shows that @a@ has exactly @n@ +-- (non-@_|_@) inhabitants, and that we have a bijection with 'fromFinite' and +-- 'toFinite' as each \'direction\'. +-- +-- For any type @a@ with an instance of @Finitary@, for every non-@_|_@ @x :: a@, we have +-- a unique /index/ @i :: Finite n@. We will also refer to any such @x@ as an +-- /inhabitant/ of @a@. We can convert inhabitants to indexes using @toFinite@, +-- and also convert indexes to inhabitants with @fromFinite@. +-- +-- __Laws__ +-- +-- The main laws state that 'fromFinite' should be a bijection, with 'toFinite' as +-- its inverse, and 'Cardinality' must be a truthful representation of the +-- cardinality of the type. Thus: +-- +-- * \[\texttt{fromFinite} \circ \texttt{toFinite} = \texttt{toFinite} \circ +-- \texttt{fromFinite} = \texttt{id}\] +-- * \[\forall x, y :: \texttt{Finite} \; n \; \texttt{fromFinite} \; x = \texttt{fromFinite} \; y +-- \rightarrow x = y\] +-- * \[\forall x :: \texttt{Finite} \; n \; \exists y :: a \mid \texttt{fromFinite} \; x +-- = y\] +-- +-- Additionally, if you define any of the other methods, these laws must hold: +-- +-- * \[ a \neq \emptyset \rightarrow \texttt{start} = \texttt{fromFinite} \; 0 \] +-- * \[ a \neq \emptyset \rightarrow \texttt{end} = \texttt{fromFinite} \; (n - 1)) \] +-- * \[ \forall x :: a \; \texttt{end} \neq x \rightarrow \texttt{next} \; x = +-- (\texttt{fromFinite} \circ + 1 \circ \texttt{toFinite}) \; x \] +-- * \[ \forall x :: a \; \texttt{start} \neq x \rightarrow \texttt{prev} \; x = +-- (\texttt{fromFinite} \circ - 1 \circ \texttt{toFinite}) \; x \] +-- * \[ \forall x :: a \; \texttt{enumerateFrom} \; x = \texttt{fromFinite <\$> [toFinite} \; x \texttt{..]} \] +-- * \[ \forall x, y :: a \; \texttt{enumerateFromThen} \; x y = +-- \texttt{fromFinite <\$> [toFinite} \; x \texttt{, }\; y \texttt{..]} \] +-- * \[ \forall x, y :: a \; \texttt{enumerateFromTo} \; x \; y = +-- \texttt{fromFinite <\$> [toFinite} \; x \texttt{..} \; y \texttt{]} \] +-- * \[ \forall x, y, z :: a \; \texttt{enumerateFromThenTo} \; x \; y \; z = +-- \texttt{fromFinite <\$> [toFinite} \; x \texttt{,} \; y \texttt{..} \; z \texttt{]} \] +-- +-- The default definitions follow these laws. Additionally, if you derive via +-- 'Generic', these are also followed for you. +-- +-- Lastly, we /strongly/ suggest that @fromFinite@ and @toFinite@ should have +-- time complexity \(\Theta(1)\), or, if that's not possible, \(O(\texttt{n})\), where @n@ is the +-- cardinality of @a@. The latter is in effect for instances generated using +-- @Generics@-based derivation, but not for \'basic\' types; thus, these +-- functions for your derived types will only be as slow as their \'structure\', +-- rather than their \'contents\', provided the contents are of these \'basic\' +-- types. +class (KnownNat (Cardinality a)) => Finitary (a :: Type) where + -- | How many (non-@_|_@) inhabitants @a@ has, as a typelevel natural number. + type Cardinality a :: Nat + type Cardinality a = GCardinality (Rep a) + -- | Converts an index into its corresponding inhabitant. + fromFinite :: Finite (Cardinality a) -> a + default fromFinite :: (Generic a, GFinitary (Rep a), Cardinality a ~ GCardinality (Rep a)) => Finite (Cardinality a) -> a + fromFinite = to . gFromFinite + -- | Converts an inhabitant to its corresponding index. + toFinite :: a -> Finite (Cardinality a) + default toFinite :: (Generic a, GFinitary (Rep a), Cardinality a ~ GCardinality (Rep a)) => a -> Finite (Cardinality a) + toFinite = gToFinite . from + -- | The first inhabitant, by index, assuming @a@ has any inhabitants. + start :: (1 <= Cardinality a) => a + start = fromFinite minBound + -- | The last inhabitant, by index, assuming @a@ has any inhabitants. + end :: (1 <= Cardinality a) => a + end = fromFinite maxBound + -- | @previous x@ gives the inhabitant whose index precedes the index of @x@, + -- or 'empty' if no such index exists. + previous :: (Alternative f) => a -> f a + previous = fmap fromFinite . guarded (== maxBound) . dec . toFinite + -- | @next x@ gives the inhabitant whose index follows the index of @x@, or + -- 'empty' if no such index exists. + next :: (Alternative f) => a -> f a + next = fmap fromFinite . guarded (== minBound) . inc . toFinite + -- | @enumerateFrom x@ gives a list of inhabitants, starting with @x@, + -- followed by all other values whose indexes follow @x@, in index order. + enumerateFrom :: a -> [a] + enumerateFrom x = fromFinite <$> [toFinite x ..] + enumerateFromThen :: a -> a -> [a] + enumerateFromThen x y = fromFinite <$> [toFinite x, toFinite y ..] + -- | @enumerateFromTo x y@ gives a list of inhabitants, starting with @x@, + -- ending with @y@, and containing all other values whose indices lie between + -- those of @x@ and @y@. The list is in index order. + enumerateFromTo :: a -> a -> [a] + enumerateFromTo x y = fromFinite <$> [toFinite x .. toFinite y] + enumerateFromThenTo :: a -> a -> a -> [a] + enumerateFromThenTo x y z = fromFinite <$> [toFinite x, toFinite y .. toFinite z] + +class (KnownNat (GCardinality a)) => GFinitary (a :: Type -> Type) where + type GCardinality a :: Nat + gFromFinite :: Finite (GCardinality a) -> a x + gToFinite :: a x -> Finite (GCardinality a) + +instance GFinitary V1 where + type GCardinality V1 = 0 + {-# INLINE gFromFinite #-} + gFromFinite = const undefined + {-# INLINE gToFinite #-} + gToFinite = const undefined + +instance GFinitary U1 where + type GCardinality U1 = 1 + {-# INLINE gFromFinite #-} + gFromFinite = const U1 + {-# INLINE gToFinite #-} + gToFinite = const 0 + +instance (Finitary a) => GFinitary (K1 _1 a) where + type GCardinality (K1 _1 a) = Cardinality a + {-# INLINE gFromFinite #-} + gFromFinite = K1 . fromFinite + {-# INLINE gToFinite #-} + gToFinite = toFinite . op K1 + +instance (GFinitary a, GFinitary b) => GFinitary (a :+: b) where + type GCardinality (a :+: b) = GCardinality a + GCardinality b + {-# INLINE gFromFinite #-} + gFromFinite = either (L1 . gFromFinite) (R1 . gFromFinite) . separateSum + {-# INLINE gToFinite #-} + gToFinite (L1 x) = weakenN . gToFinite $ x + gToFinite (R1 x) = shiftN . gToFinite $ x + +instance (GFinitary a, GFinitary b) => GFinitary (a :*: b) where + type GCardinality (a :*: b) = GCardinality a * GCardinality b + {-# INLINE gFromFinite #-} + gFromFinite i = let (x, y) = separateProduct i in + gFromFinite x :*: gFromFinite y + {-# INLINE gToFinite #-} + gToFinite (x :*: y) = combineProduct @(GCardinality a) @(GCardinality b) (weakenN . gToFinite $ x, weakenN . gToFinite $ y) + +instance (GFinitary a) => GFinitary (M1 _x _y a) where + type GCardinality (M1 _x _y a) = GCardinality a + {-# INLINE gFromFinite #-} + gFromFinite = M1 . gFromFinite + {-# INLINE gToFinite #-} + gToFinite = gToFinite . op M1 + +-- * Instances +-- Basic types + +instance Finitary Void + +instance Finitary () + +instance Finitary (Proxy a) + +instance Finitary Bool + +instance Finitary Any + +instance Finitary All + +instance Finitary B.Bit where + type Cardinality B.Bit = 2 + {-# INLINE fromFinite #-} + fromFinite = B.Bit . toEnum . fromEnum + {-# INLINE toFinite #-} + toFinite = toEnum . fromEnum . op B.Bit + {-# INLINE start #-} + start = minBound + {-# INLINE end #-} + end = maxBound + {-# INLINE next #-} + next = fmap succ . guarded (== minBound) + {-# INLINE previous #-} + previous = fmap pred . guarded (== maxBound) + {-# INLINE enumerateFrom #-} + enumerateFrom = enumFrom + {-# INLINE enumerateFromThen #-} + enumerateFromThen = enumFromThen + {-# INLINE enumerateFromTo #-} + enumerateFromTo = enumFromTo + {-# INLINE enumerateFromThenTo #-} + enumerateFromThenTo = enumFromThenTo + +instance Finitary BTS.Bit where + type Cardinality BTS.Bit = 2 + {-# INLINE fromFinite #-} + fromFinite = BTS.Bit . toEnum . fromEnum + {-# INLINE toFinite #-} + toFinite = toEnum . fromEnum . op BTS.Bit + {-# INLINE start #-} + start = minBound + {-# INLINE end #-} + end = maxBound + {-# INLINE next #-} + next = fmap succ . guarded (== minBound) + {-# INLINE previous #-} + previous = fmap pred . guarded (== maxBound) + {-# INLINE enumerateFrom #-} + enumerateFrom = enumFrom + {-# INLINE enumerateFromThen #-} + enumerateFromThen = enumFromThen + {-# INLINE enumerateFromTo #-} + enumerateFromTo = enumFromTo + {-# INLINE enumerateFromThenTo #-} + enumerateFromThenTo = enumFromThenTo + +instance Finitary Ordering + +-- | 'Char' has one inhabitant per Unicode code point. +instance Finitary Char where + type Cardinality Char = $(charCardinality) + {-# INLINE fromFinite #-} + fromFinite = toEnum . fromEnum + {-# INLINE toFinite #-} + toFinite = toEnum . fromEnum + {-# INLINE start #-} + start = minBound + {-# INLINE end #-} + end = maxBound + {-# INLINE next #-} + next = fmap succ . guarded (/= maxBound) + {-# INLINE previous #-} + previous = fmap pred . guarded (/= minBound) + {-# INLINE enumerateFrom #-} + enumerateFrom = enumFrom + {-# INLINE enumerateFromThen #-} + enumerateFromThen = enumFromThen + {-# INLINE enumerateFromTo #-} + enumerateFromTo = enumFromTo + {-# INLINE enumerateFromThenTo #-} + enumerateFromThenTo = enumFromThenTo + +instance Finitary Word8 where + type Cardinality Word8 = $(cardinalityOf @Word8) + {-# INLINE fromFinite #-} + fromFinite = toEnum . fromEnum + {-# INLINE toFinite #-} + toFinite = toEnum . fromEnum + {-# INLINE start #-} + start = minBound + {-# INLINE end #-} + end = maxBound + {-# INLINE next #-} + next = fmap succ . guarded (/= maxBound) + {-# INLINE previous #-} + previous = fmap pred . guarded (/= minBound) + {-# INLINE enumerateFrom #-} + enumerateFrom = enumFrom + {-# INLINE enumerateFromThen #-} + enumerateFromThen = enumFromThen + {-# INLINE enumerateFromTo #-} + enumerateFromTo = enumFromTo + {-# INLINE enumerateFromThenTo #-} + enumerateFromThenTo = enumFromThenTo + +instance Finitary Word16 where + type Cardinality Word16 = $(cardinalityOf @Word16) + {-# INLINE fromFinite #-} + fromFinite = toEnum . fromEnum + {-# INLINE toFinite #-} + toFinite = toEnum . fromEnum + {-# INLINE start #-} + start = minBound + {-# INLINE end #-} + end = maxBound + {-# INLINE next #-} + next = fmap succ . guarded (/= maxBound) + {-# INLINE previous #-} + previous = fmap pred . guarded (/= minBound) + {-# INLINE enumerateFrom #-} + enumerateFrom = enumFrom + {-# INLINE enumerateFromThen #-} + enumerateFromThen = enumFromThen + {-# INLINE enumerateFromTo #-} + enumerateFromTo = enumFromTo + {-# INLINE enumerateFromThenTo #-} + enumerateFromThenTo = enumFromThenTo + +instance Finitary Word32 where + type Cardinality Word32 = $(cardinalityOf @Word32) + {-# INLINE fromFinite #-} + fromFinite = fromIntegral + {-# INLINE toFinite #-} + toFinite = fromIntegral + {-# INLINE start #-} + start = minBound + {-# INLINE end #-} + end = maxBound + {-# INLINE next #-} + next = guarded (== minBound) . inc + {-# INLINE previous #-} + previous = guarded (== maxBound) . dec + {-# INLINE enumerateFrom #-} + enumerateFrom = enumFrom + {-# INLINE enumerateFromThen #-} + enumerateFromThen = enumFromThen + {-# INLINE enumerateFromTo #-} + enumerateFromTo = enumFromTo + {-# INLINE enumerateFromThenTo #-} + enumerateFromThenTo = enumFromThenTo + +instance Finitary Word64 where + type Cardinality Word64 = $(cardinalityOf @Word64) + {-# INLINE fromFinite #-} + fromFinite = fromIntegral + {-# INLINE toFinite #-} + toFinite = fromIntegral + {-# INLINE start #-} + start = minBound + {-# INLINE end #-} + end = maxBound + {-# INLINE next #-} + next = guarded (== minBound) . inc + {-# INLINE previous #-} + previous = guarded (== maxBound) . dec + {-# INLINE enumerateFrom #-} + enumerateFrom = enumFrom + {-# INLINE enumerateFromThen #-} + enumerateFromThen = enumFromThen + {-# INLINE enumerateFromTo #-} + enumerateFromTo = enumFromTo + {-# INLINE enumerateFromThenTo #-} + enumerateFromThenTo = enumFromThenTo + +instance Finitary Int8 where + type Cardinality Int8 = $(cardinalityOf @Int8) + {-# INLINE fromFinite #-} + fromFinite = fromIntegral . subtract 128 . fromIntegral @_ @Int16 + {-# INLINE toFinite #-} + toFinite = fromIntegral . (+ 128) . fromIntegral @_ @Int16 + {-# INLINE start #-} + start = minBound + {-# INLINE end #-} + end = maxBound + {-# INLINE next #-} + next = fmap succ . guarded (/= maxBound) + {-# INLINE previous #-} + previous = fmap pred . guarded (/= minBound) + {-# INLINE enumerateFrom #-} + enumerateFrom = enumFrom + {-# INLINE enumerateFromThen #-} + enumerateFromThen = enumFromThen + {-# INLINE enumerateFromTo #-} + enumerateFromTo = enumFromTo + {-# INLINE enumerateFromThenTo #-} + enumerateFromThenTo = enumFromThenTo + +instance Finitary Int16 where + type Cardinality Int16 = $(cardinalityOf @Int16) + {-# INLINE fromFinite #-} + fromFinite = fromIntegral . subtract 32768 . fromIntegral @_ @Int32 + {-# INLINE toFinite #-} + toFinite = fromIntegral . (+ 32768) . fromIntegral @_ @Int32 + {-# INLINE start #-} + start = minBound + {-# INLINE end #-} + end = maxBound + {-# INLINE next #-} + next = fmap succ . guarded (/= maxBound) + {-# INLINE previous #-} + previous = fmap pred . guarded (/= minBound) + {-# INLINE enumerateFrom #-} + enumerateFrom = enumFrom + {-# INLINE enumerateFromThen #-} + enumerateFromThen = enumFromThen + {-# INLINE enumerateFromTo #-} + enumerateFromTo = enumFromTo + {-# INLINE enumerateFromThenTo #-} + enumerateFromThenTo = enumFromThenTo + +instance Finitary Int32 where + type Cardinality Int32 = $(cardinalityOf @Int32) + {-# INLINE fromFinite #-} + fromFinite = fromIntegral @_ @Int32 . subtract $(adjustmentOf @Int32) . fromIntegral @_ @Integer + {-# INLINE toFinite #-} + toFinite = fromIntegral . (+ $(adjustmentOf @Int32)) . fromIntegral @_ @Integer . fromEnum + {-# INLINE start #-} + start = minBound + {-# INLINE end #-} + end = maxBound + {-# INLINE next #-} + next = guarded (== minBound) . inc + {-# INLINE previous #-} + previous = guarded (== maxBound) . dec + {-# INLINE enumerateFrom #-} + enumerateFrom = enumFrom + {-# INLINE enumerateFromThen #-} + enumerateFromThen = enumFromThen + {-# INLINE enumerateFromTo #-} + enumerateFromTo = enumFromTo + {-# INLINE enumerateFromThenTo #-} + enumerateFromThenTo = enumFromThenTo + +instance Finitary Int64 where + type Cardinality Int64 = $(cardinalityOf @Int64) + {-# INLINE fromFinite #-} + fromFinite = fromIntegral @_ @Int64 . subtract $(adjustmentOf @Int64) . fromIntegral @_ @Integer + {-# INLINE toFinite #-} + toFinite = fromIntegral . (+ $(adjustmentOf @Int64)) . fromIntegral @_ @Integer . fromEnum + {-# INLINE start #-} + start = minBound + {-# INLINE end #-} + end = maxBound + {-# INLINE next #-} + next = guarded (== minBound) . inc + {-# INLINE previous #-} + previous = guarded (== maxBound) . dec + {-# INLINE enumerateFrom #-} + enumerateFrom = enumFrom + {-# INLINE enumerateFromThen #-} + enumerateFromThen = enumFromThen + {-# INLINE enumerateFromTo #-} + enumerateFromTo = enumFromTo + {-# INLINE enumerateFromThenTo #-} + enumerateFromThenTo = enumFromThenTo + +-- Variable-width instances + +-- | 'Int' has a finite number of inhabitants, varying by platform. This +-- instance will determine this when the library is built. +instance Finitary Int where + type Cardinality Int = $(cardinalityOf @Int) + {-# INLINE fromFinite #-} + fromFinite = fromIntegral @_ @Int . subtract $(adjustmentOf @Int) . fromIntegral @_ @Integer + {-# INLINE toFinite #-} + toFinite = fromIntegral . (+ $(adjustmentOf @Int)) . fromIntegral @_ @Integer . fromEnum + {-# INLINE start #-} + start = minBound + {-# INLINE end #-} + end = maxBound + {-# INLINE next #-} + next = guarded (== minBound) . inc + {-# INLINE previous #-} + previous = guarded (== maxBound) . dec + {-# INLINE enumerateFrom #-} + enumerateFrom = enumFrom + {-# INLINE enumerateFromThen #-} + enumerateFromThen = enumFromThen + {-# INLINE enumerateFromTo #-} + enumerateFromTo = enumFromTo + {-# INLINE enumerateFromThenTo #-} + enumerateFromThenTo = enumFromThenTo + +-- | 'Word' has a finite number of inhabitants, varying by platform. This +-- instance will determine this when the library is built. +instance Finitary Word where + type Cardinality Word = $(cardinalityOf @Word) + {-# INLINE fromFinite #-} + fromFinite = fromIntegral + {-# INLINE toFinite #-} + toFinite = fromIntegral + {-# INLINE start #-} + start = minBound + {-# INLINE end #-} + end = maxBound + {-# INLINE next #-} + next = guarded (== minBound) . inc + {-# INLINE previous #-} + previous = guarded (== maxBound) . dec + {-# INLINE enumerateFrom #-} + enumerateFrom = enumFrom + {-# INLINE enumerateFromThen #-} + enumerateFromThen = enumFromThen + {-# INLINE enumerateFromTo #-} + enumerateFromTo = enumFromTo + {-# INLINE enumerateFromThenTo #-} + enumerateFromThenTo = enumFromThenTo + +-- | Since any type is isomorphic to itself, it follows that a \'valid\' @Finite +-- n@ (meaning that @n@ is a 'KnownNat') has finite cardinality. +instance (KnownNat n) => Finitary (Finite n) where + type Cardinality (Finite n) = n + {-# INLINE fromFinite #-} + fromFinite = id + {-# INLINE toFinite #-} + toFinite = id + {-# INLINE start #-} + start = minBound + {-# INLINE end #-} + end = maxBound + {-# INLINE next #-} + next = guarded (== minBound) . inc + {-# INLINE previous #-} + previous = guarded (== maxBound) . dec + {-# INLINE enumerateFrom #-} + enumerateFrom = enumFrom + {-# INLINE enumerateFromThen #-} + enumerateFromThen = enumFromThen + {-# INLINE enumerateFromTo #-} + enumerateFromTo = enumFromTo + {-# INLINE enumerateFromThenTo #-} + enumerateFromThenTo = enumFromThenTo + +-- | @Maybe a@ introduces one additional inhabitant (namely, 'Nothing') to @a@. +instance (Finitary a) => Finitary (Maybe a) + +-- | The sum of two finite types will also be finite, with a cardinality equal +-- to the sum of their cardinalities. +instance (Finitary a, Finitary b) => Finitary (Either a b) + +-- | The product of two finite types will also be finite, with a cardinality +-- equal to the product of their cardinalities. +instance (Finitary a, Finitary b) => Finitary (a, b) + +instance (Finitary a, Finitary b, Finitary c) => Finitary (a, b, c) + +instance (Finitary a, Finitary b, Finitary c, Finitary d) => Finitary (a, b, c, d) + +instance (Finitary a, Finitary b, Finitary c, Finitary d, Finitary e) => Finitary (a, b, c, d, e) + +instance (Finitary a, Finitary b, Finitary c, Finitary d, Finitary e, Finitary f) => Finitary (a, b, c, d, e, f) + +instance (Finitary a) => Finitary (Const a b) + +#if MIN_VERSION_base(4,12,0) +instance (Finitary a) => Finitary (Down a) +#else +instance (Finitary a) => Finitary (Down a) where + type Cardinality (Down a) = Cardinality a + {-# INLINE fromFinite #-} + fromFinite = Down . fromFinite + {-# INLINE toFinite #-} + toFinite = toFinite . op Down + {-# INLINE start #-} + start = Down start + {-# INLINE end #-} + end = Down end + {-# INLINE previous #-} + previous = fmap Down . previous . op Down + {-# INLINE next #-} + next = fmap Down . next . op Down + {-# INLINE enumerateFrom #-} + enumerateFrom = fmap Down . enumerateFrom . op Down + {-# INLINE enumerateFromThen #-} + enumerateFromThen (Down x) (Down y) = fmap Down . enumerateFromThen x $ y + {-# INLINE enumerateFromTo #-} + enumerateFromTo (Down x) (Down y) = fmap Down . enumerateFromTo x $ y + {-# INLINE enumerateFromThenTo #-} + enumerateFromThenTo (Down x) (Down y) (Down z) = fmap Down . enumerateFromThenTo x y $ z +#endif + +instance (Finitary a) => Finitary (Sum a) + +instance (Finitary a) => Finitary (Product a) + +instance (Finitary a) => Finitary (Dual a) + +instance (Finitary a) => Finitary (Last a) + +instance (Finitary a) => Finitary (First a) + +instance (Finitary a) => Finitary (Identity a) + +instance (Finitary a) => Finitary (Max a) + +instance (Finitary a) => Finitary (Min a) + +-- | We can treat explicitly-sized @Vector@s as a fixed-length string over a +-- finite alphabet, with the cardinality of the alphabet being the same as the +-- cardinality of @a@. Thus, we can \'number off\' the possible @Vector@s starting +-- with the one where every position is @start :: a@, and finishing with the one +-- where every position is @end :: a@. +instance (Finitary a, KnownNat n, Cardinality a <= Cardinality a ^ n) => Finitary (VS.Vector n a) where + type Cardinality (VS.Vector n a) = Cardinality a ^ n + {-# INLINE fromFinite #-} + fromFinite = evalState (VS.replicateM (unrank typeSize)) + where typeSize = finite @(Cardinality (VS.Vector n a)) . fromIntegral . natVal @(Cardinality a) $ Proxy + {-# INLINE toFinite #-} + toFinite v = evalState go base + where go = VS.foldM' (accumStep base) minBound v + base = finite @(Cardinality (VS.Vector n a)) . fromIntegral . natVal @(Cardinality a) $ Proxy + +instance (Finitary a, VUS.Unbox a, KnownNat n, Cardinality a <= Cardinality a ^ n) => Finitary (VUS.Vector n a) where + type Cardinality (VUS.Vector n a) = Cardinality a ^ n + {-# INLINE fromFinite #-} + fromFinite = evalState (VUS.replicateM (unrank typeSize)) + where typeSize = finite @(Cardinality (VUS.Vector n a)) . fromIntegral . natVal @(Cardinality a) $ Proxy + {-# INLINE toFinite #-} + toFinite v = evalState go base + where go = VUS.foldM' (accumStep base) minBound v + base = finite @(Cardinality (VUS.Vector n a)) . fromIntegral . natVal @(Cardinality a) $ Proxy + +instance (Finitary a, Storable a, KnownNat n, Cardinality a <= Cardinality a ^ n) => Finitary (VSS.Vector n a) where + type Cardinality (VSS.Vector n a) = Cardinality a ^ n + {-# INLINE fromFinite #-} + fromFinite = evalState (VSS.replicateM (unrank typeSize)) + where typeSize = finite @(Cardinality (VSS.Vector n a)) . fromIntegral . natVal @(Cardinality a) $ Proxy + {-# INLINE toFinite #-} + toFinite v = evalState go base + where go = VSS.foldM' (accumStep base) minBound v + base = finite @(Cardinality (VSS.Vector n a)) . fromIntegral . natVal @(Cardinality a) $ Proxy + +-- Helpers + +{-# INLINE unrank #-} +unrank :: (MonadState (Finite n) m, Finitary a, KnownNat n, (Cardinality a) <= n) => Finite n -> m a +unrank typeSize = do remaining <- get + let (d, r) = remaining `divMod` typeSize + put d + return (fromFinite . fromJust . strengthenN $ r) + +{-# INLINE accumStep #-} +accumStep :: (MonadState (Finite n) m, Finitary a, KnownNat n, (Cardinality a) <= n) => Finite n -> Finite n -> a -> m (Finite n) +accumStep base total e = do let e' = weakenN . toFinite $ e + ex <- get + modify (* base) + return (total + (e' * ex)) + +{-# INLINE inc #-} +inc :: (Num a) => a -> a +inc = (+ 1) + +{-# INLINE dec #-} +dec :: (Num a) => a -> a +dec = subtract 1 + +{-# INLINE guarded #-} +guarded :: forall (a :: Type) (f :: Type -> Type) . (Alternative f) => (a -> Bool) -> a -> f a +guarded p x = bool empty (pure x) (p x) diff --git a/src/Data/Finitary/TH.hs b/src/Data/Finitary/TH.hs new file mode 100644 --- /dev/null +++ b/src/Data/Finitary/TH.hs @@ -0,0 +1,34 @@ +{- + - Copyright (C) 2019 Koz Ross + - + - This program is free software: you can redistribute it and/or modify + - it under the terms of the GNU General Public License as published by + - the Free Software Foundation, either version 3 of the License, or + - (at your option) any later version. + - + - This program is distributed in the hope that it will be useful, + - but WITHOUT ANY WARRANTY; without even the implied warranty of + - MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + - GNU General Public License for more details. + - + - You should have received a copy of the GNU General Public License + - along with this program. If not, see . + -} + +{-# LANGUAGE AllowAmbiguousTypes #-} +{-# LANGUAGE ScopedTypeVariables #-} +{-# LANGUAGE TypeApplications #-} + +module Data.Finitary.TH where + +import Foreign.Storable (Storable, sizeOf) +import Language.Haskell.TH (Q, Type(..), TyLit(..), Exp(..), Lit(..)) + +charCardinality :: Q Type +charCardinality = pure . LitT . NumTyLit . fromIntegral . (+ 1) . fromEnum $ maxBound @Char + +cardinalityOf :: forall a . (Storable a) => Q Type +cardinalityOf = pure . LitT . NumTyLit . product . replicate (sizeOf @a undefined * 8) $ 2 + +adjustmentOf :: forall a . (Integral a, Bounded a) => Q Exp +adjustmentOf = pure . LitE . IntegerL . (+ 1) . fromIntegral @_ @Integer $ maxBound @a diff --git a/test/Main.hs b/test/Main.hs new file mode 100644 --- /dev/null +++ b/test/Main.hs @@ -0,0 +1,119 @@ +{-# LANGUAGE DeriveAnyClass #-} +{-# LANGUAGE DeriveGeneric #-} +{-# LANGUAGE TypeInType #-} +{-# LANGUAGE AllowAmbiguousTypes #-} +{-# LANGUAGE ScopedTypeVariables #-} +{-# LANGUAGE TypeApplications #-} +{-# LANGUAGE OverloadedStrings #-} +{-# LANGUAGE TypeOperators #-} +{-# LANGUAGE TypeFamilies #-} +{-# LANGUAGE GADTs #-} +{-# LANGUAGE RankNTypes #-} + +module Main where + +import Data.Maybe (isNothing) +import Data.Int (Int8, Int16, Int32, Int64) +import Data.Word (Word8, Word16, Word32, Word64) +import GHC.TypeNats +import GHC.Generics +import Data.Kind (Type) +import Data.Finite (Finite) +import Data.Proxy (Proxy(..)) +import Control.Monad.Loops (andM) +import Data.Typeable (Typeable, typeRep) +import Data.String (fromString) +import Hedgehog + +import qualified Hedgehog.Gen as G +import qualified Hedgehog.Range as R +import qualified Data.Vector.Sized as VS +import qualified Data.Vector.Unboxed.Sized as VUS +import qualified Data.Vector.Storable.Sized as VSS +import qualified Data.Bit as B +import qualified Data.Bit.ThreadSafe as BTS + +import Data.Finitary + +-- A representation of types +data SomeFinitaryRep where + SomeFinitaryRep :: forall (a :: Type) . (Finitary a, Show a, Eq a, Typeable a, 1 <= (Cardinality a)) => Proxy a -> SomeFinitaryRep + +-- A representation of test functions +data SomeTestFunction where + SomeTestFunction :: (forall (a :: Type) . (Finitary a, Show a, Eq a, 1 <= (Cardinality a)) => Proxy a -> Property) -> SomeTestFunction + +-- Some weird generic +data Foo = Bar | Baz (VS.Vector 4 Bool) | Quux Word8 + deriving (Eq, Show, Typeable, Generic, Finitary) + +-- Generators +choose :: forall (a :: Type) m . (MonadGen m, Finitary a) => m a +choose = fromFinite <$> chooseFinite + +chooseFinite :: forall (n :: Nat) m . (KnownNat n, MonadGen m) => m (Finite n) +chooseFinite = fromIntegral <$> G.integral (R.linear 0 limit) + where limit = subtract @Integer 1 . fromIntegral . natVal @n $ Proxy + +-- Data +allTheTypes :: [SomeFinitaryRep] +allTheTypes = [ + SomeFinitaryRep @() Proxy, + SomeFinitaryRep @(Proxy Int) Proxy, + SomeFinitaryRep @Bool Proxy, + SomeFinitaryRep @B.Bit Proxy, + SomeFinitaryRep @BTS.Bit Proxy, + SomeFinitaryRep @Ordering Proxy, + SomeFinitaryRep @Char Proxy, + SomeFinitaryRep @Word8 Proxy, + SomeFinitaryRep @Word16 Proxy, + SomeFinitaryRep @Word32 Proxy, + SomeFinitaryRep @Word64 Proxy, + SomeFinitaryRep @Int16 Proxy, + SomeFinitaryRep @Int8 Proxy, + SomeFinitaryRep @Int32 Proxy, + SomeFinitaryRep @Int64 Proxy, + SomeFinitaryRep @Int Proxy, + SomeFinitaryRep @Word Proxy, + SomeFinitaryRep @(Maybe Word8) Proxy, + SomeFinitaryRep @(Either Word8 Int8) Proxy, + SomeFinitaryRep @(Word8, Int8) Proxy, + SomeFinitaryRep @(VS.Vector 4 Bool) Proxy, + SomeFinitaryRep @(VUS.Vector 4 Bool) Proxy, + SomeFinitaryRep @(VSS.Vector 4 Bool) Proxy, + SomeFinitaryRep @Foo Proxy + ] + +constructTest :: SomeTestFunction -> GroupName -> IO Bool +constructTest (SomeTestFunction testFunc) name = checkParallel . Group name $ fmap go allTheTypes + where go (SomeFinitaryRep p) = (fromString . show . typeRep $ p, testFunc p) + +-- Properties +isBijection :: forall (a :: Type) . (Finitary a, Show a, Eq a) => Proxy a -> Property +isBijection _ = withTests testLimit (property $ do x <- forAll $ choose @a + x === (fromFinite . toFinite $ x)) + where testLimit = fromIntegral . (* 2) . min 32767 . natVal @(Cardinality a) $ Proxy + +startIsCorrect :: forall (a :: Type) . (Finitary a, Show a, Eq a, 1 <= (Cardinality a)) => Proxy a -> Property +startIsCorrect _ = property $ start @a === fromFinite minBound + +previousStartNothing :: forall (a :: Type) . (Finitary a, 1 <= (Cardinality a)) => Proxy a -> Property +previousStartNothing _ = property $ assert (isNothing . previous $ start @a) + +endNextNothing :: forall (a :: Type) . (Finitary a, 1 <= (Cardinality a)) => Proxy a -> Property +endNextNothing _ = property $ assert (isNothing . next $ end @a) + +endIsCorrect :: forall (a :: Type) . (Finitary a, Show a, Eq a, 1 <= (Cardinality a)) => Proxy a -> Property +endIsCorrect _ = property $ end @a === fromFinite maxBound + +allTests :: [(SomeTestFunction, GroupName)] +allTests = [ + (SomeTestFunction isBijection, "bijectivity"), + (SomeTestFunction startIsCorrect, "start"), + (SomeTestFunction endIsCorrect, "end"), + (SomeTestFunction previousStartNothing, "previous + start"), + (SomeTestFunction endNextNothing, "next + end") + ] + +main :: IO Bool +main = andM . fmap (uncurry constructTest) $ allTests