Data.Semilattice.Lower

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

Documentation

class Lower s where

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

lowerBound :: Bounded s => s

Instances

Lower Bool

Methods

lowerBound :: Bool

Lower Char

Methods

lowerBound :: Char

Lower Int

Methods

lowerBound :: Int

Lower Int8

Methods

lowerBound :: Int8

Lower Int16

Methods

lowerBound :: Int16

Lower Int32

Methods

lowerBound :: Int32

Lower Int64

Methods

lowerBound :: Int64

Lower Ordering

Methods

lowerBound :: Ordering

Lower Word8

Methods

lowerBound :: Word8

Lower Word16

Methods

lowerBound :: Word16

Lower Word32

Methods

lowerBound :: Word32

Lower Word64

Methods

lowerBound :: Word64

Lower ()

Methods

lowerBound :: ()

Lower CDev

Methods

lowerBound :: CDev

Lower CIno

Methods

lowerBound :: CIno

Lower CMode

Methods

lowerBound :: CMode

Lower COff

Methods

lowerBound :: COff

Lower CPid

Methods

lowerBound :: CPid

Lower CSsize

Methods

lowerBound :: CSsize

Lower CGid

Methods

lowerBound :: CGid

Lower CNlink

Methods

lowerBound :: CNlink

Lower CUid

Methods

lowerBound :: CUid

Lower CTcflag

Methods

lowerBound :: CTcflag

Lower CRLim

Methods

lowerBound :: CRLim

Lower CBlkSize

Methods

lowerBound :: CBlkSize

Lower CBlkCnt

Methods

lowerBound :: CBlkCnt

Lower CClockId

Methods

lowerBound :: CClockId

Lower CFsBlkCnt

Methods

lowerBound :: CFsBlkCnt

Lower CFsFilCnt

Methods

lowerBound :: CFsFilCnt

Lower CId

Methods

lowerBound :: CId

Lower CKey

Methods

lowerBound :: CKey

Lower Fd

Methods

lowerBound :: Fd

Lower All

Methods

lowerBound :: All

Lower Any

Methods

lowerBound :: Any

Lower Associativity

Methods

lowerBound :: Associativity

Lower SourceUnpackedness

Methods

lowerBound :: SourceUnpackedness

Lower SourceStrictness

Methods

lowerBound :: SourceStrictness

Lower DecidedStrictness

Methods

lowerBound :: DecidedStrictness

Lower CChar

Methods

lowerBound :: CChar

Lower CSChar

Methods

lowerBound :: CSChar

Lower CUChar

Methods

lowerBound :: CUChar

Lower CShort

Methods

lowerBound :: CShort

Lower CUShort

Methods

lowerBound :: CUShort

Lower CInt

Methods

lowerBound :: CInt

Lower CUInt

Methods

lowerBound :: CUInt

Lower CLong

Methods

lowerBound :: CLong

Lower CULong

Methods

lowerBound :: CULong

Lower CLLong

Methods

lowerBound :: CLLong

Lower CULLong

Methods

lowerBound :: CULLong

Lower CBool

Methods

lowerBound :: CBool

Lower CPtrdiff

Methods

lowerBound :: CPtrdiff

Lower CSize

Methods

lowerBound :: CSize

Lower CWchar

Methods

lowerBound :: CWchar

Lower CSigAtomic

Methods

lowerBound :: CSigAtomic

Lower CIntPtr

Methods

lowerBound :: CIntPtr

Lower CUIntPtr

Methods

lowerBound :: CUIntPtr

Lower CIntMax

Methods

lowerBound :: CIntMax

Lower CUIntMax

Methods

lowerBound :: CUIntMax

Lower WordPtr

Methods

lowerBound :: WordPtr

Lower IntPtr

Methods

lowerBound :: IntPtr

Lower GeneralCategory

Methods

lowerBound :: GeneralCategory

Lower IntSet

Methods

lowerBound :: IntSet

Lower [a]

Methods

lowerBound :: [a]

Lower (Maybe a)

Methods

lowerBound :: Maybe a

Lower a => Lower (Min a)

Methods

lowerBound :: Min a

Lower a => Lower (Max a)

Methods

lowerBound :: Max a

Lower a => Lower (First a)

Methods

lowerBound :: First a

Lower a => Lower (Last a)

Methods

lowerBound :: Last a

Lower a => Lower (WrappedMonoid a)

Methods

lowerBound :: WrappedMonoid a

Lower a => Lower (Identity a)

Methods

lowerBound :: Identity a

Lower a => Lower (Dual a)

Methods

lowerBound :: Dual a

Lower (Endo a)

Methods

lowerBound :: Endo a

Lower a => Lower (Sum a)

Methods

lowerBound :: Sum a

Lower a => Lower (Product a)

Methods

lowerBound :: Product a

Lower (First a)

Methods

lowerBound :: First a

Lower (Last a)

Methods

lowerBound :: Last a

Lower (IntMap a)

Methods

lowerBound :: IntMap a

Lower (Set a)

Methods

lowerBound :: Set a

Lower (HashSet a)

Methods

lowerBound :: HashSet a

Lower a => Lower (Joining a)

Methods

lowerBound :: Joining a

Upper a => Lower (Tumble a)

Methods

lowerBound :: Tumble a

Lower a => Lower (Order a)

Methods

lowerBound :: Order a

Bounded a => Lower (Bound a)

Methods

lowerBound :: Bound a

Lower b => Lower (a -> b)

Methods

lowerBound :: a -> b

(Lower a, Lower b) => Lower (a, b)

Methods

lowerBound :: (a, b)

Lower (Proxy k a)

Methods

lowerBound :: Proxy k a

Lower (Map k a)

Methods

lowerBound :: Map k a

Lower (HashMap k a)

Methods

lowerBound :: HashMap k a

(Lower a, Lower b, Lower c) => Lower (a, b, c)

Methods

lowerBound :: (a, b, c)

Lower a => Lower (Const k a b)

Methods

lowerBound :: Const k a b

Coercible k a b => Lower (Coercion k a b)

Methods

lowerBound :: Coercion k a b

(~) k a b => Lower ((:~:) k a b)

Methods

lowerBound :: (k :~: a) b

(Lower a, Lower b, Lower c, Lower d) => Lower (a, b, c, d)

Methods

lowerBound :: (a, b, c, d)

(~~) k1 k2 a b => Lower ((:~~:) k1 k2 a b)

Methods

lowerBound :: (k1 :~~: k2) a b

(Lower a, Lower b, Lower c, Lower d, Lower e) => Lower (a, b, c, d, e)

Methods

lowerBound :: (a, b, c, d, e)

(Lower a, Lower b, Lower c, Lower d, Lower e, Lower f) => Lower (a, b, c, d, e, f)

Methods

lowerBound :: (a, b, c, d, e, f)

(Lower a, Lower b, Lower c, Lower d, Lower e, Lower f, Lower g) => Lower (a, b, c, d, e, f, g)

Methods

lowerBound :: (a, b, c, d, e, f, g)

(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)

Methods

lowerBound :: (a, b, c, d, e, f, g, h)

(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)

Methods

lowerBound :: (a, b, c, d, e, f, g, h, i)

(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)

Methods

lowerBound :: (a, b, c, d, e, f, g, h, i, j)

(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)

Methods

lowerBound :: (a, b, c, d, e, f, g, h, i, j, k)

(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)

Methods

lowerBound :: (a, b, c, d, e, f, g, h, i, j, k, l)

(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)

Methods

lowerBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m)

(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)

Methods

lowerBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n)

(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)

Methods

lowerBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o)

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