finitary (empty) → 0.1.0.0
raw patch · 8 files changed
+1770/−0 lines, 8 filesdep +basedep +bitvecdep +coercible-utilssetup-changed
Dependencies added: base, bitvec, coercible-utils, finitary, finite-typelits, ghc-typelits-knownnat, ghc-typelits-natnormalise, hedgehog, monad-loops, mtl, template-haskell, vector-sized
Files
- CHANGELOG.md +5/−0
- LICENSE.md +675/−0
- README.md +146/−0
- Setup.hs +3/−0
- finitary.cabal +59/−0
- src/Data/Finitary.hs +729/−0
- src/Data/Finitary/TH.hs +34/−0
- test/Main.hs +119/−0
+ CHANGELOG.md view
@@ -0,0 +1,5 @@+# Revision history for finitary++## 0.1.0.0 -- 2019-09-10++* First version. Released on an unsuspecting world.
+ LICENSE.md view
@@ -0,0 +1,675 @@+### GNU GENERAL PUBLIC LICENSE++Version 3, 29 June 2007++Copyright (C) 2007 Free Software Foundation, Inc.+<https://fsf.org/>++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. By contrast,+the GNU General Public License is intended to guarantee your freedom+to share and change all versions of a program--to make sure it remains+free software for all its users. We, the Free Software Foundation, use+the GNU General Public License for most of our software; it applies+also to any other work released this way by its authors. You can apply+it to your programs, too.++When we speak of free software, we are referring to freedom, not+price. 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+ README.md view
@@ -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.
+ Setup.hs view
@@ -0,0 +1,3 @@+import Distribution.Simple++main = defaultMain
+ finitary.cabal view
@@ -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
+ src/Data/Finitary.hs view
@@ -0,0 +1,729 @@+{-+ - Copyright (C) 2019 Koz Ross <koz.ross@retro-freedom.nz>+ -+ - 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 <http://www.gnu.org/licenses/>.+ -}++{-# 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)
+ src/Data/Finitary/TH.hs view
@@ -0,0 +1,34 @@+{-+ - Copyright (C) 2019 Koz Ross <koz.ross@retro-freedom.nz>+ -+ - 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 <http://www.gnu.org/licenses/>.+ -}++{-# 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
+ test/Main.hs view
@@ -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