diff --git a/Algebra/Enumerable.hs b/Algebra/Enumerable.hs --- a/Algebra/Enumerable.hs +++ b/Algebra/Enumerable.hs @@ -1,3 +1,13 @@ +{-# LANGUAGE Safe #-} +---------------------------------------------------------------------------- +-- | +-- Module : Algebra.Enumerable +-- Copyright : (C) 2010-2015 Maximilian Bolingbroke +-- License : BSD-3-Clause (see the file LICENSE) +-- +-- Maintainer : Oleg Grenrus +-- +---------------------------------------------------------------------------- module Algebra.Enumerable ( Enumerable(..), universeBounded, Enumerated(..) diff --git a/Algebra/Lattice.hs b/Algebra/Lattice.hs --- a/Algebra/Lattice.hs +++ b/Algebra/Lattice.hs @@ -1,13 +1,31 @@ {-# LANGUAGE FlexibleInstances #-} +{-# LANGUAGE Trustworthy #-} +---------------------------------------------------------------------------- +-- | +-- Module : Algebra.Lattice +-- Copyright : (C) 2010-2015 Maximilian Bolingbroke +-- License : BSD-3-Clause (see the file LICENSE) +-- +-- Maintainer : Oleg Grenrus +-- +-- In mathematics, a lattice is a partially ordered set in which every +-- two elements have a unique supremum (also called a least upper bound +-- or @join@) and a unique infimum (also called a greatest lower bound or +-- @meet@). +-- +-- In this module lattices are defined using `meet` and `join` operators, +-- as it's constructive one. +-- +---------------------------------------------------------------------------- module Algebra.Lattice ( -- * Unbounded lattices JoinSemiLattice(..), MeetSemiLattice(..), Lattice, joinLeq, joins1, meetLeq, meets1, - + -- * Bounded lattices BoundedJoinSemiLattice(..), BoundedMeetSemiLattice(..), BoundedLattice, joins, meets, - + -- * Fixed points of chains in lattices lfp, lfpFrom, unsafeLfp, gfp, gfpFrom, unsafeGfp, @@ -21,12 +39,17 @@ import qualified Data.Map as M import qualified Data.IntMap as IM +import Data.Hashable +import qualified Data.HashSet as HS +import qualified Data.HashMap.Lazy as HM -- | A algebraic structure with element joins: -- +-- @ -- Associativity: x `join` (y `join` z) == (x `join` y) `join` z -- Commutativity: x `join` y == y `join` x -- Idempotency: x `join` x == x +-- @ class JoinSemiLattice a where join :: a -> a -> a @@ -40,9 +63,11 @@ -- | A algebraic structure with element meets: -- +-- @ -- Associativity: x `meet` (y `meet` z) == (x `meet` y) `meet` z -- Commutativity: x `meet` y == y `meet` x -- Idempotency: x `meet` x == x +-- @ class MeetSemiLattice a where meet :: a -> a -> a @@ -57,12 +82,16 @@ -- | The combination of two semi lattices makes a lattice if the absorption law holds: -- see and -- +-- @ -- Absorption: a `join` (a `meet` b) == a `meet` (a `join` b) == a +-- @ class (JoinSemiLattice a, MeetSemiLattice a) => Lattice a where -- | A join-semilattice with some element |bottom| that `join` approaches. -- +-- @ -- Identity: x `join` bottom == x +-- @ class JoinSemiLattice a => BoundedJoinSemiLattice a where bottom :: a @@ -72,7 +101,9 @@ -- | A meet-semilattice with some element |top| that `meet` approaches. -- +-- @ -- Identity: x `meet` top == x +-- @ class MeetSemiLattice a => BoundedMeetSemiLattice a where top :: a @@ -116,6 +147,19 @@ bottom = IS.empty -- +-- HashSet +-- + +instance (Eq a, Hashable a) => JoinSemiLattice (HS.HashSet a) where + join = HS.union + +instance (Eq a, Hashable a) => MeetSemiLattice (HS.HashSet a) where + meet = HS.intersection + +instance (Eq a, Hashable a) => BoundedJoinSemiLattice (HS.HashSet a) where + bottom = HS.empty + +-- -- Maps -- @@ -144,6 +188,19 @@ instance JoinSemiLattice v => BoundedJoinSemiLattice (IM.IntMap v) where bottom = IM.empty + +-- +-- HashMaps +-- + +instance (Eq k, Hashable k) => JoinSemiLattice (HM.HashMap k v) where + join = HM.union + +instance (Eq k, Hashable k) => MeetSemiLattice (HM.HashMap k v) where + meet = HM.intersection + +instance (Eq k, Hashable k) => BoundedJoinSemiLattice (HM.HashMap k v) where + bottom = HM.empty -- -- Functions diff --git a/Algebra/Lattice/Dropped.hs b/Algebra/Lattice/Dropped.hs --- a/Algebra/Lattice/Dropped.hs +++ b/Algebra/Lattice/Dropped.hs @@ -1,9 +1,42 @@ +{-# LANGUAGE CPP #-} +{-# LANGUAGE DeriveDataTypeable #-} +{-# LANGUAGE DeriveGeneric #-} +{-# LANGUAGE FlexibleContexts #-} +{-# LANGUAGE TypeOperators #-} +{-# LANGUAGE DeriveDataTypeable #-} +{-# LANGUAGE Trustworthy #-} +---------------------------------------------------------------------------- +-- | +-- Module : Algebra.Lattice.Dropped +-- Copyright : (C) 2010-2015 Maximilian Bolingbroke, 2015 Oleg Grenrus +-- License : BSD-3-Clause (see the file LICENSE) +-- +-- Maintainer : Oleg Grenrus +-- +---------------------------------------------------------------------------- module Algebra.Lattice.Dropped ( Dropped(..) ) where +#ifndef MIN_VERSION_base +#define MIN_VERSION_base(x,y,z) 1 +#endif + import Algebra.Lattice +#if MIN_VERSION_base(4,8,0) +#else +import Data.Monoid (Monoid(..)) +import Data.Foldable +import Data.Traversable +#endif + +import Control.Applicative +import Control.DeepSeq +import Data.Data +import Data.Hashable +import GHC.Generics + -- -- Dropped -- @@ -12,6 +45,29 @@ -- As a bonus, the top will be an absorbing element for the join. data Dropped a = Top | Drop a + deriving ( Eq, Ord, Show, Read, Data, Typeable, Generic +#if __GLASGOW_HASKELL__ >= 706 + , Generic1 +#endif + ) + +instance Functor Dropped where + fmap _ Top = Top + fmap f (Drop a) = Drop (f a) + +instance Foldable Dropped where + foldMap _ Top = mempty + foldMap f (Drop a) = f a + +instance Traversable Dropped where + traverse _ Top = pure Top + traverse f (Drop a) = Drop <$> f a + +instance NFData a => NFData (Dropped a) where + rnf Top = () + rnf (Drop a) = rnf a + +instance Hashable a => Hashable (Dropped a) instance JoinSemiLattice a => JoinSemiLattice (Dropped a) where Top `join` _ = Top diff --git a/Algebra/Lattice/Levitated.hs b/Algebra/Lattice/Levitated.hs --- a/Algebra/Lattice/Levitated.hs +++ b/Algebra/Lattice/Levitated.hs @@ -1,9 +1,42 @@ +{-# LANGUAGE CPP #-} +{-# LANGUAGE DeriveDataTypeable #-} +{-# LANGUAGE DeriveGeneric #-} +{-# LANGUAGE FlexibleContexts #-} +{-# LANGUAGE TypeOperators #-} +{-# LANGUAGE DeriveDataTypeable #-} +{-# LANGUAGE Trustworthy #-} +---------------------------------------------------------------------------- +-- | +-- Module : Algebra.Lattice.Levitated +-- Copyright : (C) 2010-2015 Maximilian Bolingbroke, 2015 Oleg Grenrus +-- License : BSD-3-Clause (see the file LICENSE) +-- +-- Maintainer : Oleg Grenrus +-- +---------------------------------------------------------------------------- module Algebra.Lattice.Levitated ( Levitated(..) ) where +#ifndef MIN_VERSION_base +#define MIN_VERSION_base(x,y,z) 1 +#endif + import Algebra.Lattice +#if MIN_VERSION_base(4,8,0) +#else +import Data.Monoid (Monoid(..)) +import Data.Foldable +import Data.Traversable +#endif + +import Control.Applicative +import Control.DeepSeq +import Data.Data +import Data.Hashable +import GHC.Generics + -- -- Levitated -- @@ -14,7 +47,33 @@ data Levitated a = Top | Levitate a | Bottom + deriving ( Eq, Ord, Show, Read, Data, Typeable, Generic +#if __GLASGOW_HASKELL__ >= 706 + , Generic1 +#endif + ) +instance Functor Levitated where + fmap _ Bottom = Bottom + fmap _ Top = Top + fmap f (Levitate a) = Levitate (f a) +instance Foldable Levitated where + foldMap _ Bottom = mempty + foldMap _ Top = mempty + foldMap f (Levitate a) = f a + +instance Traversable Levitated where + traverse _ Bottom = pure Bottom + traverse _ Top = pure Top + traverse f (Levitate a) = Levitate <$> f a + +instance NFData a => NFData (Levitated a) where + rnf Top = () + rnf Bottom = () + rnf (Levitate a) = rnf a + +instance Hashable a => Hashable (Levitated a) + instance JoinSemiLattice a => JoinSemiLattice (Levitated a) where Top `join` _ = Top _ `join` Top = Top @@ -37,4 +96,4 @@ instance MeetSemiLattice a => BoundedMeetSemiLattice (Levitated a) where top = Top -instance BoundedLattice a => BoundedLattice (Levitated a) where +instance Lattice a => BoundedLattice (Levitated a) where diff --git a/Algebra/Lattice/Lifted.hs b/Algebra/Lattice/Lifted.hs --- a/Algebra/Lattice/Lifted.hs +++ b/Algebra/Lattice/Lifted.hs @@ -1,9 +1,41 @@ +{-# LANGUAGE CPP #-} +{-# LANGUAGE DeriveDataTypeable #-} +{-# LANGUAGE DeriveGeneric #-} +{-# LANGUAGE FlexibleContexts #-} +{-# LANGUAGE TypeOperators #-} +{-# LANGUAGE Trustworthy #-} +---------------------------------------------------------------------------- +-- | +-- Module : Algebra.Lattice.Lifted +-- Copyright : (C) 2010-2015 Maximilian Bolingbroke, 2015 Oleg Grenrus +-- License : BSD-3-Clause (see the file LICENSE) +-- +-- Maintainer : Oleg Grenrus +-- +---------------------------------------------------------------------------- module Algebra.Lattice.Lifted ( Lifted(..) ) where +#ifndef MIN_VERSION_base +#define MIN_VERSION_base(x,y,z) 1 +#endif + import Algebra.Lattice +#if MIN_VERSION_base(4,8,0) +#else +import Data.Monoid (Monoid(..)) +import Data.Foldable +import Data.Traversable +#endif + +import Control.Applicative +import Control.DeepSeq +import Data.Data +import Data.Hashable +import GHC.Generics + -- -- Lifted -- @@ -12,6 +44,29 @@ -- As a bonus, the bottom will be an absorbing element for the meet. data Lifted a = Lift a | Bottom + deriving ( Eq, Ord, Show, Read, Data, Typeable, Generic +#if __GLASGOW_HASKELL__ >= 706 + , Generic1 +#endif + ) + +instance Functor Lifted where + fmap _ Bottom = Bottom + fmap f (Lift a) = Lift (f a) + +instance Foldable Lifted where + foldMap _ Bottom = mempty + foldMap f (Lift a) = f a + +instance Traversable Lifted where + traverse _ Bottom = pure Bottom + traverse f (Lift a) = Lift <$> f a + +instance NFData a => NFData (Lifted a) where + rnf Bottom = () + rnf (Lift a) = rnf a + +instance Hashable a => Hashable (Lifted a) instance JoinSemiLattice a => JoinSemiLattice (Lifted a) where Lift x `join` Lift y = Lift (x `join` y) diff --git a/Algebra/PartialOrd.hs b/Algebra/PartialOrd.hs --- a/Algebra/PartialOrd.hs +++ b/Algebra/PartialOrd.hs @@ -1,8 +1,18 @@ +{-# LANGUAGE Safe #-} +---------------------------------------------------------------------------- +-- | +-- Module : Algebra.PartialOrd +-- Copyright : (C) 2010-2015 Maximilian Bolingbroke +-- License : BSD-3-Clause (see the file LICENSE) +-- +-- Maintainer : Oleg Grenrus +-- +---------------------------------------------------------------------------- module Algebra.PartialOrd ( -- * Partial orderings PartialOrd(..), partialOrdEq, - + -- * Fixed points of chains in partial orders lfpFrom, unsafeLfpFrom, gfpFrom, unsafeGfpFrom @@ -21,14 +31,18 @@ -- This can be defined using either |joinLeq| or |meetLeq|, or a more efficient definition -- can be derived directly. -- +-- @ -- Reflexive: a `leq` a -- Antisymmetric: a `leq` b && b `leq` a ==> a == b -- Transitive: a `leq` b && b `leq` c ==> a `leq` c +-- @ -- -- The superclass equality (which can be defined using |partialOrdEq|) must obey these laws: -- +-- @ -- Reflexive: a == a -- Transitive: a == b && b == c ==> a == b +-- @ class Eq a => PartialOrd a where leq :: a -> a -> Bool diff --git a/CHANGELOG.md b/CHANGELOG.md new file mode 100644 --- /dev/null +++ b/CHANGELOG.md @@ -0,0 +1,8 @@ +# 1.3 (2015-05-18) + +- relaxed constraint for `BoundedLattice (Levitated a)` +- added instances to `Dropped`, `Levitated` and `Lifted`: + - from base + - `NFData` + - `Hashable` +- added `HashSet` and `HashMap` lattice instances diff --git a/LICENSE b/LICENSE --- a/LICENSE +++ b/LICENSE @@ -1,4 +1,4 @@ -Copyright (c) 2010, Maximilian Bolingbroke +Copyright (c) 2010-2015 Maximilian Bolingbroke, 2015 Oleg Grenrus All rights reserved. Redistribution and use in source and binary forms, with or without modification, are permitted diff --git a/README.md b/README.md new file mode 100644 --- /dev/null +++ b/README.md @@ -0,0 +1,5 @@ +# lattices + +[![Build Status](https://travis-ci.org/phadej/lattices.svg?branch=master)](https://travis-ci.org/phadej/lattices) + +Fine-grained library for constructing and manipulating lattices diff --git a/lattices.cabal b/lattices.cabal --- a/lattices.cabal +++ b/lattices.cabal @@ -1,21 +1,39 @@ -Name: lattices -Version: 1.2.1.1 -Cabal-Version: >= 1.2 -Category: Math -Synopsis: Fine-grained library for constructing and manipulating lattices -License: BSD3 -License-File: LICENSE -Author: Max Bolingbroke -Maintainer: Max Bolingbroke -Build-Type: Simple +name: lattices +version: 1.3 +cabal-version: >= 1.10 +category: Math +license: BSD3 +license-File: LICENSE +author: Maximilian Bolingbroke +maintainer: Oleg Grenrus +homepage: http://github.com/phadej/lattices/ +bug-reports: http://github.com/phadej/lattices.git/issues +copyright: (C) 2010-2015 Maximilian Bolingbroke +build-type: Simple +extra-source-files: README.md CHANGELOG.md +synopsis: Fine-grained library for constructing and manipulating lattices +description: + In mathematics, a lattice is a partially ordered set in which every two elements have a unique supremum (also called a least upper bound or @join@) and a unique infimum (also called a greatest lower bound or @meet@). -Library - Exposed-Modules: Algebra.Enumerable, - Algebra.Lattice, - Algebra.Lattice.Dropped, - Algebra.Lattice.Levitated, - Algebra.Lattice.Lifted, - Algebra.PartialOrd +source-repository head + type: git + location: git://github.com/phadej/lattices.git - Build-Depends: base >= 3 && < 5, - containers >= 0.3 && < 0.6 +library + exposed-modules: Algebra.Enumerable, + Algebra.Lattice, + Algebra.Lattice.Dropped, + Algebra.Lattice.Levitated, + Algebra.Lattice.Lifted, + Algebra.PartialOrd + + build-depends: base >= 3 && < 5, + containers >= 0.3 && < 0.6, + deepseq >= 1.1 && < 1.5, + hashable >= 1.2 && < 1.3, + unordered-containers >= 0.2 && < 0.3 + ghc-options: -Wall + default-language: Haskell2010 + + if impl(ghc >= 7.4 && < 7.5) + build-depends: ghc-prim