Safe Haskell	None
Language	Haskell2010

Data.Semilattice.Lower

Description

Lower bounds, related to Bounded, Join, Meet, and Ord.

Synopsis

Documentation

class Lower s where Source #

The greatest lower bound of s.

Laws:

If s is Bounded, we require lowerBound and minBound to agree:

lowerBound = minBound

If s is a Join semilattice, lowerBound must be the identity of \/:

lowerBound \/ a = a

If s is a Meet semilattice, lowerBound must be the absorbing element of /\:

lowerBound /\ a = lowerBound

If s is Ordered, lowerBound must be at least as small as every terminating value:

compare lowerBound a /= GT

Methods

lowerBound :: s Source #

lowerBound :: Bounded s => s Source #

Instances

Lower Bool Source #
Methods lowerBound :: Bool Source #
Lower Char Source #
Methods lowerBound :: Char Source #
Lower Int Source #
Methods lowerBound :: Int Source #
Lower Int8 Source #
Methods lowerBound :: Int8 Source #
Lower Int16 Source #
Methods lowerBound :: Int16 Source #
Lower Int32 Source #
Methods lowerBound :: Int32 Source #
Lower Int64 Source #
Methods lowerBound :: Int64 Source #
Lower Ordering Source #
Methods lowerBound :: Ordering Source #
Lower Word8 Source #
Methods lowerBound :: Word8 Source #
Lower Word16 Source #
Methods lowerBound :: Word16 Source #
Lower Word32 Source #
Methods lowerBound :: Word32 Source #
Lower Word64 Source #
Methods lowerBound :: Word64 Source #
Lower () Source #
Methods lowerBound :: () Source #
Lower CDev Source #
Methods lowerBound :: CDev Source #
Lower CIno Source #
Methods lowerBound :: CIno Source #
Lower CMode Source #
Methods lowerBound :: CMode Source #
Lower COff Source #
Methods lowerBound :: COff Source #
Lower CPid Source #
Methods lowerBound :: CPid Source #
Lower CSsize Source #
Methods lowerBound :: CSsize Source #
Lower CGid Source #
Methods lowerBound :: CGid Source #
Lower CNlink Source #
Methods lowerBound :: CNlink Source #
Lower CUid Source #
Methods lowerBound :: CUid Source #
Lower CTcflag Source #
Methods lowerBound :: CTcflag Source #
Lower CRLim Source #
Methods lowerBound :: CRLim Source #
Lower CBlkSize Source #
Methods lowerBound :: CBlkSize Source #
Lower CBlkCnt Source #
Methods lowerBound :: CBlkCnt Source #
Lower CClockId Source #
Methods lowerBound :: CClockId Source #
Lower CFsBlkCnt Source #
Methods lowerBound :: CFsBlkCnt Source #
Lower CFsFilCnt Source #
Methods lowerBound :: CFsFilCnt Source #
Lower CId Source #
Methods lowerBound :: CId Source #
Lower CKey Source #
Methods lowerBound :: CKey Source #
Lower Fd Source #
Methods lowerBound :: Fd Source #
Lower All Source #
Methods lowerBound :: All Source #
Lower Any Source #
Methods lowerBound :: Any Source #
Lower Associativity Source #
Methods lowerBound :: Associativity Source #
Lower SourceUnpackedness Source #
Methods lowerBound :: SourceUnpackedness Source #
Lower SourceStrictness Source #
Methods lowerBound :: SourceStrictness Source #
Lower DecidedStrictness Source #
Methods lowerBound :: DecidedStrictness Source #
Lower CChar Source #
Methods lowerBound :: CChar Source #
Lower CSChar Source #
Methods lowerBound :: CSChar Source #
Lower CUChar Source #
Methods lowerBound :: CUChar Source #
Lower CShort Source #
Methods lowerBound :: CShort Source #
Lower CUShort Source #
Methods lowerBound :: CUShort Source #
Lower CInt Source #
Methods lowerBound :: CInt Source #
Lower CUInt Source #
Methods lowerBound :: CUInt Source #
Lower CLong Source #
Methods lowerBound :: CLong Source #
Lower CULong Source #
Methods lowerBound :: CULong Source #
Lower CLLong Source #
Methods lowerBound :: CLLong Source #
Lower CULLong Source #
Methods lowerBound :: CULLong Source #
Lower CBool Source #
Methods lowerBound :: CBool Source #
Lower CPtrdiff Source #
Methods lowerBound :: CPtrdiff Source #
Lower CSize Source #
Methods lowerBound :: CSize Source #
Lower CWchar Source #
Methods lowerBound :: CWchar Source #
Lower CSigAtomic Source #
Methods lowerBound :: CSigAtomic Source #
Lower CIntPtr Source #
Methods lowerBound :: CIntPtr Source #
Lower CUIntPtr Source #
Methods lowerBound :: CUIntPtr Source #
Lower CIntMax Source #
Methods lowerBound :: CIntMax Source #
Lower CUIntMax Source #
Methods lowerBound :: CUIntMax Source #
Lower WordPtr Source #
Methods lowerBound :: WordPtr Source #
Lower IntPtr Source #
Methods lowerBound :: IntPtr Source #
Lower GeneralCategory Source #
Methods lowerBound :: GeneralCategory Source #
Lower IntSet Source #
Methods lowerBound :: IntSet Source #
Lower [a] Source #
Methods lowerBound :: [a] Source #
Lower (Maybe a) Source #
Methods lowerBound :: Maybe a Source #
Lower a => Lower (Min a) Source #
Methods lowerBound :: Min a Source #
Lower a => Lower (Max a) Source #
Methods lowerBound :: Max a Source #
Lower a => Lower (First a) Source #
Methods lowerBound :: First a Source #
Lower a => Lower (Last a) Source #
Methods lowerBound :: Last a Source #
Lower a => Lower (WrappedMonoid a) Source #
Methods lowerBound :: WrappedMonoid a Source #
Lower a => Lower (Identity a) Source #
Methods lowerBound :: Identity a Source #
Lower a => Lower (Dual a) Source #
Methods lowerBound :: Dual a Source #
Lower (Endo a) Source #
Methods lowerBound :: Endo a Source #
Lower a => Lower (Sum a) Source #
Methods lowerBound :: Sum a Source #
Lower a => Lower (Product a) Source #
Methods lowerBound :: Product a Source #
Lower (First a) Source #
Methods lowerBound :: First a Source #
Lower (Last a) Source #
Methods lowerBound :: Last a Source #
Lower (IntMap a) Source #
Methods lowerBound :: IntMap a Source #
Lower (Set a) Source #
Methods lowerBound :: Set a Source #
Lower (HashSet a) Source #
Methods lowerBound :: HashSet a Source #
Lower a => Lower (Joining a) Source #
Methods lowerBound :: Joining a Source #
Upper a => Lower (Tumble a) Source #
Methods lowerBound :: Tumble a Source #
Lower a => Lower (Order a) Source #
Methods lowerBound :: Order a Source #
Bounded a => Lower (Bound a) Source #
Methods lowerBound :: Bound a Source #
Lower b => Lower (a -> b) Source #
Methods lowerBound :: a -> b Source #
(Lower a, Lower b) => Lower (a, b) Source #
Methods lowerBound :: (a, b) Source #
Lower (Proxy k a) Source #
Methods lowerBound :: Proxy k a Source #
Lower (Map k a) Source #
Methods lowerBound :: Map k a Source #
Lower (HashMap k a) Source #
Methods lowerBound :: HashMap k a Source #
(Lower a, Lower b, Lower c) => Lower (a, b, c) Source #
Methods lowerBound :: (a, b, c) Source #
Lower a => Lower (Const k a b) Source #
Methods lowerBound :: Const k a b Source #
Coercible k a b => Lower (Coercion k a b) Source #
Methods lowerBound :: Coercion k a b Source #
(~) k a b => Lower ((:~:) k a b) Source #
Methods lowerBound :: (k :~: a) b Source #
(Lower a, Lower b, Lower c, Lower d) => Lower (a, b, c, d) Source #
Methods lowerBound :: (a, b, c, d) Source #
(~~) k1 k2 a b => Lower ((:~~:) k1 k2 a b) Source #
Methods lowerBound :: (k1 :~~: k2) a b Source #
(Lower a, Lower b, Lower c, Lower d, Lower e) => Lower (a, b, c, d, e) Source #
Methods lowerBound :: (a, b, c, d, e) Source #
(Lower a, Lower b, Lower c, Lower d, Lower e, Lower f) => Lower (a, b, c, d, e, f) Source #
Methods lowerBound :: (a, b, c, d, e, f) Source #
(Lower a, Lower b, Lower c, Lower d, Lower e, Lower f, Lower g) => Lower (a, b, c, d, e, f, g) Source #
Methods lowerBound :: (a, b, c, d, e, f, g) Source #
(Lower a, Lower b, Lower c, Lower d, Lower e, Lower f, Lower g, Lower h) => Lower (a, b, c, d, e, f, g, h) Source #
Methods lowerBound :: (a, b, c, d, e, f, g, h) Source #
(Lower a, Lower b, Lower c, Lower d, Lower e, Lower f, Lower g, Lower h, Lower i) => Lower (a, b, c, d, e, f, g, h, i) Source #
Methods lowerBound :: (a, b, c, d, e, f, g, h, i) Source #
(Lower a, Lower b, Lower c, Lower d, Lower e, Lower f, Lower g, Lower h, Lower i, Lower j) => Lower (a, b, c, d, e, f, g, h, i, j) Source #
Methods lowerBound :: (a, b, c, d, e, f, g, h, i, j) Source #
(Lower a, Lower b, Lower c, Lower d, Lower e, Lower f, Lower g, Lower h, Lower i, Lower j, Lower k) => Lower (a, b, c, d, e, f, g, h, i, j, k) Source #
Methods lowerBound :: (a, b, c, d, e, f, g, h, i, j, k) Source #
(Lower a, Lower b, Lower c, Lower d, Lower e, Lower f, Lower g, Lower h, Lower i, Lower j, Lower k, Lower l) => Lower (a, b, c, d, e, f, g, h, i, j, k, l) Source #
Methods lowerBound :: (a, b, c, d, e, f, g, h, i, j, k, l) Source #
(Lower a, Lower b, Lower c, Lower d, Lower e, Lower f, Lower g, Lower h, Lower i, Lower j, Lower k, Lower l, Lower m) => Lower (a, b, c, d, e, f, g, h, i, j, k, l, m) Source #
Methods lowerBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m) Source #
(Lower a, Lower b, Lower c, Lower d, Lower e, Lower f, Lower g, Lower h, Lower i, Lower j, Lower k, Lower l, Lower m, Lower n) => Lower (a, b, c, d, e, f, g, h, i, j, k, l, m, n) Source #
Methods lowerBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) Source #
(Lower a, Lower b, Lower c, Lower d, Lower e, Lower f, Lower g, Lower h, Lower i, Lower j, Lower k, Lower l, Lower m, Lower n, Lower o) => Lower (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) Source #
Methods lowerBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) Source #

Bounded:

lowerBound == (minBound :: Bool)

Identity of \/:

lowerBound \/ a == (a :: Bool)

Absorbing element of /\:

lowerBound /\ a == (lowerBound :: Bool)

Ord:

compare lowerBound (a :: Bool) /= GT

>>> import Data.Semilattice.Join
>>> import Data.Semilattice.Meet
>>> import Test.QuickCheck (Arbitrary(..))
>>> import Test.QuickCheck.Function